idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
|---|---|---|---|---|---|---|
54,801 | How can I generate a time series with autocorrelation at lags other than 1? | The problem is solved once you can solve it for lag 1, because you can take $k$ such independent (or at least uncorrelated) time series $X_t^{(1)},$ $X_t^{(2)},$ through $X_t^{(k)}$ and interleave them to form a time series
$$X_t = X_1^{(1)}, X_1^{(2)}, \ldots, X_1^{(k)},\ X_2^{(1)}, \ldots, X_2^{(k)},\ X_3^{(1)}, \ldo... | How can I generate a time series with autocorrelation at lags other than 1? | The problem is solved once you can solve it for lag 1, because you can take $k$ such independent (or at least uncorrelated) time series $X_t^{(1)},$ $X_t^{(2)},$ through $X_t^{(k)}$ and interleave the | How can I generate a time series with autocorrelation at lags other than 1?
The problem is solved once you can solve it for lag 1, because you can take $k$ such independent (or at least uncorrelated) time series $X_t^{(1)},$ $X_t^{(2)},$ through $X_t^{(k)}$ and interleave them to form a time series
$$X_t = X_1^{(1)}, X... | How can I generate a time series with autocorrelation at lags other than 1?
The problem is solved once you can solve it for lag 1, because you can take $k$ such independent (or at least uncorrelated) time series $X_t^{(1)},$ $X_t^{(2)},$ through $X_t^{(k)}$ and interleave the |
54,802 | How can I generate a time series with autocorrelation at lags other than 1? | Edit: It looks like I misinterpreted this question. The question appears to be asking for a method to generate a random vector with non-zero auto-correlation at one lag. My answer give a method to generate a random vector with non-zero auto-regression at only one lag, which is a different thing (and gives non-zero au... | How can I generate a time series with autocorrelation at lags other than 1? | Edit: It looks like I misinterpreted this question. The question appears to be asking for a method to generate a random vector with non-zero auto-correlation at one lag. My answer give a method to g | How can I generate a time series with autocorrelation at lags other than 1?
Edit: It looks like I misinterpreted this question. The question appears to be asking for a method to generate a random vector with non-zero auto-correlation at one lag. My answer give a method to generate a random vector with non-zero auto-r... | How can I generate a time series with autocorrelation at lags other than 1?
Edit: It looks like I misinterpreted this question. The question appears to be asking for a method to generate a random vector with non-zero auto-correlation at one lag. My answer give a method to g |
54,803 | Bayesian methods are about averaging over uncertainty rather than optimization. Explain? | When doing model selection, each model $\mathfrak M$ is given an evidence $\mathfrak e(\mathfrak M)$ that writes as the corresponding integrated likelihood
$$\mathfrak e(\mathfrak M) = \int f_{\mathfrak M}(\mathbf x|\theta_{\mathfrak M})\,\text{d}\theta_{\mathfrak M}$$Each model is then given a posterior probability $\... | Bayesian methods are about averaging over uncertainty rather than optimization. Explain? | When doing model selection, each model $\mathfrak M$ is given an evidence $\mathfrak e(\mathfrak M)$ that writes as the corresponding integrated likelihood
$$\mathfrak e(\mathfrak M) = \int f_{\mathfr | Bayesian methods are about averaging over uncertainty rather than optimization. Explain?
When doing model selection, each model $\mathfrak M$ is given an evidence $\mathfrak e(\mathfrak M)$ that writes as the corresponding integrated likelihood
$$\mathfrak e(\mathfrak M) = \int f_{\mathfrak M}(\mathbf x|\theta_{\mathfr... | Bayesian methods are about averaging over uncertainty rather than optimization. Explain?
When doing model selection, each model $\mathfrak M$ is given an evidence $\mathfrak e(\mathfrak M)$ that writes as the corresponding integrated likelihood
$$\mathfrak e(\mathfrak M) = \int f_{\mathfr |
54,804 | Bayesian methods are about averaging over uncertainty rather than optimization. Explain? | I did a cursory search for the context of the quote you give. I find it showing up a lot with slides for Gharamani.
In those slides he's using that statement to suggest that MAP is not a bayesian method. My experience with Bayesian methods has been that the results of some inference are usually a distribution of param... | Bayesian methods are about averaging over uncertainty rather than optimization. Explain? | I did a cursory search for the context of the quote you give. I find it showing up a lot with slides for Gharamani.
In those slides he's using that statement to suggest that MAP is not a bayesian met | Bayesian methods are about averaging over uncertainty rather than optimization. Explain?
I did a cursory search for the context of the quote you give. I find it showing up a lot with slides for Gharamani.
In those slides he's using that statement to suggest that MAP is not a bayesian method. My experience with Bayesia... | Bayesian methods are about averaging over uncertainty rather than optimization. Explain?
I did a cursory search for the context of the quote you give. I find it showing up a lot with slides for Gharamani.
In those slides he's using that statement to suggest that MAP is not a bayesian met |
54,805 | Is there a maximum number of independent variables for generalized additive model? | The number of predictors should reflect your understanding of the system you are modelling and the hypotheses you are testing.
Technically, you can have as many covariates in the model as observations minus 2 (one for the intercept and one to have some hope of estimating everything). In a GAM, with 100 observations and... | Is there a maximum number of independent variables for generalized additive model? | The number of predictors should reflect your understanding of the system you are modelling and the hypotheses you are testing.
Technically, you can have as many covariates in the model as observations | Is there a maximum number of independent variables for generalized additive model?
The number of predictors should reflect your understanding of the system you are modelling and the hypotheses you are testing.
Technically, you can have as many covariates in the model as observations minus 2 (one for the intercept and o... | Is there a maximum number of independent variables for generalized additive model?
The number of predictors should reflect your understanding of the system you are modelling and the hypotheses you are testing.
Technically, you can have as many covariates in the model as observations |
54,806 | Is there a maximum number of independent variables for generalized additive model? | there is no such thing as the right number. This is totally dependent on the problem.
If you want to use classical regression methods the only "real" restriction is that you should have less than 100 variables.
I usually use a lasso regression with CV lambda to select the variables for the GANMmodel. | Is there a maximum number of independent variables for generalized additive model? | there is no such thing as the right number. This is totally dependent on the problem.
If you want to use classical regression methods the only "real" restriction is that you should have less than 100 | Is there a maximum number of independent variables for generalized additive model?
there is no such thing as the right number. This is totally dependent on the problem.
If you want to use classical regression methods the only "real" restriction is that you should have less than 100 variables.
I usually use a lasso re... | Is there a maximum number of independent variables for generalized additive model?
there is no such thing as the right number. This is totally dependent on the problem.
If you want to use classical regression methods the only "real" restriction is that you should have less than 100 |
54,807 | Find mgf from joint pmf | This problem is intriguing because it indicates something symmetrical lurks. One can't help feeling there is a simple, low-computation, insightful solution. Indeed, a little staring at the pmf suggests defining
$$z = y-x.$$
We may assume $z \ge 0$ (because when $z \lt 0$ the $z!$ terms in the denominator have poles, w... | Find mgf from joint pmf | This problem is intriguing because it indicates something symmetrical lurks. One can't help feeling there is a simple, low-computation, insightful solution. Indeed, a little staring at the pmf sugges | Find mgf from joint pmf
This problem is intriguing because it indicates something symmetrical lurks. One can't help feeling there is a simple, low-computation, insightful solution. Indeed, a little staring at the pmf suggests defining
$$z = y-x.$$
We may assume $z \ge 0$ (because when $z \lt 0$ the $z!$ terms in the d... | Find mgf from joint pmf
This problem is intriguing because it indicates something symmetrical lurks. One can't help feeling there is a simple, low-computation, insightful solution. Indeed, a little staring at the pmf sugges |
54,808 | Find mgf from joint pmf | The joint pmf of $(X,Y)$ is of the form
\begin{align}
p(x,y)&=\frac{e^{-2}}{y!}\binom{y}{x}\mathbf1_{x=0,1,\ldots,y\,;\,y=0,1,\ldots}
\\&=\binom{y}{x}\frac{1}{2^y}\mathbf1_{x=0,1,\ldots,y}\,\frac{e^{-2}2^y}{y!}\mathbf1_{y=0,1,\ldots}
\end{align}
This shows that $X\mid Y\sim\mathsf{Bin}\left(Y,\frac{1}{2}\right)$, where... | Find mgf from joint pmf | The joint pmf of $(X,Y)$ is of the form
\begin{align}
p(x,y)&=\frac{e^{-2}}{y!}\binom{y}{x}\mathbf1_{x=0,1,\ldots,y\,;\,y=0,1,\ldots}
\\&=\binom{y}{x}\frac{1}{2^y}\mathbf1_{x=0,1,\ldots,y}\,\frac{e^{- | Find mgf from joint pmf
The joint pmf of $(X,Y)$ is of the form
\begin{align}
p(x,y)&=\frac{e^{-2}}{y!}\binom{y}{x}\mathbf1_{x=0,1,\ldots,y\,;\,y=0,1,\ldots}
\\&=\binom{y}{x}\frac{1}{2^y}\mathbf1_{x=0,1,\ldots,y}\,\frac{e^{-2}2^y}{y!}\mathbf1_{y=0,1,\ldots}
\end{align}
This shows that $X\mid Y\sim\mathsf{Bin}\left(Y,\f... | Find mgf from joint pmf
The joint pmf of $(X,Y)$ is of the form
\begin{align}
p(x,y)&=\frac{e^{-2}}{y!}\binom{y}{x}\mathbf1_{x=0,1,\ldots,y\,;\,y=0,1,\ldots}
\\&=\binom{y}{x}\frac{1}{2^y}\mathbf1_{x=0,1,\ldots,y}\,\frac{e^{- |
54,809 | Which R-squared value to report while using a fixed effects model - within, between or overall? | All three of these values provide some insight into your model, so you may need to report all three, but the within value is typically of main interest, as fixed-effects is known as the within estimator. At least in Stata, it comes from OLS-estimated mean-deviated model:
$$
\left ( y_{it} - \bar{y_{i}} \right ) = \lef... | Which R-squared value to report while using a fixed effects model - within, between or overall? | All three of these values provide some insight into your model, so you may need to report all three, but the within value is typically of main interest, as fixed-effects is known as the within estimat | Which R-squared value to report while using a fixed effects model - within, between or overall?
All three of these values provide some insight into your model, so you may need to report all three, but the within value is typically of main interest, as fixed-effects is known as the within estimator. At least in Stata, ... | Which R-squared value to report while using a fixed effects model - within, between or overall?
All three of these values provide some insight into your model, so you may need to report all three, but the within value is typically of main interest, as fixed-effects is known as the within estimat |
54,810 | Roots within the unit circle and non-stationarity | Not restricted to time-series analysis, characteristic equations (CE) are used in many applications or problems, such as differential/difference equation solving, signal processing, control systems etc. And, it is directly related with commonly used transforms, e.g. Z, (Disc./Cont.) Fourier, Laplace transform etc. Usin... | Roots within the unit circle and non-stationarity | Not restricted to time-series analysis, characteristic equations (CE) are used in many applications or problems, such as differential/difference equation solving, signal processing, control systems et | Roots within the unit circle and non-stationarity
Not restricted to time-series analysis, characteristic equations (CE) are used in many applications or problems, such as differential/difference equation solving, signal processing, control systems etc. And, it is directly related with commonly used transforms, e.g. Z, ... | Roots within the unit circle and non-stationarity
Not restricted to time-series analysis, characteristic equations (CE) are used in many applications or problems, such as differential/difference equation solving, signal processing, control systems et |
54,811 | Roots within the unit circle and non-stationarity | to my perspective, you can simply understand the characteristic equations as the restrictions of your target. Your target has to be the root of your characteristic equations. If you don't understand how the time series AR or MA or ARMA model come from, you can read the book "Analysis of Financial Time Series" by Ruey S... | Roots within the unit circle and non-stationarity | to my perspective, you can simply understand the characteristic equations as the restrictions of your target. Your target has to be the root of your characteristic equations. If you don't understand h | Roots within the unit circle and non-stationarity
to my perspective, you can simply understand the characteristic equations as the restrictions of your target. Your target has to be the root of your characteristic equations. If you don't understand how the time series AR or MA or ARMA model come from, you can read the ... | Roots within the unit circle and non-stationarity
to my perspective, you can simply understand the characteristic equations as the restrictions of your target. Your target has to be the root of your characteristic equations. If you don't understand h |
54,812 | Truncated Gamma Distribution | A generic if rarely mentioned result about conjugate families is that they are defined in terms of an arbitrary dominating measure $\lambda$. This means that their density wrt this dominating measure is provided by the corresponding exponential family shape
$$\exp\{A(\theta)\cdot S_0 -\lambda \psi(\theta)\}$$
but that ... | Truncated Gamma Distribution | A generic if rarely mentioned result about conjugate families is that they are defined in terms of an arbitrary dominating measure $\lambda$. This means that their density wrt this dominating measure | Truncated Gamma Distribution
A generic if rarely mentioned result about conjugate families is that they are defined in terms of an arbitrary dominating measure $\lambda$. This means that their density wrt this dominating measure is provided by the corresponding exponential family shape
$$\exp\{A(\theta)\cdot S_0 -\lamb... | Truncated Gamma Distribution
A generic if rarely mentioned result about conjugate families is that they are defined in terms of an arbitrary dominating measure $\lambda$. This means that their density wrt this dominating measure |
54,813 | Multilevel model with 4 levels? | There is no restriction to the number of "levels" in lme4. The package will be able to fit any number of levels provided that the data supports such a random effects structure.
We can demonstrate with the following simulation of a 4-level dataset similar to that as described in the OP:
> set.seed(15)
> library(lme4)
>... | Multilevel model with 4 levels? | There is no restriction to the number of "levels" in lme4. The package will be able to fit any number of levels provided that the data supports such a random effects structure.
We can demonstrate wit | Multilevel model with 4 levels?
There is no restriction to the number of "levels" in lme4. The package will be able to fit any number of levels provided that the data supports such a random effects structure.
We can demonstrate with the following simulation of a 4-level dataset similar to that as described in the OP:
... | Multilevel model with 4 levels?
There is no restriction to the number of "levels" in lme4. The package will be able to fit any number of levels provided that the data supports such a random effects structure.
We can demonstrate wit |
54,814 | How to account for temporal autocorrelation in logistic regression with longitudinal data? | If you would include the time variable in the specification of your random effects you would account for the correlations in the repeated measurements of your outcome variable ThermalResponse, e.g., something like
fm1 <- glmer(ThermalResponse ~ Temperature + Humidity + (TimeSeries | Location),
data = t... | How to account for temporal autocorrelation in logistic regression with longitudinal data? | If you would include the time variable in the specification of your random effects you would account for the correlations in the repeated measurements of your outcome variable ThermalResponse, e.g., s | How to account for temporal autocorrelation in logistic regression with longitudinal data?
If you would include the time variable in the specification of your random effects you would account for the correlations in the repeated measurements of your outcome variable ThermalResponse, e.g., something like
fm1 <- glmer(Th... | How to account for temporal autocorrelation in logistic regression with longitudinal data?
If you would include the time variable in the specification of your random effects you would account for the correlations in the repeated measurements of your outcome variable ThermalResponse, e.g., s |
54,815 | How to account for temporal autocorrelation in logistic regression with longitudinal data? | Switch to GLMMTMB package it allows for different covariance structures like AR1 with random effects and the use of multiple different distribution including the binomial. I use it all the time for logistic mixed models with temporal autocorrelation. Also, the reason LME freaked out is that your data are not normal (wh... | How to account for temporal autocorrelation in logistic regression with longitudinal data? | Switch to GLMMTMB package it allows for different covariance structures like AR1 with random effects and the use of multiple different distribution including the binomial. I use it all the time for lo | How to account for temporal autocorrelation in logistic regression with longitudinal data?
Switch to GLMMTMB package it allows for different covariance structures like AR1 with random effects and the use of multiple different distribution including the binomial. I use it all the time for logistic mixed models with temp... | How to account for temporal autocorrelation in logistic regression with longitudinal data?
Switch to GLMMTMB package it allows for different covariance structures like AR1 with random effects and the use of multiple different distribution including the binomial. I use it all the time for lo |
54,816 | How to account for temporal autocorrelation in logistic regression with longitudinal data? | If I understand you correctly, You want to argue that there is an effect of the temperature controlling for time and the location. Thus, you could use a fixed effect interaction between time and the location like in this example
n_times <- 100L # number of time periods
n_sites <- 10L # number of sites
n_sub <- 2L ... | How to account for temporal autocorrelation in logistic regression with longitudinal data? | If I understand you correctly, You want to argue that there is an effect of the temperature controlling for time and the location. Thus, you could use a fixed effect interaction between time and the l | How to account for temporal autocorrelation in logistic regression with longitudinal data?
If I understand you correctly, You want to argue that there is an effect of the temperature controlling for time and the location. Thus, you could use a fixed effect interaction between time and the location like in this example ... | How to account for temporal autocorrelation in logistic regression with longitudinal data?
If I understand you correctly, You want to argue that there is an effect of the temperature controlling for time and the location. Thus, you could use a fixed effect interaction between time and the l |
54,817 | Limits of a density function | Yes.
Suppose the limit is anything else, so $\lim_{t \rightarrow \infty} f(t) = a \neq 0$. Then, by the definition of the limit, there is an $N$ so that for all $t > N$, $| f(t) - a | < \frac{a}{2}$. In particular, $f(t) > \frac{a}{2}$ in this reigon.
But then:
$$
\int_{\mathbf{R}} f(t) dt \geq \int_{N}^{\infty} f(t)... | Limits of a density function | Yes.
Suppose the limit is anything else, so $\lim_{t \rightarrow \infty} f(t) = a \neq 0$. Then, by the definition of the limit, there is an $N$ so that for all $t > N$, $| f(t) - a | < \frac{a}{2}$. | Limits of a density function
Yes.
Suppose the limit is anything else, so $\lim_{t \rightarrow \infty} f(t) = a \neq 0$. Then, by the definition of the limit, there is an $N$ so that for all $t > N$, $| f(t) - a | < \frac{a}{2}$. In particular, $f(t) > \frac{a}{2}$ in this reigon.
But then:
$$
\int_{\mathbf{R}} f(t) d... | Limits of a density function
Yes.
Suppose the limit is anything else, so $\lim_{t \rightarrow \infty} f(t) = a \neq 0$. Then, by the definition of the limit, there is an $N$ so that for all $t > N$, $| f(t) - a | < \frac{a}{2}$. |
54,818 | Variance of unbiased estimator for the shape parameter of Pareto distribution | I will write the standard Pareto distribution with density
$$
f(x;\alpha,x_m)=\frac{\alpha x_m^\alpha}{x^{\alpha+1}}\cdot I(x > x_m),
$$ for some $\alpha>0, x_m>0$. Then the loglikelihood function can be written
$$
\ell(\alpha,x_m)=n\log\alpha + n\alpha\log x_m - (\alpha+1) \sum_i \log x_i
$$ (for $x_m<\min_i x_i$, ... | Variance of unbiased estimator for the shape parameter of Pareto distribution | I will write the standard Pareto distribution with density
$$
f(x;\alpha,x_m)=\frac{\alpha x_m^\alpha}{x^{\alpha+1}}\cdot I(x > x_m),
$$ for some $\alpha>0, x_m>0$. Then the loglikelihood function | Variance of unbiased estimator for the shape parameter of Pareto distribution
I will write the standard Pareto distribution with density
$$
f(x;\alpha,x_m)=\frac{\alpha x_m^\alpha}{x^{\alpha+1}}\cdot I(x > x_m),
$$ for some $\alpha>0, x_m>0$. Then the loglikelihood function can be written
$$
\ell(\alpha,x_m)=n\log\a... | Variance of unbiased estimator for the shape parameter of Pareto distribution
I will write the standard Pareto distribution with density
$$
f(x;\alpha,x_m)=\frac{\alpha x_m^\alpha}{x^{\alpha+1}}\cdot I(x > x_m),
$$ for some $\alpha>0, x_m>0$. Then the loglikelihood function |
54,819 | Interpreting BLUPs or VarCorr estimates in mixed models? | As explained in the answer you cited above, the covariance matrices are referring to two different models, one in the marginal model (integrating out the random effects), and the other on the conditional model on the random effects.
It is not that one is better than the other because they are not referring to the same... | Interpreting BLUPs or VarCorr estimates in mixed models? | As explained in the answer you cited above, the covariance matrices are referring to two different models, one in the marginal model (integrating out the random effects), and the other on the conditio | Interpreting BLUPs or VarCorr estimates in mixed models?
As explained in the answer you cited above, the covariance matrices are referring to two different models, one in the marginal model (integrating out the random effects), and the other on the conditional model on the random effects.
It is not that one is better ... | Interpreting BLUPs or VarCorr estimates in mixed models?
As explained in the answer you cited above, the covariance matrices are referring to two different models, one in the marginal model (integrating out the random effects), and the other on the conditio |
54,820 | What is a consequence of an ill-conditioned Hessian matrix? | It is easiest understood when considering solving the linear problem,
$$
Ax = b
$$
where $b$ and $A$ are the problem data, and $x$ the parameters we are trying to estimate. In practice you have errors in $b$ which propagate through $A$. How?
Assume we have only errors in the measurements, $b$, and denote $\delta b$ and... | What is a consequence of an ill-conditioned Hessian matrix? | It is easiest understood when considering solving the linear problem,
$$
Ax = b
$$
where $b$ and $A$ are the problem data, and $x$ the parameters we are trying to estimate. In practice you have errors | What is a consequence of an ill-conditioned Hessian matrix?
It is easiest understood when considering solving the linear problem,
$$
Ax = b
$$
where $b$ and $A$ are the problem data, and $x$ the parameters we are trying to estimate. In practice you have errors in $b$ which propagate through $A$. How?
Assume we have onl... | What is a consequence of an ill-conditioned Hessian matrix?
It is easiest understood when considering solving the linear problem,
$$
Ax = b
$$
where $b$ and $A$ are the problem data, and $x$ the parameters we are trying to estimate. In practice you have errors |
54,821 | What is a consequence of an ill-conditioned Hessian matrix? | Many optimization methods, such as Newton's, require the computation of the inverse of the Hessian.
The conditioning of a matrix $H$ is usually defined as the ratio between the largest and smallest singular values,
$$
\kappa(H)=\frac{\sigma_1}{\sigma_n}.
$$
If this number is large, that is, $\sigma_n$ is small with res... | What is a consequence of an ill-conditioned Hessian matrix? | Many optimization methods, such as Newton's, require the computation of the inverse of the Hessian.
The conditioning of a matrix $H$ is usually defined as the ratio between the largest and smallest si | What is a consequence of an ill-conditioned Hessian matrix?
Many optimization methods, such as Newton's, require the computation of the inverse of the Hessian.
The conditioning of a matrix $H$ is usually defined as the ratio between the largest and smallest singular values,
$$
\kappa(H)=\frac{\sigma_1}{\sigma_n}.
$$
If... | What is a consequence of an ill-conditioned Hessian matrix?
Many optimization methods, such as Newton's, require the computation of the inverse of the Hessian.
The conditioning of a matrix $H$ is usually defined as the ratio between the largest and smallest si |
54,822 | lmer for repeated measures | This seems to be a longitudinal study, with measurements over time for each pair. As a first step, based on the date variable you could construct the follow-up time variable, which is the time from the first measurement. Think however carefully if the first measurement really is the time 0 for each pair for your experi... | lmer for repeated measures | This seems to be a longitudinal study, with measurements over time for each pair. As a first step, based on the date variable you could construct the follow-up time variable, which is the time from th | lmer for repeated measures
This seems to be a longitudinal study, with measurements over time for each pair. As a first step, based on the date variable you could construct the follow-up time variable, which is the time from the first measurement. Think however carefully if the first measurement really is the time 0 fo... | lmer for repeated measures
This seems to be a longitudinal study, with measurements over time for each pair. As a first step, based on the date variable you could construct the follow-up time variable, which is the time from th |
54,823 | lmer for repeated measures | (my first attempted answer on stackexchange...fingers crossed that this works)
I'm not an expert, but I'll offer some feeback. I don't have enough reputation to put this in a comment, so here's an answer.
I guess the first question to ask is, what do you wish to learn from the data? You say you want to compare them. ... | lmer for repeated measures | (my first attempted answer on stackexchange...fingers crossed that this works)
I'm not an expert, but I'll offer some feeback. I don't have enough reputation to put this in a comment, so here's an an | lmer for repeated measures
(my first attempted answer on stackexchange...fingers crossed that this works)
I'm not an expert, but I'll offer some feeback. I don't have enough reputation to put this in a comment, so here's an answer.
I guess the first question to ask is, what do you wish to learn from the data? You say... | lmer for repeated measures
(my first attempted answer on stackexchange...fingers crossed that this works)
I'm not an expert, but I'll offer some feeback. I don't have enough reputation to put this in a comment, so here's an an |
54,824 | pymc3: acceptance probabilities and divergencies after tuning | You might have better luck on our discourse: https://discourse.pymc.io/
A couple of notes: You need to use: pm.sample(..., nuts_kwargs=dict(target_accept=0.95)) instead to have the target_accept be applied (this behavior is changed in line with what you tried in the next release). That might already solve your problem.... | pymc3: acceptance probabilities and divergencies after tuning | You might have better luck on our discourse: https://discourse.pymc.io/
A couple of notes: You need to use: pm.sample(..., nuts_kwargs=dict(target_accept=0.95)) instead to have the target_accept be ap | pymc3: acceptance probabilities and divergencies after tuning
You might have better luck on our discourse: https://discourse.pymc.io/
A couple of notes: You need to use: pm.sample(..., nuts_kwargs=dict(target_accept=0.95)) instead to have the target_accept be applied (this behavior is changed in line with what you trie... | pymc3: acceptance probabilities and divergencies after tuning
You might have better luck on our discourse: https://discourse.pymc.io/
A couple of notes: You need to use: pm.sample(..., nuts_kwargs=dict(target_accept=0.95)) instead to have the target_accept be ap |
54,825 | Central limit theorem (CLT) writing | The notation $\stackrel{d}{\rightarrow}$ in the CLT is shorthand for the formal limit statement:
$$\lim_{n \rightarrow \infty} \mathbb{P} \Big( \sqrt{n} (\bar{X}_n - \mu) \leqslant t \Big) = \Phi(t | 0, \sigma^2).$$
You will notice that the formal statement is a limit statement in $n$ and so all of the values of $n$ ar... | Central limit theorem (CLT) writing | The notation $\stackrel{d}{\rightarrow}$ in the CLT is shorthand for the formal limit statement:
$$\lim_{n \rightarrow \infty} \mathbb{P} \Big( \sqrt{n} (\bar{X}_n - \mu) \leqslant t \Big) = \Phi(t | | Central limit theorem (CLT) writing
The notation $\stackrel{d}{\rightarrow}$ in the CLT is shorthand for the formal limit statement:
$$\lim_{n \rightarrow \infty} \mathbb{P} \Big( \sqrt{n} (\bar{X}_n - \mu) \leqslant t \Big) = \Phi(t | 0, \sigma^2).$$
You will notice that the formal statement is a limit statement in $n... | Central limit theorem (CLT) writing
The notation $\stackrel{d}{\rightarrow}$ in the CLT is shorthand for the formal limit statement:
$$\lim_{n \rightarrow \infty} \mathbb{P} \Big( \sqrt{n} (\bar{X}_n - \mu) \leqslant t \Big) = \Phi(t | |
54,826 | Simple linear regression: If Y and X are both normal, what's the exact null distribution of the parameters? | Since you have specified that $X$ and $Y$ are independent, the conditional mean of $Y$ given $X$ is:
$$\mathbb{E}(Y|X) = \mathbb{E}(Y) = c,$$
which implies that:
$$\beta_0 = c \quad \quad \quad \beta_1 = 0 \quad \quad \quad \varepsilon \sim \text{N}(0, d).$$
In this case there is nothing to test --- your regression par... | Simple linear regression: If Y and X are both normal, what's the exact null distribution of the para | Since you have specified that $X$ and $Y$ are independent, the conditional mean of $Y$ given $X$ is:
$$\mathbb{E}(Y|X) = \mathbb{E}(Y) = c,$$
which implies that:
$$\beta_0 = c \quad \quad \quad \beta_ | Simple linear regression: If Y and X are both normal, what's the exact null distribution of the parameters?
Since you have specified that $X$ and $Y$ are independent, the conditional mean of $Y$ given $X$ is:
$$\mathbb{E}(Y|X) = \mathbb{E}(Y) = c,$$
which implies that:
$$\beta_0 = c \quad \quad \quad \beta_1 = 0 \quad ... | Simple linear regression: If Y and X are both normal, what's the exact null distribution of the para
Since you have specified that $X$ and $Y$ are independent, the conditional mean of $Y$ given $X$ is:
$$\mathbb{E}(Y|X) = \mathbb{E}(Y) = c,$$
which implies that:
$$\beta_0 = c \quad \quad \quad \beta_ |
54,827 | Simple linear regression: If Y and X are both normal, what's the exact null distribution of the parameters? | In simple linear regression the computation of the estimate of $\beta_0$ is:
$$\hat\beta_0 = \frac {1}{n} S_y + \frac {1}{n} S_x \frac {n S_{xy} - S_x S_y}{ n S_{xx} - S_x S_x}$$
with $S_x = \sum x_i $, $S_y = \sum y_i $, $S_{xx} = \sum x_i x_i $, $S_{xy} = \sum x_i y_i $
You could say it will be a linear sum of the $y... | Simple linear regression: If Y and X are both normal, what's the exact null distribution of the para | In simple linear regression the computation of the estimate of $\beta_0$ is:
$$\hat\beta_0 = \frac {1}{n} S_y + \frac {1}{n} S_x \frac {n S_{xy} - S_x S_y}{ n S_{xx} - S_x S_x}$$
with $S_x = \sum x_i | Simple linear regression: If Y and X are both normal, what's the exact null distribution of the parameters?
In simple linear regression the computation of the estimate of $\beta_0$ is:
$$\hat\beta_0 = \frac {1}{n} S_y + \frac {1}{n} S_x \frac {n S_{xy} - S_x S_y}{ n S_{xx} - S_x S_x}$$
with $S_x = \sum x_i $, $S_y = \s... | Simple linear regression: If Y and X are both normal, what's the exact null distribution of the para
In simple linear regression the computation of the estimate of $\beta_0$ is:
$$\hat\beta_0 = \frac {1}{n} S_y + \frac {1}{n} S_x \frac {n S_{xy} - S_x S_y}{ n S_{xx} - S_x S_x}$$
with $S_x = \sum x_i |
54,828 | Is a neural network consisting of a single softmax classification layer only a linear classifier? | A neural network with no hidden layers and a softmax output layer is exactly logistic regression (possibly with more than 2 classes), when trained to minimize categorical cross-entropy (equivalently maximize the log-likelihood of a multinomial model).
Your explanation is right on the money: a linear combination of inpu... | Is a neural network consisting of a single softmax classification layer only a linear classifier? | A neural network with no hidden layers and a softmax output layer is exactly logistic regression (possibly with more than 2 classes), when trained to minimize categorical cross-entropy (equivalently m | Is a neural network consisting of a single softmax classification layer only a linear classifier?
A neural network with no hidden layers and a softmax output layer is exactly logistic regression (possibly with more than 2 classes), when trained to minimize categorical cross-entropy (equivalently maximize the log-likeli... | Is a neural network consisting of a single softmax classification layer only a linear classifier?
A neural network with no hidden layers and a softmax output layer is exactly logistic regression (possibly with more than 2 classes), when trained to minimize categorical cross-entropy (equivalently m |
54,829 | Asymmetric cost function in neural networks | This might explain why there are not many papers on asymmetric loss functions.
That's not true. Cross-entropy is used as loss function in most classification problems (and problems that aren't standard classification, like for example autoencoder training and segmentation problems), and it's not symmetric. | Asymmetric cost function in neural networks | This might explain why there are not many papers on asymmetric loss functions.
That's not true. Cross-entropy is used as loss function in most classification problems (and problems that aren't standa | Asymmetric cost function in neural networks
This might explain why there are not many papers on asymmetric loss functions.
That's not true. Cross-entropy is used as loss function in most classification problems (and problems that aren't standard classification, like for example autoencoder training and segmentation pr... | Asymmetric cost function in neural networks
This might explain why there are not many papers on asymmetric loss functions.
That's not true. Cross-entropy is used as loss function in most classification problems (and problems that aren't standa |
54,830 | Asymmetric cost function in neural networks | It's not correct that there are few papers that use an asymmetric loss function. For instance, the cross-entropy loss is asymmetric, and there are gazillions of papers that use neural networks with a cross-entropy loss. Same for the hinge loss.
It's not correct that neural networks necessarily perform badly if you us... | Asymmetric cost function in neural networks | It's not correct that there are few papers that use an asymmetric loss function. For instance, the cross-entropy loss is asymmetric, and there are gazillions of papers that use neural networks with a | Asymmetric cost function in neural networks
It's not correct that there are few papers that use an asymmetric loss function. For instance, the cross-entropy loss is asymmetric, and there are gazillions of papers that use neural networks with a cross-entropy loss. Same for the hinge loss.
It's not correct that neural ... | Asymmetric cost function in neural networks
It's not correct that there are few papers that use an asymmetric loss function. For instance, the cross-entropy loss is asymmetric, and there are gazillions of papers that use neural networks with a |
54,831 | Asymmetric cost function in neural networks | There are some examples for research papers using asymmetric cost functions / loss functions. One example is "Residual value forecasting using asymmetric cost functions" published in the International Journal for Forecasting. Various estimation methods considering asymmetric costs were used and compared - including neu... | Asymmetric cost function in neural networks | There are some examples for research papers using asymmetric cost functions / loss functions. One example is "Residual value forecasting using asymmetric cost functions" published in the International | Asymmetric cost function in neural networks
There are some examples for research papers using asymmetric cost functions / loss functions. One example is "Residual value forecasting using asymmetric cost functions" published in the International Journal for Forecasting. Various estimation methods considering asymmetric ... | Asymmetric cost function in neural networks
There are some examples for research papers using asymmetric cost functions / loss functions. One example is "Residual value forecasting using asymmetric cost functions" published in the International |
54,832 | Separate Models vs Flags in the same model | I will write an answer assuming some form of regression (-like) model. You say neural network, much the same will apply, nevertheless it will be helpful to understand the issues in a simpler setting. And you should probably try some simpler model before throwing the data at a neural network ...
So let $Y_i$ be the resp... | Separate Models vs Flags in the same model | I will write an answer assuming some form of regression (-like) model. You say neural network, much the same will apply, nevertheless it will be helpful to understand the issues in a simpler setting. | Separate Models vs Flags in the same model
I will write an answer assuming some form of regression (-like) model. You say neural network, much the same will apply, nevertheless it will be helpful to understand the issues in a simpler setting. And you should probably try some simpler model before throwing the data at a ... | Separate Models vs Flags in the same model
I will write an answer assuming some form of regression (-like) model. You say neural network, much the same will apply, nevertheless it will be helpful to understand the issues in a simpler setting. |
54,833 | Association, relationship and correlation | They may sometimes be used as if they mean the same thing but correlation is more specific, and association is more general, with relationship being between the two.
Correlation means that they move together (positive correlation indicates increasing and decreasing together, negative correlation means they move in oppo... | Association, relationship and correlation | They may sometimes be used as if they mean the same thing but correlation is more specific, and association is more general, with relationship being between the two.
Correlation means that they move t | Association, relationship and correlation
They may sometimes be used as if they mean the same thing but correlation is more specific, and association is more general, with relationship being between the two.
Correlation means that they move together (positive correlation indicates increasing and decreasing together, ne... | Association, relationship and correlation
They may sometimes be used as if they mean the same thing but correlation is more specific, and association is more general, with relationship being between the two.
Correlation means that they move t |
54,834 | Question about the latent variable in EM algorithm | There is a lot of confusion in the question, confusion that could be reduced by looking at a textbook on the paper, or even the original 1977 paper by Dempster, Laird and Rubin.
Here is an excerpt of our book, Introducing Monte Carlo Methods with R, followed by my answer:
Assume that we observe $X_1, \ldots, X_n$, jo... | Question about the latent variable in EM algorithm | There is a lot of confusion in the question, confusion that could be reduced by looking at a textbook on the paper, or even the original 1977 paper by Dempster, Laird and Rubin.
Here is an excerpt of | Question about the latent variable in EM algorithm
There is a lot of confusion in the question, confusion that could be reduced by looking at a textbook on the paper, or even the original 1977 paper by Dempster, Laird and Rubin.
Here is an excerpt of our book, Introducing Monte Carlo Methods with R, followed by my ans... | Question about the latent variable in EM algorithm
There is a lot of confusion in the question, confusion that could be reduced by looking at a textbook on the paper, or even the original 1977 paper by Dempster, Laird and Rubin.
Here is an excerpt of |
54,835 | Question about the latent variable in EM algorithm | If I correctly read between the lines, your question is about the difference between the distribution of $[z]$ (i.e., the prior distribution of the latent variable), and the distribution of $[z \mid y]$ (i.e., the posterior distribution of the latent variable given the data $y$).
The prior probabilities are the same fo... | Question about the latent variable in EM algorithm | If I correctly read between the lines, your question is about the difference between the distribution of $[z]$ (i.e., the prior distribution of the latent variable), and the distribution of $[z \mid y | Question about the latent variable in EM algorithm
If I correctly read between the lines, your question is about the difference between the distribution of $[z]$ (i.e., the prior distribution of the latent variable), and the distribution of $[z \mid y]$ (i.e., the posterior distribution of the latent variable given the... | Question about the latent variable in EM algorithm
If I correctly read between the lines, your question is about the difference between the distribution of $[z]$ (i.e., the prior distribution of the latent variable), and the distribution of $[z \mid y |
54,836 | Ways of Testing Linearity Assumption in Multiple Regression apart from Residual Plots | What you can do is fit a model that relaxes the linearity assumption, using, e.g., splines, and compare it with the model that assumes linearity. For example, in R, for a linear regression model you can do something like that:
library("splines")
# linear effect of age on y
fm_linear <- lm(y ~ age + sex, data = your_da... | Ways of Testing Linearity Assumption in Multiple Regression apart from Residual Plots | What you can do is fit a model that relaxes the linearity assumption, using, e.g., splines, and compare it with the model that assumes linearity. For example, in R, for a linear regression model you c | Ways of Testing Linearity Assumption in Multiple Regression apart from Residual Plots
What you can do is fit a model that relaxes the linearity assumption, using, e.g., splines, and compare it with the model that assumes linearity. For example, in R, for a linear regression model you can do something like that:
library... | Ways of Testing Linearity Assumption in Multiple Regression apart from Residual Plots
What you can do is fit a model that relaxes the linearity assumption, using, e.g., splines, and compare it with the model that assumes linearity. For example, in R, for a linear regression model you c |
54,837 | How to interpret the result of Friedman's test? | The problem is that the row and column labels for the matrix make the results difficult to understand. ‡
In the following, since there are no column labels, the columns will be labeled V1 to V7 by default. This will make it easy to evaluate the comparisons between them.
if(!require(PMCMR)){install.packages("PMCMR")}
... | How to interpret the result of Friedman's test? | The problem is that the row and column labels for the matrix make the results difficult to understand. ‡
In the following, since there are no column labels, the columns will be labeled V1 to V7 by def | How to interpret the result of Friedman's test?
The problem is that the row and column labels for the matrix make the results difficult to understand. ‡
In the following, since there are no column labels, the columns will be labeled V1 to V7 by default. This will make it easy to evaluate the comparisons between them.
... | How to interpret the result of Friedman's test?
The problem is that the row and column labels for the matrix make the results difficult to understand. ‡
In the following, since there are no column labels, the columns will be labeled V1 to V7 by def |
54,838 | Confidence intervals for autocorrelation function | A quick google search with "confidence intervals for acfs" yielded
Janet M. Box-Steffensmeier, John R. Freeman, Matthew P. Hitt, Jon C. W. Pevehouse: Time Series Analysis for the Social Sciences.
In there, on page 38, the standard error of an AC estimator at lag k is stated to be
$AC_{SE,k} = \sqrt{N^{-1}\left(1+2\sum_... | Confidence intervals for autocorrelation function | A quick google search with "confidence intervals for acfs" yielded
Janet M. Box-Steffensmeier, John R. Freeman, Matthew P. Hitt, Jon C. W. Pevehouse: Time Series Analysis for the Social Sciences.
In t | Confidence intervals for autocorrelation function
A quick google search with "confidence intervals for acfs" yielded
Janet M. Box-Steffensmeier, John R. Freeman, Matthew P. Hitt, Jon C. W. Pevehouse: Time Series Analysis for the Social Sciences.
In there, on page 38, the standard error of an AC estimator at lag k is st... | Confidence intervals for autocorrelation function
A quick google search with "confidence intervals for acfs" yielded
Janet M. Box-Steffensmeier, John R. Freeman, Matthew P. Hitt, Jon C. W. Pevehouse: Time Series Analysis for the Social Sciences.
In t |
54,839 | Confidence intervals for autocorrelation function | When the ACF is estimated from data I think also the error should be directly computed from the same data. I think that is generally the safest and most conservative approach. I would just store the resulting products of the signal with itself after each shift in the row of a matrix. Then you have the full distribution... | Confidence intervals for autocorrelation function | When the ACF is estimated from data I think also the error should be directly computed from the same data. I think that is generally the safest and most conservative approach. I would just store the r | Confidence intervals for autocorrelation function
When the ACF is estimated from data I think also the error should be directly computed from the same data. I think that is generally the safest and most conservative approach. I would just store the resulting products of the signal with itself after each shift in the ro... | Confidence intervals for autocorrelation function
When the ACF is estimated from data I think also the error should be directly computed from the same data. I think that is generally the safest and most conservative approach. I would just store the r |
54,840 | Build a (normal?) distribution from $n$, quartiles and mean? | The answer is No, not exactly anyhow.
If you have two quartiles of a normal population then you can find $\mu$ and $\sigma.$ For example the lower and upper quantiles of $\mathsf{Norm}(\mu = 100,\, \sigma = 10)$ are $93.255$ and $106.745,$ respectively.
qnorm(c(.25, .75), 100, 10)
[1] 93.2551 106.7449
Then $P\left(... | Build a (normal?) distribution from $n$, quartiles and mean? | The answer is No, not exactly anyhow.
If you have two quartiles of a normal population then you can find $\mu$ and $\sigma.$ For example the lower and upper quantiles of $\mathsf{Norm}(\mu = 100,\, \s | Build a (normal?) distribution from $n$, quartiles and mean?
The answer is No, not exactly anyhow.
If you have two quartiles of a normal population then you can find $\mu$ and $\sigma.$ For example the lower and upper quantiles of $\mathsf{Norm}(\mu = 100,\, \sigma = 10)$ are $93.255$ and $106.745,$ respectively.
qnor... | Build a (normal?) distribution from $n$, quartiles and mean?
The answer is No, not exactly anyhow.
If you have two quartiles of a normal population then you can find $\mu$ and $\sigma.$ For example the lower and upper quantiles of $\mathsf{Norm}(\mu = 100,\, \s |
54,841 | Build a (normal?) distribution from $n$, quartiles and mean? | Based on @whuber's Comments about 'modeling', I gave some thought to relatively elementary methods that might be used to estimate the parameters of a normal distribution given the sample size, sample quartiles, and sample mean, assuming that data are normal.
Most of this will work better for very large $n.$ After some ... | Build a (normal?) distribution from $n$, quartiles and mean? | Based on @whuber's Comments about 'modeling', I gave some thought to relatively elementary methods that might be used to estimate the parameters of a normal distribution given the sample size, sample | Build a (normal?) distribution from $n$, quartiles and mean?
Based on @whuber's Comments about 'modeling', I gave some thought to relatively elementary methods that might be used to estimate the parameters of a normal distribution given the sample size, sample quartiles, and sample mean, assuming that data are normal.
... | Build a (normal?) distribution from $n$, quartiles and mean?
Based on @whuber's Comments about 'modeling', I gave some thought to relatively elementary methods that might be used to estimate the parameters of a normal distribution given the sample size, sample |
54,842 | Build a (normal?) distribution from $n$, quartiles and mean? | It is possible to estimate the parameters based on this information, but to construct some (approximate) likelihood function based on the given information $n,Q_1, Q_3, \bar{X}_n$ do not see easy. In a way this is a followup on the answer by @BruceET, trying to formalize ideas in that answer.
Using the theory of order ... | Build a (normal?) distribution from $n$, quartiles and mean? | It is possible to estimate the parameters based on this information, but to construct some (approximate) likelihood function based on the given information $n,Q_1, Q_3, \bar{X}_n$ do not see easy. In | Build a (normal?) distribution from $n$, quartiles and mean?
It is possible to estimate the parameters based on this information, but to construct some (approximate) likelihood function based on the given information $n,Q_1, Q_3, \bar{X}_n$ do not see easy. In a way this is a followup on the answer by @BruceET, trying ... | Build a (normal?) distribution from $n$, quartiles and mean?
It is possible to estimate the parameters based on this information, but to construct some (approximate) likelihood function based on the given information $n,Q_1, Q_3, \bar{X}_n$ do not see easy. In |
54,843 | What is intuition behind high variance of Monte Carlo method? [closed] | In RL, for value functions, the bias and variance refer to behaviour of different kinds of estimate for the value function. The value function's true value is the expected return from a specific starting state (and action for action values), assuming that all actions are selected according to the policy being evaluated... | What is intuition behind high variance of Monte Carlo method? [closed] | In RL, for value functions, the bias and variance refer to behaviour of different kinds of estimate for the value function. The value function's true value is the expected return from a specific start | What is intuition behind high variance of Monte Carlo method? [closed]
In RL, for value functions, the bias and variance refer to behaviour of different kinds of estimate for the value function. The value function's true value is the expected return from a specific starting state (and action for action values), assumin... | What is intuition behind high variance of Monte Carlo method? [closed]
In RL, for value functions, the bias and variance refer to behaviour of different kinds of estimate for the value function. The value function's true value is the expected return from a specific start |
54,844 | Why do descriptive statistics contradict with regression coefficents? | This not an issue with L1 norms nor with logistic regression specifically; it will happen with ordinary L2-norm multiple linear regression. The direction of an unconditional relationship can change once you condition on another variable (include an additional feature).
Consider 4 groups, where the $p=\text{Pr}(Y=1)$ i... | Why do descriptive statistics contradict with regression coefficents? | This not an issue with L1 norms nor with logistic regression specifically; it will happen with ordinary L2-norm multiple linear regression. The direction of an unconditional relationship can change on | Why do descriptive statistics contradict with regression coefficents?
This not an issue with L1 norms nor with logistic regression specifically; it will happen with ordinary L2-norm multiple linear regression. The direction of an unconditional relationship can change once you condition on another variable (include an a... | Why do descriptive statistics contradict with regression coefficents?
This not an issue with L1 norms nor with logistic regression specifically; it will happen with ordinary L2-norm multiple linear regression. The direction of an unconditional relationship can change on |
54,845 | In propensity score matching, should a variable used in exact matching also be used in the model? | I always fall back on the propensity score tautology (Ho, Imai. King, & Stuart, 2007): a propensity score (model) should be evaluated for its ability to yield balance samples. Try both methods and see which yields better balance. It's hard to make a general rule when every dataset is different and might have peculiarit... | In propensity score matching, should a variable used in exact matching also be used in the model? | I always fall back on the propensity score tautology (Ho, Imai. King, & Stuart, 2007): a propensity score (model) should be evaluated for its ability to yield balance samples. Try both methods and see | In propensity score matching, should a variable used in exact matching also be used in the model?
I always fall back on the propensity score tautology (Ho, Imai. King, & Stuart, 2007): a propensity score (model) should be evaluated for its ability to yield balance samples. Try both methods and see which yields better b... | In propensity score matching, should a variable used in exact matching also be used in the model?
I always fall back on the propensity score tautology (Ho, Imai. King, & Stuart, 2007): a propensity score (model) should be evaluated for its ability to yield balance samples. Try both methods and see |
54,846 | In propensity score matching, should a variable used in exact matching also be used in the model? | Yes, we can/is recommended to use a variable $x$ that we used for matching in our final model. The matching itself can also have different steps as here, both exact and then PSM. Using multiple procedures in our analysis does not necessitate using a variable $x$ only in one of the steps.
Using certain covariates with ... | In propensity score matching, should a variable used in exact matching also be used in the model? | Yes, we can/is recommended to use a variable $x$ that we used for matching in our final model. The matching itself can also have different steps as here, both exact and then PSM. Using multiple proce | In propensity score matching, should a variable used in exact matching also be used in the model?
Yes, we can/is recommended to use a variable $x$ that we used for matching in our final model. The matching itself can also have different steps as here, both exact and then PSM. Using multiple procedures in our analysis ... | In propensity score matching, should a variable used in exact matching also be used in the model?
Yes, we can/is recommended to use a variable $x$ that we used for matching in our final model. The matching itself can also have different steps as here, both exact and then PSM. Using multiple proce |
54,847 | Simple Linear Regression: how does $\Sigma\hat{u_i}^2/\sigma^2$ follow chi squared distribution with df (n-2)? | The correct expression for the variance of the $i$th residual is explained here in detail.
I am using a slightly different notation but in the end it will all match with what you are working with.
Suppose we have a simple linear regression model $$y=\alpha+\beta x+\epsilon$$
where $\alpha+\beta x$ is the part of $y$ ex... | Simple Linear Regression: how does $\Sigma\hat{u_i}^2/\sigma^2$ follow chi squared distribution with | The correct expression for the variance of the $i$th residual is explained here in detail.
I am using a slightly different notation but in the end it will all match with what you are working with.
Sup | Simple Linear Regression: how does $\Sigma\hat{u_i}^2/\sigma^2$ follow chi squared distribution with df (n-2)?
The correct expression for the variance of the $i$th residual is explained here in detail.
I am using a slightly different notation but in the end it will all match with what you are working with.
Suppose we h... | Simple Linear Regression: how does $\Sigma\hat{u_i}^2/\sigma^2$ follow chi squared distribution with
The correct expression for the variance of the $i$th residual is explained here in detail.
I am using a slightly different notation but in the end it will all match with what you are working with.
Sup |
54,848 | Does it make sense to use an Early Stopping Metric like “mae” instaed of “val_loss” for regression problems? | In order to prevent overfitting, EarlyStopping should monitor a validation metric. Because your loss function is the mse, by monitoring val_loss you are essentially monitoring the validation Mean Squared Error. If you think that mae is a better metric for your task, you should monitor val_mae instead.
Why monitor a va... | Does it make sense to use an Early Stopping Metric like “mae” instaed of “val_loss” for regression p | In order to prevent overfitting, EarlyStopping should monitor a validation metric. Because your loss function is the mse, by monitoring val_loss you are essentially monitoring the validation Mean Squa | Does it make sense to use an Early Stopping Metric like “mae” instaed of “val_loss” for regression problems?
In order to prevent overfitting, EarlyStopping should monitor a validation metric. Because your loss function is the mse, by monitoring val_loss you are essentially monitoring the validation Mean Squared Error. ... | Does it make sense to use an Early Stopping Metric like “mae” instaed of “val_loss” for regression p
In order to prevent overfitting, EarlyStopping should monitor a validation metric. Because your loss function is the mse, by monitoring val_loss you are essentially monitoring the validation Mean Squa |
54,849 | Why is multicollinearity so bad for machine learning models and what can we do about it? | Multicollinearity simply imlies that one or more of the features in your dataset are useless to the model. Thus you get all the problems associated with more features (i.e. curse of dimensionality), but none of the benefits (e.g. making the classes easier separable).
Many ML algorithms are impervious to problems of thi... | Why is multicollinearity so bad for machine learning models and what can we do about it? | Multicollinearity simply imlies that one or more of the features in your dataset are useless to the model. Thus you get all the problems associated with more features (i.e. curse of dimensionality), b | Why is multicollinearity so bad for machine learning models and what can we do about it?
Multicollinearity simply imlies that one or more of the features in your dataset are useless to the model. Thus you get all the problems associated with more features (i.e. curse of dimensionality), but none of the benefits (e.g. m... | Why is multicollinearity so bad for machine learning models and what can we do about it?
Multicollinearity simply imlies that one or more of the features in your dataset are useless to the model. Thus you get all the problems associated with more features (i.e. curse of dimensionality), b |
54,850 | Why is multicollinearity so bad for machine learning models and what can we do about it? | The easiest way to understand is to imagine that you have two identical features, e.g. temperature in Celsius and Fehrenheits. This is a case of perfect collinearity.
Two things will happen, both bad. One is that at the very least you're going to waste some neurons. In the first layer you have $a^{[0]}_i$ inputs for $... | Why is multicollinearity so bad for machine learning models and what can we do about it? | The easiest way to understand is to imagine that you have two identical features, e.g. temperature in Celsius and Fehrenheits. This is a case of perfect collinearity.
Two things will happen, both bad | Why is multicollinearity so bad for machine learning models and what can we do about it?
The easiest way to understand is to imagine that you have two identical features, e.g. temperature in Celsius and Fehrenheits. This is a case of perfect collinearity.
Two things will happen, both bad. One is that at the very least... | Why is multicollinearity so bad for machine learning models and what can we do about it?
The easiest way to understand is to imagine that you have two identical features, e.g. temperature in Celsius and Fehrenheits. This is a case of perfect collinearity.
Two things will happen, both bad |
54,851 | Conditional expectation on an estimator for defensive sampling | Yeah that’s what I thought when I first looked at it. But the conditional expectation is taken with respect to the conditional pmf of $Y$ given $X_i =x_i$. If $y=1$ the weight for $f(x_i) g_1^{-1}(x_i)$ is $\frac{\varrho g_1(x_i)}{g_1(x_i)\varrho + g_2(x_i) (1-\varrho)}$. You can follow a similar path to obtain the wei... | Conditional expectation on an estimator for defensive sampling | Yeah that’s what I thought when I first looked at it. But the conditional expectation is taken with respect to the conditional pmf of $Y$ given $X_i =x_i$. If $y=1$ the weight for $f(x_i) g_1^{-1}(x_i | Conditional expectation on an estimator for defensive sampling
Yeah that’s what I thought when I first looked at it. But the conditional expectation is taken with respect to the conditional pmf of $Y$ given $X_i =x_i$. If $y=1$ the weight for $f(x_i) g_1^{-1}(x_i)$ is $\frac{\varrho g_1(x_i)}{g_1(x_i)\varrho + g_2(x_i)... | Conditional expectation on an estimator for defensive sampling
Yeah that’s what I thought when I first looked at it. But the conditional expectation is taken with respect to the conditional pmf of $Y$ given $X_i =x_i$. If $y=1$ the weight for $f(x_i) g_1^{-1}(x_i |
54,852 | Conditional expectation on an estimator for defensive sampling | Hopefully a correct derivation based on Taylor's answer...
$$E\left[\frac{f(X_i)}{g_{Y_i}(X_i)}|X_i\right]=\int \frac{f(X_i)}{g_{Y_i}(X_i)}k(X_i,dY_i)=\sum_{j=1}^2 \frac{f(X_i)}{g_j(X_i)}\frac{p(X_i|Y_{i}=j)p(Y_{i}=j)}{p(X_i)}$$
where $k$ is a regular conditional distribution, $X_i$ is cont. and $Y_i$ is discrete,
$$\s... | Conditional expectation on an estimator for defensive sampling | Hopefully a correct derivation based on Taylor's answer...
$$E\left[\frac{f(X_i)}{g_{Y_i}(X_i)}|X_i\right]=\int \frac{f(X_i)}{g_{Y_i}(X_i)}k(X_i,dY_i)=\sum_{j=1}^2 \frac{f(X_i)}{g_j(X_i)}\frac{p(X_i|Y | Conditional expectation on an estimator for defensive sampling
Hopefully a correct derivation based on Taylor's answer...
$$E\left[\frac{f(X_i)}{g_{Y_i}(X_i)}|X_i\right]=\int \frac{f(X_i)}{g_{Y_i}(X_i)}k(X_i,dY_i)=\sum_{j=1}^2 \frac{f(X_i)}{g_j(X_i)}\frac{p(X_i|Y_{i}=j)p(Y_{i}=j)}{p(X_i)}$$
where $k$ is a regular condi... | Conditional expectation on an estimator for defensive sampling
Hopefully a correct derivation based on Taylor's answer...
$$E\left[\frac{f(X_i)}{g_{Y_i}(X_i)}|X_i\right]=\int \frac{f(X_i)}{g_{Y_i}(X_i)}k(X_i,dY_i)=\sum_{j=1}^2 \frac{f(X_i)}{g_j(X_i)}\frac{p(X_i|Y |
54,853 | Conditional expectation on an estimator for defensive sampling | Just to step in a wee bit late,
\begin{align*}
\mathbb{E}\left[\dfrac{f(X_i)}{g_{Y_i}(X_i)}\big|X_i\right]
&= \dfrac{f(X_i)}{g_{1}(X_i)} \mathbb{P}(Y_i=1|X_i) + \dfrac{f(X_i)}{g_{2}(X_i)} \mathbb{P}(Y_i=2|X_i)\\
&= \dfrac{f(X_i)}{g_{1}(X_i)} \dfrac{\rho g_1(X_i)}{\rho g_1(X_i) +(1-\rho) g_2(X_i)} + \dfrac{f(X_i)}{g_{2... | Conditional expectation on an estimator for defensive sampling | Just to step in a wee bit late,
\begin{align*}
\mathbb{E}\left[\dfrac{f(X_i)}{g_{Y_i}(X_i)}\big|X_i\right]
&= \dfrac{f(X_i)}{g_{1}(X_i)} \mathbb{P}(Y_i=1|X_i) + \dfrac{f(X_i)}{g_{2}(X_i)} \mathbb{P}( | Conditional expectation on an estimator for defensive sampling
Just to step in a wee bit late,
\begin{align*}
\mathbb{E}\left[\dfrac{f(X_i)}{g_{Y_i}(X_i)}\big|X_i\right]
&= \dfrac{f(X_i)}{g_{1}(X_i)} \mathbb{P}(Y_i=1|X_i) + \dfrac{f(X_i)}{g_{2}(X_i)} \mathbb{P}(Y_i=2|X_i)\\
&= \dfrac{f(X_i)}{g_{1}(X_i)} \dfrac{\rho g_... | Conditional expectation on an estimator for defensive sampling
Just to step in a wee bit late,
\begin{align*}
\mathbb{E}\left[\dfrac{f(X_i)}{g_{Y_i}(X_i)}\big|X_i\right]
&= \dfrac{f(X_i)}{g_{1}(X_i)} \mathbb{P}(Y_i=1|X_i) + \dfrac{f(X_i)}{g_{2}(X_i)} \mathbb{P}( |
54,854 | Why is Kendall's tau not consistent? | This is an issue of a measure (and hence the test based on it) not being able to pick up an association (an alternative under the test) it's not designed for.
In the same sense a t-test of means is not "consistent" against a difference in distributions that only related to a change in the spread. Almost any test or sta... | Why is Kendall's tau not consistent? | This is an issue of a measure (and hence the test based on it) not being able to pick up an association (an alternative under the test) it's not designed for.
In the same sense a t-test of means is no | Why is Kendall's tau not consistent?
This is an issue of a measure (and hence the test based on it) not being able to pick up an association (an alternative under the test) it's not designed for.
In the same sense a t-test of means is not "consistent" against a difference in distributions that only related to a change ... | Why is Kendall's tau not consistent?
This is an issue of a measure (and hence the test based on it) not being able to pick up an association (an alternative under the test) it's not designed for.
In the same sense a t-test of means is no |
54,855 | Eicker-Huber-White Robust Variance Estimator | There is a little mistake in your statement, as your $s_t^2$, $t=0,1$, define the sum of squared residuals belonging to the two groups of observations. The formula you refer to (unless your textbook has a typo) defines $s_t^2$ as the estimate of the error variances of the two groups (which, under heteroskedasticity, ar... | Eicker-Huber-White Robust Variance Estimator | There is a little mistake in your statement, as your $s_t^2$, $t=0,1$, define the sum of squared residuals belonging to the two groups of observations. The formula you refer to (unless your textbook h | Eicker-Huber-White Robust Variance Estimator
There is a little mistake in your statement, as your $s_t^2$, $t=0,1$, define the sum of squared residuals belonging to the two groups of observations. The formula you refer to (unless your textbook has a typo) defines $s_t^2$ as the estimate of the error variances of the tw... | Eicker-Huber-White Robust Variance Estimator
There is a little mistake in your statement, as your $s_t^2$, $t=0,1$, define the sum of squared residuals belonging to the two groups of observations. The formula you refer to (unless your textbook h |
54,856 | Direction of correlation | I believe that a Pearson correlation is not capable of telling you which 'direction' the relationship is.
A Pearson correlation is essentially looking for the tendency of one variable to vary in a certain way with another variable, but can not establish a causal link in that way.
For example, it is possible that having... | Direction of correlation | I believe that a Pearson correlation is not capable of telling you which 'direction' the relationship is.
A Pearson correlation is essentially looking for the tendency of one variable to vary in a cer | Direction of correlation
I believe that a Pearson correlation is not capable of telling you which 'direction' the relationship is.
A Pearson correlation is essentially looking for the tendency of one variable to vary in a certain way with another variable, but can not establish a causal link in that way.
For example, i... | Direction of correlation
I believe that a Pearson correlation is not capable of telling you which 'direction' the relationship is.
A Pearson correlation is essentially looking for the tendency of one variable to vary in a cer |
54,857 | Direction of correlation | The short answer is that you can't use Pearson correlation to determine causality. This is directly related to the popular saying that causation means correlation, but not vise versa.
To give a reason, I think it's best to look at Wilk's lambda as a test of significance. Briefly, Wilk's lambda can be used as a signifi... | Direction of correlation | The short answer is that you can't use Pearson correlation to determine causality. This is directly related to the popular saying that causation means correlation, but not vise versa.
To give a reaso | Direction of correlation
The short answer is that you can't use Pearson correlation to determine causality. This is directly related to the popular saying that causation means correlation, but not vise versa.
To give a reason, I think it's best to look at Wilk's lambda as a test of significance. Briefly, Wilk's lambda... | Direction of correlation
The short answer is that you can't use Pearson correlation to determine causality. This is directly related to the popular saying that causation means correlation, but not vise versa.
To give a reaso |
54,858 | Direction of correlation | You always have to remember that correlation is not causality! No correlation coefficient will tell you the causal relationship of your variables. The only way you can identify causation might be to run linear regression with lagged variables (if you have time series data) and see what seems to predict the other based ... | Direction of correlation | You always have to remember that correlation is not causality! No correlation coefficient will tell you the causal relationship of your variables. The only way you can identify causation might be to r | Direction of correlation
You always have to remember that correlation is not causality! No correlation coefficient will tell you the causal relationship of your variables. The only way you can identify causation might be to run linear regression with lagged variables (if you have time series data) and see what seems to... | Direction of correlation
You always have to remember that correlation is not causality! No correlation coefficient will tell you the causal relationship of your variables. The only way you can identify causation might be to r |
54,859 | Maximum likelihood and Gumbel distribution. Does the likelihood have a global maximum? | I will prove a more general result: if a density is log-concave, then
the log-likelihood of the corresponding location-scale family has a
global maximum. The wanted result then follows,
since the Gumbel density is log-concave.
Consider a univariate density $f^\star(y)$ which is log-concave and
smooth on the real line; ... | Maximum likelihood and Gumbel distribution. Does the likelihood have a global maximum? | I will prove a more general result: if a density is log-concave, then
the log-likelihood of the corresponding location-scale family has a
global maximum. The wanted result then follows,
since the Gumb | Maximum likelihood and Gumbel distribution. Does the likelihood have a global maximum?
I will prove a more general result: if a density is log-concave, then
the log-likelihood of the corresponding location-scale family has a
global maximum. The wanted result then follows,
since the Gumbel density is log-concave.
Consid... | Maximum likelihood and Gumbel distribution. Does the likelihood have a global maximum?
I will prove a more general result: if a density is log-concave, then
the log-likelihood of the corresponding location-scale family has a
global maximum. The wanted result then follows,
since the Gumb |
54,860 | Maximum likelihood and Gumbel distribution. Does the likelihood have a global maximum? | Here is the (log-)likelihood surface in $(u,\alpha)$ for a sample of 100 points from a standard Gumbel:
As you can see, the mode is located near $(0,1)$ which is the true value of the parameter. The graph was made by the following R code
library(VGAM)
obs=rgumbel(1e3)
loca=seq(min(obs),max(obs),le=1e2)
scala=seq(.1*sd... | Maximum likelihood and Gumbel distribution. Does the likelihood have a global maximum? | Here is the (log-)likelihood surface in $(u,\alpha)$ for a sample of 100 points from a standard Gumbel:
As you can see, the mode is located near $(0,1)$ which is the true value of the parameter. The | Maximum likelihood and Gumbel distribution. Does the likelihood have a global maximum?
Here is the (log-)likelihood surface in $(u,\alpha)$ for a sample of 100 points from a standard Gumbel:
As you can see, the mode is located near $(0,1)$ which is the true value of the parameter. The graph was made by the following R... | Maximum likelihood and Gumbel distribution. Does the likelihood have a global maximum?
Here is the (log-)likelihood surface in $(u,\alpha)$ for a sample of 100 points from a standard Gumbel:
As you can see, the mode is located near $(0,1)$ which is the true value of the parameter. The |
54,861 | Binary logistic regression: Interpreting odds ratio vs. comparing predictive probabilities | We often interpret the odds ratio like you did: $\newcommand{\Odds}{\text{Odds}}\newcommand{\event}{\text{event}}\newcommand{\noevent}{\text{no event}}$
people with an x score of 1 are 12 times as likely then people with an x score of 0 to have a positive outcome on y
But likely is purposefully vague here so as not t... | Binary logistic regression: Interpreting odds ratio vs. comparing predictive probabilities | We often interpret the odds ratio like you did: $\newcommand{\Odds}{\text{Odds}}\newcommand{\event}{\text{event}}\newcommand{\noevent}{\text{no event}}$
people with an x score of 1 are 12 times as li | Binary logistic regression: Interpreting odds ratio vs. comparing predictive probabilities
We often interpret the odds ratio like you did: $\newcommand{\Odds}{\text{Odds}}\newcommand{\event}{\text{event}}\newcommand{\noevent}{\text{no event}}$
people with an x score of 1 are 12 times as likely then people with an x sc... | Binary logistic regression: Interpreting odds ratio vs. comparing predictive probabilities
We often interpret the odds ratio like you did: $\newcommand{\Odds}{\text{Odds}}\newcommand{\event}{\text{event}}\newcommand{\noevent}{\text{no event}}$
people with an x score of 1 are 12 times as li |
54,862 | Interpretation of modes in periodogram | My apologies in advance, I wrote a bit of a novel.
tl;dr
1) Likely there is a mean or trend in the data. This is usually represented at the zero-frequency.
2) Yes, you could say there's a periodic component at this point with a period of 200 time units (seconds).
3) Yes, you can do this, it depends on the method. If ... | Interpretation of modes in periodogram | My apologies in advance, I wrote a bit of a novel.
tl;dr
1) Likely there is a mean or trend in the data. This is usually represented at the zero-frequency.
2) Yes, you could say there's a periodic co | Interpretation of modes in periodogram
My apologies in advance, I wrote a bit of a novel.
tl;dr
1) Likely there is a mean or trend in the data. This is usually represented at the zero-frequency.
2) Yes, you could say there's a periodic component at this point with a period of 200 time units (seconds).
3) Yes, you can ... | Interpretation of modes in periodogram
My apologies in advance, I wrote a bit of a novel.
tl;dr
1) Likely there is a mean or trend in the data. This is usually represented at the zero-frequency.
2) Yes, you could say there's a periodic co |
54,863 | How to choose a way to obtain maximum likelihood estimation | There is nothing special about MLEs here, since what you're asking really applies to any optimisation problem. In this broader sense, you want to know what methods are desirable to maximise/minimise a function.
Applying standard calculus methods for optimisation, you should be able to get an equation for the critical ... | How to choose a way to obtain maximum likelihood estimation | There is nothing special about MLEs here, since what you're asking really applies to any optimisation problem. In this broader sense, you want to know what methods are desirable to maximise/minimise | How to choose a way to obtain maximum likelihood estimation
There is nothing special about MLEs here, since what you're asking really applies to any optimisation problem. In this broader sense, you want to know what methods are desirable to maximise/minimise a function.
Applying standard calculus methods for optimisat... | How to choose a way to obtain maximum likelihood estimation
There is nothing special about MLEs here, since what you're asking really applies to any optimisation problem. In this broader sense, you want to know what methods are desirable to maximise/minimise |
54,864 | Coordinate prediction parameterization in object detection networks | The parametrization seems to originate from the R-CNN paper, Girschick et al., 2013: Rich feature hierarchies for accurate object detection and semantic segmentation. Note that SSD is also using this parametrization (see Eq. (2) in the paper).
Using this parametrization, size of a bounding box is computed as $w=w_a\exp... | Coordinate prediction parameterization in object detection networks | The parametrization seems to originate from the R-CNN paper, Girschick et al., 2013: Rich feature hierarchies for accurate object detection and semantic segmentation. Note that SSD is also using this | Coordinate prediction parameterization in object detection networks
The parametrization seems to originate from the R-CNN paper, Girschick et al., 2013: Rich feature hierarchies for accurate object detection and semantic segmentation. Note that SSD is also using this parametrization (see Eq. (2) in the paper).
Using th... | Coordinate prediction parameterization in object detection networks
The parametrization seems to originate from the R-CNN paper, Girschick et al., 2013: Rich feature hierarchies for accurate object detection and semantic segmentation. Note that SSD is also using this |
54,865 | Random forest - short text classification | Generally speaking, in a machine learning approach, it is recommended to test several models regardless of their theoretical performance, because their accuracy is dependent of the training dataset. True enough, a couple of algorithms are generally preferred for text classification (SVM, Naive Bayes, multinomial regres... | Random forest - short text classification | Generally speaking, in a machine learning approach, it is recommended to test several models regardless of their theoretical performance, because their accuracy is dependent of the training dataset. T | Random forest - short text classification
Generally speaking, in a machine learning approach, it is recommended to test several models regardless of their theoretical performance, because their accuracy is dependent of the training dataset. True enough, a couple of algorithms are generally preferred for text classifica... | Random forest - short text classification
Generally speaking, in a machine learning approach, it is recommended to test several models regardless of their theoretical performance, because their accuracy is dependent of the training dataset. T |
54,866 | How to scale for SelectKBest for feature selection | I think the problem is that you're using the chi2 scoring function. If you instead use the f_classif scoring function, then there will not be any errors due to having negative values in your dataset. So if you want to use chi2, then you would need to transform your data somehow to get rid of negatives (you could normal... | How to scale for SelectKBest for feature selection | I think the problem is that you're using the chi2 scoring function. If you instead use the f_classif scoring function, then there will not be any errors due to having negative values in your dataset. | How to scale for SelectKBest for feature selection
I think the problem is that you're using the chi2 scoring function. If you instead use the f_classif scoring function, then there will not be any errors due to having negative values in your dataset. So if you want to use chi2, then you would need to transform your dat... | How to scale for SelectKBest for feature selection
I think the problem is that you're using the chi2 scoring function. If you instead use the f_classif scoring function, then there will not be any errors due to having negative values in your dataset. |
54,867 | How to scale for SelectKBest for feature selection | You can use MinMaxScaler. By default, it will scale the data within the range $[0,1]$:
from sklearn.preprocessing import MinMaxScaler
scaler = MinMaxScaler()
scaler.fit(X)
scaler.transform(X) | How to scale for SelectKBest for feature selection | You can use MinMaxScaler. By default, it will scale the data within the range $[0,1]$:
from sklearn.preprocessing import MinMaxScaler
scaler = MinMaxScaler()
scaler.fit(X)
scaler.transform(X) | How to scale for SelectKBest for feature selection
You can use MinMaxScaler. By default, it will scale the data within the range $[0,1]$:
from sklearn.preprocessing import MinMaxScaler
scaler = MinMaxScaler()
scaler.fit(X)
scaler.transform(X) | How to scale for SelectKBest for feature selection
You can use MinMaxScaler. By default, it will scale the data within the range $[0,1]$:
from sklearn.preprocessing import MinMaxScaler
scaler = MinMaxScaler()
scaler.fit(X)
scaler.transform(X) |
54,868 | Are observations independent in bootstrapped resamples? | Think of it this way:
You have a population of individuals. You select an individual at random from the population, measure his weight and return him back to the population. You then select a second individual at random from the population, measure his weight and return him to the population. You continue this proce... | Are observations independent in bootstrapped resamples? | Think of it this way:
You have a population of individuals. You select an individual at random from the population, measure his weight and return him back to the population. You then select a second | Are observations independent in bootstrapped resamples?
Think of it this way:
You have a population of individuals. You select an individual at random from the population, measure his weight and return him back to the population. You then select a second individual at random from the population, measure his weight an... | Are observations independent in bootstrapped resamples?
Think of it this way:
You have a population of individuals. You select an individual at random from the population, measure his weight and return him back to the population. You then select a second |
54,869 | Are observations independent in bootstrapped resamples? | Independence is a property of a collection of random variables defined on the same probability space. Whether or not your bootstrap samples are independent depends on which random variables you are considering to be underlying your samples.
Consider the random experiment:
Toss a coin twice, write down the outcomes, an... | Are observations independent in bootstrapped resamples? | Independence is a property of a collection of random variables defined on the same probability space. Whether or not your bootstrap samples are independent depends on which random variables you are co | Are observations independent in bootstrapped resamples?
Independence is a property of a collection of random variables defined on the same probability space. Whether or not your bootstrap samples are independent depends on which random variables you are considering to be underlying your samples.
Consider the random exp... | Are observations independent in bootstrapped resamples?
Independence is a property of a collection of random variables defined on the same probability space. Whether or not your bootstrap samples are independent depends on which random variables you are co |
54,870 | Are observations independent in bootstrapped resamples? | I'm the OP. The answers from others were very good, and I have accepted one of them. I am also answering here to unite what I have learned.
Yes. In this context, the observations are independent. I believe the key issue is whether we are conditioning on cluster membership.
A formal answer
Above, I tried to check whet... | Are observations independent in bootstrapped resamples? | I'm the OP. The answers from others were very good, and I have accepted one of them. I am also answering here to unite what I have learned.
Yes. In this context, the observations are independent. I b | Are observations independent in bootstrapped resamples?
I'm the OP. The answers from others were very good, and I have accepted one of them. I am also answering here to unite what I have learned.
Yes. In this context, the observations are independent. I believe the key issue is whether we are conditioning on cluster m... | Are observations independent in bootstrapped resamples?
I'm the OP. The answers from others were very good, and I have accepted one of them. I am also answering here to unite what I have learned.
Yes. In this context, the observations are independent. I b |
54,871 | Expected number of wins until $k$ consecutive wins | The answer is the expected number of games times the expected number of wins per game.
It would be reasonable to doubt this result: sure, it might be close; but couldn't it miss the mark slightly due to the fact that the game ends (by design) with a large streak of wins? Let's find a rigorous way to address this quest... | Expected number of wins until $k$ consecutive wins | The answer is the expected number of games times the expected number of wins per game.
It would be reasonable to doubt this result: sure, it might be close; but couldn't it miss the mark slightly due | Expected number of wins until $k$ consecutive wins
The answer is the expected number of games times the expected number of wins per game.
It would be reasonable to doubt this result: sure, it might be close; but couldn't it miss the mark slightly due to the fact that the game ends (by design) with a large streak of win... | Expected number of wins until $k$ consecutive wins
The answer is the expected number of games times the expected number of wins per game.
It would be reasonable to doubt this result: sure, it might be close; but couldn't it miss the mark slightly due |
54,872 | Expected number of wins until $k$ consecutive wins | The fact that it is the win probability $p$ times the expected number of games is a simple application of the optional stopping theorem
Let
$X_n$ be the total number of wins at round $n$. The recentered random variable $Y_n = X_n - p\ n$ is a martingale.
$\tau$ be the time till you win $k$ consecutive games. $\tau$ is... | Expected number of wins until $k$ consecutive wins | The fact that it is the win probability $p$ times the expected number of games is a simple application of the optional stopping theorem
Let
$X_n$ be the total number of wins at round $n$. The recente | Expected number of wins until $k$ consecutive wins
The fact that it is the win probability $p$ times the expected number of games is a simple application of the optional stopping theorem
Let
$X_n$ be the total number of wins at round $n$. The recentered random variable $Y_n = X_n - p\ n$ is a martingale.
$\tau$ be the... | Expected number of wins until $k$ consecutive wins
The fact that it is the win probability $p$ times the expected number of games is a simple application of the optional stopping theorem
Let
$X_n$ be the total number of wins at round $n$. The recente |
54,873 | If you're only interested in predicting $Y$ when $X>n$, should you use all $X$ in a regression anyway? | The point of regression is to learn from data points with other predictor values than those for which you want to make a prediction. So, the fact that you are not interested in predicting for certain predictor values is no reason in itself to restrict your dataset in that way.
Consider a more extreme example: Say you a... | If you're only interested in predicting $Y$ when $X>n$, should you use all $X$ in a regression anywa | The point of regression is to learn from data points with other predictor values than those for which you want to make a prediction. So, the fact that you are not interested in predicting for certain | If you're only interested in predicting $Y$ when $X>n$, should you use all $X$ in a regression anyway?
The point of regression is to learn from data points with other predictor values than those for which you want to make a prediction. So, the fact that you are not interested in predicting for certain predictor values ... | If you're only interested in predicting $Y$ when $X>n$, should you use all $X$ in a regression anywa
The point of regression is to learn from data points with other predictor values than those for which you want to make a prediction. So, the fact that you are not interested in predicting for certain |
54,874 | If you're only interested in predicting $Y$ when $X>n$, should you use all $X$ in a regression anyway? | If there is reason to think that a relationship between $X$ and $Y$ holds over the entire range of $X$ (possibly after transforming $X$), then yes, you should use all your data. This may hold, for instance, in physical systems.
However, if there is no such constant relationship, then using the full range of $X$ will lu... | If you're only interested in predicting $Y$ when $X>n$, should you use all $X$ in a regression anywa | If there is reason to think that a relationship between $X$ and $Y$ holds over the entire range of $X$ (possibly after transforming $X$), then yes, you should use all your data. This may hold, for ins | If you're only interested in predicting $Y$ when $X>n$, should you use all $X$ in a regression anyway?
If there is reason to think that a relationship between $X$ and $Y$ holds over the entire range of $X$ (possibly after transforming $X$), then yes, you should use all your data. This may hold, for instance, in physica... | If you're only interested in predicting $Y$ when $X>n$, should you use all $X$ in a regression anywa
If there is reason to think that a relationship between $X$ and $Y$ holds over the entire range of $X$ (possibly after transforming $X$), then yes, you should use all your data. This may hold, for ins |
54,875 | Why GLM Poisson model predict negative value for count data? | The Poisson GLM fits a model $y_i \sim \text{Pois}(\mu_i)$ with $\log(\mu_i) = x_i^\top \beta$, i.e., a log links the expectation $\mu_i$ to the so-called "linear predictor" $x_i^\top \beta$, often denoted $\eta_i$ in the GLM literature. Hence, at least two types of predictions may be of interest based on the coefficie... | Why GLM Poisson model predict negative value for count data? | The Poisson GLM fits a model $y_i \sim \text{Pois}(\mu_i)$ with $\log(\mu_i) = x_i^\top \beta$, i.e., a log links the expectation $\mu_i$ to the so-called "linear predictor" $x_i^\top \beta$, often de | Why GLM Poisson model predict negative value for count data?
The Poisson GLM fits a model $y_i \sim \text{Pois}(\mu_i)$ with $\log(\mu_i) = x_i^\top \beta$, i.e., a log links the expectation $\mu_i$ to the so-called "linear predictor" $x_i^\top \beta$, often denoted $\eta_i$ in the GLM literature. Hence, at least two t... | Why GLM Poisson model predict negative value for count data?
The Poisson GLM fits a model $y_i \sim \text{Pois}(\mu_i)$ with $\log(\mu_i) = x_i^\top \beta$, i.e., a log links the expectation $\mu_i$ to the so-called "linear predictor" $x_i^\top \beta$, often de |
54,876 | Theoretical justification for training a multi-class classification model to be used for multi-label classification | A softmax output layer does not seem to make sense. The total probability of all classes would then be coerced to sum to 1. This does not make sense in a multi-label setting. Using a sigmoid instead would seem more logical (allows multiple classes to have high probability e.g. close to 1).
Perhaps what is being done i... | Theoretical justification for training a multi-class classification model to be used for multi-label | A softmax output layer does not seem to make sense. The total probability of all classes would then be coerced to sum to 1. This does not make sense in a multi-label setting. Using a sigmoid instead w | Theoretical justification for training a multi-class classification model to be used for multi-label classification
A softmax output layer does not seem to make sense. The total probability of all classes would then be coerced to sum to 1. This does not make sense in a multi-label setting. Using a sigmoid instead would... | Theoretical justification for training a multi-class classification model to be used for multi-label
A softmax output layer does not seem to make sense. The total probability of all classes would then be coerced to sum to 1. This does not make sense in a multi-label setting. Using a sigmoid instead w |
54,877 | How to reduce type I and II error for determining bias of loaded dice for reduced legal costs? | Concerning the Type I and Type II error comparison, a die roll of an unbiased die yields an outcome from a discrete uniform distribution. To test a candidate die for bias, one has to assume a type of bias distribution that is a discrete nonuniform distribution. Since there are several different ways of biasing a die, ... | How to reduce type I and II error for determining bias of loaded dice for reduced legal costs? | Concerning the Type I and Type II error comparison, a die roll of an unbiased die yields an outcome from a discrete uniform distribution. To test a candidate die for bias, one has to assume a type of | How to reduce type I and II error for determining bias of loaded dice for reduced legal costs?
Concerning the Type I and Type II error comparison, a die roll of an unbiased die yields an outcome from a discrete uniform distribution. To test a candidate die for bias, one has to assume a type of bias distribution that is... | How to reduce type I and II error for determining bias of loaded dice for reduced legal costs?
Concerning the Type I and Type II error comparison, a die roll of an unbiased die yields an outcome from a discrete uniform distribution. To test a candidate die for bias, one has to assume a type of |
54,878 | How to reduce type I and II error for determining bias of loaded dice for reduced legal costs? | I'm not sure I'd approach the problem this way.
First, you have two hypotheses: the die is fair or not fair. If it is not fair, the distribution of throws will not be uniform (taking a mean of the throws is not an efficient way to measure this). Rather, I'd record the distribution of throws and after a few dozen, sta... | How to reduce type I and II error for determining bias of loaded dice for reduced legal costs? | I'm not sure I'd approach the problem this way.
First, you have two hypotheses: the die is fair or not fair. If it is not fair, the distribution of throws will not be uniform (taking a mean of the t | How to reduce type I and II error for determining bias of loaded dice for reduced legal costs?
I'm not sure I'd approach the problem this way.
First, you have two hypotheses: the die is fair or not fair. If it is not fair, the distribution of throws will not be uniform (taking a mean of the throws is not an efficient... | How to reduce type I and II error for determining bias of loaded dice for reduced legal costs?
I'm not sure I'd approach the problem this way.
First, you have two hypotheses: the die is fair or not fair. If it is not fair, the distribution of throws will not be uniform (taking a mean of the t |
54,879 | How to reduce type I and II error for determining bias of loaded dice for reduced legal costs? | TLDR – the problem is underdefined
Aim
The details provided in the question can only lead to a relative balance of errors. Simply rearrange the equation and $ P(TypeII Error) ≈ 3P(TypeI Error)/240000$.
This is not what is wanted or needed, rather it is to know what threshold for mean that would be used as a cut off. I... | How to reduce type I and II error for determining bias of loaded dice for reduced legal costs? | TLDR – the problem is underdefined
Aim
The details provided in the question can only lead to a relative balance of errors. Simply rearrange the equation and $ P(TypeII Error) ≈ 3P(TypeI Error)/240000$ | How to reduce type I and II error for determining bias of loaded dice for reduced legal costs?
TLDR – the problem is underdefined
Aim
The details provided in the question can only lead to a relative balance of errors. Simply rearrange the equation and $ P(TypeII Error) ≈ 3P(TypeI Error)/240000$.
This is not what is wa... | How to reduce type I and II error for determining bias of loaded dice for reduced legal costs?
TLDR – the problem is underdefined
Aim
The details provided in the question can only lead to a relative balance of errors. Simply rearrange the equation and $ P(TypeII Error) ≈ 3P(TypeI Error)/240000$ |
54,880 | How to reduce type I and II error for determining bias of loaded dice for reduced legal costs? | As I understand, the core part of the question is "how to choose $\alpha$ and/or $\beta$"?
Maybe it's me, that is (non-statistically) biased to interpret the question like this. But recently I had numerous discussions and thoughts about this very question. In a nutshell: there is no general rule, it depends on each and... | How to reduce type I and II error for determining bias of loaded dice for reduced legal costs? | As I understand, the core part of the question is "how to choose $\alpha$ and/or $\beta$"?
Maybe it's me, that is (non-statistically) biased to interpret the question like this. But recently I had num | How to reduce type I and II error for determining bias of loaded dice for reduced legal costs?
As I understand, the core part of the question is "how to choose $\alpha$ and/or $\beta$"?
Maybe it's me, that is (non-statistically) biased to interpret the question like this. But recently I had numerous discussions and tho... | How to reduce type I and II error for determining bias of loaded dice for reduced legal costs?
As I understand, the core part of the question is "how to choose $\alpha$ and/or $\beta$"?
Maybe it's me, that is (non-statistically) biased to interpret the question like this. But recently I had num |
54,881 | Find a matrix with orthonormal columns with minimal Frobenius distance to a given matrix | Q1. Proof
Given $\mathbf A$ that is square or tall, we want to maximize $\operatorname{tr}(\mathbf A^\top \mathbf X)$ subject to $\mathbf X^\top \mathbf X=\mathbf I$.
Let us denote by $\mathbf A = \mathbf{USV}^\top=\mathbf{\tilde U}\mathbf{\tilde S}\mathbf V^\top$ the "thin" and the "full" SVD of $\mathbf A$. Now we h... | Find a matrix with orthonormal columns with minimal Frobenius distance to a given matrix | Q1. Proof
Given $\mathbf A$ that is square or tall, we want to maximize $\operatorname{tr}(\mathbf A^\top \mathbf X)$ subject to $\mathbf X^\top \mathbf X=\mathbf I$.
Let us denote by $\mathbf A = \m | Find a matrix with orthonormal columns with minimal Frobenius distance to a given matrix
Q1. Proof
Given $\mathbf A$ that is square or tall, we want to maximize $\operatorname{tr}(\mathbf A^\top \mathbf X)$ subject to $\mathbf X^\top \mathbf X=\mathbf I$.
Let us denote by $\mathbf A = \mathbf{USV}^\top=\mathbf{\tilde ... | Find a matrix with orthonormal columns with minimal Frobenius distance to a given matrix
Q1. Proof
Given $\mathbf A$ that is square or tall, we want to maximize $\operatorname{tr}(\mathbf A^\top \mathbf X)$ subject to $\mathbf X^\top \mathbf X=\mathbf I$.
Let us denote by $\mathbf A = \m |
54,882 | Find a matrix with orthonormal columns with minimal Frobenius distance to a given matrix | Suppose we are given (square or tall) matrix $\mathrm B \in \mathbb R^{n \times p}$, where $n \geq p$. We have the following optimization problem in semi-orthogonal matrix $\mathrm X_1 \in \mathbb R^{n \times p}$
$$\begin{array}{ll} \text{minimize} & \| \mathrm X_1 - \mathrm B \|_{\text{F}}^2\\ \text{subject to} & \mat... | Find a matrix with orthonormal columns with minimal Frobenius distance to a given matrix | Suppose we are given (square or tall) matrix $\mathrm B \in \mathbb R^{n \times p}$, where $n \geq p$. We have the following optimization problem in semi-orthogonal matrix $\mathrm X_1 \in \mathbb R^{ | Find a matrix with orthonormal columns with minimal Frobenius distance to a given matrix
Suppose we are given (square or tall) matrix $\mathrm B \in \mathbb R^{n \times p}$, where $n \geq p$. We have the following optimization problem in semi-orthogonal matrix $\mathrm X_1 \in \mathbb R^{n \times p}$
$$\begin{array}{ll... | Find a matrix with orthonormal columns with minimal Frobenius distance to a given matrix
Suppose we are given (square or tall) matrix $\mathrm B \in \mathbb R^{n \times p}$, where $n \geq p$. We have the following optimization problem in semi-orthogonal matrix $\mathrm X_1 \in \mathbb R^{ |
54,883 | The dirty coins and the three judges | If you rephrase the question,
not asking about the 'true' $p_{coin}$ how often the coin is heads or tails
but instead you analyze the 'effective' $p_{judges}$ the probability how often the judges say heads or tails
, then the regular analysis becomes 'ok'.
This analysis does not become more difficult. Even if the $... | The dirty coins and the three judges | If you rephrase the question,
not asking about the 'true' $p_{coin}$ how often the coin is heads or tails
but instead you analyze the 'effective' $p_{judges}$ the probability how often the judges sa | The dirty coins and the three judges
If you rephrase the question,
not asking about the 'true' $p_{coin}$ how often the coin is heads or tails
but instead you analyze the 'effective' $p_{judges}$ the probability how often the judges say heads or tails
, then the regular analysis becomes 'ok'.
This analysis does not... | The dirty coins and the three judges
If you rephrase the question,
not asking about the 'true' $p_{coin}$ how often the coin is heads or tails
but instead you analyze the 'effective' $p_{judges}$ the probability how often the judges sa |
54,884 | The dirty coins and the three judges | The problem simplifies if we quantify agreement, where by agreement we mean the fraction of $0$'s and $1$'s of the total number of trials that are the same between any two measurements. In specific, we quantify how each (equally good) judge’s judgments agree with the median judgments, and how well median judgements agr... | The dirty coins and the three judges | The problem simplifies if we quantify agreement, where by agreement we mean the fraction of $0$'s and $1$'s of the total number of trials that are the same between any two measurements. In specific, w | The dirty coins and the three judges
The problem simplifies if we quantify agreement, where by agreement we mean the fraction of $0$'s and $1$'s of the total number of trials that are the same between any two measurements. In specific, we quantify how each (equally good) judge’s judgments agree with the median judgment... | The dirty coins and the three judges
The problem simplifies if we quantify agreement, where by agreement we mean the fraction of $0$'s and $1$'s of the total number of trials that are the same between any two measurements. In specific, w |
54,885 | An unbiased estimator of σ³ | Let us consider a Normal sample. Since$$\sigma^{-2}\sum_{i=1}^n (x_i-\bar{x}_n)^2\sim\chi^2_{n-1}$$which is also a Gamma $\mathcal{Ga}(n-1,1/2)$ variate, the $3/2$ moment of this variate is
$$\int_0^\infty z^{3/2}z^{n-1-1}\exp\{-z/2\}2^{-(n-1)}\Gamma(n-1)^{-1}\text{d}z=\frac{2^{(n-1)+3/2}\Gamma(n-1+3/2)}{2^{n-1}\Gamma(... | An unbiased estimator of σ³ | Let us consider a Normal sample. Since$$\sigma^{-2}\sum_{i=1}^n (x_i-\bar{x}_n)^2\sim\chi^2_{n-1}$$which is also a Gamma $\mathcal{Ga}(n-1,1/2)$ variate, the $3/2$ moment of this variate is
$$\int_0^\ | An unbiased estimator of σ³
Let us consider a Normal sample. Since$$\sigma^{-2}\sum_{i=1}^n (x_i-\bar{x}_n)^2\sim\chi^2_{n-1}$$which is also a Gamma $\mathcal{Ga}(n-1,1/2)$ variate, the $3/2$ moment of this variate is
$$\int_0^\infty z^{3/2}z^{n-1-1}\exp\{-z/2\}2^{-(n-1)}\Gamma(n-1)^{-1}\text{d}z=\frac{2^{(n-1)+3/2}\Ga... | An unbiased estimator of σ³
Let us consider a Normal sample. Since$$\sigma^{-2}\sum_{i=1}^n (x_i-\bar{x}_n)^2\sim\chi^2_{n-1}$$which is also a Gamma $\mathcal{Ga}(n-1,1/2)$ variate, the $3/2$ moment of this variate is
$$\int_0^\ |
54,886 | Selecting alpha and beta parameters for a beta distribution, based on a mode and a 95% credible interval | This is an optimisation problem to match a distribution to 3 parameters: 2 quantiles and the mode.
In fact, even the function you used earlier returns estimates from an optimisation. If you calculate the quantile values from those $\alpha, \beta$ parameters it gave you, you'll see they don't match up exactly:
> qbeta(p... | Selecting alpha and beta parameters for a beta distribution, based on a mode and a 95% credible inte | This is an optimisation problem to match a distribution to 3 parameters: 2 quantiles and the mode.
In fact, even the function you used earlier returns estimates from an optimisation. If you calculate | Selecting alpha and beta parameters for a beta distribution, based on a mode and a 95% credible interval
This is an optimisation problem to match a distribution to 3 parameters: 2 quantiles and the mode.
In fact, even the function you used earlier returns estimates from an optimisation. If you calculate the quantile va... | Selecting alpha and beta parameters for a beta distribution, based on a mode and a 95% credible inte
This is an optimisation problem to match a distribution to 3 parameters: 2 quantiles and the mode.
In fact, even the function you used earlier returns estimates from an optimisation. If you calculate |
54,887 | Difference between stochastic variational inference and variational inference? | Have a look at the paper Stochastic Variational Inference:
The coordinate ascent algorithm in Figure 3 is inefficient for large data sets because we must optimize the local variational parameters for each data point before re-estimating the global variational parameters. Stochastic variational inference uses stochasti... | Difference between stochastic variational inference and variational inference? | Have a look at the paper Stochastic Variational Inference:
The coordinate ascent algorithm in Figure 3 is inefficient for large data sets because we must optimize the local variational parameters for | Difference between stochastic variational inference and variational inference?
Have a look at the paper Stochastic Variational Inference:
The coordinate ascent algorithm in Figure 3 is inefficient for large data sets because we must optimize the local variational parameters for each data point before re-estimating the... | Difference between stochastic variational inference and variational inference?
Have a look at the paper Stochastic Variational Inference:
The coordinate ascent algorithm in Figure 3 is inefficient for large data sets because we must optimize the local variational parameters for |
54,888 | Difference between stochastic variational inference and variational inference? | Stochastic VI means you don't use the exact, complete, information you have [because it's too complicated, or computationally expensive] but rather a stochastic version of it.
While the paper about SVI only deals with the Exponential Family, and one type of stochasticity, I think the term should also apply to any gener... | Difference between stochastic variational inference and variational inference? | Stochastic VI means you don't use the exact, complete, information you have [because it's too complicated, or computationally expensive] but rather a stochastic version of it.
While the paper about SV | Difference between stochastic variational inference and variational inference?
Stochastic VI means you don't use the exact, complete, information you have [because it's too complicated, or computationally expensive] but rather a stochastic version of it.
While the paper about SVI only deals with the Exponential Family,... | Difference between stochastic variational inference and variational inference?
Stochastic VI means you don't use the exact, complete, information you have [because it's too complicated, or computationally expensive] but rather a stochastic version of it.
While the paper about SV |
54,889 | Can my standard laptop be used to run deep learning projects? | I have an hulking old refurbished T520 with the CD drive ripped out and the plastic busted out of the corner from when I dropped it. 8 GB of RAM. You know what? I've done quite a lot with keras, tensorflow and theano on that machine. Things start to go south with CNNs on bigger images, but the point is: no excuses! Ins... | Can my standard laptop be used to run deep learning projects? | I have an hulking old refurbished T520 with the CD drive ripped out and the plastic busted out of the corner from when I dropped it. 8 GB of RAM. You know what? I've done quite a lot with keras, tenso | Can my standard laptop be used to run deep learning projects?
I have an hulking old refurbished T520 with the CD drive ripped out and the plastic busted out of the corner from when I dropped it. 8 GB of RAM. You know what? I've done quite a lot with keras, tensorflow and theano on that machine. Things start to go south... | Can my standard laptop be used to run deep learning projects?
I have an hulking old refurbished T520 with the CD drive ripped out and the plastic busted out of the corner from when I dropped it. 8 GB of RAM. You know what? I've done quite a lot with keras, tenso |
54,890 | Can my standard laptop be used to run deep learning projects? | The benchmarks described in
https://github.com/jcjohnson/cnn-benchmarks
are very instructive. If you want to estimate how much slower your model will be,a rough guideline is to do one forward and backward pass on the code described above, divide it by the time taken on a GPU, and you will get an idea of how many X yo... | Can my standard laptop be used to run deep learning projects? | The benchmarks described in
https://github.com/jcjohnson/cnn-benchmarks
are very instructive. If you want to estimate how much slower your model will be,a rough guideline is to do one forward and ba | Can my standard laptop be used to run deep learning projects?
The benchmarks described in
https://github.com/jcjohnson/cnn-benchmarks
are very instructive. If you want to estimate how much slower your model will be,a rough guideline is to do one forward and backward pass on the code described above, divide it by the ... | Can my standard laptop be used to run deep learning projects?
The benchmarks described in
https://github.com/jcjohnson/cnn-benchmarks
are very instructive. If you want to estimate how much slower your model will be,a rough guideline is to do one forward and ba |
54,891 | Can my standard laptop be used to run deep learning projects? | As other have said in their answers, using your laptop should be perfectly fine for running inference on trained models. However, training a network from scratch (or even fine-tuning one) takes quite a long time, and having a training occupying 100% of your laptop's CPU for a week just to find out you need to change so... | Can my standard laptop be used to run deep learning projects? | As other have said in their answers, using your laptop should be perfectly fine for running inference on trained models. However, training a network from scratch (or even fine-tuning one) takes quite | Can my standard laptop be used to run deep learning projects?
As other have said in their answers, using your laptop should be perfectly fine for running inference on trained models. However, training a network from scratch (or even fine-tuning one) takes quite a long time, and having a training occupying 100% of your ... | Can my standard laptop be used to run deep learning projects?
As other have said in their answers, using your laptop should be perfectly fine for running inference on trained models. However, training a network from scratch (or even fine-tuning one) takes quite |
54,892 | Can my standard laptop be used to run deep learning projects? | The key question is: are you going to train models yourself or use pretrained models?
If you can stick to pretrained models and do transfer learning, you should be fine - you can do this in any framework, for example see pretrained models in Keras. You can actually do lots of interesting stuff with pretrained models - ... | Can my standard laptop be used to run deep learning projects? | The key question is: are you going to train models yourself or use pretrained models?
If you can stick to pretrained models and do transfer learning, you should be fine - you can do this in any framew | Can my standard laptop be used to run deep learning projects?
The key question is: are you going to train models yourself or use pretrained models?
If you can stick to pretrained models and do transfer learning, you should be fine - you can do this in any framework, for example see pretrained models in Keras. You can a... | Can my standard laptop be used to run deep learning projects?
The key question is: are you going to train models yourself or use pretrained models?
If you can stick to pretrained models and do transfer learning, you should be fine - you can do this in any framew |
54,893 | Using column weights to achieve a different LASSO penalty per coefficient | To simplify the discussion below, I will first consider the case that all $\lambda_i > 0$, and then show how to deal with some unpenalized predictors.
Part 1: All predictors are penalized ($\lambda_i > 0$ for all $i$)
This case indeed works in exactly the way you described in your question.
Let $\Lambda = \text{Diag}(\... | Using column weights to achieve a different LASSO penalty per coefficient | To simplify the discussion below, I will first consider the case that all $\lambda_i > 0$, and then show how to deal with some unpenalized predictors.
Part 1: All predictors are penalized ($\lambda_i | Using column weights to achieve a different LASSO penalty per coefficient
To simplify the discussion below, I will first consider the case that all $\lambda_i > 0$, and then show how to deal with some unpenalized predictors.
Part 1: All predictors are penalized ($\lambda_i > 0$ for all $i$)
This case indeed works in ex... | Using column weights to achieve a different LASSO penalty per coefficient
To simplify the discussion below, I will first consider the case that all $\lambda_i > 0$, and then show how to deal with some unpenalized predictors.
Part 1: All predictors are penalized ($\lambda_i |
54,894 | Is choice of machine learning algorithm a secondary issue? | You want citations for the claims, but I think this advice, while useful, stems from this context specifically.
The fact that these methods work so well on Kaggle and other competitions has to do with the type of datasets in those competitions. Often, especially in elementary competitions, data consists of many exampl... | Is choice of machine learning algorithm a secondary issue? | You want citations for the claims, but I think this advice, while useful, stems from this context specifically.
The fact that these methods work so well on Kaggle and other competitions has to do wit | Is choice of machine learning algorithm a secondary issue?
You want citations for the claims, but I think this advice, while useful, stems from this context specifically.
The fact that these methods work so well on Kaggle and other competitions has to do with the type of datasets in those competitions. Often, especial... | Is choice of machine learning algorithm a secondary issue?
You want citations for the claims, but I think this advice, while useful, stems from this context specifically.
The fact that these methods work so well on Kaggle and other competitions has to do wit |
54,895 | Is choice of machine learning algorithm a secondary issue? | Isn't the NFL concerned with algorithms which are data-independent? Feature engineering is completely data-dependent, because it's not a rigorous, well-defined algorithm, expecially in the sense meant by Kagglers. For different data sets they choose different features based on expertise, Intuition and a lot of hand-wav... | Is choice of machine learning algorithm a secondary issue? | Isn't the NFL concerned with algorithms which are data-independent? Feature engineering is completely data-dependent, because it's not a rigorous, well-defined algorithm, expecially in the sense meant | Is choice of machine learning algorithm a secondary issue?
Isn't the NFL concerned with algorithms which are data-independent? Feature engineering is completely data-dependent, because it's not a rigorous, well-defined algorithm, expecially in the sense meant by Kagglers. For different data sets they choose different f... | Is choice of machine learning algorithm a secondary issue?
Isn't the NFL concerned with algorithms which are data-independent? Feature engineering is completely data-dependent, because it's not a rigorous, well-defined algorithm, expecially in the sense meant |
54,896 | Is choice of machine learning algorithm a secondary issue? | Thank you for the interesting question. I think the question will be hard to conclusively answer without a more rigorous definition of feature engineering which seems hard to give.
I don't think there is any tension with no free lunch, since I think that feature engineering involves changing the optimisation problem. T... | Is choice of machine learning algorithm a secondary issue? | Thank you for the interesting question. I think the question will be hard to conclusively answer without a more rigorous definition of feature engineering which seems hard to give.
I don't think there | Is choice of machine learning algorithm a secondary issue?
Thank you for the interesting question. I think the question will be hard to conclusively answer without a more rigorous definition of feature engineering which seems hard to give.
I don't think there is any tension with no free lunch, since I think that featur... | Is choice of machine learning algorithm a secondary issue?
Thank you for the interesting question. I think the question will be hard to conclusively answer without a more rigorous definition of feature engineering which seems hard to give.
I don't think there |
54,897 | Term for "extent to which a test throws away information"? | The term is simply "loss of information" (or "information loss"), & was introduced by Fisher shortly after he came up with the concept of sufficiency. See Fisher (1925), "Theory of Statistical Estimation", Proc. Camb. Philos. Soc., 22, pp 700 – 725. The usual way to measure it is in terms of Fisher information, the va... | Term for "extent to which a test throws away information"? | The term is simply "loss of information" (or "information loss"), & was introduced by Fisher shortly after he came up with the concept of sufficiency. See Fisher (1925), "Theory of Statistical Estima | Term for "extent to which a test throws away information"?
The term is simply "loss of information" (or "information loss"), & was introduced by Fisher shortly after he came up with the concept of sufficiency. See Fisher (1925), "Theory of Statistical Estimation", Proc. Camb. Philos. Soc., 22, pp 700 – 725. The usual ... | Term for "extent to which a test throws away information"?
The term is simply "loss of information" (or "information loss"), & was introduced by Fisher shortly after he came up with the concept of sufficiency. See Fisher (1925), "Theory of Statistical Estima |
54,898 | Term for "extent to which a test throws away information"? | Simple answer to Q. Is there a term for the "extent to which we lose information" when reducing D to a test statistic t or to a rejection or non-rejection R? is that first that there is no simple loss of information and measuring it can be difficult and deceptive. Secondly, when we complete hypothesis testing we have o... | Term for "extent to which a test throws away information"? | Simple answer to Q. Is there a term for the "extent to which we lose information" when reducing D to a test statistic t or to a rejection or non-rejection R? is that first that there is no simple loss | Term for "extent to which a test throws away information"?
Simple answer to Q. Is there a term for the "extent to which we lose information" when reducing D to a test statistic t or to a rejection or non-rejection R? is that first that there is no simple loss of information and measuring it can be difficult and decepti... | Term for "extent to which a test throws away information"?
Simple answer to Q. Is there a term for the "extent to which we lose information" when reducing D to a test statistic t or to a rejection or non-rejection R? is that first that there is no simple loss |
54,899 | A better model has higher residual deviance and AIC. How is it possible? | You do not reject model 2 because there is no effect, but because the effect is not significant enough.
The results are consistent.
Note that an insignificant result for an anova model can still acknowledge an insignificant difference between the two models, e.g. that the likelihood ratio for the small and big model i... | A better model has higher residual deviance and AIC. How is it possible? | You do not reject model 2 because there is no effect, but because the effect is not significant enough.
The results are consistent.
Note that an insignificant result for an anova model can still ackn | A better model has higher residual deviance and AIC. How is it possible?
You do not reject model 2 because there is no effect, but because the effect is not significant enough.
The results are consistent.
Note that an insignificant result for an anova model can still acknowledge an insignificant difference between the... | A better model has higher residual deviance and AIC. How is it possible?
You do not reject model 2 because there is no effect, but because the effect is not significant enough.
The results are consistent.
Note that an insignificant result for an anova model can still ackn |
54,900 | A better model has higher residual deviance and AIC. How is it possible? | The residual deviance will always be smaller (or at least equal to) for the larger model. Similar to adding variables will only increase R-Squared in regression.
AIC is only slightly better for Model B, I bet BIC is actually worse as it more severely punishes additional variables.
Different model fit statistics will n... | A better model has higher residual deviance and AIC. How is it possible? | The residual deviance will always be smaller (or at least equal to) for the larger model. Similar to adding variables will only increase R-Squared in regression.
AIC is only slightly better for Model | A better model has higher residual deviance and AIC. How is it possible?
The residual deviance will always be smaller (or at least equal to) for the larger model. Similar to adding variables will only increase R-Squared in regression.
AIC is only slightly better for Model B, I bet BIC is actually worse as it more seve... | A better model has higher residual deviance and AIC. How is it possible?
The residual deviance will always be smaller (or at least equal to) for the larger model. Similar to adding variables will only increase R-Squared in regression.
AIC is only slightly better for Model |
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