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 |
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47,701 | How to fit an autoregressive (AR(1)) model with trend and/or seasonality to a time series? | My suggestion is to parameterise the function $f(t)$ and use the methodology of state space models and the Kalman filter. For example, a second order autoregressive, AR(2), process is a relatively general, yet simple, specification that can capture smooth cycles.
Then, you would deal with a Gaussian linear model with a... | How to fit an autoregressive (AR(1)) model with trend and/or seasonality to a time series? | My suggestion is to parameterise the function $f(t)$ and use the methodology of state space models and the Kalman filter. For example, a second order autoregressive, AR(2), process is a relatively gen | How to fit an autoregressive (AR(1)) model with trend and/or seasonality to a time series?
My suggestion is to parameterise the function $f(t)$ and use the methodology of state space models and the Kalman filter. For example, a second order autoregressive, AR(2), process is a relatively general, yet simple, specificati... | How to fit an autoregressive (AR(1)) model with trend and/or seasonality to a time series?
My suggestion is to parameterise the function $f(t)$ and use the methodology of state space models and the Kalman filter. For example, a second order autoregressive, AR(2), process is a relatively gen |
47,702 | How to fit an autoregressive (AR(1)) model with trend and/or seasonality to a time series? | From the graphs you have shown in your question, it appears that there may be some periodic signal in your data with a fixed frequency value. To determine whether this is the case, you should generate the Discrete Fourier Transform (DFT) of your data and plot its periodogram. From the plotted periodogram below, it is... | How to fit an autoregressive (AR(1)) model with trend and/or seasonality to a time series? | From the graphs you have shown in your question, it appears that there may be some periodic signal in your data with a fixed frequency value. To determine whether this is the case, you should generat | How to fit an autoregressive (AR(1)) model with trend and/or seasonality to a time series?
From the graphs you have shown in your question, it appears that there may be some periodic signal in your data with a fixed frequency value. To determine whether this is the case, you should generate the Discrete Fourier Transf... | How to fit an autoregressive (AR(1)) model with trend and/or seasonality to a time series?
From the graphs you have shown in your question, it appears that there may be some periodic signal in your data with a fixed frequency value. To determine whether this is the case, you should generat |
47,703 | How to fit an autoregressive (AR(1)) model with trend and/or seasonality to a time series? | This answer is not theoretical but practical and might work in some cases. Use with cautions since it is not guaranteed to work for all cases.
Since $f(t)$ change slowly, it is possible to split it into several order 2 polynomials and still have many points. Instead of decomposing the time series in trend + seasonalit... | How to fit an autoregressive (AR(1)) model with trend and/or seasonality to a time series? | This answer is not theoretical but practical and might work in some cases. Use with cautions since it is not guaranteed to work for all cases.
Since $f(t)$ change slowly, it is possible to split it i | How to fit an autoregressive (AR(1)) model with trend and/or seasonality to a time series?
This answer is not theoretical but practical and might work in some cases. Use with cautions since it is not guaranteed to work for all cases.
Since $f(t)$ change slowly, it is possible to split it into several order 2 polynomia... | How to fit an autoregressive (AR(1)) model with trend and/or seasonality to a time series?
This answer is not theoretical but practical and might work in some cases. Use with cautions since it is not guaranteed to work for all cases.
Since $f(t)$ change slowly, it is possible to split it i |
47,704 | What is "Adjusted CV" or "Bias-corrected CV"? | In this context, bias correction refers to the fact that, when we do perform resampling (bootstrap or cross-validation) we almost certainly do not use our whole sample of size $N$; this potential leads to the biased estimates of the MSEP (Mean Squared Error of Prediction).
There are various methodologies that can cont... | What is "Adjusted CV" or "Bias-corrected CV"? | In this context, bias correction refers to the fact that, when we do perform resampling (bootstrap or cross-validation) we almost certainly do not use our whole sample of size $N$; this potential lead | What is "Adjusted CV" or "Bias-corrected CV"?
In this context, bias correction refers to the fact that, when we do perform resampling (bootstrap or cross-validation) we almost certainly do not use our whole sample of size $N$; this potential leads to the biased estimates of the MSEP (Mean Squared Error of Prediction). ... | What is "Adjusted CV" or "Bias-corrected CV"?
In this context, bias correction refers to the fact that, when we do perform resampling (bootstrap or cross-validation) we almost certainly do not use our whole sample of size $N$; this potential lead |
47,705 | Correcting Kullback-Leibler divergence for size of datasets | The fundamental issue is that the KL divergence between the true underlying distributions is zero, as they are the same in your code ($U(0,1)$,) but sampling variation (almost) ensures that in finite samples the KL divergence between the two empirical distributions will be positive, as the empirical distributions will ... | Correcting Kullback-Leibler divergence for size of datasets | The fundamental issue is that the KL divergence between the true underlying distributions is zero, as they are the same in your code ($U(0,1)$,) but sampling variation (almost) ensures that in finite | Correcting Kullback-Leibler divergence for size of datasets
The fundamental issue is that the KL divergence between the true underlying distributions is zero, as they are the same in your code ($U(0,1)$,) but sampling variation (almost) ensures that in finite samples the KL divergence between the two empirical distribu... | Correcting Kullback-Leibler divergence for size of datasets
The fundamental issue is that the KL divergence between the true underlying distributions is zero, as they are the same in your code ($U(0,1)$,) but sampling variation (almost) ensures that in finite |
47,706 | Correcting Kullback-Leibler divergence for size of datasets | The KL divergence doesn't really produce smaller distances with larger datasets or vice-versa. In your example, the distances are incomparable because of the sampling step in your code (in generate_histogram).
Essentially, when you use that function to generate a probability mass function with 100 data points, there's ... | Correcting Kullback-Leibler divergence for size of datasets | The KL divergence doesn't really produce smaller distances with larger datasets or vice-versa. In your example, the distances are incomparable because of the sampling step in your code (in generate_hi | Correcting Kullback-Leibler divergence for size of datasets
The KL divergence doesn't really produce smaller distances with larger datasets or vice-versa. In your example, the distances are incomparable because of the sampling step in your code (in generate_histogram).
Essentially, when you use that function to generat... | Correcting Kullback-Leibler divergence for size of datasets
The KL divergence doesn't really produce smaller distances with larger datasets or vice-versa. In your example, the distances are incomparable because of the sampling step in your code (in generate_hi |
47,707 | How do I interpret the coefficients of a log-linear regression with quadratic terms? | By "impact" of $x$ I understand you want to estimate the change in the predicted value when $x$ changes by some (small) amount $\delta x.$ This is a simple calculation beginning with the fitted model
$$\log(\hat y(x)) = \hat a + \hat b x + \hat c x^2$$
where the "hats" on the terms designate estimated values. Pluggin... | How do I interpret the coefficients of a log-linear regression with quadratic terms? | By "impact" of $x$ I understand you want to estimate the change in the predicted value when $x$ changes by some (small) amount $\delta x.$ This is a simple calculation beginning with the fitted model | How do I interpret the coefficients of a log-linear regression with quadratic terms?
By "impact" of $x$ I understand you want to estimate the change in the predicted value when $x$ changes by some (small) amount $\delta x.$ This is a simple calculation beginning with the fitted model
$$\log(\hat y(x)) = \hat a + \hat ... | How do I interpret the coefficients of a log-linear regression with quadratic terms?
By "impact" of $x$ I understand you want to estimate the change in the predicted value when $x$ changes by some (small) amount $\delta x.$ This is a simple calculation beginning with the fitted model |
47,708 | What is the difference between monte carlo integration and gibbs sampling? | Monte Carlo integration is a technique for numerically integrating a function by evaluating it at many randomly chosen points. It's useful for computing integrals when a closed form solution doesn't exist, and when the problem is high dimensional (in this case, standard numerical integration methods based on quadtratur... | What is the difference between monte carlo integration and gibbs sampling? | Monte Carlo integration is a technique for numerically integrating a function by evaluating it at many randomly chosen points. It's useful for computing integrals when a closed form solution doesn't e | What is the difference between monte carlo integration and gibbs sampling?
Monte Carlo integration is a technique for numerically integrating a function by evaluating it at many randomly chosen points. It's useful for computing integrals when a closed form solution doesn't exist, and when the problem is high dimensiona... | What is the difference between monte carlo integration and gibbs sampling?
Monte Carlo integration is a technique for numerically integrating a function by evaluating it at many randomly chosen points. It's useful for computing integrals when a closed form solution doesn't e |
47,709 | K-nearest neighbor supervised or unsupervised machine learning? | Assuming K is given, strictly speaking, KNN does not have any learning involved, i.e., there are no parameters we can tune to make the performance better. Or we are not trying to optimize an objective function from the training data set. This is a major differences from most supervised learning algorithms.
It is a rule... | K-nearest neighbor supervised or unsupervised machine learning? | Assuming K is given, strictly speaking, KNN does not have any learning involved, i.e., there are no parameters we can tune to make the performance better. Or we are not trying to optimize an objective | K-nearest neighbor supervised or unsupervised machine learning?
Assuming K is given, strictly speaking, KNN does not have any learning involved, i.e., there are no parameters we can tune to make the performance better. Or we are not trying to optimize an objective function from the training data set. This is a major di... | K-nearest neighbor supervised or unsupervised machine learning?
Assuming K is given, strictly speaking, KNN does not have any learning involved, i.e., there are no parameters we can tune to make the performance better. Or we are not trying to optimize an objective |
47,710 | How to back-transform a log transformed regression model in R with bias correction | You didn't give any details about why you think the outputs are wildly unlikely, but my guess is that your errors are not normally distributed. That "smearing adjustment" (bias correction) you're using is only valid if the errors are normal.
There is a more general smearing adjustment you can use, which is easy to imp... | How to back-transform a log transformed regression model in R with bias correction | You didn't give any details about why you think the outputs are wildly unlikely, but my guess is that your errors are not normally distributed. That "smearing adjustment" (bias correction) you're usi | How to back-transform a log transformed regression model in R with bias correction
You didn't give any details about why you think the outputs are wildly unlikely, but my guess is that your errors are not normally distributed. That "smearing adjustment" (bias correction) you're using is only valid if the errors are no... | How to back-transform a log transformed regression model in R with bias correction
You didn't give any details about why you think the outputs are wildly unlikely, but my guess is that your errors are not normally distributed. That "smearing adjustment" (bias correction) you're usi |
47,711 | Optimal proposal for self-normalized importance sampling | It should be noted that $q_{opt}$ actually minimizes the approximate variance given by the Delta method. You can get this by solving
$$
q_{opt} = \arg\min_q\mathbb{E}_q[w^2(X)(f(X)-I)^2], \; \text{ s.t.} \int q(x)dx=1
$$
Now, since:
$$
\mathbb{E}_q[w^2(X)(f(X)-I)^2] = \int\frac{p^2(x)}{q(x)}(f(x)-I)^2dx = \int L(x,q(x... | Optimal proposal for self-normalized importance sampling | It should be noted that $q_{opt}$ actually minimizes the approximate variance given by the Delta method. You can get this by solving
$$
q_{opt} = \arg\min_q\mathbb{E}_q[w^2(X)(f(X)-I)^2], \; \text{ s | Optimal proposal for self-normalized importance sampling
It should be noted that $q_{opt}$ actually minimizes the approximate variance given by the Delta method. You can get this by solving
$$
q_{opt} = \arg\min_q\mathbb{E}_q[w^2(X)(f(X)-I)^2], \; \text{ s.t.} \int q(x)dx=1
$$
Now, since:
$$
\mathbb{E}_q[w^2(X)(f(X)-I... | Optimal proposal for self-normalized importance sampling
It should be noted that $q_{opt}$ actually minimizes the approximate variance given by the Delta method. You can get this by solving
$$
q_{opt} = \arg\min_q\mathbb{E}_q[w^2(X)(f(X)-I)^2], \; \text{ s |
47,712 | Finding a function minimizing the expected value | Note: Normally for self-study questions we try to give hints rather than full solutions. However, in the present case you are dealing with a functional-optimisation problem where I think most students would not have any idea how to do any of this, without seeing a full solution for a few cases. In view of this, I hav... | Finding a function minimizing the expected value | Note: Normally for self-study questions we try to give hints rather than full solutions. However, in the present case you are dealing with a functional-optimisation problem where I think most student | Finding a function minimizing the expected value
Note: Normally for self-study questions we try to give hints rather than full solutions. However, in the present case you are dealing with a functional-optimisation problem where I think most students would not have any idea how to do any of this, without seeing a full ... | Finding a function minimizing the expected value
Note: Normally for self-study questions we try to give hints rather than full solutions. However, in the present case you are dealing with a functional-optimisation problem where I think most student |
47,713 | Finding a function minimizing the expected value | Interpreting the question as @whuber did in his comment, here is a quite vague hint:
https://en.wikipedia.org/wiki/Law_of_total_expectation
Edit after the spoilers: graphical illustration of the application of the hint, as well as shorter version of Ben's answer:
Here are the two dependent random variables $X$ and $Y... | Finding a function minimizing the expected value | Interpreting the question as @whuber did in his comment, here is a quite vague hint:
https://en.wikipedia.org/wiki/Law_of_total_expectation
Edit after the spoilers: graphical illustration of the appl | Finding a function minimizing the expected value
Interpreting the question as @whuber did in his comment, here is a quite vague hint:
https://en.wikipedia.org/wiki/Law_of_total_expectation
Edit after the spoilers: graphical illustration of the application of the hint, as well as shorter version of Ben's answer:
Here ... | Finding a function minimizing the expected value
Interpreting the question as @whuber did in his comment, here is a quite vague hint:
https://en.wikipedia.org/wiki/Law_of_total_expectation
Edit after the spoilers: graphical illustration of the appl |
47,714 | Correlation between Ornstein-Uhlenbeck processes | They are not perfectly positively correlated: Even when random variables are deterministically related (which would require $X$ to be deterministic in this case), perfect correlation requires them to be related via an affine transformation. This would require a relationship of the form:
$$V(t) = \ln \Big[ 1+\frac{U(t... | Correlation between Ornstein-Uhlenbeck processes | They are not perfectly positively correlated: Even when random variables are deterministically related (which would require $X$ to be deterministic in this case), perfect correlation requires them to | Correlation between Ornstein-Uhlenbeck processes
They are not perfectly positively correlated: Even when random variables are deterministically related (which would require $X$ to be deterministic in this case), perfect correlation requires them to be related via an affine transformation. This would require a relation... | Correlation between Ornstein-Uhlenbeck processes
They are not perfectly positively correlated: Even when random variables are deterministically related (which would require $X$ to be deterministic in this case), perfect correlation requires them to |
47,715 | Mean square convergence of linear processes | Absolute summability will allow you to show that the sequence (in $n$)
$$
X_t^n = \sum_{j=-n}^{n} \psi_jZ_{t-j}
$$
has a mean-square limit (we are not talking about almost-sure convergence, here). That is, we want to show that there exists some $X_t$ (we don't know it exists yet,because it's an infinite sum) such that
... | Mean square convergence of linear processes | Absolute summability will allow you to show that the sequence (in $n$)
$$
X_t^n = \sum_{j=-n}^{n} \psi_jZ_{t-j}
$$
has a mean-square limit (we are not talking about almost-sure convergence, here). Tha | Mean square convergence of linear processes
Absolute summability will allow you to show that the sequence (in $n$)
$$
X_t^n = \sum_{j=-n}^{n} \psi_jZ_{t-j}
$$
has a mean-square limit (we are not talking about almost-sure convergence, here). That is, we want to show that there exists some $X_t$ (we don't know it exists ... | Mean square convergence of linear processes
Absolute summability will allow you to show that the sequence (in $n$)
$$
X_t^n = \sum_{j=-n}^{n} \psi_jZ_{t-j}
$$
has a mean-square limit (we are not talking about almost-sure convergence, here). Tha |
47,716 | Compare a diagnostic test to gold standard | If you use McNemar's test you are testing whether the table is symmetric: whether more people are diagnosed sick by the new method and well by the old versus well by the new and sick by the old. This is a perfectly reasonable scientific question to have.For a concrete situation suppose the two methods being compared ar... | Compare a diagnostic test to gold standard | If you use McNemar's test you are testing whether the table is symmetric: whether more people are diagnosed sick by the new method and well by the old versus well by the new and sick by the old. This | Compare a diagnostic test to gold standard
If you use McNemar's test you are testing whether the table is symmetric: whether more people are diagnosed sick by the new method and well by the old versus well by the new and sick by the old. This is a perfectly reasonable scientific question to have.For a concrete situatio... | Compare a diagnostic test to gold standard
If you use McNemar's test you are testing whether the table is symmetric: whether more people are diagnosed sick by the new method and well by the old versus well by the new and sick by the old. This |
47,717 | Compare a diagnostic test to gold standard | You are asking about agreement, so you should use a test for agreement. With just two diagnostic measures ('raters') that are categorical in nature, the standard test is Cohen's kappa. Here's a version applied to your data, coded in R:
tab2 = as.data.frame(tab)
library(irr)
kappa2(tab2[rep(1:4, times=tab2[,3]),1:2]... | Compare a diagnostic test to gold standard | You are asking about agreement, so you should use a test for agreement. With just two diagnostic measures ('raters') that are categorical in nature, the standard test is Cohen's kappa. Here's a vers | Compare a diagnostic test to gold standard
You are asking about agreement, so you should use a test for agreement. With just two diagnostic measures ('raters') that are categorical in nature, the standard test is Cohen's kappa. Here's a version applied to your data, coded in R:
tab2 = as.data.frame(tab)
library(irr... | Compare a diagnostic test to gold standard
You are asking about agreement, so you should use a test for agreement. With just two diagnostic measures ('raters') that are categorical in nature, the standard test is Cohen's kappa. Here's a vers |
47,718 | Unbiased Estimation of $\mu^2$ under certain conditions | Only the third question remains to be answered, the case where $X$ has infinite variance.
When $n \gt 1,$ you can split the data into two smaller nonoverlapping (and therefore independent) samples, estimate $\mu$ separately in each subsample, and multiply the estimates. The independence assures the expectation of that... | Unbiased Estimation of $\mu^2$ under certain conditions | Only the third question remains to be answered, the case where $X$ has infinite variance.
When $n \gt 1,$ you can split the data into two smaller nonoverlapping (and therefore independent) samples, es | Unbiased Estimation of $\mu^2$ under certain conditions
Only the third question remains to be answered, the case where $X$ has infinite variance.
When $n \gt 1,$ you can split the data into two smaller nonoverlapping (and therefore independent) samples, estimate $\mu$ separately in each subsample, and multiply the esti... | Unbiased Estimation of $\mu^2$ under certain conditions
Only the third question remains to be answered, the case where $X$ has infinite variance.
When $n \gt 1,$ you can split the data into two smaller nonoverlapping (and therefore independent) samples, es |
47,719 | Randomly choose between numbers that yields a specific amount of binary 1's | The algorithm to use depends on (a) the capabilities of your software platform; (b) how many such random draws you need; (c) how large the number of digits $n$ is; and (d) how large the number of possible results $\binom{n}{k}$ (where $k$ is the number of ones) is.
Most statistical work is done with 32 or 64 signed int... | Randomly choose between numbers that yields a specific amount of binary 1's | The algorithm to use depends on (a) the capabilities of your software platform; (b) how many such random draws you need; (c) how large the number of digits $n$ is; and (d) how large the number of poss | Randomly choose between numbers that yields a specific amount of binary 1's
The algorithm to use depends on (a) the capabilities of your software platform; (b) how many such random draws you need; (c) how large the number of digits $n$ is; and (d) how large the number of possible results $\binom{n}{k}$ (where $k$ is th... | Randomly choose between numbers that yields a specific amount of binary 1's
The algorithm to use depends on (a) the capabilities of your software platform; (b) how many such random draws you need; (c) how large the number of digits $n$ is; and (d) how large the number of poss |
47,720 | Is $\theta$ a location or a scale parameter in the $\mathcal N(\theta,\theta)$ and $\mathcal N(\theta,\theta^2)$ densities? | Since, when $X\sim{\cal N}(\theta,\theta^2)$,$$Z=\dfrac{X-\theta}{\theta}=\dfrac{X}{\theta}-1\sim{\cal N}(0,1)$$and assuming $\theta\ne 0$, since $\theta=0$ is a special case that results in a Dirac mass at zero, the parameter $\theta$ is a scale parameter as $$X=\theta(Z+1)$$ is the scaled version of $Z+1$ that has a ... | Is $\theta$ a location or a scale parameter in the $\mathcal N(\theta,\theta)$ and $\mathcal N(\thet | Since, when $X\sim{\cal N}(\theta,\theta^2)$,$$Z=\dfrac{X-\theta}{\theta}=\dfrac{X}{\theta}-1\sim{\cal N}(0,1)$$and assuming $\theta\ne 0$, since $\theta=0$ is a special case that results in a Dirac m | Is $\theta$ a location or a scale parameter in the $\mathcal N(\theta,\theta)$ and $\mathcal N(\theta,\theta^2)$ densities?
Since, when $X\sim{\cal N}(\theta,\theta^2)$,$$Z=\dfrac{X-\theta}{\theta}=\dfrac{X}{\theta}-1\sim{\cal N}(0,1)$$and assuming $\theta\ne 0$, since $\theta=0$ is a special case that results in a Dir... | Is $\theta$ a location or a scale parameter in the $\mathcal N(\theta,\theta)$ and $\mathcal N(\thet
Since, when $X\sim{\cal N}(\theta,\theta^2)$,$$Z=\dfrac{X-\theta}{\theta}=\dfrac{X}{\theta}-1\sim{\cal N}(0,1)$$and assuming $\theta\ne 0$, since $\theta=0$ is a special case that results in a Dirac m |
47,721 | How is a ROCAUC=1.0 possible with imperfect accuracy? [duplicate] | ROC AUC and the $c$-statistic are equivalent, and measure the probability that a randomly-chosen positive sample is ranked higher than a randomly-chosen negative sample. If all positives have score 0.49 and all negatives have score 0.48, then the ROC AUC is 1.0 because of this property. This can lead to counter-intuiti... | How is a ROCAUC=1.0 possible with imperfect accuracy? [duplicate] | ROC AUC and the $c$-statistic are equivalent, and measure the probability that a randomly-chosen positive sample is ranked higher than a randomly-chosen negative sample. If all positives have score 0. | How is a ROCAUC=1.0 possible with imperfect accuracy? [duplicate]
ROC AUC and the $c$-statistic are equivalent, and measure the probability that a randomly-chosen positive sample is ranked higher than a randomly-chosen negative sample. If all positives have score 0.49 and all negatives have score 0.48, then the ROC AUC... | How is a ROCAUC=1.0 possible with imperfect accuracy? [duplicate]
ROC AUC and the $c$-statistic are equivalent, and measure the probability that a randomly-chosen positive sample is ranked higher than a randomly-chosen negative sample. If all positives have score 0. |
47,722 | Why do planned comparisons and post-hoc tests differ? | They aren't really the same. A planned comparison is something you are committing to before you see your data, and will run no matter what the results look like. A post-hoc comparison is more opportunistic. You look at that because, when you looked at the data, that particular comparison looked interesting. The ide... | Why do planned comparisons and post-hoc tests differ? | They aren't really the same. A planned comparison is something you are committing to before you see your data, and will run no matter what the results look like. A post-hoc comparison is more opport | Why do planned comparisons and post-hoc tests differ?
They aren't really the same. A planned comparison is something you are committing to before you see your data, and will run no matter what the results look like. A post-hoc comparison is more opportunistic. You look at that because, when you looked at the data, t... | Why do planned comparisons and post-hoc tests differ?
They aren't really the same. A planned comparison is something you are committing to before you see your data, and will run no matter what the results look like. A post-hoc comparison is more opport |
47,723 | How to understand SE of regression slope equation | The intuitive understanding is indeed as you suggest in the comment. If you think about the value of the slope for the regression as something that will change every time you draw a new sample (which it does), then the standard deviation of the resulting sampling distribution is the standard error for that parameter. ... | How to understand SE of regression slope equation | The intuitive understanding is indeed as you suggest in the comment. If you think about the value of the slope for the regression as something that will change every time you draw a new sample (which | How to understand SE of regression slope equation
The intuitive understanding is indeed as you suggest in the comment. If you think about the value of the slope for the regression as something that will change every time you draw a new sample (which it does), then the standard deviation of the resulting sampling distr... | How to understand SE of regression slope equation
The intuitive understanding is indeed as you suggest in the comment. If you think about the value of the slope for the regression as something that will change every time you draw a new sample (which |
47,724 | A question on probability involving Binomial distribution | Your intuition is correct. Algebraic demonstration of that fact can proceed as follows:
$$\begin{equation} \begin{aligned}
\mathbb{P}(X = i)
&= \sum_{j=i}^n {j \choose i} s^i (1-s)^{j-i} {n \choose j} p^j (1-p)^{n-j} \\[8pt]
&= \sum_{j=i}^n \frac{j!}{i! (j-i)!} \frac{n!}{j! (n-j)!} s^i (1-s)^{j-i} p^j (1-p)^{n-j} \\[... | A question on probability involving Binomial distribution | Your intuition is correct. Algebraic demonstration of that fact can proceed as follows:
$$\begin{equation} \begin{aligned}
\mathbb{P}(X = i)
&= \sum_{j=i}^n {j \choose i} s^i (1-s)^{j-i} {n \choose | A question on probability involving Binomial distribution
Your intuition is correct. Algebraic demonstration of that fact can proceed as follows:
$$\begin{equation} \begin{aligned}
\mathbb{P}(X = i)
&= \sum_{j=i}^n {j \choose i} s^i (1-s)^{j-i} {n \choose j} p^j (1-p)^{n-j} \\[8pt]
&= \sum_{j=i}^n \frac{j!}{i! (j-i)!... | A question on probability involving Binomial distribution
Your intuition is correct. Algebraic demonstration of that fact can proceed as follows:
$$\begin{equation} \begin{aligned}
\mathbb{P}(X = i)
&= \sum_{j=i}^n {j \choose i} s^i (1-s)^{j-i} {n \choose |
47,725 | An example of a bivariate pdf, where marginals are triangular distributions | A nice way to do this is to use copulae.
In your case:
let $X \sim \text{Triangular}(0,1)$ with pdf $f(x)$ and parameter $b$, and
let $Y \sim \text{Triangular}(0,1)$ with pdf $g(y)$ and parameter $c$:
with cdf's $F(x)$ and $G(y)$:
... where I am using the Prob function (from the mathStatica package for Mathematica... | An example of a bivariate pdf, where marginals are triangular distributions | A nice way to do this is to use copulae.
In your case:
let $X \sim \text{Triangular}(0,1)$ with pdf $f(x)$ and parameter $b$, and
let $Y \sim \text{Triangular}(0,1)$ with pdf $g(y)$ and parameter $c | An example of a bivariate pdf, where marginals are triangular distributions
A nice way to do this is to use copulae.
In your case:
let $X \sim \text{Triangular}(0,1)$ with pdf $f(x)$ and parameter $b$, and
let $Y \sim \text{Triangular}(0,1)$ with pdf $g(y)$ and parameter $c$:
with cdf's $F(x)$ and $G(y)$:
... wher... | An example of a bivariate pdf, where marginals are triangular distributions
A nice way to do this is to use copulae.
In your case:
let $X \sim \text{Triangular}(0,1)$ with pdf $f(x)$ and parameter $b$, and
let $Y \sim \text{Triangular}(0,1)$ with pdf $g(y)$ and parameter $c |
47,726 | Why is it valid to use CV to set parameters and hyperparameters but not seeds? | Provided you do your cross-validation properly (i.e. cross validate the whole procedure) I don't think it's "wrong", I think the most likely result is just that it won't be helpful. Doing this CV properly though means you have to be careful to include these decisions in each fold. It's common to see people forgetting t... | Why is it valid to use CV to set parameters and hyperparameters but not seeds? | Provided you do your cross-validation properly (i.e. cross validate the whole procedure) I don't think it's "wrong", I think the most likely result is just that it won't be helpful. Doing this CV prop | Why is it valid to use CV to set parameters and hyperparameters but not seeds?
Provided you do your cross-validation properly (i.e. cross validate the whole procedure) I don't think it's "wrong", I think the most likely result is just that it won't be helpful. Doing this CV properly though means you have to be careful ... | Why is it valid to use CV to set parameters and hyperparameters but not seeds?
Provided you do your cross-validation properly (i.e. cross validate the whole procedure) I don't think it's "wrong", I think the most likely result is just that it won't be helpful. Doing this CV prop |
47,727 | How is the minimum $\lambda$ computed in group LASSO? | If a change of $\beta$ in any direction will not decrease the cost/objective function then you have found yourself in, at least, a local minimum. The calculations below will show for which λ the solution/point $\beta = 0$ stops to be a minimum.
Consider the effect of 'a change of $\beta^{(l)}$ by an infinitesimal dista... | How is the minimum $\lambda$ computed in group LASSO? | If a change of $\beta$ in any direction will not decrease the cost/objective function then you have found yourself in, at least, a local minimum. The calculations below will show for which λ the solut | How is the minimum $\lambda$ computed in group LASSO?
If a change of $\beta$ in any direction will not decrease the cost/objective function then you have found yourself in, at least, a local minimum. The calculations below will show for which λ the solution/point $\beta = 0$ stops to be a minimum.
Consider the effect o... | How is the minimum $\lambda$ computed in group LASSO?
If a change of $\beta$ in any direction will not decrease the cost/objective function then you have found yourself in, at least, a local minimum. The calculations below will show for which λ the solut |
47,728 | Mix of text and numeric data | You have two main options here:
As you said, create some numeric features out of the text description and merge it with the rest of the numeric data. The features created out of the text description can be either the document-term matrix (with tf-idf or not), can be SVD components or even averaged word-vectors (look f... | Mix of text and numeric data | You have two main options here:
As you said, create some numeric features out of the text description and merge it with the rest of the numeric data. The features created out of the text description | Mix of text and numeric data
You have two main options here:
As you said, create some numeric features out of the text description and merge it with the rest of the numeric data. The features created out of the text description can be either the document-term matrix (with tf-idf or not), can be SVD components or even ... | Mix of text and numeric data
You have two main options here:
As you said, create some numeric features out of the text description and merge it with the rest of the numeric data. The features created out of the text description |
47,729 | Mix of text and numeric data | I think there is a more satisfying solution than what has been suggested already, one that creates a single model that properly deals with the two kinds of input data and their relationship to the output class. Use a sequence model like an RNN to convert text into a kind of embedding. That embedding output is used di... | Mix of text and numeric data | I think there is a more satisfying solution than what has been suggested already, one that creates a single model that properly deals with the two kinds of input data and their relationship to the out | Mix of text and numeric data
I think there is a more satisfying solution than what has been suggested already, one that creates a single model that properly deals with the two kinds of input data and their relationship to the output class. Use a sequence model like an RNN to convert text into a kind of embedding. Tha... | Mix of text and numeric data
I think there is a more satisfying solution than what has been suggested already, one that creates a single model that properly deals with the two kinds of input data and their relationship to the out |
47,730 | Integrate out missing variables in Gaussian Processing? | The linked question is discussing data imputation for the purposes of building a predictive model. What I believe the accepted answer is referring to is using a Gaussian Process as a model for the missing data, conditional on the observed data.
"Integrating out" these missing variables then means marginalising the pre... | Integrate out missing variables in Gaussian Processing? | The linked question is discussing data imputation for the purposes of building a predictive model. What I believe the accepted answer is referring to is using a Gaussian Process as a model for the mis | Integrate out missing variables in Gaussian Processing?
The linked question is discussing data imputation for the purposes of building a predictive model. What I believe the accepted answer is referring to is using a Gaussian Process as a model for the missing data, conditional on the observed data.
"Integrating out" ... | Integrate out missing variables in Gaussian Processing?
The linked question is discussing data imputation for the purposes of building a predictive model. What I believe the accepted answer is referring to is using a Gaussian Process as a model for the mis |
47,731 | Regularization on weights without bias | Here's my understanding of this quote. This is sort of a hand-wavy argument, but still gives some intuition. Let's consider a simple linear layer:
$$y = Wx + b$$
... or equivalently:
$$y_i = x_{1}W_{i,1} + ... + x_{n}W_{i,n} + b_i$$
If we focus on one weight $W_{i,j}$, its value is determined by observing two variables... | Regularization on weights without bias | Here's my understanding of this quote. This is sort of a hand-wavy argument, but still gives some intuition. Let's consider a simple linear layer:
$$y = Wx + b$$
... or equivalently:
$$y_i = x_{1}W_{i | Regularization on weights without bias
Here's my understanding of this quote. This is sort of a hand-wavy argument, but still gives some intuition. Let's consider a simple linear layer:
$$y = Wx + b$$
... or equivalently:
$$y_i = x_{1}W_{i,1} + ... + x_{n}W_{i,n} + b_i$$
If we focus on one weight $W_{i,j}$, its value i... | Regularization on weights without bias
Here's my understanding of this quote. This is sort of a hand-wavy argument, but still gives some intuition. Let's consider a simple linear layer:
$$y = Wx + b$$
... or equivalently:
$$y_i = x_{1}W_{i |
47,732 | Regularization on weights without bias | In ML lingo a weight is a coefficient of a bona fide regression variable and bias is the intercept. Also, in regression language interaction has a specific meaning, not the same as used in the text quoted.
In your text how variables interact means simply that there is a function that into translates inputs $x$ into ou... | Regularization on weights without bias | In ML lingo a weight is a coefficient of a bona fide regression variable and bias is the intercept. Also, in regression language interaction has a specific meaning, not the same as used in the text qu | Regularization on weights without bias
In ML lingo a weight is a coefficient of a bona fide regression variable and bias is the intercept. Also, in regression language interaction has a specific meaning, not the same as used in the text quoted.
In your text how variables interact means simply that there is a function t... | Regularization on weights without bias
In ML lingo a weight is a coefficient of a bona fide regression variable and bias is the intercept. Also, in regression language interaction has a specific meaning, not the same as used in the text qu |
47,733 | Prove that the squared exponential covariance is non-negative definite | I am not an expert but I'll sketch a standard argument which is explained in more detail in Rasmussen and Williams, Chapter 4 Section 2.1 (that book has answered a ton of my question about GPs). So we are working with the squared exponential function right? We have:
$$K_{i,j}= \alpha \cdot \mathrm{exp}(\frac{-(x_i-x_j)... | Prove that the squared exponential covariance is non-negative definite | I am not an expert but I'll sketch a standard argument which is explained in more detail in Rasmussen and Williams, Chapter 4 Section 2.1 (that book has answered a ton of my question about GPs). So we | Prove that the squared exponential covariance is non-negative definite
I am not an expert but I'll sketch a standard argument which is explained in more detail in Rasmussen and Williams, Chapter 4 Section 2.1 (that book has answered a ton of my question about GPs). So we are working with the squared exponential functio... | Prove that the squared exponential covariance is non-negative definite
I am not an expert but I'll sketch a standard argument which is explained in more detail in Rasmussen and Williams, Chapter 4 Section 2.1 (that book has answered a ton of my question about GPs). So we |
47,734 | Prove that the squared exponential covariance is non-negative definite | There are also 3 more proofs here:
How to prove that the radial basis function is a kernel?
Note that the "squared exponential" kernel is also called a "radial basis function" (RBF) kernel and a "Gaussian" kernel. | Prove that the squared exponential covariance is non-negative definite | There are also 3 more proofs here:
How to prove that the radial basis function is a kernel?
Note that the "squared exponential" kernel is also called a "radial basis function" (RBF) kernel and a "Gaus | Prove that the squared exponential covariance is non-negative definite
There are also 3 more proofs here:
How to prove that the radial basis function is a kernel?
Note that the "squared exponential" kernel is also called a "radial basis function" (RBF) kernel and a "Gaussian" kernel. | Prove that the squared exponential covariance is non-negative definite
There are also 3 more proofs here:
How to prove that the radial basis function is a kernel?
Note that the "squared exponential" kernel is also called a "radial basis function" (RBF) kernel and a "Gaus |
47,735 | How are ergodicity and "weak dependence" related? | The concepts are not interchangeable. Ergodicity deals with studying the systems where different realizations of the process are not available. For instance, in coin toss we could reasonably argue that we could generate any number of realizations of the sequence of coin tosses. We'll toss 10 coins 1000 times, and it gi... | How are ergodicity and "weak dependence" related? | The concepts are not interchangeable. Ergodicity deals with studying the systems where different realizations of the process are not available. For instance, in coin toss we could reasonably argue tha | How are ergodicity and "weak dependence" related?
The concepts are not interchangeable. Ergodicity deals with studying the systems where different realizations of the process are not available. For instance, in coin toss we could reasonably argue that we could generate any number of realizations of the sequence of coin... | How are ergodicity and "weak dependence" related?
The concepts are not interchangeable. Ergodicity deals with studying the systems where different realizations of the process are not available. For instance, in coin toss we could reasonably argue tha |
47,736 | How are ergodicity and "weak dependence" related? | I had the same question, and found these lecture notes. Page 8 states that a mixing process is ergodic (called Theorem 7) and that a mixing process is also called weakly dependent.
In other words, a weakly dependent process is ergodic.
It is my understanding that we require ergodicity to estimate the asymptotic covaria... | How are ergodicity and "weak dependence" related? | I had the same question, and found these lecture notes. Page 8 states that a mixing process is ergodic (called Theorem 7) and that a mixing process is also called weakly dependent.
In other words, a w | How are ergodicity and "weak dependence" related?
I had the same question, and found these lecture notes. Page 8 states that a mixing process is ergodic (called Theorem 7) and that a mixing process is also called weakly dependent.
In other words, a weakly dependent process is ergodic.
It is my understanding that we req... | How are ergodicity and "weak dependence" related?
I had the same question, and found these lecture notes. Page 8 states that a mixing process is ergodic (called Theorem 7) and that a mixing process is also called weakly dependent.
In other words, a w |
47,737 | How do I show this using the Cauchy-Schwarz inequality | I am able to use Cauchy-Schwartz inequality, but I not quite getting the same result. I may have made a mistake, so here are all the steps.
Note that for positive semi-definite matrices, trace defines an inner product. That is $tr(AB) = \langle B^T, A \rangle$.
Then by Cauchy-Schwarz for $A$ and $B$ positive semi-defi... | How do I show this using the Cauchy-Schwarz inequality | I am able to use Cauchy-Schwartz inequality, but I not quite getting the same result. I may have made a mistake, so here are all the steps.
Note that for positive semi-definite matrices, trace define | How do I show this using the Cauchy-Schwarz inequality
I am able to use Cauchy-Schwartz inequality, but I not quite getting the same result. I may have made a mistake, so here are all the steps.
Note that for positive semi-definite matrices, trace defines an inner product. That is $tr(AB) = \langle B^T, A \rangle$.
Th... | How do I show this using the Cauchy-Schwarz inequality
I am able to use Cauchy-Schwartz inequality, but I not quite getting the same result. I may have made a mistake, so here are all the steps.
Note that for positive semi-definite matrices, trace define |
47,738 | For what types of research designs should (Days|Subject) vs. (1|Days:Subject) random effect specification be used? | Your fit2 does not really fit a random slope. Instead, it sets a random intercept for each combination of Days and Subject. This implies that for the computation of the random effects fit2 treats Days as a categorical rather than continuous variable.
You can check the difference by comparing the output of ranef(fit1) a... | For what types of research designs should (Days|Subject) vs. (1|Days:Subject) random effect specific | Your fit2 does not really fit a random slope. Instead, it sets a random intercept for each combination of Days and Subject. This implies that for the computation of the random effects fit2 treats Days | For what types of research designs should (Days|Subject) vs. (1|Days:Subject) random effect specification be used?
Your fit2 does not really fit a random slope. Instead, it sets a random intercept for each combination of Days and Subject. This implies that for the computation of the random effects fit2 treats Days as a... | For what types of research designs should (Days|Subject) vs. (1|Days:Subject) random effect specific
Your fit2 does not really fit a random slope. Instead, it sets a random intercept for each combination of Days and Subject. This implies that for the computation of the random effects fit2 treats Days |
47,739 | Prove that the vector $(X_{n},Y_{n})$ converges in probability if and only if each component converges in probability | Both directions can be proved simply using definitions.
For the $\Rightarrow$ direction, use $\Pr\left(|X_n-X| > \epsilon\right) \le \Pr\left(\sqrt{|X_n-X|^2+|Y_n-Y|^2}> \epsilon\right) $.
For the $\Leftarrow$ direction, note $\Pr\left(\sqrt{|X_n-X|^2+|Y_n-Y|^2}> 2\epsilon \right)\le \Pr(|X_n-X| > \epsilon$ or$ |Y_n-... | Prove that the vector $(X_{n},Y_{n})$ converges in probability if and only if each component converg | Both directions can be proved simply using definitions.
For the $\Rightarrow$ direction, use $\Pr\left(|X_n-X| > \epsilon\right) \le \Pr\left(\sqrt{|X_n-X|^2+|Y_n-Y|^2}> \epsilon\right) $.
For the $\L | Prove that the vector $(X_{n},Y_{n})$ converges in probability if and only if each component converges in probability
Both directions can be proved simply using definitions.
For the $\Rightarrow$ direction, use $\Pr\left(|X_n-X| > \epsilon\right) \le \Pr\left(\sqrt{|X_n-X|^2+|Y_n-Y|^2}> \epsilon\right) $.
For the $\Lef... | Prove that the vector $(X_{n},Y_{n})$ converges in probability if and only if each component converg
Both directions can be proved simply using definitions.
For the $\Rightarrow$ direction, use $\Pr\left(|X_n-X| > \epsilon\right) \le \Pr\left(\sqrt{|X_n-X|^2+|Y_n-Y|^2}> \epsilon\right) $.
For the $\L |
47,740 | ntree parameter in predict.gbm | A good use of that parameter is saving time on hyperparameter tuning. Suppose you want to tune the model on number of trees with a test data set. And you want to try from 1000 to 5000 trees, step by 1000.
Instead of building 5 models, you can just build one model with 5000 tree, and use this ntree parameter to see the... | ntree parameter in predict.gbm | A good use of that parameter is saving time on hyperparameter tuning. Suppose you want to tune the model on number of trees with a test data set. And you want to try from 1000 to 5000 trees, step by 1 | ntree parameter in predict.gbm
A good use of that parameter is saving time on hyperparameter tuning. Suppose you want to tune the model on number of trees with a test data set. And you want to try from 1000 to 5000 trees, step by 1000.
Instead of building 5 models, you can just build one model with 5000 tree, and use ... | ntree parameter in predict.gbm
A good use of that parameter is saving time on hyperparameter tuning. Suppose you want to tune the model on number of trees with a test data set. And you want to try from 1000 to 5000 trees, step by 1 |
47,741 | ntree parameter in predict.gbm | From the documentation:
predict.gbm produces predicted values for each observation in newdata
using the the first n.trees iterations of the boosting sequence. If
n.trees is a vector than the result is a matrix with each column
representing the predictions from gbm models with n.trees[1]
iterations, n.trees[2] ... | ntree parameter in predict.gbm | From the documentation:
predict.gbm produces predicted values for each observation in newdata
using the the first n.trees iterations of the boosting sequence. If
n.trees is a vector than the resu | ntree parameter in predict.gbm
From the documentation:
predict.gbm produces predicted values for each observation in newdata
using the the first n.trees iterations of the boosting sequence. If
n.trees is a vector than the result is a matrix with each column
representing the predictions from gbm models with n.tre... | ntree parameter in predict.gbm
From the documentation:
predict.gbm produces predicted values for each observation in newdata
using the the first n.trees iterations of the boosting sequence. If
n.trees is a vector than the resu |
47,742 | How do we characterize probabilities on this infinite sample space | [Note: I think this answer is correct. If it's wrong, then hopefully at least it will be a starting point for further discussions.]
It's not possible to talk about the "fraction of sequences with infinitely many 1s" unless you have some way of defining "fraction". This can't be done consistently without using measure t... | How do we characterize probabilities on this infinite sample space | [Note: I think this answer is correct. If it's wrong, then hopefully at least it will be a starting point for further discussions.]
It's not possible to talk about the "fraction of sequences with infi | How do we characterize probabilities on this infinite sample space
[Note: I think this answer is correct. If it's wrong, then hopefully at least it will be a starting point for further discussions.]
It's not possible to talk about the "fraction of sequences with infinitely many 1s" unless you have some way of defining ... | How do we characterize probabilities on this infinite sample space
[Note: I think this answer is correct. If it's wrong, then hopefully at least it will be a starting point for further discussions.]
It's not possible to talk about the "fraction of sequences with infi |
47,743 | How do we characterize probabilities on this infinite sample space | I would say that to ask this question, we must ask the probability that any sequence has finite ones. I think it's sufficient to show that the probability of generating a sequence, as you described, that has finite ones, by rolling a dice at each step, is zero. If that's true then drawing any element of $S$ should guar... | How do we characterize probabilities on this infinite sample space | I would say that to ask this question, we must ask the probability that any sequence has finite ones. I think it's sufficient to show that the probability of generating a sequence, as you described, t | How do we characterize probabilities on this infinite sample space
I would say that to ask this question, we must ask the probability that any sequence has finite ones. I think it's sufficient to show that the probability of generating a sequence, as you described, that has finite ones, by rolling a dice at each step, ... | How do we characterize probabilities on this infinite sample space
I would say that to ask this question, we must ask the probability that any sequence has finite ones. I think it's sufficient to show that the probability of generating a sequence, as you described, t |
47,744 | A Coin Flip Problem | Let your coin be $X_1$ and denote sum of heads as $S$.
As I have written in the comment the answers seems to be
$$P(X_1 = 1| S \ge k) = \frac{\sum_{i = k}^{n} \binom{n-1}{i-1}}{\sum_{i=k}^{n}\binom{n}{i}}$$
Here is a plot of theoretical vs sample probabilities with $n = 20$ and 1e^7 trials
We can see that with low v... | A Coin Flip Problem | Let your coin be $X_1$ and denote sum of heads as $S$.
As I have written in the comment the answers seems to be
$$P(X_1 = 1| S \ge k) = \frac{\sum_{i = k}^{n} \binom{n-1}{i-1}}{\sum_{i=k}^{n}\binom{ | A Coin Flip Problem
Let your coin be $X_1$ and denote sum of heads as $S$.
As I have written in the comment the answers seems to be
$$P(X_1 = 1| S \ge k) = \frac{\sum_{i = k}^{n} \binom{n-1}{i-1}}{\sum_{i=k}^{n}\binom{n}{i}}$$
Here is a plot of theoretical vs sample probabilities with $n = 20$ and 1e^7 trials
We can... | A Coin Flip Problem
Let your coin be $X_1$ and denote sum of heads as $S$.
As I have written in the comment the answers seems to be
$$P(X_1 = 1| S \ge k) = \frac{\sum_{i = k}^{n} \binom{n-1}{i-1}}{\sum_{i=k}^{n}\binom{ |
47,745 | Two measurement devices vs 1 device multiple measurements | Regardless of how these devices behave, an additive model of variability provides useful insight.
Such a model supposes that the response of an instrument is the sum of three independent quantities (none of which we necessarily know):
The true value it is trying to measure, $\mu$.
A random measurement error $X$ with m... | Two measurement devices vs 1 device multiple measurements | Regardless of how these devices behave, an additive model of variability provides useful insight.
Such a model supposes that the response of an instrument is the sum of three independent quantities (n | Two measurement devices vs 1 device multiple measurements
Regardless of how these devices behave, an additive model of variability provides useful insight.
Such a model supposes that the response of an instrument is the sum of three independent quantities (none of which we necessarily know):
The true value it is tryin... | Two measurement devices vs 1 device multiple measurements
Regardless of how these devices behave, an additive model of variability provides useful insight.
Such a model supposes that the response of an instrument is the sum of three independent quantities (n |
47,746 | Understanding the GARCH(1,1) model: the constant, the ARCH term and the GARCH term | A GARCH(1,1) model is
\begin{aligned}
y_t &= \mu_t + u_t, \\
\mu_t &= \dots \text{(e.g. a constant or an ARMA equation without the term $u_t$)}, \\
u_t &= \sigma_t \varepsilon_t, \\
\sigma_t^2 &= \omega + \alpha_1 u_{t-1}^2 + \beta_1 \sigma_{t-1}^2, \\
\varepsilon_t &\sim i.i.d(0,1). \\
\end{aligned}
The three componen... | Understanding the GARCH(1,1) model: the constant, the ARCH term and the GARCH term | A GARCH(1,1) model is
\begin{aligned}
y_t &= \mu_t + u_t, \\
\mu_t &= \dots \text{(e.g. a constant or an ARMA equation without the term $u_t$)}, \\
u_t &= \sigma_t \varepsilon_t, \\
\sigma_t^2 &= \ome | Understanding the GARCH(1,1) model: the constant, the ARCH term and the GARCH term
A GARCH(1,1) model is
\begin{aligned}
y_t &= \mu_t + u_t, \\
\mu_t &= \dots \text{(e.g. a constant or an ARMA equation without the term $u_t$)}, \\
u_t &= \sigma_t \varepsilon_t, \\
\sigma_t^2 &= \omega + \alpha_1 u_{t-1}^2 + \beta_1 \si... | Understanding the GARCH(1,1) model: the constant, the ARCH term and the GARCH term
A GARCH(1,1) model is
\begin{aligned}
y_t &= \mu_t + u_t, \\
\mu_t &= \dots \text{(e.g. a constant or an ARMA equation without the term $u_t$)}, \\
u_t &= \sigma_t \varepsilon_t, \\
\sigma_t^2 &= \ome |
47,747 | Understanding the GARCH(1,1) model: the constant, the ARCH term and the GARCH term | Think you have it backwards on sigma squared. The "beta" of the GARCH model is the coefficient of historical variance. | Understanding the GARCH(1,1) model: the constant, the ARCH term and the GARCH term | Think you have it backwards on sigma squared. The "beta" of the GARCH model is the coefficient of historical variance. | Understanding the GARCH(1,1) model: the constant, the ARCH term and the GARCH term
Think you have it backwards on sigma squared. The "beta" of the GARCH model is the coefficient of historical variance. | Understanding the GARCH(1,1) model: the constant, the ARCH term and the GARCH term
Think you have it backwards on sigma squared. The "beta" of the GARCH model is the coefficient of historical variance. |
47,748 | Skewness of Tweedie distribution | Exponential dispersion family is a broad family of distributions allowed in GLMs. The general form of the PDF can be written as follows:
$$f(x;\theta,\phi)=a(x,\phi)\exp\Big[\frac{1}{\phi}\big(x\theta-\kappa(\theta)\big)\Big].$$
The term $\kappa(\theta)$ is denoted with kappa because it is intimately related to the cum... | Skewness of Tweedie distribution | Exponential dispersion family is a broad family of distributions allowed in GLMs. The general form of the PDF can be written as follows:
$$f(x;\theta,\phi)=a(x,\phi)\exp\Big[\frac{1}{\phi}\big(x\theta | Skewness of Tweedie distribution
Exponential dispersion family is a broad family of distributions allowed in GLMs. The general form of the PDF can be written as follows:
$$f(x;\theta,\phi)=a(x,\phi)\exp\Big[\frac{1}{\phi}\big(x\theta-\kappa(\theta)\big)\Big].$$
The term $\kappa(\theta)$ is denoted with kappa because it... | Skewness of Tweedie distribution
Exponential dispersion family is a broad family of distributions allowed in GLMs. The general form of the PDF can be written as follows:
$$f(x;\theta,\phi)=a(x,\phi)\exp\Big[\frac{1}{\phi}\big(x\theta |
47,749 | If in this problem I regress $x$ on $y$ instead than $y$ on $x$, do I need to use an error-in-variables model? | The direction of regression may be important to prevent attenuation bias.
Your question about the regression $x \sim y$ versus $y \sim x$ has many angles. A problem which you might encounter is regression attenuation or regression dilution.
This does not depend on which variable the experiment was controlled in the e... | If in this problem I regress $x$ on $y$ instead than $y$ on $x$, do I need to use an error-in-variab | The direction of regression may be important to prevent attenuation bias.
Your question about the regression $x \sim y$ versus $y \sim x$ has many angles. A problem which you might encounter is regres | If in this problem I regress $x$ on $y$ instead than $y$ on $x$, do I need to use an error-in-variables model?
The direction of regression may be important to prevent attenuation bias.
Your question about the regression $x \sim y$ versus $y \sim x$ has many angles. A problem which you might encounter is regression atte... | If in this problem I regress $x$ on $y$ instead than $y$ on $x$, do I need to use an error-in-variab
The direction of regression may be important to prevent attenuation bias.
Your question about the regression $x \sim y$ versus $y \sim x$ has many angles. A problem which you might encounter is regres |
47,750 | Proposal distribution in Hamiltonian Monte Carlo | The proposal distribution for the original Hamiltonian Monte Carlo algorithm is just a delta function around the final point in the numerical trajectory with the momentum negated,
$$K(z' | z) = \delta \, (z' - R(\Phi_{\epsilon, L}(z))), $$
where $z = (q, p)$ is a point on phase space, $\Phi_{\epsilon, L}(z)$ is the act... | Proposal distribution in Hamiltonian Monte Carlo | The proposal distribution for the original Hamiltonian Monte Carlo algorithm is just a delta function around the final point in the numerical trajectory with the momentum negated,
$$K(z' | z) = \delta | Proposal distribution in Hamiltonian Monte Carlo
The proposal distribution for the original Hamiltonian Monte Carlo algorithm is just a delta function around the final point in the numerical trajectory with the momentum negated,
$$K(z' | z) = \delta \, (z' - R(\Phi_{\epsilon, L}(z))), $$
where $z = (q, p)$ is a point o... | Proposal distribution in Hamiltonian Monte Carlo
The proposal distribution for the original Hamiltonian Monte Carlo algorithm is just a delta function around the final point in the numerical trajectory with the momentum negated,
$$K(z' | z) = \delta |
47,751 | Proposal distribution in Hamiltonian Monte Carlo | The proposal distribution in Hamiltonian Monte Carlo does not have an explicit form in general. Instead, samples from it are defined operationally: first sample an initial velocity and then move the position using a number of leap-frog steps. The final position is a sample from the proposal distribution. | Proposal distribution in Hamiltonian Monte Carlo | The proposal distribution in Hamiltonian Monte Carlo does not have an explicit form in general. Instead, samples from it are defined operationally: first sample an initial velocity and then move the p | Proposal distribution in Hamiltonian Monte Carlo
The proposal distribution in Hamiltonian Monte Carlo does not have an explicit form in general. Instead, samples from it are defined operationally: first sample an initial velocity and then move the position using a number of leap-frog steps. The final position is a samp... | Proposal distribution in Hamiltonian Monte Carlo
The proposal distribution in Hamiltonian Monte Carlo does not have an explicit form in general. Instead, samples from it are defined operationally: first sample an initial velocity and then move the p |
47,752 | Uniform distribution on $\mathbb{Q} \cap [0, 1]$ (sort of) [duplicate] | No it is not possible.
If such a random variable exists, we would have $\Pr(X=q)=0$ for every $q \in \mathbb{Q} \cap [0,1]$, because we can write the singleton $\{q\}$ as a decreasing intersection of intervals $[a_n, b_n]$ whose length $b_n-a_n$ goes to $0$, and then $\Pr(X = q) = \lim \Pr(X \in [a_n,b_n])=0$.
Now, the... | Uniform distribution on $\mathbb{Q} \cap [0, 1]$ (sort of) [duplicate] | No it is not possible.
If such a random variable exists, we would have $\Pr(X=q)=0$ for every $q \in \mathbb{Q} \cap [0,1]$, because we can write the singleton $\{q\}$ as a decreasing intersection of | Uniform distribution on $\mathbb{Q} \cap [0, 1]$ (sort of) [duplicate]
No it is not possible.
If such a random variable exists, we would have $\Pr(X=q)=0$ for every $q \in \mathbb{Q} \cap [0,1]$, because we can write the singleton $\{q\}$ as a decreasing intersection of intervals $[a_n, b_n]$ whose length $b_n-a_n$ goe... | Uniform distribution on $\mathbb{Q} \cap [0, 1]$ (sort of) [duplicate]
No it is not possible.
If such a random variable exists, we would have $\Pr(X=q)=0$ for every $q \in \mathbb{Q} \cap [0,1]$, because we can write the singleton $\{q\}$ as a decreasing intersection of |
47,753 | Why in Box-Cox method we try to make x and y normally distributed, but that's not an assumption for linear regression? | In reality the box-cox transformation finds a transformation that homogenize variance. And constant variance is really an important assumption! The comment of @whuber: The Box-Cox transform is a data transformation (usually for positive data) defined by $Y^{(\lambda)}= \frac{y^\lambda - 1}{\lambda}$ (when $\lambda\no... | Why in Box-Cox method we try to make x and y normally distributed, but that's not an assumption for | In reality the box-cox transformation finds a transformation that homogenize variance. And constant variance is really an important assumption! The comment of @whuber: The Box-Cox transform is a dat | Why in Box-Cox method we try to make x and y normally distributed, but that's not an assumption for linear regression?
In reality the box-cox transformation finds a transformation that homogenize variance. And constant variance is really an important assumption! The comment of @whuber: The Box-Cox transform is a data... | Why in Box-Cox method we try to make x and y normally distributed, but that's not an assumption for
In reality the box-cox transformation finds a transformation that homogenize variance. And constant variance is really an important assumption! The comment of @whuber: The Box-Cox transform is a dat |
47,754 | Why in Box-Cox method we try to make x and y normally distributed, but that's not an assumption for linear regression? | I'm assuming you're referring to Box-Cox normality plots by "method" in your question. It is true that normality assumption in OLS is not required for the method to be useful. For instance, regardless of the error distribution it will produce the coefficients that are unbiased under certain other conditions.
With that ... | Why in Box-Cox method we try to make x and y normally distributed, but that's not an assumption for | I'm assuming you're referring to Box-Cox normality plots by "method" in your question. It is true that normality assumption in OLS is not required for the method to be useful. For instance, regardless | Why in Box-Cox method we try to make x and y normally distributed, but that's not an assumption for linear regression?
I'm assuming you're referring to Box-Cox normality plots by "method" in your question. It is true that normality assumption in OLS is not required for the method to be useful. For instance, regardless ... | Why in Box-Cox method we try to make x and y normally distributed, but that's not an assumption for
I'm assuming you're referring to Box-Cox normality plots by "method" in your question. It is true that normality assumption in OLS is not required for the method to be useful. For instance, regardless |
47,755 | Why in Box-Cox method we try to make x and y normally distributed, but that's not an assumption for linear regression? | Sorry that my question is a bit unorganized, but one of my question(and most confused part) is why do we want our predictors and responses variable to be symmetric or normally distributed. And after dwelling on this for two days, I think now I quite got the answer.
Here is what I found is most useful: https://stats.st... | Why in Box-Cox method we try to make x and y normally distributed, but that's not an assumption for | Sorry that my question is a bit unorganized, but one of my question(and most confused part) is why do we want our predictors and responses variable to be symmetric or normally distributed. And after d | Why in Box-Cox method we try to make x and y normally distributed, but that's not an assumption for linear regression?
Sorry that my question is a bit unorganized, but one of my question(and most confused part) is why do we want our predictors and responses variable to be symmetric or normally distributed. And after dw... | Why in Box-Cox method we try to make x and y normally distributed, but that's not an assumption for
Sorry that my question is a bit unorganized, but one of my question(and most confused part) is why do we want our predictors and responses variable to be symmetric or normally distributed. And after d |
47,756 | Connecting scatter plots with linear interpolation? | I'll phrase this, following your example, in terms of plotting with time on the $x$ or horizontal axis: that is pleasantly easy to imagine and discuss and (I guess) the most common example of this issue in practice. Translation to other variables on that axis, such as position in space, seems straightforward (until som... | Connecting scatter plots with linear interpolation? | I'll phrase this, following your example, in terms of plotting with time on the $x$ or horizontal axis: that is pleasantly easy to imagine and discuss and (I guess) the most common example of this iss | Connecting scatter plots with linear interpolation?
I'll phrase this, following your example, in terms of plotting with time on the $x$ or horizontal axis: that is pleasantly easy to imagine and discuss and (I guess) the most common example of this issue in practice. Translation to other variables on that axis, such as... | Connecting scatter plots with linear interpolation?
I'll phrase this, following your example, in terms of plotting with time on the $x$ or horizontal axis: that is pleasantly easy to imagine and discuss and (I guess) the most common example of this iss |
47,757 | Strange variance weights for Poisson GLM for square root link | The weights in the glm function are
$$
w_i = \left.\frac{(\partial \mu_i/\partial\eta_i)^2}{\text{var}(\mu_i)}\right|_{\mu_i=h(\eta_i) = \eta_i^2}
$$
So if $\mu_i = \eta_i^2$ and you recall that $\text{var}(\mu_i)=\mu_i$ then $\partial \mu_i/\partial\eta_i = 2\eta_i$ so $w_i = 4$. This is what you get from glm
> counts... | Strange variance weights for Poisson GLM for square root link | The weights in the glm function are
$$
w_i = \left.\frac{(\partial \mu_i/\partial\eta_i)^2}{\text{var}(\mu_i)}\right|_{\mu_i=h(\eta_i) = \eta_i^2}
$$
So if $\mu_i = \eta_i^2$ and you recall that $\tex | Strange variance weights for Poisson GLM for square root link
The weights in the glm function are
$$
w_i = \left.\frac{(\partial \mu_i/\partial\eta_i)^2}{\text{var}(\mu_i)}\right|_{\mu_i=h(\eta_i) = \eta_i^2}
$$
So if $\mu_i = \eta_i^2$ and you recall that $\text{var}(\mu_i)=\mu_i$ then $\partial \mu_i/\partial\eta_i =... | Strange variance weights for Poisson GLM for square root link
The weights in the glm function are
$$
w_i = \left.\frac{(\partial \mu_i/\partial\eta_i)^2}{\text{var}(\mu_i)}\right|_{\mu_i=h(\eta_i) = \eta_i^2}
$$
So if $\mu_i = \eta_i^2$ and you recall that $\tex |
47,758 | Standard Deviation in Neural Network Regression | First of all you want to get standard deviations that says something about test errors not training errors. There are different aproaches to solve the problem.
Ensampling/bootstrapping: multiple different splits of your training data and get out of bag estimates for each split. Then for each observation calculate the s... | Standard Deviation in Neural Network Regression | First of all you want to get standard deviations that says something about test errors not training errors. There are different aproaches to solve the problem.
Ensampling/bootstrapping: multiple diffe | Standard Deviation in Neural Network Regression
First of all you want to get standard deviations that says something about test errors not training errors. There are different aproaches to solve the problem.
Ensampling/bootstrapping: multiple different splits of your training data and get out of bag estimates for each ... | Standard Deviation in Neural Network Regression
First of all you want to get standard deviations that says something about test errors not training errors. There are different aproaches to solve the problem.
Ensampling/bootstrapping: multiple diffe |
47,759 | Overfitting in polynomial regression and other concerns | There is no such rule about specific order polynomials which is agnostic to your dataset. If any such rule existed, I would expect it to be a function of your data or your data generating process - without knowing something about that, it's hard to say. Without saying anything about specific order polynomials, your gen... | Overfitting in polynomial regression and other concerns | There is no such rule about specific order polynomials which is agnostic to your dataset. If any such rule existed, I would expect it to be a function of your data or your data generating process - wi | Overfitting in polynomial regression and other concerns
There is no such rule about specific order polynomials which is agnostic to your dataset. If any such rule existed, I would expect it to be a function of your data or your data generating process - without knowing something about that, it's hard to say. Without sa... | Overfitting in polynomial regression and other concerns
There is no such rule about specific order polynomials which is agnostic to your dataset. If any such rule existed, I would expect it to be a function of your data or your data generating process - wi |
47,760 | How to use hyper-geometric test | You can look at wikipedia.
The hypergeometric test uses the hypergeometric distribution to measure the statistical significance of having drawn a sample consisting of a specific number of k successes (out of n total draws) from a population of size N containing K successes. In a test for over-representation of success... | How to use hyper-geometric test | You can look at wikipedia.
The hypergeometric test uses the hypergeometric distribution to measure the statistical significance of having drawn a sample consisting of a specific number of k successes | How to use hyper-geometric test
You can look at wikipedia.
The hypergeometric test uses the hypergeometric distribution to measure the statistical significance of having drawn a sample consisting of a specific number of k successes (out of n total draws) from a population of size N containing K successes. In a test fo... | How to use hyper-geometric test
You can look at wikipedia.
The hypergeometric test uses the hypergeometric distribution to measure the statistical significance of having drawn a sample consisting of a specific number of k successes |
47,761 | Why does skew and heteroscedasticity lead to bias? | In this context "biased" essentially means "disproportionately influenced by". RMSE, a commonly used error metric, sums the total squared error across all predictions. In this case if your model were to predict with 90% accuracy the value of a \$100,000 home and a \$1,000,000 home respectively, you would be penalized 1... | Why does skew and heteroscedasticity lead to bias? | In this context "biased" essentially means "disproportionately influenced by". RMSE, a commonly used error metric, sums the total squared error across all predictions. In this case if your model were | Why does skew and heteroscedasticity lead to bias?
In this context "biased" essentially means "disproportionately influenced by". RMSE, a commonly used error metric, sums the total squared error across all predictions. In this case if your model were to predict with 90% accuracy the value of a \$100,000 home and a \$1,... | Why does skew and heteroscedasticity lead to bias?
In this context "biased" essentially means "disproportionately influenced by". RMSE, a commonly used error metric, sums the total squared error across all predictions. In this case if your model were |
47,762 | When and why do we use sparse coding? | Parsimony. Sparse representations of a signal are easier to describe because they're short and highlight the essential features. This can be helpful if one wants to understand the signal, the process that generated it, or other systems that interact with it.
Denoising. In this context, the measured signal is a mixture ... | When and why do we use sparse coding? | Parsimony. Sparse representations of a signal are easier to describe because they're short and highlight the essential features. This can be helpful if one wants to understand the signal, the process | When and why do we use sparse coding?
Parsimony. Sparse representations of a signal are easier to describe because they're short and highlight the essential features. This can be helpful if one wants to understand the signal, the process that generated it, or other systems that interact with it.
Denoising. In this cont... | When and why do we use sparse coding?
Parsimony. Sparse representations of a signal are easier to describe because they're short and highlight the essential features. This can be helpful if one wants to understand the signal, the process |
47,763 | When and why do we use sparse coding? | "In numerical analysis and computer science, a sparse matrix or sparse array is a matrix in which most of the elements are zero." Wikipedia
There are some datasets where instances have a large number of attributes. This dataset can be thought of as a sparse matrix if most of the recorded attribute are zero. In this sce... | When and why do we use sparse coding? | "In numerical analysis and computer science, a sparse matrix or sparse array is a matrix in which most of the elements are zero." Wikipedia
There are some datasets where instances have a large number | When and why do we use sparse coding?
"In numerical analysis and computer science, a sparse matrix or sparse array is a matrix in which most of the elements are zero." Wikipedia
There are some datasets where instances have a large number of attributes. This dataset can be thought of as a sparse matrix if most of the re... | When and why do we use sparse coding?
"In numerical analysis and computer science, a sparse matrix or sparse array is a matrix in which most of the elements are zero." Wikipedia
There are some datasets where instances have a large number |
47,764 | Does correlation correlate with causation? | The sentence "correlation does not imply causation" is usually understood much broader than it should be. If two variables A and B are highly correlated, then something is causing something else. You just cannot conclude that A causes B because there are a number of other possibilities:
B causes A
A and B are both cau... | Does correlation correlate with causation? | The sentence "correlation does not imply causation" is usually understood much broader than it should be. If two variables A and B are highly correlated, then something is causing something else. You | Does correlation correlate with causation?
The sentence "correlation does not imply causation" is usually understood much broader than it should be. If two variables A and B are highly correlated, then something is causing something else. You just cannot conclude that A causes B because there are a number of other poss... | Does correlation correlate with causation?
The sentence "correlation does not imply causation" is usually understood much broader than it should be. If two variables A and B are highly correlated, then something is causing something else. You |
47,765 | Does correlation correlate with causation? | Does correlation (any statistical association) correlate with (related
to) causation?
This question (words in parentheses are mine) is quite general and essentially the answer seem me yes. Causal inference in statistics framework exist exactly because the answer to that question is yes.
However in order to give more... | Does correlation correlate with causation? | Does correlation (any statistical association) correlate with (related
to) causation?
This question (words in parentheses are mine) is quite general and essentially the answer seem me yes. Causal i | Does correlation correlate with causation?
Does correlation (any statistical association) correlate with (related
to) causation?
This question (words in parentheses are mine) is quite general and essentially the answer seem me yes. Causal inference in statistics framework exist exactly because the answer to that que... | Does correlation correlate with causation?
Does correlation (any statistical association) correlate with (related
to) causation?
This question (words in parentheses are mine) is quite general and essentially the answer seem me yes. Causal i |
47,766 | Does correlation correlate with causation? | Correlation is a special type of association and association is different from causation which can be only inferred from a randomized experiment(the reason would be the confounder).
References:
1. Association and Correlation
2. Openintro-Statistics | Does correlation correlate with causation? | Correlation is a special type of association and association is different from causation which can be only inferred from a randomized experiment(the reason would be the confounder).
References:
1. As | Does correlation correlate with causation?
Correlation is a special type of association and association is different from causation which can be only inferred from a randomized experiment(the reason would be the confounder).
References:
1. Association and Correlation
2. Openintro-Statistics | Does correlation correlate with causation?
Correlation is a special type of association and association is different from causation which can be only inferred from a randomized experiment(the reason would be the confounder).
References:
1. As |
47,767 | Intuitive explanation of the relationship between standard error of model coefficient and residual variance | When you simulate the the data, you know the population coefficients, because you chose them. But if I simulate the data and only give you the data, you don't know the population coefficients. You only have the data - just as it is with real data.
When you look at data that has noise about a linear relationship, there'... | Intuitive explanation of the relationship between standard error of model coefficient and residual v | When you simulate the the data, you know the population coefficients, because you chose them. But if I simulate the data and only give you the data, you don't know the population coefficients. You onl | Intuitive explanation of the relationship between standard error of model coefficient and residual variance
When you simulate the the data, you know the population coefficients, because you chose them. But if I simulate the data and only give you the data, you don't know the population coefficients. You only have the d... | Intuitive explanation of the relationship between standard error of model coefficient and residual v
When you simulate the the data, you know the population coefficients, because you chose them. But if I simulate the data and only give you the data, you don't know the population coefficients. You onl |
47,768 | Difference between R² and Chi-Square | Found this after a quick google: "R^2 is used to quantify the amount of variability in the data that is explained by your model. It's useful for comparing the fits of different models.
The Chi-square goodness of fit test is used to test if your data follows a particular distribution. It's more useful for testing model ... | Difference between R² and Chi-Square | Found this after a quick google: "R^2 is used to quantify the amount of variability in the data that is explained by your model. It's useful for comparing the fits of different models.
The Chi-square | Difference between R² and Chi-Square
Found this after a quick google: "R^2 is used to quantify the amount of variability in the data that is explained by your model. It's useful for comparing the fits of different models.
The Chi-square goodness of fit test is used to test if your data follows a particular distribution... | Difference between R² and Chi-Square
Found this after a quick google: "R^2 is used to quantify the amount of variability in the data that is explained by your model. It's useful for comparing the fits of different models.
The Chi-square |
47,769 | Difference between R² and Chi-Square | Chi^2 provides a per-feature measurement of dependency with the target. This is useful at the feature-selection stage, for a classification model. We'd like to weed out the low-dependent features.
(scikit-learn guide for additional such measurements for classification and regression models).
R^2 provides a model-level ... | Difference between R² and Chi-Square | Chi^2 provides a per-feature measurement of dependency with the target. This is useful at the feature-selection stage, for a classification model. We'd like to weed out the low-dependent features.
(sc | Difference between R² and Chi-Square
Chi^2 provides a per-feature measurement of dependency with the target. This is useful at the feature-selection stage, for a classification model. We'd like to weed out the low-dependent features.
(scikit-learn guide for additional such measurements for classification and regression... | Difference between R² and Chi-Square
Chi^2 provides a per-feature measurement of dependency with the target. This is useful at the feature-selection stage, for a classification model. We'd like to weed out the low-dependent features.
(sc |
47,770 | Why accuracy gradually increase then suddenly drop with dropout | When you increase dropout beyond a certain threshold, it results in the model not being able to fit properly. Intuitively, a higher dropout rate would result in a higher variance to some of the layers, which also degrades training. Dropout is like all other forms of regularization in that it reduces model capacity. If ... | Why accuracy gradually increase then suddenly drop with dropout | When you increase dropout beyond a certain threshold, it results in the model not being able to fit properly. Intuitively, a higher dropout rate would result in a higher variance to some of the layers | Why accuracy gradually increase then suddenly drop with dropout
When you increase dropout beyond a certain threshold, it results in the model not being able to fit properly. Intuitively, a higher dropout rate would result in a higher variance to some of the layers, which also degrades training. Dropout is like all othe... | Why accuracy gradually increase then suddenly drop with dropout
When you increase dropout beyond a certain threshold, it results in the model not being able to fit properly. Intuitively, a higher dropout rate would result in a higher variance to some of the layers |
47,771 | Why accuracy gradually increase then suddenly drop with dropout | I think I met the same problem with this dramatic-drop-in-accuracy issue. I think the problem with this issue might be related to the softmax function and the cross-entropy that you defined(loss function). Mine issue comes exactly from this cross-entropy function, and I used one-hot-format labels BTW. Taken that classi... | Why accuracy gradually increase then suddenly drop with dropout | I think I met the same problem with this dramatic-drop-in-accuracy issue. I think the problem with this issue might be related to the softmax function and the cross-entropy that you defined(loss funct | Why accuracy gradually increase then suddenly drop with dropout
I think I met the same problem with this dramatic-drop-in-accuracy issue. I think the problem with this issue might be related to the softmax function and the cross-entropy that you defined(loss function). Mine issue comes exactly from this cross-entropy f... | Why accuracy gradually increase then suddenly drop with dropout
I think I met the same problem with this dramatic-drop-in-accuracy issue. I think the problem with this issue might be related to the softmax function and the cross-entropy that you defined(loss funct |
47,772 | H2O: Can I use the h2o for time series predictions? | You can use H2O for time series, and you would normally do some data engineering to create time-based features. In my book (Practical Machine Learning with H2O) one of the three main data sets is prediction of football match results, so that shows some of the techniques.
I normally do things like arima and adf.test in ... | H2O: Can I use the h2o for time series predictions? | You can use H2O for time series, and you would normally do some data engineering to create time-based features. In my book (Practical Machine Learning with H2O) one of the three main data sets is pred | H2O: Can I use the h2o for time series predictions?
You can use H2O for time series, and you would normally do some data engineering to create time-based features. In my book (Practical Machine Learning with H2O) one of the three main data sets is prediction of football match results, so that shows some of the techniqu... | H2O: Can I use the h2o for time series predictions?
You can use H2O for time series, and you would normally do some data engineering to create time-based features. In my book (Practical Machine Learning with H2O) one of the three main data sets is pred |
47,773 | H2O: Can I use the h2o for time series predictions? | Methods designed especially for time series work better for such data then black-box machine learning algorithms as shown, for example, in this blog entry. The time-series models take into consideration the time-dependence of your data, while the general purpose methods do not. Of course, you can add to your data addit... | H2O: Can I use the h2o for time series predictions? | Methods designed especially for time series work better for such data then black-box machine learning algorithms as shown, for example, in this blog entry. The time-series models take into considerati | H2O: Can I use the h2o for time series predictions?
Methods designed especially for time series work better for such data then black-box machine learning algorithms as shown, for example, in this blog entry. The time-series models take into consideration the time-dependence of your data, while the general purpose metho... | H2O: Can I use the h2o for time series predictions?
Methods designed especially for time series work better for such data then black-box machine learning algorithms as shown, for example, in this blog entry. The time-series models take into considerati |
47,774 | (Nomenclature) Are there two different Weak Laws of Large Numbers? | Many results in statistics have generic names that apply to a collection of theorems asserting some result under different conditions. My understanding is that a "weak law of large numbers" can refer to any theorem that shows convergence-in-probability of the sequence of sample means to a corresponding mean. Any theo... | (Nomenclature) Are there two different Weak Laws of Large Numbers? | Many results in statistics have generic names that apply to a collection of theorems asserting some result under different conditions. My understanding is that a "weak law of large numbers" can refer | (Nomenclature) Are there two different Weak Laws of Large Numbers?
Many results in statistics have generic names that apply to a collection of theorems asserting some result under different conditions. My understanding is that a "weak law of large numbers" can refer to any theorem that shows convergence-in-probability... | (Nomenclature) Are there two different Weak Laws of Large Numbers?
Many results in statistics have generic names that apply to a collection of theorems asserting some result under different conditions. My understanding is that a "weak law of large numbers" can refer |
47,775 | Two-way repeated measures linear mixed model | A linear mixed model is what you want. First, make sure that Subject is a factor:
Mydata$Subject <- as.factor(Mydata$Subject)
Then, I would fit the model with saturated fixed- and random-effects structures:
mod1 <- lmer(Estimate ~ Condition + Size + Condition * Size + # Fixed effects
(1 + Condition + S... | Two-way repeated measures linear mixed model | A linear mixed model is what you want. First, make sure that Subject is a factor:
Mydata$Subject <- as.factor(Mydata$Subject)
Then, I would fit the model with saturated fixed- and random-effects stru | Two-way repeated measures linear mixed model
A linear mixed model is what you want. First, make sure that Subject is a factor:
Mydata$Subject <- as.factor(Mydata$Subject)
Then, I would fit the model with saturated fixed- and random-effects structures:
mod1 <- lmer(Estimate ~ Condition + Size + Condition * Size + # Fi... | Two-way repeated measures linear mixed model
A linear mixed model is what you want. First, make sure that Subject is a factor:
Mydata$Subject <- as.factor(Mydata$Subject)
Then, I would fit the model with saturated fixed- and random-effects stru |
47,776 | A Kernel Two Sample Test and Curse of Dimensionality | Just happen to see this post while going over MMD papers. In the context of two-sample testing and considering the test power under a given level, the answer is it does suffer from high dimension.
Previous experiment might be misleading because they did not select a fair alternative for testing. For example, consider $... | A Kernel Two Sample Test and Curse of Dimensionality | Just happen to see this post while going over MMD papers. In the context of two-sample testing and considering the test power under a given level, the answer is it does suffer from high dimension.
Pre | A Kernel Two Sample Test and Curse of Dimensionality
Just happen to see this post while going over MMD papers. In the context of two-sample testing and considering the test power under a given level, the answer is it does suffer from high dimension.
Previous experiment might be misleading because they did not select a ... | A Kernel Two Sample Test and Curse of Dimensionality
Just happen to see this post while going over MMD papers. In the context of two-sample testing and considering the test power under a given level, the answer is it does suffer from high dimension.
Pre |
47,777 | A Kernel Two Sample Test and Curse of Dimensionality | Oh, of course the method strongly suffers from the curse of dimensionality. It's just that they derive their results under what essentially is a parametric alternative, hidden behind the RKHS notation and not made too explicit.
Indeed, motivated by exactly the same question as yours, Ery Arias-Castro, Bruno Pelletier a... | A Kernel Two Sample Test and Curse of Dimensionality | Oh, of course the method strongly suffers from the curse of dimensionality. It's just that they derive their results under what essentially is a parametric alternative, hidden behind the RKHS notation | A Kernel Two Sample Test and Curse of Dimensionality
Oh, of course the method strongly suffers from the curse of dimensionality. It's just that they derive their results under what essentially is a parametric alternative, hidden behind the RKHS notation and not made too explicit.
Indeed, motivated by exactly the same q... | A Kernel Two Sample Test and Curse of Dimensionality
Oh, of course the method strongly suffers from the curse of dimensionality. It's just that they derive their results under what essentially is a parametric alternative, hidden behind the RKHS notation |
47,778 | A Kernel Two Sample Test and Curse of Dimensionality | I found the introduction of paper, "Can Shared-Neighbor Distances Defeat the Curse of Dimensionality" by Houle et al (2010) to be helpful. Particularly, they make the distinction between dimensions bearing relevant information and irrelevant information. For example, two Gaussian distribution clusters with separated ... | A Kernel Two Sample Test and Curse of Dimensionality | I found the introduction of paper, "Can Shared-Neighbor Distances Defeat the Curse of Dimensionality" by Houle et al (2010) to be helpful. Particularly, they make the distinction between dimensions b | A Kernel Two Sample Test and Curse of Dimensionality
I found the introduction of paper, "Can Shared-Neighbor Distances Defeat the Curse of Dimensionality" by Houle et al (2010) to be helpful. Particularly, they make the distinction between dimensions bearing relevant information and irrelevant information. For exampl... | A Kernel Two Sample Test and Curse of Dimensionality
I found the introduction of paper, "Can Shared-Neighbor Distances Defeat the Curse of Dimensionality" by Houle et al (2010) to be helpful. Particularly, they make the distinction between dimensions b |
47,779 | Big O and little o notation explained? | Definition
The sequence $a_n = o(x_n)$ if $a_n/x_n \to 0$. We would read it as $a_n$ is of smaller order than $1/n$, or $a_n$ is little-oh of $1/n$. In your case, if some term $a_n$ is $o(1/n)$ that means that $n a_n \to 0$. A few examples of sequences that are $o(1/n)$ are $c/n^p$ where $p > 1$, $1/(n\log(n))$, and $1... | Big O and little o notation explained? | Definition
The sequence $a_n = o(x_n)$ if $a_n/x_n \to 0$. We would read it as $a_n$ is of smaller order than $1/n$, or $a_n$ is little-oh of $1/n$. In your case, if some term $a_n$ is $o(1/n)$ that m | Big O and little o notation explained?
Definition
The sequence $a_n = o(x_n)$ if $a_n/x_n \to 0$. We would read it as $a_n$ is of smaller order than $1/n$, or $a_n$ is little-oh of $1/n$. In your case, if some term $a_n$ is $o(1/n)$ that means that $n a_n \to 0$. A few examples of sequences that are $o(1/n)$ are $c/n^p... | Big O and little o notation explained?
Definition
The sequence $a_n = o(x_n)$ if $a_n/x_n \to 0$. We would read it as $a_n$ is of smaller order than $1/n$, or $a_n$ is little-oh of $1/n$. In your case, if some term $a_n$ is $o(1/n)$ that m |
47,780 | Vanishing gradient vs. dying ReLU? [duplicate] | ELU and ReLU both have zero or vanishing gradient "on the left". This is still a marked departure from $\tanh$ or logistic units, because those functions are bounded above and below; for ELU and ReLU units, the gradient updates will be larger "on the right". As a demonstration, work out the derivatives for each and not... | Vanishing gradient vs. dying ReLU? [duplicate] | ELU and ReLU both have zero or vanishing gradient "on the left". This is still a marked departure from $\tanh$ or logistic units, because those functions are bounded above and below; for ELU and ReLU | Vanishing gradient vs. dying ReLU? [duplicate]
ELU and ReLU both have zero or vanishing gradient "on the left". This is still a marked departure from $\tanh$ or logistic units, because those functions are bounded above and below; for ELU and ReLU units, the gradient updates will be larger "on the right". As a demonstra... | Vanishing gradient vs. dying ReLU? [duplicate]
ELU and ReLU both have zero or vanishing gradient "on the left". This is still a marked departure from $\tanh$ or logistic units, because those functions are bounded above and below; for ELU and ReLU |
47,781 | Why not use modulus for variance? [duplicate] | Let $\mu=\operatorname{E}(X).$
The main reason for using $\sqrt{\operatorname{var}(X)} = \sqrt{\operatorname{E}((X-\mu)^2)}$ as a measure of dispersion, rather that using the mean absolute deviation $\operatorname{E}(|X-\mu|),$ is that if $X_1,\ldots,X_n$ are independent, then
$$
\operatorname{var}(X_1+\cdots+X_n) = \o... | Why not use modulus for variance? [duplicate] | Let $\mu=\operatorname{E}(X).$
The main reason for using $\sqrt{\operatorname{var}(X)} = \sqrt{\operatorname{E}((X-\mu)^2)}$ as a measure of dispersion, rather that using the mean absolute deviation $ | Why not use modulus for variance? [duplicate]
Let $\mu=\operatorname{E}(X).$
The main reason for using $\sqrt{\operatorname{var}(X)} = \sqrt{\operatorname{E}((X-\mu)^2)}$ as a measure of dispersion, rather that using the mean absolute deviation $\operatorname{E}(|X-\mu|),$ is that if $X_1,\ldots,X_n$ are independent, t... | Why not use modulus for variance? [duplicate]
Let $\mu=\operatorname{E}(X).$
The main reason for using $\sqrt{\operatorname{var}(X)} = \sqrt{\operatorname{E}((X-\mu)^2)}$ as a measure of dispersion, rather that using the mean absolute deviation $ |
47,782 | Why not use modulus for variance? [duplicate] | There are already several good answers here, including in the comments. However as the OP requested a "simpler" justification, here I will expand on my comment.
To me this is a very natural distinction between root-mean-square vs. mean-absolute deviations, and why we might prefer one vs. the other when measuring dispe... | Why not use modulus for variance? [duplicate] | There are already several good answers here, including in the comments. However as the OP requested a "simpler" justification, here I will expand on my comment.
To me this is a very natural distincti | Why not use modulus for variance? [duplicate]
There are already several good answers here, including in the comments. However as the OP requested a "simpler" justification, here I will expand on my comment.
To me this is a very natural distinction between root-mean-square vs. mean-absolute deviations, and why we might... | Why not use modulus for variance? [duplicate]
There are already several good answers here, including in the comments. However as the OP requested a "simpler" justification, here I will expand on my comment.
To me this is a very natural distincti |
47,783 | Derivative of a quadratic form wrt a parameter in the matrix | For typing convenience, define
$$\eqalign{
Y &= yy^T,\,\,\,\,
A=C^{-1},\,\,\,\,
J = \frac{\partial C}{\partial\theta} \cr
\lambda &= y^TC^{-1}y = {\rm Tr}(Y^TA)= Y:A \cr
}$$ Notice that $(A,C,Y)$ are symmetric matrices. Also note that the colon in the final expression is just a convenient (Frobenius product) notation f... | Derivative of a quadratic form wrt a parameter in the matrix | For typing convenience, define
$$\eqalign{
Y &= yy^T,\,\,\,\,
A=C^{-1},\,\,\,\,
J = \frac{\partial C}{\partial\theta} \cr
\lambda &= y^TC^{-1}y = {\rm Tr}(Y^TA)= Y:A \cr
}$$ Notice that $(A,C,Y)$ are | Derivative of a quadratic form wrt a parameter in the matrix
For typing convenience, define
$$\eqalign{
Y &= yy^T,\,\,\,\,
A=C^{-1},\,\,\,\,
J = \frac{\partial C}{\partial\theta} \cr
\lambda &= y^TC^{-1}y = {\rm Tr}(Y^TA)= Y:A \cr
}$$ Notice that $(A,C,Y)$ are symmetric matrices. Also note that the colon in the final e... | Derivative of a quadratic form wrt a parameter in the matrix
For typing convenience, define
$$\eqalign{
Y &= yy^T,\,\,\,\,
A=C^{-1},\,\,\,\,
J = \frac{\partial C}{\partial\theta} \cr
\lambda &= y^TC^{-1}y = {\rm Tr}(Y^TA)= Y:A \cr
}$$ Notice that $(A,C,Y)$ are |
47,784 | Derivative of a quadratic form wrt a parameter in the matrix | I guess the correct chain rule is
$$\frac{\partial y^T C^{-1}(\theta)y}{\partial \theta_k} = \sum_{i, j} \frac{\partial y^T C^{-1}(\theta)y}{\partial C_{i,j}(\theta)} \frac{\partial C_{i,j}(\theta)}{\partial \theta_k} = Tr\Big[\Big(\frac{\partial y^T C^{-1}(\theta)y}{\partial C(\theta)}\Big)^T \Big(\frac{\partial C(\t... | Derivative of a quadratic form wrt a parameter in the matrix | I guess the correct chain rule is
$$\frac{\partial y^T C^{-1}(\theta)y}{\partial \theta_k} = \sum_{i, j} \frac{\partial y^T C^{-1}(\theta)y}{\partial C_{i,j}(\theta)} \frac{\partial C_{i,j}(\theta)}{ | Derivative of a quadratic form wrt a parameter in the matrix
I guess the correct chain rule is
$$\frac{\partial y^T C^{-1}(\theta)y}{\partial \theta_k} = \sum_{i, j} \frac{\partial y^T C^{-1}(\theta)y}{\partial C_{i,j}(\theta)} \frac{\partial C_{i,j}(\theta)}{\partial \theta_k} = Tr\Big[\Big(\frac{\partial y^T C^{-1}(... | Derivative of a quadratic form wrt a parameter in the matrix
I guess the correct chain rule is
$$\frac{\partial y^T C^{-1}(\theta)y}{\partial \theta_k} = \sum_{i, j} \frac{\partial y^T C^{-1}(\theta)y}{\partial C_{i,j}(\theta)} \frac{\partial C_{i,j}(\theta)}{ |
47,785 | Why Gaussian process has marginalisation/consistency property? | A Gaussian process $\{X(t)\colon t \in \mathbb T\}$ is not defined as just a collection of Gaussian random variables; there is also the requirement that
for every $n \geq 1$, every finite collection $\{X(t_1), X(t_2), \cdots, X(t_n)\colon t_1, t_2, \cdots, t_n \in \mathbb T\}$ of $n$ random variables from the process ... | Why Gaussian process has marginalisation/consistency property? | A Gaussian process $\{X(t)\colon t \in \mathbb T\}$ is not defined as just a collection of Gaussian random variables; there is also the requirement that
for every $n \geq 1$, every finite collection | Why Gaussian process has marginalisation/consistency property?
A Gaussian process $\{X(t)\colon t \in \mathbb T\}$ is not defined as just a collection of Gaussian random variables; there is also the requirement that
for every $n \geq 1$, every finite collection $\{X(t_1), X(t_2), \cdots, X(t_n)\colon t_1, t_2, \cdots,... | Why Gaussian process has marginalisation/consistency property?
A Gaussian process $\{X(t)\colon t \in \mathbb T\}$ is not defined as just a collection of Gaussian random variables; there is also the requirement that
for every $n \geq 1$, every finite collection |
47,786 | Why Gaussian process has marginalisation/consistency property? | It is actually a good question which shows a subtlety of the definition of a general(not necessarily Gaussian) stochastic process. And I hope it is not too late for you.
In GPML, it says
A stochastic process is defined as a collection of random variables with a law. Since these random variables are themselves mappings... | Why Gaussian process has marginalisation/consistency property? | It is actually a good question which shows a subtlety of the definition of a general(not necessarily Gaussian) stochastic process. And I hope it is not too late for you.
In GPML, it says
A stochastic | Why Gaussian process has marginalisation/consistency property?
It is actually a good question which shows a subtlety of the definition of a general(not necessarily Gaussian) stochastic process. And I hope it is not too late for you.
In GPML, it says
A stochastic process is defined as a collection of random variables w... | Why Gaussian process has marginalisation/consistency property?
It is actually a good question which shows a subtlety of the definition of a general(not necessarily Gaussian) stochastic process. And I hope it is not too late for you.
In GPML, it says
A stochastic |
47,787 | What is Box-Cox regression? | What is box-cox regression? Is it apply box-cox power transformation then run a linear regression?
It could be used to describe that but it will typically mean more than that.
Consider that if you just look at $Y$ and find a Box-Cox transformation before you consider your $x$-variables, you're looking at the marginal... | What is Box-Cox regression? | What is box-cox regression? Is it apply box-cox power transformation then run a linear regression?
It could be used to describe that but it will typically mean more than that.
Consider that if you j | What is Box-Cox regression?
What is box-cox regression? Is it apply box-cox power transformation then run a linear regression?
It could be used to describe that but it will typically mean more than that.
Consider that if you just look at $Y$ and find a Box-Cox transformation before you consider your $x$-variables, yo... | What is Box-Cox regression?
What is box-cox regression? Is it apply box-cox power transformation then run a linear regression?
It could be used to describe that but it will typically mean more than that.
Consider that if you j |
47,788 | What is the point of Root Mean Absolute Error, RMAE, when evaluating forecasting errors? | I think it seems like a misunderstanding, AFAIK rMAE is "relative Mean Absolute Error" not "root Mean Absolute Error" and as a result it has no unit (e.g. dollars)
And it might be useful for comparison of classifiers which were tested on completely different datasets (with different units etc.)
See this link for more i... | What is the point of Root Mean Absolute Error, RMAE, when evaluating forecasting errors? | I think it seems like a misunderstanding, AFAIK rMAE is "relative Mean Absolute Error" not "root Mean Absolute Error" and as a result it has no unit (e.g. dollars)
And it might be useful for compariso | What is the point of Root Mean Absolute Error, RMAE, when evaluating forecasting errors?
I think it seems like a misunderstanding, AFAIK rMAE is "relative Mean Absolute Error" not "root Mean Absolute Error" and as a result it has no unit (e.g. dollars)
And it might be useful for comparison of classifiers which were tes... | What is the point of Root Mean Absolute Error, RMAE, when evaluating forecasting errors?
I think it seems like a misunderstanding, AFAIK rMAE is "relative Mean Absolute Error" not "root Mean Absolute Error" and as a result it has no unit (e.g. dollars)
And it might be useful for compariso |
47,789 | What if do not use any activation function in the neural network? [duplicate] | Consider a two layer neural network. Let $x \in \mathbb{R}^n$ be your input vector, and consider a single layer without an activation function and weight matrix $A$ and bias $b$, it would computer
$$Ax + b$$
A second layer (without activation and weight matrix $C$ and bias $d$) would then compute $$C(Ax + b)+d$$
This i... | What if do not use any activation function in the neural network? [duplicate] | Consider a two layer neural network. Let $x \in \mathbb{R}^n$ be your input vector, and consider a single layer without an activation function and weight matrix $A$ and bias $b$, it would computer
$$A | What if do not use any activation function in the neural network? [duplicate]
Consider a two layer neural network. Let $x \in \mathbb{R}^n$ be your input vector, and consider a single layer without an activation function and weight matrix $A$ and bias $b$, it would computer
$$Ax + b$$
A second layer (without activation... | What if do not use any activation function in the neural network? [duplicate]
Consider a two layer neural network. Let $x \in \mathbb{R}^n$ be your input vector, and consider a single layer without an activation function and weight matrix $A$ and bias $b$, it would computer
$$A |
47,790 | Comparisons of circular means | You can do Watson's large sample nonparametric test or Bootstrap version of Watson's nonparametric test. Both these tests are available in R "circular" package. There is a good book named "Circular statistics in R" written by Arthur Pewsey et al. There you will find the details on what functions to use and how to do th... | Comparisons of circular means | You can do Watson's large sample nonparametric test or Bootstrap version of Watson's nonparametric test. Both these tests are available in R "circular" package. There is a good book named "Circular st | Comparisons of circular means
You can do Watson's large sample nonparametric test or Bootstrap version of Watson's nonparametric test. Both these tests are available in R "circular" package. There is a good book named "Circular statistics in R" written by Arthur Pewsey et al. There you will find the details on what fun... | Comparisons of circular means
You can do Watson's large sample nonparametric test or Bootstrap version of Watson's nonparametric test. Both these tests are available in R "circular" package. There is a good book named "Circular st |
47,791 | Comparisons of circular means | Philipp Berens' CircStat toolbox for MATLAB offers circ_cmtest, which is a non-parametric multi-sample test for equal medians. It says it is similar to a Kruskal-Wallis test for linear data. Becuase it assumes data are non-parametric, comparison of medians rather than means makes good sense. It's quite simple to use. | Comparisons of circular means | Philipp Berens' CircStat toolbox for MATLAB offers circ_cmtest, which is a non-parametric multi-sample test for equal medians. It says it is similar to a Kruskal-Wallis test for linear data. Becuase i | Comparisons of circular means
Philipp Berens' CircStat toolbox for MATLAB offers circ_cmtest, which is a non-parametric multi-sample test for equal medians. It says it is similar to a Kruskal-Wallis test for linear data. Becuase it assumes data are non-parametric, comparison of medians rather than means makes good sens... | Comparisons of circular means
Philipp Berens' CircStat toolbox for MATLAB offers circ_cmtest, which is a non-parametric multi-sample test for equal medians. It says it is similar to a Kruskal-Wallis test for linear data. Becuase i |
47,792 | Are Neural Nets a Special Case Of Graphical Models? | If you focus on the generative part, GANs and VAEs are actually mathematically the same object (1), i.e. Gaussian latent variable models, where $z$ is a latent Gaussian random variable pointing to an observed $x$:
The difference is that VAEs are prescribed models that output a random variable $x$ with a probability de... | Are Neural Nets a Special Case Of Graphical Models? | If you focus on the generative part, GANs and VAEs are actually mathematically the same object (1), i.e. Gaussian latent variable models, where $z$ is a latent Gaussian random variable pointing to an | Are Neural Nets a Special Case Of Graphical Models?
If you focus on the generative part, GANs and VAEs are actually mathematically the same object (1), i.e. Gaussian latent variable models, where $z$ is a latent Gaussian random variable pointing to an observed $x$:
The difference is that VAEs are prescribed models tha... | Are Neural Nets a Special Case Of Graphical Models?
If you focus on the generative part, GANs and VAEs are actually mathematically the same object (1), i.e. Gaussian latent variable models, where $z$ is a latent Gaussian random variable pointing to an |
47,793 | Are Neural Nets a Special Case Of Graphical Models? | You can view a deep neural network as a graphical model, but here, the CPDs are not probabilistic but are deterministic. Consider for example that the input to a neuron is $\vec{x}$ and the output of the neuron is y. In the CPD for this neuron we have, $p(\vec{x},y)=1$, and $p(\vec{x},\hat{y})=0$ for $\hat{y}\neq y$. R... | Are Neural Nets a Special Case Of Graphical Models? | You can view a deep neural network as a graphical model, but here, the CPDs are not probabilistic but are deterministic. Consider for example that the input to a neuron is $\vec{x}$ and the output of | Are Neural Nets a Special Case Of Graphical Models?
You can view a deep neural network as a graphical model, but here, the CPDs are not probabilistic but are deterministic. Consider for example that the input to a neuron is $\vec{x}$ and the output of the neuron is y. In the CPD for this neuron we have, $p(\vec{x},y)=1... | Are Neural Nets a Special Case Of Graphical Models?
You can view a deep neural network as a graphical model, but here, the CPDs are not probabilistic but are deterministic. Consider for example that the input to a neuron is $\vec{x}$ and the output of |
47,794 | interpreting causality() in R for Granger Test | [W]hat is this Granger test for and how to interpret it?
Basically, Granger causality $x \xrightarrow{Granger} y$ exists when using lags of $x$ next to the lags of $y$ for forecasting $y$ delivers better forecast accuracy than using only the lags of $y$ (without the lags of $x$).
You can find definitions and details i... | interpreting causality() in R for Granger Test | [W]hat is this Granger test for and how to interpret it?
Basically, Granger causality $x \xrightarrow{Granger} y$ exists when using lags of $x$ next to the lags of $y$ for forecasting $y$ delivers be | interpreting causality() in R for Granger Test
[W]hat is this Granger test for and how to interpret it?
Basically, Granger causality $x \xrightarrow{Granger} y$ exists when using lags of $x$ next to the lags of $y$ for forecasting $y$ delivers better forecast accuracy than using only the lags of $y$ (without the lags ... | interpreting causality() in R for Granger Test
[W]hat is this Granger test for and how to interpret it?
Basically, Granger causality $x \xrightarrow{Granger} y$ exists when using lags of $x$ next to the lags of $y$ for forecasting $y$ delivers be |
47,795 | What is the difference between complete statistics and complete family of distributions? | Suppose $X_1,\ldots,X_n \sim \text{i.i.d. } N(\mu,\sigma^2).$
The family of distributions is $$\left\{ N_n\left(\begin{bmatrix} \mu \\ \vdots \\ \mu \end{bmatrix},\sigma^2 \begin{bmatrix} 1 & 0 & 0 & \cdots & 0 \\ 0 & 1 & 0 & \cdots & 0 \\ 0 & 0 & 1 & \cdots & 0 \\ \vdots & \vdots & \vdots & & \vdots \\ 0 & 0 & 0 & \c... | What is the difference between complete statistics and complete family of distributions? | Suppose $X_1,\ldots,X_n \sim \text{i.i.d. } N(\mu,\sigma^2).$
The family of distributions is $$\left\{ N_n\left(\begin{bmatrix} \mu \\ \vdots \\ \mu \end{bmatrix},\sigma^2 \begin{bmatrix} 1 & 0 & 0 & | What is the difference between complete statistics and complete family of distributions?
Suppose $X_1,\ldots,X_n \sim \text{i.i.d. } N(\mu,\sigma^2).$
The family of distributions is $$\left\{ N_n\left(\begin{bmatrix} \mu \\ \vdots \\ \mu \end{bmatrix},\sigma^2 \begin{bmatrix} 1 & 0 & 0 & \cdots & 0 \\ 0 & 1 & 0 & \cdo... | What is the difference between complete statistics and complete family of distributions?
Suppose $X_1,\ldots,X_n \sim \text{i.i.d. } N(\mu,\sigma^2).$
The family of distributions is $$\left\{ N_n\left(\begin{bmatrix} \mu \\ \vdots \\ \mu \end{bmatrix},\sigma^2 \begin{bmatrix} 1 & 0 & 0 & |
47,796 | Performance of the Wilcoxon-Mann-Whitney test with large sample sizes (> 100,000) from medical data warehouses | Your sample sizes are so large it would be surprising not to find differences on almost any reasonable measure of difference between the population distributions.
In the medical literature one typically sees a Wilcoxon-Mann-Whitney test being used in comparing the LOS of the two groups and reports it as a test of the ... | Performance of the Wilcoxon-Mann-Whitney test with large sample sizes (> 100,000) from medical data | Your sample sizes are so large it would be surprising not to find differences on almost any reasonable measure of difference between the population distributions.
In the medical literature one typica | Performance of the Wilcoxon-Mann-Whitney test with large sample sizes (> 100,000) from medical data warehouses
Your sample sizes are so large it would be surprising not to find differences on almost any reasonable measure of difference between the population distributions.
In the medical literature one typically sees ... | Performance of the Wilcoxon-Mann-Whitney test with large sample sizes (> 100,000) from medical data
Your sample sizes are so large it would be surprising not to find differences on almost any reasonable measure of difference between the population distributions.
In the medical literature one typica |
47,797 | High correlation among two variables but VIFs do not indicate collinearity | I would use condition indexes rather than either VIFs or correlations; I wrote my dissertation about this, but you can also see the work of David Belsley, e.g. this book. But if I had to choose between VIFs and correlations, I'd go with VIFs. Belsley shows that fairly high correlations are not always problematic.
If ... | High correlation among two variables but VIFs do not indicate collinearity | I would use condition indexes rather than either VIFs or correlations; I wrote my dissertation about this, but you can also see the work of David Belsley, e.g. this book. But if I had to choose betwe | High correlation among two variables but VIFs do not indicate collinearity
I would use condition indexes rather than either VIFs or correlations; I wrote my dissertation about this, but you can also see the work of David Belsley, e.g. this book. But if I had to choose between VIFs and correlations, I'd go with VIFs. ... | High correlation among two variables but VIFs do not indicate collinearity
I would use condition indexes rather than either VIFs or correlations; I wrote my dissertation about this, but you can also see the work of David Belsley, e.g. this book. But if I had to choose betwe |
47,798 | Log-linear regression vs. Poisson regression | A Poisson regression is a regression where the outcome variable consists of non-negative integers, and it is sensible to assume that the variance and mean of the model are the same.
A log-linear regression is usually a model estimated using linear regression, where the response variable is replaced by a new variable t... | Log-linear regression vs. Poisson regression | A Poisson regression is a regression where the outcome variable consists of non-negative integers, and it is sensible to assume that the variance and mean of the model are the same.
A log-linear regr | Log-linear regression vs. Poisson regression
A Poisson regression is a regression where the outcome variable consists of non-negative integers, and it is sensible to assume that the variance and mean of the model are the same.
A log-linear regression is usually a model estimated using linear regression, where the resp... | Log-linear regression vs. Poisson regression
A Poisson regression is a regression where the outcome variable consists of non-negative integers, and it is sensible to assume that the variance and mean of the model are the same.
A log-linear regr |
47,799 | Does Fisher's Exact test for a $2\times 2$ table use the Non-central Hypergeometric or the Hypergeometric distribution? | This is what the R help says.
For 2 by 2 tables, the null of conditional independence is
equivalent to the hypothesis that the odds ratio equals one.
‘Exact’ inference can be based on observing that in general, given
all marginal totals fixed, the first element of the contingency
table has ... | Does Fisher's Exact test for a $2\times 2$ table use the Non-central Hypergeometric or the Hypergeom | This is what the R help says.
For 2 by 2 tables, the null of conditional independence is
equivalent to the hypothesis that the odds ratio equals one.
‘Exact’ inference can be based on o | Does Fisher's Exact test for a $2\times 2$ table use the Non-central Hypergeometric or the Hypergeometric distribution?
This is what the R help says.
For 2 by 2 tables, the null of conditional independence is
equivalent to the hypothesis that the odds ratio equals one.
‘Exact’ inference can be based on o... | Does Fisher's Exact test for a $2\times 2$ table use the Non-central Hypergeometric or the Hypergeom
This is what the R help says.
For 2 by 2 tables, the null of conditional independence is
equivalent to the hypothesis that the odds ratio equals one.
‘Exact’ inference can be based on o |
47,800 | Does Fisher's Exact test for a $2\times 2$ table use the Non-central Hypergeometric or the Hypergeometric distribution? | The noncentral hypergeometric distribution is a generalization of the hypergeometric distribution. The latter is used for the Fisher exact test. However, it frequently seems to be referred to as the hypergeometric distribution as if the question of noncentrality did not exist. I suppose that the thinking for this is th... | Does Fisher's Exact test for a $2\times 2$ table use the Non-central Hypergeometric or the Hypergeom | The noncentral hypergeometric distribution is a generalization of the hypergeometric distribution. The latter is used for the Fisher exact test. However, it frequently seems to be referred to as the h | Does Fisher's Exact test for a $2\times 2$ table use the Non-central Hypergeometric or the Hypergeometric distribution?
The noncentral hypergeometric distribution is a generalization of the hypergeometric distribution. The latter is used for the Fisher exact test. However, it frequently seems to be referred to as the h... | Does Fisher's Exact test for a $2\times 2$ table use the Non-central Hypergeometric or the Hypergeom
The noncentral hypergeometric distribution is a generalization of the hypergeometric distribution. The latter is used for the Fisher exact test. However, it frequently seems to be referred to as the h |
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