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 |
|---|---|---|---|---|---|---|
55,801 | Calculate variance of $X^2$ when $X$ is a random variable with mean $0$ and variance $\sigma_x^2$ | If you have only the mean and variance of $X$ as 0 and $\sigma_x^2$, then there is insufficient information to calculate the variance of $X^2$, which is
$$
E[X^4] - E[X^2]^2 = E[X^4] - \sigma_x^4.
$$
For a normal R.V. $\sim N(0, \sigma_x^2)$, $E[X] = 0, E[X^2] = \sigma_x^2, E[X^4] = 3 \sigma_x^4$.
For a uniform R.V. ... | Calculate variance of $X^2$ when $X$ is a random variable with mean $0$ and variance $\sigma_x^2$ | If you have only the mean and variance of $X$ as 0 and $\sigma_x^2$, then there is insufficient information to calculate the variance of $X^2$, which is
$$
E[X^4] - E[X^2]^2 = E[X^4] - \sigma_x^4.
$$
| Calculate variance of $X^2$ when $X$ is a random variable with mean $0$ and variance $\sigma_x^2$
If you have only the mean and variance of $X$ as 0 and $\sigma_x^2$, then there is insufficient information to calculate the variance of $X^2$, which is
$$
E[X^4] - E[X^2]^2 = E[X^4] - \sigma_x^4.
$$
For a normal R.V. $\s... | Calculate variance of $X^2$ when $X$ is a random variable with mean $0$ and variance $\sigma_x^2$
If you have only the mean and variance of $X$ as 0 and $\sigma_x^2$, then there is insufficient information to calculate the variance of $X^2$, which is
$$
E[X^4] - E[X^2]^2 = E[X^4] - \sigma_x^4.
$$
|
55,802 | Calculating pooled p-values manually | This is for anyone who is interested, after reading pp. 37-43 in Flexible Imputation of Missing Data by Stef van Buuren. If we call the adjusted degrees of freedom nu
m <- nrow(mat)
lambda <- (betweenVar + (betweenVar/m))/totVar
n <- nrow(nhimp$data)
k <- length(coef(lm(chl~bmi,data = complete(nhimp,1))))
nu_... | Calculating pooled p-values manually | This is for anyone who is interested, after reading pp. 37-43 in Flexible Imputation of Missing Data by Stef van Buuren. If we call the adjusted degrees of freedom nu
m <- nrow(mat)
lambda <- (bet | Calculating pooled p-values manually
This is for anyone who is interested, after reading pp. 37-43 in Flexible Imputation of Missing Data by Stef van Buuren. If we call the adjusted degrees of freedom nu
m <- nrow(mat)
lambda <- (betweenVar + (betweenVar/m))/totVar
n <- nrow(nhimp$data)
k <- length(coef(lm(chl~... | Calculating pooled p-values manually
This is for anyone who is interested, after reading pp. 37-43 in Flexible Imputation of Missing Data by Stef van Buuren. If we call the adjusted degrees of freedom nu
m <- nrow(mat)
lambda <- (bet |
55,803 | Visualizing model fit for multidimensional data | I think a good approach in your case could be to
Fit the multivariate GP model on a few training points, as you do now
Take advantage of the fact you have the ground truth function in order to generate true values and predicted values for a range of inputs.
Plot comparisons of the "marginal" and "joint" outputs for t... | Visualizing model fit for multidimensional data | I think a good approach in your case could be to
Fit the multivariate GP model on a few training points, as you do now
Take advantage of the fact you have the ground truth function in order to gener | Visualizing model fit for multidimensional data
I think a good approach in your case could be to
Fit the multivariate GP model on a few training points, as you do now
Take advantage of the fact you have the ground truth function in order to generate true values and predicted values for a range of inputs.
Plot compari... | Visualizing model fit for multidimensional data
I think a good approach in your case could be to
Fit the multivariate GP model on a few training points, as you do now
Take advantage of the fact you have the ground truth function in order to gener |
55,804 | How to un-transform exponential plot data to get back to original data scale? | You are going about this modelling exercise from the wrong direction. You are transforming x which is causing among other things trouble with big values. Instead you could transform y.
Anyway, the reason your attempts are failing is because you are trying to apply the back transformation to the fitted values, but you t... | How to un-transform exponential plot data to get back to original data scale? | You are going about this modelling exercise from the wrong direction. You are transforming x which is causing among other things trouble with big values. Instead you could transform y.
Anyway, the rea | How to un-transform exponential plot data to get back to original data scale?
You are going about this modelling exercise from the wrong direction. You are transforming x which is causing among other things trouble with big values. Instead you could transform y.
Anyway, the reason your attempts are failing is because y... | How to un-transform exponential plot data to get back to original data scale?
You are going about this modelling exercise from the wrong direction. You are transforming x which is causing among other things trouble with big values. Instead you could transform y.
Anyway, the rea |
55,805 | Proof that $E(|X_1 - X_2|)$ is bound by twice the mean | as pointed out in the comments by @zhanxiong, the triangle inequality is sufficient here, take:
$|X_1 -X_2| \leq |X_1| +|X_2|$ and take expectations to get
$\mathbb{E}(|X_1 -X_2|) \leq \mathbb{E}(|X_1|) +\mathbb{E}(|X_2|)$. However, you cannot equate the two marginal expectations to be the same value without assuming t... | Proof that $E(|X_1 - X_2|)$ is bound by twice the mean | as pointed out in the comments by @zhanxiong, the triangle inequality is sufficient here, take:
$|X_1 -X_2| \leq |X_1| +|X_2|$ and take expectations to get
$\mathbb{E}(|X_1 -X_2|) \leq \mathbb{E}(|X_1 | Proof that $E(|X_1 - X_2|)$ is bound by twice the mean
as pointed out in the comments by @zhanxiong, the triangle inequality is sufficient here, take:
$|X_1 -X_2| \leq |X_1| +|X_2|$ and take expectations to get
$\mathbb{E}(|X_1 -X_2|) \leq \mathbb{E}(|X_1|) +\mathbb{E}(|X_2|)$. However, you cannot equate the two margin... | Proof that $E(|X_1 - X_2|)$ is bound by twice the mean
as pointed out in the comments by @zhanxiong, the triangle inequality is sufficient here, take:
$|X_1 -X_2| \leq |X_1| +|X_2|$ and take expectations to get
$\mathbb{E}(|X_1 -X_2|) \leq \mathbb{E}(|X_1 |
55,806 | Calculate standard deviation from sample size, mean, and confidence interval? | The standard deviation for percentage/proportion is:
\begin{align}
\sigma &= \sqrt{p(1-p)} \\[5pt]
&= \sqrt{0.642(1-0.642)} \\[5pt]
&= 0.4792
\end{align}
Thus when given a percentage, you can directly find the std deviation.
For back tracking, we know, $CI = p \pm z \frac{\sigma}{\sqrt{N}}$
For 95%, $z = 1.96$, ... | Calculate standard deviation from sample size, mean, and confidence interval? | The standard deviation for percentage/proportion is:
\begin{align}
\sigma &= \sqrt{p(1-p)} \\[5pt]
&= \sqrt{0.642(1-0.642)} \\[5pt]
&= 0.4792
\end{align}
Thus when given a percentage, you can dire | Calculate standard deviation from sample size, mean, and confidence interval?
The standard deviation for percentage/proportion is:
\begin{align}
\sigma &= \sqrt{p(1-p)} \\[5pt]
&= \sqrt{0.642(1-0.642)} \\[5pt]
&= 0.4792
\end{align}
Thus when given a percentage, you can directly find the std deviation.
For back tra... | Calculate standard deviation from sample size, mean, and confidence interval?
The standard deviation for percentage/proportion is:
\begin{align}
\sigma &= \sqrt{p(1-p)} \\[5pt]
&= \sqrt{0.642(1-0.642)} \\[5pt]
&= 0.4792
\end{align}
Thus when given a percentage, you can dire |
55,807 | Calculate standard deviation from sample size, mean, and confidence interval? | From the description you provided, your first question is about the distribution of people's age. Normal (i.e. Gaussian) distribution applies to such kind of applications.
It will be helpful if you know how the confidence interval (CI) was calculated, because there are many different possible ways that the CI was calcu... | Calculate standard deviation from sample size, mean, and confidence interval? | From the description you provided, your first question is about the distribution of people's age. Normal (i.e. Gaussian) distribution applies to such kind of applications.
It will be helpful if you kn | Calculate standard deviation from sample size, mean, and confidence interval?
From the description you provided, your first question is about the distribution of people's age. Normal (i.e. Gaussian) distribution applies to such kind of applications.
It will be helpful if you know how the confidence interval (CI) was ca... | Calculate standard deviation from sample size, mean, and confidence interval?
From the description you provided, your first question is about the distribution of people's age. Normal (i.e. Gaussian) distribution applies to such kind of applications.
It will be helpful if you kn |
55,808 | Calculate standard deviation from sample size, mean, and confidence interval? | A bit late to the party, but I noticed that the second part of the question was not fully addressed - "can it be apply to percentage measure"?
Following the OPs comment, I am assuming that by "percentage measure" we are referring to some binary outcome (Male/Female, Right handed/Left handed etc.).
In that case the va... | Calculate standard deviation from sample size, mean, and confidence interval? | A bit late to the party, but I noticed that the second part of the question was not fully addressed - "can it be apply to percentage measure"?
Following the OPs comment, I am assuming that by "percen | Calculate standard deviation from sample size, mean, and confidence interval?
A bit late to the party, but I noticed that the second part of the question was not fully addressed - "can it be apply to percentage measure"?
Following the OPs comment, I am assuming that by "percentage measure" we are referring to some bin... | Calculate standard deviation from sample size, mean, and confidence interval?
A bit late to the party, but I noticed that the second part of the question was not fully addressed - "can it be apply to percentage measure"?
Following the OPs comment, I am assuming that by "percen |
55,809 | How can't the Softmax layer never converge using hard targets | The wording never converge may sound a bit too strong, but the actual statement is
... the softmax can never predict a probability of exactly $0$ or exactly $1$, ...
This is certainly true in almost all cases. In this context, a convergence means fitting the training data perfectly and outputting a one-hot vector of ... | How can't the Softmax layer never converge using hard targets | The wording never converge may sound a bit too strong, but the actual statement is
... the softmax can never predict a probability of exactly $0$ or exactly $1$, ...
This is certainly true in almost | How can't the Softmax layer never converge using hard targets
The wording never converge may sound a bit too strong, but the actual statement is
... the softmax can never predict a probability of exactly $0$ or exactly $1$, ...
This is certainly true in almost all cases. In this context, a convergence means fitting t... | How can't the Softmax layer never converge using hard targets
The wording never converge may sound a bit too strong, but the actual statement is
... the softmax can never predict a probability of exactly $0$ or exactly $1$, ...
This is certainly true in almost |
55,810 | How can't the Softmax layer never converge using hard targets | why don't we face that in practice?
The predictions for multiclass classification are done by taking argmax over probability vector, so this is not really an issue.
Do frameworks "terminate" the gradient descent algorithm earlier and handle this issue internally?
In deep learning usually you don't have any converge... | How can't the Softmax layer never converge using hard targets | why don't we face that in practice?
The predictions for multiclass classification are done by taking argmax over probability vector, so this is not really an issue.
Do frameworks "terminate" the gr | How can't the Softmax layer never converge using hard targets
why don't we face that in practice?
The predictions for multiclass classification are done by taking argmax over probability vector, so this is not really an issue.
Do frameworks "terminate" the gradient descent algorithm earlier and handle this issue int... | How can't the Softmax layer never converge using hard targets
why don't we face that in practice?
The predictions for multiclass classification are done by taking argmax over probability vector, so this is not really an issue.
Do frameworks "terminate" the gr |
55,811 | How to deal when you have too many outliers? | These are not outliers. I am an economist and this is the way the data should look, based on your comments. It is a poor dataset to start a beginner on.
What you are looking at is called "price discrimination." In particular, it is third degree price discrimination. Another real world example, although it is an exa... | How to deal when you have too many outliers? | These are not outliers. I am an economist and this is the way the data should look, based on your comments. It is a poor dataset to start a beginner on.
What you are looking at is called "price disc | How to deal when you have too many outliers?
These are not outliers. I am an economist and this is the way the data should look, based on your comments. It is a poor dataset to start a beginner on.
What you are looking at is called "price discrimination." In particular, it is third degree price discrimination. Anot... | How to deal when you have too many outliers?
These are not outliers. I am an economist and this is the way the data should look, based on your comments. It is a poor dataset to start a beginner on.
What you are looking at is called "price disc |
55,812 | Noncentral chi² with a noncentral chi² noncentrality parameter | Let's do it with characteristic functions. We'll start out with the definition of the characteristic function for an arbitrary distribution $F(x)$:
$$\phi_x(it) = \int e^{itx}dF(x)$$
The ch.f. of a noncentral $\chi^2(\nu, \Lambda)$ is:
$$\phi_{X|\Lambda}(it) = \frac{\exp\{\frac{it\Lambda}{1-2it}\}}{(1-2it)^{\nu/2}}$$
... | Noncentral chi² with a noncentral chi² noncentrality parameter | Let's do it with characteristic functions. We'll start out with the definition of the characteristic function for an arbitrary distribution $F(x)$:
$$\phi_x(it) = \int e^{itx}dF(x)$$
The ch.f. of a n | Noncentral chi² with a noncentral chi² noncentrality parameter
Let's do it with characteristic functions. We'll start out with the definition of the characteristic function for an arbitrary distribution $F(x)$:
$$\phi_x(it) = \int e^{itx}dF(x)$$
The ch.f. of a noncentral $\chi^2(\nu, \Lambda)$ is:
$$\phi_{X|\Lambda}(i... | Noncentral chi² with a noncentral chi² noncentrality parameter
Let's do it with characteristic functions. We'll start out with the definition of the characteristic function for an arbitrary distribution $F(x)$:
$$\phi_x(it) = \int e^{itx}dF(x)$$
The ch.f. of a n |
55,813 | Does exponential family of distributions have finite expected value? | As fairly well-explained on Wikipedia, for any exponential family, there exists a parameterisation such that the density of the family is$$f(x|\theta)=\exp\{\theta\cdot T(x)-\Psi(\theta)\}$$wrt a constant measure $\text{d}\mu(x)$, where the components of $T(\cdot)$ are linearly independent. In this representation, the ... | Does exponential family of distributions have finite expected value? | As fairly well-explained on Wikipedia, for any exponential family, there exists a parameterisation such that the density of the family is$$f(x|\theta)=\exp\{\theta\cdot T(x)-\Psi(\theta)\}$$wrt a cons | Does exponential family of distributions have finite expected value?
As fairly well-explained on Wikipedia, for any exponential family, there exists a parameterisation such that the density of the family is$$f(x|\theta)=\exp\{\theta\cdot T(x)-\Psi(\theta)\}$$wrt a constant measure $\text{d}\mu(x)$, where the components... | Does exponential family of distributions have finite expected value?
As fairly well-explained on Wikipedia, for any exponential family, there exists a parameterisation such that the density of the family is$$f(x|\theta)=\exp\{\theta\cdot T(x)-\Psi(\theta)\}$$wrt a cons |
55,814 | Is there an equivalent to Fourier decomposition using normal distributions instead of sin / cos? | You might want to try out Gaussian Mixture models for your data.
For example, to decompose a mixture of $\mathcal{N}(10, 5), \mathcal{N}(22, 3)$, using flexmix package
library(flexmix)
set.seed(42)
m1 <- 10
m2 <- 22
sd1 <- 5
sd2 <- 3
N1 <- 1000
N2 <- 5000
D <- c(rnorm(mean = m1, sd = sd1, n = N1), rnorm(mean = m2,... | Is there an equivalent to Fourier decomposition using normal distributions instead of sin / cos? | You might want to try out Gaussian Mixture models for your data.
For example, to decompose a mixture of $\mathcal{N}(10, 5), \mathcal{N}(22, 3)$, using flexmix package
library(flexmix)
set.seed(42)
| Is there an equivalent to Fourier decomposition using normal distributions instead of sin / cos?
You might want to try out Gaussian Mixture models for your data.
For example, to decompose a mixture of $\mathcal{N}(10, 5), \mathcal{N}(22, 3)$, using flexmix package
library(flexmix)
set.seed(42)
m1 <- 10
m2 <- 22
sd1 ... | Is there an equivalent to Fourier decomposition using normal distributions instead of sin / cos?
You might want to try out Gaussian Mixture models for your data.
For example, to decompose a mixture of $\mathcal{N}(10, 5), \mathcal{N}(22, 3)$, using flexmix package
library(flexmix)
set.seed(42)
|
55,815 | Is there an equivalent to Fourier decomposition using normal distributions instead of sin / cos? | There are several important differences between sinusoidal functions are normal distributions. Sinusoidal functions provide an orthogonal basis for "nice" functions (I won't go into defining "nice" rigorously). So not only can every "nice" function be written as a linear combination, but the coefficients can be calcula... | Is there an equivalent to Fourier decomposition using normal distributions instead of sin / cos? | There are several important differences between sinusoidal functions are normal distributions. Sinusoidal functions provide an orthogonal basis for "nice" functions (I won't go into defining "nice" ri | Is there an equivalent to Fourier decomposition using normal distributions instead of sin / cos?
There are several important differences between sinusoidal functions are normal distributions. Sinusoidal functions provide an orthogonal basis for "nice" functions (I won't go into defining "nice" rigorously). So not only ... | Is there an equivalent to Fourier decomposition using normal distributions instead of sin / cos?
There are several important differences between sinusoidal functions are normal distributions. Sinusoidal functions provide an orthogonal basis for "nice" functions (I won't go into defining "nice" ri |
55,816 | How to perform a Binomial Test when having replicates? | Try fitting a binomial Generalized Linear Model - in R , if you have a dataframe called DF with numbers of successes (called "irregular") and failures ("regular") , and a column for treatment/group called Treat, with one Petri dish in each row, you can then do
Mod <- glm(data = DF, cbind(irregular,regular) ~ Treat, fa... | How to perform a Binomial Test when having replicates? | Try fitting a binomial Generalized Linear Model - in R , if you have a dataframe called DF with numbers of successes (called "irregular") and failures ("regular") , and a column for treatment/group ca | How to perform a Binomial Test when having replicates?
Try fitting a binomial Generalized Linear Model - in R , if you have a dataframe called DF with numbers of successes (called "irregular") and failures ("regular") , and a column for treatment/group called Treat, with one Petri dish in each row, you can then do
Mod... | How to perform a Binomial Test when having replicates?
Try fitting a binomial Generalized Linear Model - in R , if you have a dataframe called DF with numbers of successes (called "irregular") and failures ("regular") , and a column for treatment/group ca |
55,817 | How to perform a Binomial Test when having replicates? | There are many times in basic science (and other) research designs, where experiments are replicated and, at first glance, repeated measures seem appropriate. However, most procedures designed to handle data derived from non-independent units, such as the paired t-test, require more than one observation taken on the sa... | How to perform a Binomial Test when having replicates? | There are many times in basic science (and other) research designs, where experiments are replicated and, at first glance, repeated measures seem appropriate. However, most procedures designed to hand | How to perform a Binomial Test when having replicates?
There are many times in basic science (and other) research designs, where experiments are replicated and, at first glance, repeated measures seem appropriate. However, most procedures designed to handle data derived from non-independent units, such as the paired t-... | How to perform a Binomial Test when having replicates?
There are many times in basic science (and other) research designs, where experiments are replicated and, at first glance, repeated measures seem appropriate. However, most procedures designed to hand |
55,818 | How to perform a Binomial Test when having replicates? | If I understand correctly, you have 2 experimental conditions. Within each condition, you have three petry-dishes and within each petry-dish, you have the cells which you're counting. Assuming I understand correctly, You need to account for the fact that you have clustering in your data (cells are nested within dish). ... | How to perform a Binomial Test when having replicates? | If I understand correctly, you have 2 experimental conditions. Within each condition, you have three petry-dishes and within each petry-dish, you have the cells which you're counting. Assuming I under | How to perform a Binomial Test when having replicates?
If I understand correctly, you have 2 experimental conditions. Within each condition, you have three petry-dishes and within each petry-dish, you have the cells which you're counting. Assuming I understand correctly, You need to account for the fact that you have c... | How to perform a Binomial Test when having replicates?
If I understand correctly, you have 2 experimental conditions. Within each condition, you have three petry-dishes and within each petry-dish, you have the cells which you're counting. Assuming I under |
55,819 | How to perform a Binomial Test when having replicates? | Problem Statement:
As I understand it you have 6 petri dishes. You split them into 2 groups (A,B). Each group is identically treated, and you could $N_{irregular}/ N_{total} $.
You then want to compare treatments.
So sample data might be:
$$
\begin{matrix}
\mathbf{Dish } & \mathbf{Group} & \mathbf{N_{irregular}} &... | How to perform a Binomial Test when having replicates? | Problem Statement:
As I understand it you have 6 petri dishes. You split them into 2 groups (A,B). Each group is identically treated, and you could $N_{irregular}/ N_{total} $.
You then want to co | How to perform a Binomial Test when having replicates?
Problem Statement:
As I understand it you have 6 petri dishes. You split them into 2 groups (A,B). Each group is identically treated, and you could $N_{irregular}/ N_{total} $.
You then want to compare treatments.
So sample data might be:
$$
\begin{matrix}
\ma... | How to perform a Binomial Test when having replicates?
Problem Statement:
As I understand it you have 6 petri dishes. You split them into 2 groups (A,B). Each group is identically treated, and you could $N_{irregular}/ N_{total} $.
You then want to co |
55,820 | Negative eigenvalues in principle component analysis in the presence of missing data | If you calculate pairwise correlation coefficients in presence of missing values, you correlation matrix may end up being non positive definite. In fact it's a very common phenomenon in quant finance. One way to deal with this issue is Ledoit Wolf procedure, see here. They developed a method for a different issue, but ... | Negative eigenvalues in principle component analysis in the presence of missing data | If you calculate pairwise correlation coefficients in presence of missing values, you correlation matrix may end up being non positive definite. In fact it's a very common phenomenon in quant finance. | Negative eigenvalues in principle component analysis in the presence of missing data
If you calculate pairwise correlation coefficients in presence of missing values, you correlation matrix may end up being non positive definite. In fact it's a very common phenomenon in quant finance. One way to deal with this issue is... | Negative eigenvalues in principle component analysis in the presence of missing data
If you calculate pairwise correlation coefficients in presence of missing values, you correlation matrix may end up being non positive definite. In fact it's a very common phenomenon in quant finance. |
55,821 | Negative eigenvalues in principle component analysis in the presence of missing data | After the discussion here, I can provide at least a partial answer.
Apparently, pairwise calculation of correlation coefficients, especially if the data matrix has missing data, leads to a correlation matrix that is only positive semi-definite, not positive definite. Eigenvalues that are too extreme. According to http... | Negative eigenvalues in principle component analysis in the presence of missing data | After the discussion here, I can provide at least a partial answer.
Apparently, pairwise calculation of correlation coefficients, especially if the data matrix has missing data, leads to a correlatio | Negative eigenvalues in principle component analysis in the presence of missing data
After the discussion here, I can provide at least a partial answer.
Apparently, pairwise calculation of correlation coefficients, especially if the data matrix has missing data, leads to a correlation matrix that is only positive semi... | Negative eigenvalues in principle component analysis in the presence of missing data
After the discussion here, I can provide at least a partial answer.
Apparently, pairwise calculation of correlation coefficients, especially if the data matrix has missing data, leads to a correlatio |
55,822 | Is there a Bayesian analogue to a simultaneous confidence band? | Given a prior distribution $\pi$ on a functional space and observations about the function values at some points, or noisy observations of the function itself, the posterior distribution $\pi(\cdot|\mathcal{D})$ can be used to derive an HPD region,
$$\left\{f\in\mathcal{F}\,,\ \pi(f |\mathcal{D})\ge k_\alpha\right\}$$
... | Is there a Bayesian analogue to a simultaneous confidence band? | Given a prior distribution $\pi$ on a functional space and observations about the function values at some points, or noisy observations of the function itself, the posterior distribution $\pi(\cdot|\m | Is there a Bayesian analogue to a simultaneous confidence band?
Given a prior distribution $\pi$ on a functional space and observations about the function values at some points, or noisy observations of the function itself, the posterior distribution $\pi(\cdot|\mathcal{D})$ can be used to derive an HPD region,
$$\left... | Is there a Bayesian analogue to a simultaneous confidence band?
Given a prior distribution $\pi$ on a functional space and observations about the function values at some points, or noisy observations of the function itself, the posterior distribution $\pi(\cdot|\m |
55,823 | BIC vs. intuition | It's not an obvious question at all! In fact, I think there may be some disagreement even among statisticians.
My view is that you should never let the computer do your thinking for you. Don't blindly accept anything. However, don't blindly reject anything, either. My favorite professor in grad school, Herman Fried... | BIC vs. intuition | It's not an obvious question at all! In fact, I think there may be some disagreement even among statisticians.
My view is that you should never let the computer do your thinking for you. Don't blind | BIC vs. intuition
It's not an obvious question at all! In fact, I think there may be some disagreement even among statisticians.
My view is that you should never let the computer do your thinking for you. Don't blindly accept anything. However, don't blindly reject anything, either. My favorite professor in grad sc... | BIC vs. intuition
It's not an obvious question at all! In fact, I think there may be some disagreement even among statisticians.
My view is that you should never let the computer do your thinking for you. Don't blind |
55,824 | Comparing estimators of equal risk | The statement as reported is wrong: A most standard example is provided by the James-Stein estimator: given $X\sim\mathcal{N}_p(\theta,I_p)$ $(p>2)$, assuming $\theta$ is estimated under the square error loss,$$L(\theta,\delta)=||\theta-\delta||^2$$the estimators$$\delta_0(x)=x\qquad\text{and}\qquad \delta_{2(p-2)}(x)=... | Comparing estimators of equal risk | The statement as reported is wrong: A most standard example is provided by the James-Stein estimator: given $X\sim\mathcal{N}_p(\theta,I_p)$ $(p>2)$, assuming $\theta$ is estimated under the square er | Comparing estimators of equal risk
The statement as reported is wrong: A most standard example is provided by the James-Stein estimator: given $X\sim\mathcal{N}_p(\theta,I_p)$ $(p>2)$, assuming $\theta$ is estimated under the square error loss,$$L(\theta,\delta)=||\theta-\delta||^2$$the estimators$$\delta_0(x)=x\qquad\... | Comparing estimators of equal risk
The statement as reported is wrong: A most standard example is provided by the James-Stein estimator: given $X\sim\mathcal{N}_p(\theta,I_p)$ $(p>2)$, assuming $\theta$ is estimated under the square er |
55,825 | Expectation of Sum of Gamma over Product of Inverse-Gamma | This is rather straightforward (when the $X_i$'s are independent):
\begin{align*}\mathbb{E}\left(\cfrac{\sum_{i=1}^n X_i}{(\prod_{j=1}^n X_j)^{1/n}}\right) &= \sum_{i=1}^n \mathbb{E}\left(\cfrac{ X_i}{(\prod_{j=1}^n X_j)^{1/n}}\right)\\
&= \sum_{i=1}^n \mathbb{E}[X_i^{1-1/n}]\times \mathbb{E}\left(\cfrac{1}{(\prod_{j... | Expectation of Sum of Gamma over Product of Inverse-Gamma | This is rather straightforward (when the $X_i$'s are independent):
\begin{align*}\mathbb{E}\left(\cfrac{\sum_{i=1}^n X_i}{(\prod_{j=1}^n X_j)^{1/n}}\right) &= \sum_{i=1}^n \mathbb{E}\left(\cfrac{ X_i | Expectation of Sum of Gamma over Product of Inverse-Gamma
This is rather straightforward (when the $X_i$'s are independent):
\begin{align*}\mathbb{E}\left(\cfrac{\sum_{i=1}^n X_i}{(\prod_{j=1}^n X_j)^{1/n}}\right) &= \sum_{i=1}^n \mathbb{E}\left(\cfrac{ X_i}{(\prod_{j=1}^n X_j)^{1/n}}\right)\\
&= \sum_{i=1}^n \mathbb... | Expectation of Sum of Gamma over Product of Inverse-Gamma
This is rather straightforward (when the $X_i$'s are independent):
\begin{align*}\mathbb{E}\left(\cfrac{\sum_{i=1}^n X_i}{(\prod_{j=1}^n X_j)^{1/n}}\right) &= \sum_{i=1}^n \mathbb{E}\left(\cfrac{ X_i |
55,826 | Simulation of a Poisson Process | You want to get a function of $t$ that gives the count of events. So simply do
n_func <- function(t, S) sapply(t, function(t) sum(S <= t))
t_series <- seq(0, max(S), by = max(S)/100)
plot(t_series, n_func(t_series, S)
$S$ is basically the time stamps of each Poisson events in your sample. So you want to just count the... | Simulation of a Poisson Process | You want to get a function of $t$ that gives the count of events. So simply do
n_func <- function(t, S) sapply(t, function(t) sum(S <= t))
t_series <- seq(0, max(S), by = max(S)/100)
plot(t_series, n_ | Simulation of a Poisson Process
You want to get a function of $t$ that gives the count of events. So simply do
n_func <- function(t, S) sapply(t, function(t) sum(S <= t))
t_series <- seq(0, max(S), by = max(S)/100)
plot(t_series, n_func(t_series, S)
$S$ is basically the time stamps of each Poisson events in your sampl... | Simulation of a Poisson Process
You want to get a function of $t$ that gives the count of events. So simply do
n_func <- function(t, S) sapply(t, function(t) sum(S <= t))
t_series <- seq(0, max(S), by = max(S)/100)
plot(t_series, n_ |
55,827 | Simulation of a Poisson Process | The Poisson process is describing how events occur over time. The inter-arrival times (i.e., the times between each successive event) are distributed as an exponential. In the algorithm provided, $S_n$ is the total amount of time that has elapsed since you started recording until the $n$th event occurred. Since your... | Simulation of a Poisson Process | The Poisson process is describing how events occur over time. The inter-arrival times (i.e., the times between each successive event) are distributed as an exponential. In the algorithm provided, $S | Simulation of a Poisson Process
The Poisson process is describing how events occur over time. The inter-arrival times (i.e., the times between each successive event) are distributed as an exponential. In the algorithm provided, $S_n$ is the total amount of time that has elapsed since you started recording until the $... | Simulation of a Poisson Process
The Poisson process is describing how events occur over time. The inter-arrival times (i.e., the times between each successive event) are distributed as an exponential. In the algorithm provided, $S |
55,828 | Policy Iteration Diagram in Jack’s Car Rental (in reinforcement learning) | The stepped curves are showing the contours of the different policy actions, as a map over the state space. They are a choice of visualisation of the policy, which has 441 states, and would not look quite so intuitive listed as a table.
The numbers are the number of cars that the policy decides to move from first locat... | Policy Iteration Diagram in Jack’s Car Rental (in reinforcement learning) | The stepped curves are showing the contours of the different policy actions, as a map over the state space. They are a choice of visualisation of the policy, which has 441 states, and would not look q | Policy Iteration Diagram in Jack’s Car Rental (in reinforcement learning)
The stepped curves are showing the contours of the different policy actions, as a map over the state space. They are a choice of visualisation of the policy, which has 441 states, and would not look quite so intuitive listed as a table.
The numbe... | Policy Iteration Diagram in Jack’s Car Rental (in reinforcement learning)
The stepped curves are showing the contours of the different policy actions, as a map over the state space. They are a choice of visualisation of the policy, which has 441 states, and would not look q |
55,829 | Intuitive reason why jointly normal and uncorrelated imply independence | Well, what intuition can there be? For a bivariate normal distribution (for $X$ and $Y$, say), uncorrelated means independence of $X$ and $Y$, while for the quite similar bivariate t distribution, with say 100 degrees of freedom, independence do not follow from correlation zero. Plotted this two distributions will loo... | Intuitive reason why jointly normal and uncorrelated imply independence | Well, what intuition can there be? For a bivariate normal distribution (for $X$ and $Y$, say), uncorrelated means independence of $X$ and $Y$, while for the quite similar bivariate t distribution, wit | Intuitive reason why jointly normal and uncorrelated imply independence
Well, what intuition can there be? For a bivariate normal distribution (for $X$ and $Y$, say), uncorrelated means independence of $X$ and $Y$, while for the quite similar bivariate t distribution, with say 100 degrees of freedom, independence do no... | Intuitive reason why jointly normal and uncorrelated imply independence
Well, what intuition can there be? For a bivariate normal distribution (for $X$ and $Y$, say), uncorrelated means independence of $X$ and $Y$, while for the quite similar bivariate t distribution, wit |
55,830 | Expected value of SRSWOR sample maximum | Just about all answers will have to be mathematically equivalent. The point of this one is to develop a solution in the laziest possible way: that is, by pure reasoning unaccompanied by any calculation at all.
There are $\binom{N}{n}$ possible and equally likely samples, since each sample is a subset of $n$ of the $N... | Expected value of SRSWOR sample maximum | Just about all answers will have to be mathematically equivalent. The point of this one is to develop a solution in the laziest possible way: that is, by pure reasoning unaccompanied by any calculati | Expected value of SRSWOR sample maximum
Just about all answers will have to be mathematically equivalent. The point of this one is to develop a solution in the laziest possible way: that is, by pure reasoning unaccompanied by any calculation at all.
There are $\binom{N}{n}$ possible and equally likely samples, since ... | Expected value of SRSWOR sample maximum
Just about all answers will have to be mathematically equivalent. The point of this one is to develop a solution in the laziest possible way: that is, by pure reasoning unaccompanied by any calculati |
55,831 | Expected value of SRSWOR sample maximum | If you are sampling from the discrete uniform population (without replacement, as you have stipulated), then it is the German Tank Problem.
Let the sample be $X_1, X_2, \ldots , X_n$ with $Y=\textrm{max} \left( X_1, X_2, \ldots , X_n \right).$
The joint mass function is $$f \left( x_1, x_2, \ldots , x_n \right)=\frac... | Expected value of SRSWOR sample maximum | If you are sampling from the discrete uniform population (without replacement, as you have stipulated), then it is the German Tank Problem.
Let the sample be $X_1, X_2, \ldots , X_n$ with $Y=\textrm{ | Expected value of SRSWOR sample maximum
If you are sampling from the discrete uniform population (without replacement, as you have stipulated), then it is the German Tank Problem.
Let the sample be $X_1, X_2, \ldots , X_n$ with $Y=\textrm{max} \left( X_1, X_2, \ldots , X_n \right).$
The joint mass function is $$f \le... | Expected value of SRSWOR sample maximum
If you are sampling from the discrete uniform population (without replacement, as you have stipulated), then it is the German Tank Problem.
Let the sample be $X_1, X_2, \ldots , X_n$ with $Y=\textrm{ |
55,832 | Expected value of SRSWOR sample maximum | As with each and every sampling problem, the answer is "Yes, if you have access to the population and to an algorithm that efficiently enumerates all possible samples". So if you are talking about samples of size 3 out of population of size 7, then yes, you can probably derive that. If you are talking about realistic s... | Expected value of SRSWOR sample maximum | As with each and every sampling problem, the answer is "Yes, if you have access to the population and to an algorithm that efficiently enumerates all possible samples". So if you are talking about sam | Expected value of SRSWOR sample maximum
As with each and every sampling problem, the answer is "Yes, if you have access to the population and to an algorithm that efficiently enumerates all possible samples". So if you are talking about samples of size 3 out of population of size 7, then yes, you can probably derive th... | Expected value of SRSWOR sample maximum
As with each and every sampling problem, the answer is "Yes, if you have access to the population and to an algorithm that efficiently enumerates all possible samples". So if you are talking about sam |
55,833 | Variational Autoencoder and validation loss | The short answer is: Don't drop the KL term.
The reconstruction error plus KL term optimized by a VAE is a lower bound on the log-likelihood (also called the "evidence lower bound", or ELBO) [1]. Log-likelihood is one way to measure how well your model explains the data. If that's what you're after, it makes sense to ... | Variational Autoencoder and validation loss | The short answer is: Don't drop the KL term.
The reconstruction error plus KL term optimized by a VAE is a lower bound on the log-likelihood (also called the "evidence lower bound", or ELBO) [1]. Log | Variational Autoencoder and validation loss
The short answer is: Don't drop the KL term.
The reconstruction error plus KL term optimized by a VAE is a lower bound on the log-likelihood (also called the "evidence lower bound", or ELBO) [1]. Log-likelihood is one way to measure how well your model explains the data. If ... | Variational Autoencoder and validation loss
The short answer is: Don't drop the KL term.
The reconstruction error plus KL term optimized by a VAE is a lower bound on the log-likelihood (also called the "evidence lower bound", or ELBO) [1]. Log |
55,834 | Variational Autoencoder and validation loss | If you ignore the regularization part (KL divergence ) you will not be able to compare it with the train loss.
It is true that regularization is added to better optimize the parameters of the model and not for better approximation of the loss function.
You could add 'mse' metric for this,
Model.compile(...,metric=['... | Variational Autoencoder and validation loss | If you ignore the regularization part (KL divergence ) you will not be able to compare it with the train loss.
It is true that regularization is added to better optimize the parameters of the model a | Variational Autoencoder and validation loss
If you ignore the regularization part (KL divergence ) you will not be able to compare it with the train loss.
It is true that regularization is added to better optimize the parameters of the model and not for better approximation of the loss function.
You could add 'mse' m... | Variational Autoencoder and validation loss
If you ignore the regularization part (KL divergence ) you will not be able to compare it with the train loss.
It is true that regularization is added to better optimize the parameters of the model a |
55,835 | Where does the Kullback-Leibler come from? [duplicate] | KL divergence is very closely related to entropy. It helps to understand the motivation behind the expression for entropy.
For some distribution $p(x)$ we call $h(x) = -\log p(x)$ the information received by observing variable $x$. It's called "information" because it has the nice property that if we observe two comple... | Where does the Kullback-Leibler come from? [duplicate] | KL divergence is very closely related to entropy. It helps to understand the motivation behind the expression for entropy.
For some distribution $p(x)$ we call $h(x) = -\log p(x)$ the information rece | Where does the Kullback-Leibler come from? [duplicate]
KL divergence is very closely related to entropy. It helps to understand the motivation behind the expression for entropy.
For some distribution $p(x)$ we call $h(x) = -\log p(x)$ the information received by observing variable $x$. It's called "information" because... | Where does the Kullback-Leibler come from? [duplicate]
KL divergence is very closely related to entropy. It helps to understand the motivation behind the expression for entropy.
For some distribution $p(x)$ we call $h(x) = -\log p(x)$ the information rece |
55,836 | hidden markov model with multiple factors | Important References
I would strongly suggest you to check the Bayesian Network or probabilistic graphical model literature, which can answer your question perfectly.
If you have limited time, this page by Kevin Murphy, A Brief Introduction to Graphical Models and Bayesian Networks is a good start. The page gives bas... | hidden markov model with multiple factors | Important References
I would strongly suggest you to check the Bayesian Network or probabilistic graphical model literature, which can answer your question perfectly.
If you have limited time, this | hidden markov model with multiple factors
Important References
I would strongly suggest you to check the Bayesian Network or probabilistic graphical model literature, which can answer your question perfectly.
If you have limited time, this page by Kevin Murphy, A Brief Introduction to Graphical Models and Bayesian Ne... | hidden markov model with multiple factors
Important References
I would strongly suggest you to check the Bayesian Network or probabilistic graphical model literature, which can answer your question perfectly.
If you have limited time, this |
55,837 | Use continuous variables or buckets in neural net? | The non-linearity you are concerned about can be effectively handled by neural nets. That is one of the key points with using them instead of a linear model. A neural net can , at least theoretically, approximate any continuous function. It is called the Universal approximation theorem. Of course it might still be hard... | Use continuous variables or buckets in neural net? | The non-linearity you are concerned about can be effectively handled by neural nets. That is one of the key points with using them instead of a linear model. A neural net can , at least theoretically, | Use continuous variables or buckets in neural net?
The non-linearity you are concerned about can be effectively handled by neural nets. That is one of the key points with using them instead of a linear model. A neural net can , at least theoretically, approximate any continuous function. It is called the Universal appr... | Use continuous variables or buckets in neural net?
The non-linearity you are concerned about can be effectively handled by neural nets. That is one of the key points with using them instead of a linear model. A neural net can , at least theoretically, |
55,838 | Use continuous variables or buckets in neural net? | There are probably no principled ways to determine when to create buckets or use the value as continuous like the 'age' feature, since the predictiveness of age in different tasks vary a lot.
Trial and error is always good if having enough time and computation resources. If not, manually decide how many buckets to cre... | Use continuous variables or buckets in neural net? | There are probably no principled ways to determine when to create buckets or use the value as continuous like the 'age' feature, since the predictiveness of age in different tasks vary a lot.
Trial a | Use continuous variables or buckets in neural net?
There are probably no principled ways to determine when to create buckets or use the value as continuous like the 'age' feature, since the predictiveness of age in different tasks vary a lot.
Trial and error is always good if having enough time and computation resourc... | Use continuous variables or buckets in neural net?
There are probably no principled ways to determine when to create buckets or use the value as continuous like the 'age' feature, since the predictiveness of age in different tasks vary a lot.
Trial a |
55,839 | factor loadings = eigenvectors in R output? | However, my understanding is that loadings are computed as the product
of the eigenvector and the square root of the eigenvalue.
I depends on definition of loading you use. In princomp loadings are simply coefficients of principal components (recall that principal components are linear combinations of original varia... | factor loadings = eigenvectors in R output? | However, my understanding is that loadings are computed as the product
of the eigenvector and the square root of the eigenvalue.
I depends on definition of loading you use. In princomp loadings are | factor loadings = eigenvectors in R output?
However, my understanding is that loadings are computed as the product
of the eigenvector and the square root of the eigenvalue.
I depends on definition of loading you use. In princomp loadings are simply coefficients of principal components (recall that principal componen... | factor loadings = eigenvectors in R output?
However, my understanding is that loadings are computed as the product
of the eigenvector and the square root of the eigenvalue.
I depends on definition of loading you use. In princomp loadings are |
55,840 | ML estimator for chi square distribution | The problem is that you haven't written down the correct likelihood.
Suppose $X$ is a positive multiple $\theta$ ($=\sigma^2$) of a variable $Y$ with distribution function $F_Y$ and density $f_Y$. To find the density of $X$ itself, resort to the definition of the distribution function:
$$F_X(x) = \Pr(X\le x) = \Pr(\th... | ML estimator for chi square distribution | The problem is that you haven't written down the correct likelihood.
Suppose $X$ is a positive multiple $\theta$ ($=\sigma^2$) of a variable $Y$ with distribution function $F_Y$ and density $f_Y$. To | ML estimator for chi square distribution
The problem is that you haven't written down the correct likelihood.
Suppose $X$ is a positive multiple $\theta$ ($=\sigma^2$) of a variable $Y$ with distribution function $F_Y$ and density $f_Y$. To find the density of $X$ itself, resort to the definition of the distribution f... | ML estimator for chi square distribution
The problem is that you haven't written down the correct likelihood.
Suppose $X$ is a positive multiple $\theta$ ($=\sigma^2$) of a variable $Y$ with distribution function $F_Y$ and density $f_Y$. To |
55,841 | Expectation of the absolute difference of two i.i.d Normal distributions | If $X$ and $Y$ are independent normal random variables, then $X - Y$ is normal.
$$ X - Y \sim Normal(0, \sqrt{2}) $$
From here, the expectation of the absolute value of a standard normal is:
$$ E \left[ | X | \right] = \sqrt{\frac{2}{\pi}} $$
So for the difference
$$ E \left[ | X - Y | \right] = \sqrt{2} E \left[ | X... | Expectation of the absolute difference of two i.i.d Normal distributions | If $X$ and $Y$ are independent normal random variables, then $X - Y$ is normal.
$$ X - Y \sim Normal(0, \sqrt{2}) $$
From here, the expectation of the absolute value of a standard normal is:
$$ E \l | Expectation of the absolute difference of two i.i.d Normal distributions
If $X$ and $Y$ are independent normal random variables, then $X - Y$ is normal.
$$ X - Y \sim Normal(0, \sqrt{2}) $$
From here, the expectation of the absolute value of a standard normal is:
$$ E \left[ | X | \right] = \sqrt{\frac{2}{\pi}} $$
So... | Expectation of the absolute difference of two i.i.d Normal distributions
If $X$ and $Y$ are independent normal random variables, then $X - Y$ is normal.
$$ X - Y \sim Normal(0, \sqrt{2}) $$
From here, the expectation of the absolute value of a standard normal is:
$$ E \l |
55,842 | The Defective Lock Problem | This problem, as I have interpreted it, has an easy one-line solution. This answer states my interpretation, outlines the background theory, presents the solution, gives a worked example, and appends an alternative solution (also a one-liner) for those familiar with generating functions.
Statement of the problem
Let's... | The Defective Lock Problem | This problem, as I have interpreted it, has an easy one-line solution. This answer states my interpretation, outlines the background theory, presents the solution, gives a worked example, and appends | The Defective Lock Problem
This problem, as I have interpreted it, has an easy one-line solution. This answer states my interpretation, outlines the background theory, presents the solution, gives a worked example, and appends an alternative solution (also a one-liner) for those familiar with generating functions.
Sta... | The Defective Lock Problem
This problem, as I have interpreted it, has an easy one-line solution. This answer states my interpretation, outlines the background theory, presents the solution, gives a worked example, and appends |
55,843 | What is the difference between support vector machines and support vector regression? | a support vector machine performs classification
support vector regression performs regression
Related:
How does support vector regression work intuitively?
Support vector machines and regression | What is the difference between support vector machines and support vector regression? | a support vector machine performs classification
support vector regression performs regression
Related:
How does support vector regression work intuitively?
Support vector machines and regression | What is the difference between support vector machines and support vector regression?
a support vector machine performs classification
support vector regression performs regression
Related:
How does support vector regression work intuitively?
Support vector machines and regression | What is the difference between support vector machines and support vector regression?
a support vector machine performs classification
support vector regression performs regression
Related:
How does support vector regression work intuitively?
Support vector machines and regression |
55,844 | What is the difference between support vector machines and support vector regression? | I think this query is well addressed on the following link:
SVM vs. SVR | What is the difference between support vector machines and support vector regression? | I think this query is well addressed on the following link:
SVM vs. SVR | What is the difference between support vector machines and support vector regression?
I think this query is well addressed on the following link:
SVM vs. SVR | What is the difference between support vector machines and support vector regression?
I think this query is well addressed on the following link:
SVM vs. SVR |
55,845 | What does it mean to say that the t-distribution provides an "adjustment" or "estimate" for a normal distribution? | If the data are normally distributed, the test statistic with the sample standard deviation in the denominator will have a $t$ distribution with $n-1$ degrees of freedom. For large $n$, the $t$ distribution is approximately normal. But in small samples, it will be symmetric with heavier tails than those of the normal... | What does it mean to say that the t-distribution provides an "adjustment" or "estimate" for a normal | If the data are normally distributed, the test statistic with the sample standard deviation in the denominator will have a $t$ distribution with $n-1$ degrees of freedom. For large $n$, the $t$ distr | What does it mean to say that the t-distribution provides an "adjustment" or "estimate" for a normal distribution?
If the data are normally distributed, the test statistic with the sample standard deviation in the denominator will have a $t$ distribution with $n-1$ degrees of freedom. For large $n$, the $t$ distributi... | What does it mean to say that the t-distribution provides an "adjustment" or "estimate" for a normal
If the data are normally distributed, the test statistic with the sample standard deviation in the denominator will have a $t$ distribution with $n-1$ degrees of freedom. For large $n$, the $t$ distr |
55,846 | What does it mean to say that the t-distribution provides an "adjustment" or "estimate" for a normal distribution? | It is conventional to have the sample variance calculated to be an unbiased estimator of the population variance by dividing by $n-1$ rather than $n$.
But then the sample standard deviation is not an unbiased estimator of the population standard deviation, and the reciprocal of the sample standard deviation is even m... | What does it mean to say that the t-distribution provides an "adjustment" or "estimate" for a normal | It is conventional to have the sample variance calculated to be an unbiased estimator of the population variance by dividing by $n-1$ rather than $n$.
But then the sample standard deviation is not a | What does it mean to say that the t-distribution provides an "adjustment" or "estimate" for a normal distribution?
It is conventional to have the sample variance calculated to be an unbiased estimator of the population variance by dividing by $n-1$ rather than $n$.
But then the sample standard deviation is not an unb... | What does it mean to say that the t-distribution provides an "adjustment" or "estimate" for a normal
It is conventional to have the sample variance calculated to be an unbiased estimator of the population variance by dividing by $n-1$ rather than $n$.
But then the sample standard deviation is not a |
55,847 | Does permutation permute also dependence? | The dependence structure is simply the values of $f(x_1,\cdots,x_n):=P(X_1,\cdots,X_n)$. So by permuting the vectors, you are also permuting the dependence. Nothing is lost (unless you can't keep track of your permutation indices). For example, if $Y=(Y_1,\cdots,Y_n)$ with $Y_i=X_{\pi(i)}$, where $\pi$ is your permutat... | Does permutation permute also dependence? | The dependence structure is simply the values of $f(x_1,\cdots,x_n):=P(X_1,\cdots,X_n)$. So by permuting the vectors, you are also permuting the dependence. Nothing is lost (unless you can't keep trac | Does permutation permute also dependence?
The dependence structure is simply the values of $f(x_1,\cdots,x_n):=P(X_1,\cdots,X_n)$. So by permuting the vectors, you are also permuting the dependence. Nothing is lost (unless you can't keep track of your permutation indices). For example, if $Y=(Y_1,\cdots,Y_n)$ with $Y_i... | Does permutation permute also dependence?
The dependence structure is simply the values of $f(x_1,\cdots,x_n):=P(X_1,\cdots,X_n)$. So by permuting the vectors, you are also permuting the dependence. Nothing is lost (unless you can't keep trac |
55,848 | Convergence of Metropolis Hastings with time varying proposal density | What you are describing is adaptive MCMC if your proposal distribution depends on the history of the chain, and is thus time dependent. There is a lot of theory about ergodicity of adaptive mcmc. There are essentially two main conditions:
Diminishing Adaptation: The adaptation on the proposal distribution should dimin... | Convergence of Metropolis Hastings with time varying proposal density | What you are describing is adaptive MCMC if your proposal distribution depends on the history of the chain, and is thus time dependent. There is a lot of theory about ergodicity of adaptive mcmc. Ther | Convergence of Metropolis Hastings with time varying proposal density
What you are describing is adaptive MCMC if your proposal distribution depends on the history of the chain, and is thus time dependent. There is a lot of theory about ergodicity of adaptive mcmc. There are essentially two main conditions:
Diminishin... | Convergence of Metropolis Hastings with time varying proposal density
What you are describing is adaptive MCMC if your proposal distribution depends on the history of the chain, and is thus time dependent. There is a lot of theory about ergodicity of adaptive mcmc. Ther |
55,849 | Are two Random Variables Independent if their support has a dependency? | I've convinced myself of the answer, so I'm answering my own question.
I've determined that if there is a dependency between $X$ and $Y$ in the support of a bivariate pdf, then $X$ and $Y$ cannot be independent. To be sure, there is a Lemma (4.2.7 in Casella and Berger's Statistical Inference, 2d) that states: Let ... | Are two Random Variables Independent if their support has a dependency? | I've convinced myself of the answer, so I'm answering my own question.
I've determined that if there is a dependency between $X$ and $Y$ in the support of a bivariate pdf, then $X$ and $Y$ cannot be | Are two Random Variables Independent if their support has a dependency?
I've convinced myself of the answer, so I'm answering my own question.
I've determined that if there is a dependency between $X$ and $Y$ in the support of a bivariate pdf, then $X$ and $Y$ cannot be independent. To be sure, there is a Lemma (4.2... | Are two Random Variables Independent if their support has a dependency?
I've convinced myself of the answer, so I'm answering my own question.
I've determined that if there is a dependency between $X$ and $Y$ in the support of a bivariate pdf, then $X$ and $Y$ cannot be |
55,850 | When you do PCA (or any dimensionality reduction), what is "the number of dimensions"? | (I cannot watch the video right now so this answer is to some extent a guess of what is meant)
First of all, yes we mostly talk about variates spanning the dimensions. However, it is also possible to take the opposite view (this is sometimes calles R-mode vs. Q-mode analysis).
Let me take a detour to cluster analysis ... | When you do PCA (or any dimensionality reduction), what is "the number of dimensions"? | (I cannot watch the video right now so this answer is to some extent a guess of what is meant)
First of all, yes we mostly talk about variates spanning the dimensions. However, it is also possible to | When you do PCA (or any dimensionality reduction), what is "the number of dimensions"?
(I cannot watch the video right now so this answer is to some extent a guess of what is meant)
First of all, yes we mostly talk about variates spanning the dimensions. However, it is also possible to take the opposite view (this is s... | When you do PCA (or any dimensionality reduction), what is "the number of dimensions"?
(I cannot watch the video right now so this answer is to some extent a guess of what is meant)
First of all, yes we mostly talk about variates spanning the dimensions. However, it is also possible to |
55,851 | When you do PCA (or any dimensionality reduction), what is "the number of dimensions"? | An extensive discussion is already provided here in the answer by cbeleites, and under similar questions (PCA and Correspondence analysis in their relation to Biplot), so I'll just comment briefly on the specific video.
As the narrator never mentions "scores" or "loadings" explicitly throughout the video, and the term ... | When you do PCA (or any dimensionality reduction), what is "the number of dimensions"? | An extensive discussion is already provided here in the answer by cbeleites, and under similar questions (PCA and Correspondence analysis in their relation to Biplot), so I'll just comment briefly on | When you do PCA (or any dimensionality reduction), what is "the number of dimensions"?
An extensive discussion is already provided here in the answer by cbeleites, and under similar questions (PCA and Correspondence analysis in their relation to Biplot), so I'll just comment briefly on the specific video.
As the narrat... | When you do PCA (or any dimensionality reduction), what is "the number of dimensions"?
An extensive discussion is already provided here in the answer by cbeleites, and under similar questions (PCA and Correspondence analysis in their relation to Biplot), so I'll just comment briefly on |
55,852 | When you do PCA (or any dimensionality reduction), what is "the number of dimensions"? | The definition of a vector space is quite general and there are numerous ways to represent data as vectors in a vector space.
From my cursory examination, they may be doing the following?
Let $i = 1, \ldots, m$ index the gene.
Let $j = 1, \ldots, n$ index the cell.
Let $x_{i,j}$ denote the gene expression level of gen... | When you do PCA (or any dimensionality reduction), what is "the number of dimensions"? | The definition of a vector space is quite general and there are numerous ways to represent data as vectors in a vector space.
From my cursory examination, they may be doing the following?
Let $i = 1, | When you do PCA (or any dimensionality reduction), what is "the number of dimensions"?
The definition of a vector space is quite general and there are numerous ways to represent data as vectors in a vector space.
From my cursory examination, they may be doing the following?
Let $i = 1, \ldots, m$ index the gene.
Let $... | When you do PCA (or any dimensionality reduction), what is "the number of dimensions"?
The definition of a vector space is quite general and there are numerous ways to represent data as vectors in a vector space.
From my cursory examination, they may be doing the following?
Let $i = 1, |
55,853 | When you do PCA (or any dimensionality reduction), what is "the number of dimensions"? | I don't like these videos. They only make understanding PCA more difficult by bringing in irrelevant details. Also, they're long and wordy.
The idea of PCA is very simple when it comes to applications. You have a several series of data, call them variables. Say you have N variables (series) $x_1(t),x_2(t),\dots,x_N(t)$... | When you do PCA (or any dimensionality reduction), what is "the number of dimensions"? | I don't like these videos. They only make understanding PCA more difficult by bringing in irrelevant details. Also, they're long and wordy.
The idea of PCA is very simple when it comes to applications | When you do PCA (or any dimensionality reduction), what is "the number of dimensions"?
I don't like these videos. They only make understanding PCA more difficult by bringing in irrelevant details. Also, they're long and wordy.
The idea of PCA is very simple when it comes to applications. You have a several series of da... | When you do PCA (or any dimensionality reduction), what is "the number of dimensions"?
I don't like these videos. They only make understanding PCA more difficult by bringing in irrelevant details. Also, they're long and wordy.
The idea of PCA is very simple when it comes to applications |
55,854 | Derivation of Gini Impurity Formula | I remember reading this exact thing on Wikipedia thinking it was a typo. It's not though. And the math is really simple. Note that $f_if_k$ corresponds to the probability of observing an $i$ followed by a $k$ from two independent draws from the distribution $f$. Therefore, if you sum over the probabilities of all $(i,k... | Derivation of Gini Impurity Formula | I remember reading this exact thing on Wikipedia thinking it was a typo. It's not though. And the math is really simple. Note that $f_if_k$ corresponds to the probability of observing an $i$ followed | Derivation of Gini Impurity Formula
I remember reading this exact thing on Wikipedia thinking it was a typo. It's not though. And the math is really simple. Note that $f_if_k$ corresponds to the probability of observing an $i$ followed by a $k$ from two independent draws from the distribution $f$. Therefore, if you sum... | Derivation of Gini Impurity Formula
I remember reading this exact thing on Wikipedia thinking it was a typo. It's not though. And the math is really simple. Note that $f_if_k$ corresponds to the probability of observing an $i$ followed |
55,855 | Derivation of Gini Impurity Formula | Here is a snippet from my answer here. The easiest way (for me at least) to understand
$1-\sum f_i^2$ = $\sum_{i \neq k} f_if_k$
is by visually representing each of the elements in this equation. We'll assume that there are 4 labels below; however, this will scale to n values.
The value 1 is simply the sum of all p... | Derivation of Gini Impurity Formula | Here is a snippet from my answer here. The easiest way (for me at least) to understand
$1-\sum f_i^2$ = $\sum_{i \neq k} f_if_k$
is by visually representing each of the elements in this equation. W | Derivation of Gini Impurity Formula
Here is a snippet from my answer here. The easiest way (for me at least) to understand
$1-\sum f_i^2$ = $\sum_{i \neq k} f_if_k$
is by visually representing each of the elements in this equation. We'll assume that there are 4 labels below; however, this will scale to n values.
Th... | Derivation of Gini Impurity Formula
Here is a snippet from my answer here. The easiest way (for me at least) to understand
$1-\sum f_i^2$ = $\sum_{i \neq k} f_if_k$
is by visually representing each of the elements in this equation. W |
55,856 | What are shortcomings of PCA as a dimensionality reduction technique compared to t-SNE? | It all depends on how you understand "similarity" and what the goal of your transformation into the low-dimensional representation is.
PCA does not attempt to group "similar" points, whatever this "similarity" may be. PCA is a method of constructing a particular linear transformation which results in new coordinates o... | What are shortcomings of PCA as a dimensionality reduction technique compared to t-SNE? | It all depends on how you understand "similarity" and what the goal of your transformation into the low-dimensional representation is.
PCA does not attempt to group "similar" points, whatever this "s | What are shortcomings of PCA as a dimensionality reduction technique compared to t-SNE?
It all depends on how you understand "similarity" and what the goal of your transformation into the low-dimensional representation is.
PCA does not attempt to group "similar" points, whatever this "similarity" may be. PCA is a meth... | What are shortcomings of PCA as a dimensionality reduction technique compared to t-SNE?
It all depends on how you understand "similarity" and what the goal of your transformation into the low-dimensional representation is.
PCA does not attempt to group "similar" points, whatever this "s |
55,857 | rpart, Cross Validation. [closed] | The rpart package's plotcp function plots the Complexity Parameter Table for an rpart tree fit on the training dataset. You don't need to supply any additional validation datasets when using the plotcp function.
The Rpart implementation first fits a fully grown tree on the entire data $D$ with $T$ terminal nodes. After... | rpart, Cross Validation. [closed] | The rpart package's plotcp function plots the Complexity Parameter Table for an rpart tree fit on the training dataset. You don't need to supply any additional validation datasets when using the plotc | rpart, Cross Validation. [closed]
The rpart package's plotcp function plots the Complexity Parameter Table for an rpart tree fit on the training dataset. You don't need to supply any additional validation datasets when using the plotcp function.
The Rpart implementation first fits a fully grown tree on the entire data ... | rpart, Cross Validation. [closed]
The rpart package's plotcp function plots the Complexity Parameter Table for an rpart tree fit on the training dataset. You don't need to supply any additional validation datasets when using the plotc |
55,858 | Combining uncertain measurements | If I'm understanding your question properly, this sounds like you need Inverse variance weighting.
https://en.wikipedia.org/wiki/Inverse-variance_weighting
The estimate of your $x'$ that would minimize the variance (so giving you the "best guess") will be given by
\begin{equation}
\hat{x} = \frac{\Sigma_ix_i/\sigma^2_... | Combining uncertain measurements | If I'm understanding your question properly, this sounds like you need Inverse variance weighting.
https://en.wikipedia.org/wiki/Inverse-variance_weighting
The estimate of your $x'$ that would minimiz | Combining uncertain measurements
If I'm understanding your question properly, this sounds like you need Inverse variance weighting.
https://en.wikipedia.org/wiki/Inverse-variance_weighting
The estimate of your $x'$ that would minimize the variance (so giving you the "best guess") will be given by
\begin{equation}
\hat... | Combining uncertain measurements
If I'm understanding your question properly, this sounds like you need Inverse variance weighting.
https://en.wikipedia.org/wiki/Inverse-variance_weighting
The estimate of your $x'$ that would minimiz |
55,859 | Combining uncertain measurements | And the inverse square of the error on the combined value is the sum of the inverse squares of the individual errors:
$$ \frac{1}{\sigma^2} = \sum_i \frac{1}{\sigma_{x,i}^2}$$
For a derivation, see the section on statistical methods of any experimental physics handbook.
(The fact that you have each measurement has an x... | Combining uncertain measurements | And the inverse square of the error on the combined value is the sum of the inverse squares of the individual errors:
$$ \frac{1}{\sigma^2} = \sum_i \frac{1}{\sigma_{x,i}^2}$$
For a derivation, see th | Combining uncertain measurements
And the inverse square of the error on the combined value is the sum of the inverse squares of the individual errors:
$$ \frac{1}{\sigma^2} = \sum_i \frac{1}{\sigma_{x,i}^2}$$
For a derivation, see the section on statistical methods of any experimental physics handbook.
(The fact that y... | Combining uncertain measurements
And the inverse square of the error on the combined value is the sum of the inverse squares of the individual errors:
$$ \frac{1}{\sigma^2} = \sum_i \frac{1}{\sigma_{x,i}^2}$$
For a derivation, see th |
55,860 | How to interpret the clusplot in R | The clusplot uses PCA to draw the data. It uses the first two principal components to explain the data.
You can read more about it here Making sense of principal component analysis, eigenvectors & eigenvalues.
Principal components are the (orthogonal) axes that along them the data has the most variability, if your d... | How to interpret the clusplot in R | The clusplot uses PCA to draw the data. It uses the first two principal components to explain the data.
You can read more about it here Making sense of principal component analysis, eigenvectors & e | How to interpret the clusplot in R
The clusplot uses PCA to draw the data. It uses the first two principal components to explain the data.
You can read more about it here Making sense of principal component analysis, eigenvectors & eigenvalues.
Principal components are the (orthogonal) axes that along them the data ... | How to interpret the clusplot in R
The clusplot uses PCA to draw the data. It uses the first two principal components to explain the data.
You can read more about it here Making sense of principal component analysis, eigenvectors & e |
55,861 | In layman's terms, why is Naive Bayes the dominant algorithm used for text-classification? | I'm taking your word for Naive Bayes' popularity here as language processing isn't my specialty:
One reason NB is useful is the bias–variance tradeoff. Spam/sentiment type data are often noisy and usually high-dimensional (more predictors than samples, $n \ll p$). The naive assumption that predictors are independent o... | In layman's terms, why is Naive Bayes the dominant algorithm used for text-classification? | I'm taking your word for Naive Bayes' popularity here as language processing isn't my specialty:
One reason NB is useful is the bias–variance tradeoff. Spam/sentiment type data are often noisy and us | In layman's terms, why is Naive Bayes the dominant algorithm used for text-classification?
I'm taking your word for Naive Bayes' popularity here as language processing isn't my specialty:
One reason NB is useful is the bias–variance tradeoff. Spam/sentiment type data are often noisy and usually high-dimensional (more ... | In layman's terms, why is Naive Bayes the dominant algorithm used for text-classification?
I'm taking your word for Naive Bayes' popularity here as language processing isn't my specialty:
One reason NB is useful is the bias–variance tradeoff. Spam/sentiment type data are often noisy and us |
55,862 | Are there any implementations/examples of hierarchical classifiers? | I couldn't find an implementation of Hierarchical Classification on scikit-learn official documentation. But I found this repository recently. This module is based on scikit-learn's interfaces and conventions. I hope this will be useful.
https://github.com/globality-corp/sklearn-hierarchical-classification
It's possibl... | Are there any implementations/examples of hierarchical classifiers? | I couldn't find an implementation of Hierarchical Classification on scikit-learn official documentation. But I found this repository recently. This module is based on scikit-learn's interfaces and con | Are there any implementations/examples of hierarchical classifiers?
I couldn't find an implementation of Hierarchical Classification on scikit-learn official documentation. But I found this repository recently. This module is based on scikit-learn's interfaces and conventions. I hope this will be useful.
https://github... | Are there any implementations/examples of hierarchical classifiers?
I couldn't find an implementation of Hierarchical Classification on scikit-learn official documentation. But I found this repository recently. This module is based on scikit-learn's interfaces and con |
55,863 | Are there any implementations/examples of hierarchical classifiers? | If anyone stumbles across this, check out the package I developed to handle this type of data.
Here's the tutorial investigating antibiotic resistance
The peer-reviewed publication is Espinoza-Dupont et al. 2021 | Are there any implementations/examples of hierarchical classifiers? | If anyone stumbles across this, check out the package I developed to handle this type of data.
Here's the tutorial investigating antibiotic resistance
The peer-reviewed publication is Espinoza-Dupont | Are there any implementations/examples of hierarchical classifiers?
If anyone stumbles across this, check out the package I developed to handle this type of data.
Here's the tutorial investigating antibiotic resistance
The peer-reviewed publication is Espinoza-Dupont et al. 2021 | Are there any implementations/examples of hierarchical classifiers?
If anyone stumbles across this, check out the package I developed to handle this type of data.
Here's the tutorial investigating antibiotic resistance
The peer-reviewed publication is Espinoza-Dupont |
55,864 | Are there any implementations/examples of hierarchical classifiers? | We just released a new library compatible with scikit-learn to create local hierarchical classifiers.
It can be easily installed with pip install hiclass or conda install hiclass. Documentation and examples can be found at https://gitlab.com/dacs-hpi/hiclass.
I hope this will be useful for future readers. :) | Are there any implementations/examples of hierarchical classifiers? | We just released a new library compatible with scikit-learn to create local hierarchical classifiers.
It can be easily installed with pip install hiclass or conda install hiclass. Documentation and ex | Are there any implementations/examples of hierarchical classifiers?
We just released a new library compatible with scikit-learn to create local hierarchical classifiers.
It can be easily installed with pip install hiclass or conda install hiclass. Documentation and examples can be found at https://gitlab.com/dacs-hpi/h... | Are there any implementations/examples of hierarchical classifiers?
We just released a new library compatible with scikit-learn to create local hierarchical classifiers.
It can be easily installed with pip install hiclass or conda install hiclass. Documentation and ex |
55,865 | What is a hypothesis class in SVM? | In classification in general, the hypothesis class is the set of possible classification functions you're considering; the learning algorithm picks a function from the hypothesis class.
For a decision tree learner, the hypothesis class would just be the set of all possible decision trees.
For a primal SVM, this is the ... | What is a hypothesis class in SVM? | In classification in general, the hypothesis class is the set of possible classification functions you're considering; the learning algorithm picks a function from the hypothesis class.
For a decision | What is a hypothesis class in SVM?
In classification in general, the hypothesis class is the set of possible classification functions you're considering; the learning algorithm picks a function from the hypothesis class.
For a decision tree learner, the hypothesis class would just be the set of all possible decision tr... | What is a hypothesis class in SVM?
In classification in general, the hypothesis class is the set of possible classification functions you're considering; the learning algorithm picks a function from the hypothesis class.
For a decision |
55,866 | How to determine if a matrix is close to being negative (semi-)definite? | As Wikipedia says: "A Hermitian $n \times n$ matrix $A$ is defined as being positive-definite (PD) if the scalar $b^T A b$ is positive for every non-zero column vector $b$ of $n$ real numbers". In addition, $A$ can be equivalently be defined as PD in terms of its eigenvalues $\lambda$ (all being positive) and in terms ... | How to determine if a matrix is close to being negative (semi-)definite? | As Wikipedia says: "A Hermitian $n \times n$ matrix $A$ is defined as being positive-definite (PD) if the scalar $b^T A b$ is positive for every non-zero column vector $b$ of $n$ real numbers". In add | How to determine if a matrix is close to being negative (semi-)definite?
As Wikipedia says: "A Hermitian $n \times n$ matrix $A$ is defined as being positive-definite (PD) if the scalar $b^T A b$ is positive for every non-zero column vector $b$ of $n$ real numbers". In addition, $A$ can be equivalently be defined as PD... | How to determine if a matrix is close to being negative (semi-)definite?
As Wikipedia says: "A Hermitian $n \times n$ matrix $A$ is defined as being positive-definite (PD) if the scalar $b^T A b$ is positive for every non-zero column vector $b$ of $n$ real numbers". In add |
55,867 | How to determine if a matrix is close to being negative (semi-)definite? | For a real symmetric matrix $M=P\,\text{diag}(\lambda_1,\dots,\lambda_n)\, P^T$, the nearest (in Frobenius norm) PSD matrix is obtained by thresholding the eigenvalues at 0:$$\text{Proj}_{\mathcal{S}_n^+}(M)=P\,\text{diag}\big(\max(\lambda_1,0),\dots,\max(\lambda_n,0)\big)\, P^T.$$
See e.g. here. Hence, one interpretab... | How to determine if a matrix is close to being negative (semi-)definite? | For a real symmetric matrix $M=P\,\text{diag}(\lambda_1,\dots,\lambda_n)\, P^T$, the nearest (in Frobenius norm) PSD matrix is obtained by thresholding the eigenvalues at 0:$$\text{Proj}_{\mathcal{S}_ | How to determine if a matrix is close to being negative (semi-)definite?
For a real symmetric matrix $M=P\,\text{diag}(\lambda_1,\dots,\lambda_n)\, P^T$, the nearest (in Frobenius norm) PSD matrix is obtained by thresholding the eigenvalues at 0:$$\text{Proj}_{\mathcal{S}_n^+}(M)=P\,\text{diag}\big(\max(\lambda_1,0),\d... | How to determine if a matrix is close to being negative (semi-)definite?
For a real symmetric matrix $M=P\,\text{diag}(\lambda_1,\dots,\lambda_n)\, P^T$, the nearest (in Frobenius norm) PSD matrix is obtained by thresholding the eigenvalues at 0:$$\text{Proj}_{\mathcal{S}_ |
55,868 | How to show the inconsistency of the OLS estimator for unit-root AR(1) processes by simulation? | You will not be able to show this result (by simulation or otherwise) because it does not hold. When the true AR parameter is unity, the OLS estimator is superconsistent, not inconsistent. See for example the discussion in Hamilton's Time Series Analysis, section "Asymptotic Properties of a First-Order Autoregression w... | How to show the inconsistency of the OLS estimator for unit-root AR(1) processes by simulation? | You will not be able to show this result (by simulation or otherwise) because it does not hold. When the true AR parameter is unity, the OLS estimator is superconsistent, not inconsistent. See for exa | How to show the inconsistency of the OLS estimator for unit-root AR(1) processes by simulation?
You will not be able to show this result (by simulation or otherwise) because it does not hold. When the true AR parameter is unity, the OLS estimator is superconsistent, not inconsistent. See for example the discussion in H... | How to show the inconsistency of the OLS estimator for unit-root AR(1) processes by simulation?
You will not be able to show this result (by simulation or otherwise) because it does not hold. When the true AR parameter is unity, the OLS estimator is superconsistent, not inconsistent. See for exa |
55,869 | How to show the inconsistency of the OLS estimator for unit-root AR(1) processes by simulation? | The unit root issues in regression are usually associated with the presence of it in the dependent or independent variables. For instance, if you regress one variable on another and both of them have unit roots, then you'll likely to end up with a spurious regression.
Otherwise, the way the answers went on so war was o... | How to show the inconsistency of the OLS estimator for unit-root AR(1) processes by simulation? | The unit root issues in regression are usually associated with the presence of it in the dependent or independent variables. For instance, if you regress one variable on another and both of them have | How to show the inconsistency of the OLS estimator for unit-root AR(1) processes by simulation?
The unit root issues in regression are usually associated with the presence of it in the dependent or independent variables. For instance, if you regress one variable on another and both of them have unit roots, then you'll ... | How to show the inconsistency of the OLS estimator for unit-root AR(1) processes by simulation?
The unit root issues in regression are usually associated with the presence of it in the dependent or independent variables. For instance, if you regress one variable on another and both of them have |
55,870 | Expected value of $h(X)$. When can the order of $E$ and $h$ be inverted? | In real analysis and probability theory there is an elegant result called Jensen's inequality. What this says is that for any random variable $X$ and a convex function $h$ we have
$$h\left(\mathbb{E} [X]\right) \leq \mathbb{E} \left[ h(X) \right]$$
and the inequality is reversed if $h$ is concave, i.e.
$$h\left(\mathbb... | Expected value of $h(X)$. When can the order of $E$ and $h$ be inverted? | In real analysis and probability theory there is an elegant result called Jensen's inequality. What this says is that for any random variable $X$ and a convex function $h$ we have
$$h\left(\mathbb{E} | Expected value of $h(X)$. When can the order of $E$ and $h$ be inverted?
In real analysis and probability theory there is an elegant result called Jensen's inequality. What this says is that for any random variable $X$ and a convex function $h$ we have
$$h\left(\mathbb{E} [X]\right) \leq \mathbb{E} \left[ h(X) \right]$... | Expected value of $h(X)$. When can the order of $E$ and $h$ be inverted?
In real analysis and probability theory there is an elegant result called Jensen's inequality. What this says is that for any random variable $X$ and a convex function $h$ we have
$$h\left(\mathbb{E} |
55,871 | Understanding Word2Vec | what are my actual word vectors in the end?
The actual word vectors are the hidden representations $h$
Basically, multiplying a one hot vector with $\mathbf{W_{V\times N}}$ will give you a $1$$\times$$N$ vector which represents the word vector for the one hot you entered.
Here we multiply the one hot $1$$\times$$5$ f... | Understanding Word2Vec | what are my actual word vectors in the end?
The actual word vectors are the hidden representations $h$
Basically, multiplying a one hot vector with $\mathbf{W_{V\times N}}$ will give you a $1$$\times | Understanding Word2Vec
what are my actual word vectors in the end?
The actual word vectors are the hidden representations $h$
Basically, multiplying a one hot vector with $\mathbf{W_{V\times N}}$ will give you a $1$$\times$$N$ vector which represents the word vector for the one hot you entered.
Here we multiply the o... | Understanding Word2Vec
what are my actual word vectors in the end?
The actual word vectors are the hidden representations $h$
Basically, multiplying a one hot vector with $\mathbf{W_{V\times N}}$ will give you a $1$$\times |
55,872 | How to fit a generalized logistic function? | Given the binary response $y_i$ and the covariate $x_i$, $i=1,2,\dots,n$, the likelihood for your model is
$$
L(\beta_0,\beta_1,p_\text{min},p_\text{max})=\prod_{i=1}^n p_i^{y_i}(1-p_i)^{1-y_i}
$$
where each
$$
p_i=p_\text{min} + (p_\text{max} - p_\text{min})\frac1{1+\exp(-(\beta_0 + \beta_1 x_i)}.
$$
Just write a func... | How to fit a generalized logistic function? | Given the binary response $y_i$ and the covariate $x_i$, $i=1,2,\dots,n$, the likelihood for your model is
$$
L(\beta_0,\beta_1,p_\text{min},p_\text{max})=\prod_{i=1}^n p_i^{y_i}(1-p_i)^{1-y_i}
$$
whe | How to fit a generalized logistic function?
Given the binary response $y_i$ and the covariate $x_i$, $i=1,2,\dots,n$, the likelihood for your model is
$$
L(\beta_0,\beta_1,p_\text{min},p_\text{max})=\prod_{i=1}^n p_i^{y_i}(1-p_i)^{1-y_i}
$$
where each
$$
p_i=p_\text{min} + (p_\text{max} - p_\text{min})\frac1{1+\exp(-(\... | How to fit a generalized logistic function?
Given the binary response $y_i$ and the covariate $x_i$, $i=1,2,\dots,n$, the likelihood for your model is
$$
L(\beta_0,\beta_1,p_\text{min},p_\text{max})=\prod_{i=1}^n p_i^{y_i}(1-p_i)^{1-y_i}
$$
whe |
55,873 | Is house price prediction a regression or a time series problem? | While the other answer is correct that the response variable can be modelled as a linear regression - you are dealing with house prices. As such, your dataset will likely suffer from what is called time series induced heteroscedasticity.
What this basically means is that since your houses will vary by age - i.e. some h... | Is house price prediction a regression or a time series problem? | While the other answer is correct that the response variable can be modelled as a linear regression - you are dealing with house prices. As such, your dataset will likely suffer from what is called ti | Is house price prediction a regression or a time series problem?
While the other answer is correct that the response variable can be modelled as a linear regression - you are dealing with house prices. As such, your dataset will likely suffer from what is called time series induced heteroscedasticity.
What this basical... | Is house price prediction a regression or a time series problem?
While the other answer is correct that the response variable can be modelled as a linear regression - you are dealing with house prices. As such, your dataset will likely suffer from what is called ti |
55,874 | Is house price prediction a regression or a time series problem? | You needn't choose one or the other. Price can be modeled as a function both of its own past values and of independent variables. The latter may themselves have lagged values that additionally help predict price. | Is house price prediction a regression or a time series problem? | You needn't choose one or the other. Price can be modeled as a function both of its own past values and of independent variables. The latter may themselves have lagged values that additionally help | Is house price prediction a regression or a time series problem?
You needn't choose one or the other. Price can be modeled as a function both of its own past values and of independent variables. The latter may themselves have lagged values that additionally help predict price. | Is house price prediction a regression or a time series problem?
You needn't choose one or the other. Price can be modeled as a function both of its own past values and of independent variables. The latter may themselves have lagged values that additionally help |
55,875 | Is house price prediction a regression or a time series problem? | Your response variable - house price, and predictors - year, city. Am I correct on this? You could model this as a linear regression and predict the house price. | Is house price prediction a regression or a time series problem? | Your response variable - house price, and predictors - year, city. Am I correct on this? You could model this as a linear regression and predict the house price. | Is house price prediction a regression or a time series problem?
Your response variable - house price, and predictors - year, city. Am I correct on this? You could model this as a linear regression and predict the house price. | Is house price prediction a regression or a time series problem?
Your response variable - house price, and predictors - year, city. Am I correct on this? You could model this as a linear regression and predict the house price. |
55,876 | Difference of $R^2$ between OLS with individual dummies to panel fixed effect model? | In essence, yes. The $R^2$ value given for fixed effects regressions is often called the "within $R^2$". If you use stata, the output will give overall, within, and between $R^2$. If you use the plm package in R, it just give the within $R^2$. The basic difference between the overall and within $R^2$ is that the within... | Difference of $R^2$ between OLS with individual dummies to panel fixed effect model? | In essence, yes. The $R^2$ value given for fixed effects regressions is often called the "within $R^2$". If you use stata, the output will give overall, within, and between $R^2$. If you use the plm p | Difference of $R^2$ between OLS with individual dummies to panel fixed effect model?
In essence, yes. The $R^2$ value given for fixed effects regressions is often called the "within $R^2$". If you use stata, the output will give overall, within, and between $R^2$. If you use the plm package in R, it just give the withi... | Difference of $R^2$ between OLS with individual dummies to panel fixed effect model?
In essence, yes. The $R^2$ value given for fixed effects regressions is often called the "within $R^2$". If you use stata, the output will give overall, within, and between $R^2$. If you use the plm p |
55,877 | Difference of $R^2$ between OLS with individual dummies to panel fixed effect model? | I have been looking for the three types of R-squared of the Fixed Effects model outputs in R as well.
Thanks to the help of @paqmo, I was able to manually calculate and reproduce lfe's full and proj R-squared using the model fit from the standard lm package. That said, I am quite certain that the full R-sq is straightf... | Difference of $R^2$ between OLS with individual dummies to panel fixed effect model? | I have been looking for the three types of R-squared of the Fixed Effects model outputs in R as well.
Thanks to the help of @paqmo, I was able to manually calculate and reproduce lfe's full and proj R | Difference of $R^2$ between OLS with individual dummies to panel fixed effect model?
I have been looking for the three types of R-squared of the Fixed Effects model outputs in R as well.
Thanks to the help of @paqmo, I was able to manually calculate and reproduce lfe's full and proj R-squared using the model fit from t... | Difference of $R^2$ between OLS with individual dummies to panel fixed effect model?
I have been looking for the three types of R-squared of the Fixed Effects model outputs in R as well.
Thanks to the help of @paqmo, I was able to manually calculate and reproduce lfe's full and proj R |
55,878 | Hypothesis Testing: Permutation Testing Justification | Generally hypothesis tests are accompanied by extra assumptions that will need to hold (at least when the null is true), so that the null distribution of the test statistic can be obtained; this is as true for nonparametric tests as for parametric ones.
So for example, the usual two sample t-test comes with assumption... | Hypothesis Testing: Permutation Testing Justification | Generally hypothesis tests are accompanied by extra assumptions that will need to hold (at least when the null is true), so that the null distribution of the test statistic can be obtained; this is as | Hypothesis Testing: Permutation Testing Justification
Generally hypothesis tests are accompanied by extra assumptions that will need to hold (at least when the null is true), so that the null distribution of the test statistic can be obtained; this is as true for nonparametric tests as for parametric ones.
So for exam... | Hypothesis Testing: Permutation Testing Justification
Generally hypothesis tests are accompanied by extra assumptions that will need to hold (at least when the null is true), so that the null distribution of the test statistic can be obtained; this is as |
55,879 | Hypothesis Testing: Permutation Testing Justification | You are right that you are testing much broader assumption that the group labels are "random" and play no role in your results. As a proxy to test such hypothesis you use some test statistic that is evaluated on the permuted samples. In this case it is median, but it could something else as well. So you test if the la... | Hypothesis Testing: Permutation Testing Justification | You are right that you are testing much broader assumption that the group labels are "random" and play no role in your results. As a proxy to test such hypothesis you use some test statistic that is | Hypothesis Testing: Permutation Testing Justification
You are right that you are testing much broader assumption that the group labels are "random" and play no role in your results. As a proxy to test such hypothesis you use some test statistic that is evaluated on the permuted samples. In this case it is median, but ... | Hypothesis Testing: Permutation Testing Justification
You are right that you are testing much broader assumption that the group labels are "random" and play no role in your results. As a proxy to test such hypothesis you use some test statistic that is |
55,880 | What is the intuitive sense of the expected value of the sum of two random variables | Recall that for any random variables $X$ and $Y$ with a joint probability distribution function $p(x,y)$, the expected value of $X+Y$ is
$$ \mathbb{E}_{X,Y}[X+Y] = \int_x\int_y (x+y) p(x,y) dydx = \int_x x \int_y p(x,y)dydx + \int_y y \int_x p(x,y) dxdy$$
In the special case that $x$ and $y$ are independent, $p(x,y) = ... | What is the intuitive sense of the expected value of the sum of two random variables | Recall that for any random variables $X$ and $Y$ with a joint probability distribution function $p(x,y)$, the expected value of $X+Y$ is
$$ \mathbb{E}_{X,Y}[X+Y] = \int_x\int_y (x+y) p(x,y) dydx = \in | What is the intuitive sense of the expected value of the sum of two random variables
Recall that for any random variables $X$ and $Y$ with a joint probability distribution function $p(x,y)$, the expected value of $X+Y$ is
$$ \mathbb{E}_{X,Y}[X+Y] = \int_x\int_y (x+y) p(x,y) dydx = \int_x x \int_y p(x,y)dydx + \int_y y ... | What is the intuitive sense of the expected value of the sum of two random variables
Recall that for any random variables $X$ and $Y$ with a joint probability distribution function $p(x,y)$, the expected value of $X+Y$ is
$$ \mathbb{E}_{X,Y}[X+Y] = \int_x\int_y (x+y) p(x,y) dydx = \in |
55,881 | What is the intuitive sense of the expected value of the sum of two random variables | If $X$ and $Y$ are random variables (defined on the same probability space: ignore this remark if it confuses you), then we can regard $(X,Y)$ as a random vector (also called a bivariate random variable) and $X$ and $Y$ individually as special kinds of functions of $(X,Y)$ -- called projections or projection maps if yo... | What is the intuitive sense of the expected value of the sum of two random variables | If $X$ and $Y$ are random variables (defined on the same probability space: ignore this remark if it confuses you), then we can regard $(X,Y)$ as a random vector (also called a bivariate random variab | What is the intuitive sense of the expected value of the sum of two random variables
If $X$ and $Y$ are random variables (defined on the same probability space: ignore this remark if it confuses you), then we can regard $(X,Y)$ as a random vector (also called a bivariate random variable) and $X$ and $Y$ individually as... | What is the intuitive sense of the expected value of the sum of two random variables
If $X$ and $Y$ are random variables (defined on the same probability space: ignore this remark if it confuses you), then we can regard $(X,Y)$ as a random vector (also called a bivariate random variab |
55,882 | Why does pre-training help avoid the vanishing gradient problem? | Your question touches on two topics:
Preprocessing of the data.
Initialization of weights. For this question there are already good answers: What are good initial weights in a neural network?.
As for the first question, I shall refer to the paper: LeCun et al., Efficient Backprop, section 4.3. It is explained in grea... | Why does pre-training help avoid the vanishing gradient problem? | Your question touches on two topics:
Preprocessing of the data.
Initialization of weights. For this question there are already good answers: What are good initial weights in a neural network?.
As fo | Why does pre-training help avoid the vanishing gradient problem?
Your question touches on two topics:
Preprocessing of the data.
Initialization of weights. For this question there are already good answers: What are good initial weights in a neural network?.
As for the first question, I shall refer to the paper: LeCun... | Why does pre-training help avoid the vanishing gradient problem?
Your question touches on two topics:
Preprocessing of the data.
Initialization of weights. For this question there are already good answers: What are good initial weights in a neural network?.
As fo |
55,883 | Why does pre-training help avoid the vanishing gradient problem? | I think it does not solve the vanishing gradient problem. The main difference between DBN and a fully-connected feed-forward neural net is that DBN uses a stack of pre-trained restricted Boltzmann machines to initialize the network’s weights. But the root of the vanishing gradient problem is not about the weight initia... | Why does pre-training help avoid the vanishing gradient problem? | I think it does not solve the vanishing gradient problem. The main difference between DBN and a fully-connected feed-forward neural net is that DBN uses a stack of pre-trained restricted Boltzmann mac | Why does pre-training help avoid the vanishing gradient problem?
I think it does not solve the vanishing gradient problem. The main difference between DBN and a fully-connected feed-forward neural net is that DBN uses a stack of pre-trained restricted Boltzmann machines to initialize the network’s weights. But the root... | Why does pre-training help avoid the vanishing gradient problem?
I think it does not solve the vanishing gradient problem. The main difference between DBN and a fully-connected feed-forward neural net is that DBN uses a stack of pre-trained restricted Boltzmann mac |
55,884 | Forecasting/estimating daily hotel room demand | Yes
Yes - but you incorrectly assume ARIMA is the 'standard". There are no standard models. I'd highly recommend reading a time series book (of which there are a number of excellent free books online). They typically will cover using ARIMA models with external regressors, dynamic regression, ETS models, etc.
NA
Maybe;... | Forecasting/estimating daily hotel room demand | Yes
Yes - but you incorrectly assume ARIMA is the 'standard". There are no standard models. I'd highly recommend reading a time series book (of which there are a number of excellent free books online) | Forecasting/estimating daily hotel room demand
Yes
Yes - but you incorrectly assume ARIMA is the 'standard". There are no standard models. I'd highly recommend reading a time series book (of which there are a number of excellent free books online). They typically will cover using ARIMA models with external regressors, ... | Forecasting/estimating daily hotel room demand
Yes
Yes - but you incorrectly assume ARIMA is the 'standard". There are no standard models. I'd highly recommend reading a time series book (of which there are a number of excellent free books online) |
55,885 | Forecasting/estimating daily hotel room demand | Forecasting daily data is the objective which seems on the surface to be an everyday (pun) standard problem. Standard this ain't ! Even free online texts might not be very helpful as "model identification is the problem/opportunity" . Time series models (ARIMA) incorporating predictor series (X) is the suggested answer... | Forecasting/estimating daily hotel room demand | Forecasting daily data is the objective which seems on the surface to be an everyday (pun) standard problem. Standard this ain't ! Even free online texts might not be very helpful as "model identifica | Forecasting/estimating daily hotel room demand
Forecasting daily data is the objective which seems on the surface to be an everyday (pun) standard problem. Standard this ain't ! Even free online texts might not be very helpful as "model identification is the problem/opportunity" . Time series models (ARIMA) incorporati... | Forecasting/estimating daily hotel room demand
Forecasting daily data is the objective which seems on the surface to be an everyday (pun) standard problem. Standard this ain't ! Even free online texts might not be very helpful as "model identifica |
55,886 | Granger test: do I need stationarity? | Some types of nonstationarity are allowed, as long as we can build a model and a testing procedure that account for the specific type of nonstationarity. See Dave Giles' famous blog post "Testing for Granger causality" for the case of unit-root nonstationarity.
But obviously, not all types of nonstationarity can be al... | Granger test: do I need stationarity? | Some types of nonstationarity are allowed, as long as we can build a model and a testing procedure that account for the specific type of nonstationarity. See Dave Giles' famous blog post "Testing for | Granger test: do I need stationarity?
Some types of nonstationarity are allowed, as long as we can build a model and a testing procedure that account for the specific type of nonstationarity. See Dave Giles' famous blog post "Testing for Granger causality" for the case of unit-root nonstationarity.
But obviously, not ... | Granger test: do I need stationarity?
Some types of nonstationarity are allowed, as long as we can build a model and a testing procedure that account for the specific type of nonstationarity. See Dave Giles' famous blog post "Testing for |
55,887 | What's the difference between $\ell_1$-SVM, $\ell_2$-SVM and LS-SVM loss functions? | Consider the input $\{x_i,y_i\}^N:x_i\in \mathbb{R}^p,y_i\in\{-1,1\}$.
The common $\ell_2$-regularized $\ell_1$-SVM minimizes the following loss:
$$
\left\{\begin{matrix}
\min_{w_i,e_i}{1\over2}\|w\|_2^2+{C\over2}\sum_{i=1}^n\xi_i
\\
\xi_i=\max{(0,1-y_i\cdot w\cdot(\phi(x)+b))}\space\forall i
\end{matrix}\right.
$$
O... | What's the difference between $\ell_1$-SVM, $\ell_2$-SVM and LS-SVM loss functions? | Consider the input $\{x_i,y_i\}^N:x_i\in \mathbb{R}^p,y_i\in\{-1,1\}$.
The common $\ell_2$-regularized $\ell_1$-SVM minimizes the following loss:
$$
\left\{\begin{matrix}
\min_{w_i,e_i}{1\over2}\|w\| | What's the difference between $\ell_1$-SVM, $\ell_2$-SVM and LS-SVM loss functions?
Consider the input $\{x_i,y_i\}^N:x_i\in \mathbb{R}^p,y_i\in\{-1,1\}$.
The common $\ell_2$-regularized $\ell_1$-SVM minimizes the following loss:
$$
\left\{\begin{matrix}
\min_{w_i,e_i}{1\over2}\|w\|_2^2+{C\over2}\sum_{i=1}^n\xi_i
\\
... | What's the difference between $\ell_1$-SVM, $\ell_2$-SVM and LS-SVM loss functions?
Consider the input $\{x_i,y_i\}^N:x_i\in \mathbb{R}^p,y_i\in\{-1,1\}$.
The common $\ell_2$-regularized $\ell_1$-SVM minimizes the following loss:
$$
\left\{\begin{matrix}
\min_{w_i,e_i}{1\over2}\|w\| |
55,888 | How and When to Use Marginalization in Stan | Stan only samples from continuous parameter spaces, so for something like a finite mixture model, it is necessary to do marginalization to use Stan. On the other hand, if you have a hierarchical model where a small number of parameters control the distribution of a large number of parameters, marginalization is probabl... | How and When to Use Marginalization in Stan | Stan only samples from continuous parameter spaces, so for something like a finite mixture model, it is necessary to do marginalization to use Stan. On the other hand, if you have a hierarchical model | How and When to Use Marginalization in Stan
Stan only samples from continuous parameter spaces, so for something like a finite mixture model, it is necessary to do marginalization to use Stan. On the other hand, if you have a hierarchical model where a small number of parameters control the distribution of a large numb... | How and When to Use Marginalization in Stan
Stan only samples from continuous parameter spaces, so for something like a finite mixture model, it is necessary to do marginalization to use Stan. On the other hand, if you have a hierarchical model |
55,889 | Modeling reaction time with glmer | The high AIC value is not a problem in itself: the AIC is a measure of the relative quality of a model; it says something about how good is the fit of a model but only with respect to another model fit on the same dataset. You cannot compare it to other RT models if these are not fit on the same dataset because - for e... | Modeling reaction time with glmer | The high AIC value is not a problem in itself: the AIC is a measure of the relative quality of a model; it says something about how good is the fit of a model but only with respect to another model fi | Modeling reaction time with glmer
The high AIC value is not a problem in itself: the AIC is a measure of the relative quality of a model; it says something about how good is the fit of a model but only with respect to another model fit on the same dataset. You cannot compare it to other RT models if these are not fit o... | Modeling reaction time with glmer
The high AIC value is not a problem in itself: the AIC is a measure of the relative quality of a model; it says something about how good is the fit of a model but only with respect to another model fi |
55,890 | Modeling reaction time with glmer | It is not correct to say what you propose. The point estimate of the effect of treatments is 4.614. So the model is not saying "no effect". The standard error of that estimate is 2.709, so the p-value is 0.08 (which many people would say was suggestive of "significance".) You only had 22 subjects (presumably 11 per gro... | Modeling reaction time with glmer | It is not correct to say what you propose. The point estimate of the effect of treatments is 4.614. So the model is not saying "no effect". The standard error of that estimate is 2.709, so the p-value | Modeling reaction time with glmer
It is not correct to say what you propose. The point estimate of the effect of treatments is 4.614. So the model is not saying "no effect". The standard error of that estimate is 2.709, so the p-value is 0.08 (which many people would say was suggestive of "significance".) You only had ... | Modeling reaction time with glmer
It is not correct to say what you propose. The point estimate of the effect of treatments is 4.614. So the model is not saying "no effect". The standard error of that estimate is 2.709, so the p-value |
55,891 | Asymptotic normality: do the following convergences hold? | This can be solved from basic principles. At the end I'll explain the underlying idea.
Let $X_n$ be a sequence of iid standard Normal variables and, independently of it, let $Y_n$ also be such a sequence. Independently of both of them let $U_n$ be a sequence of independent Bernoulli variables with parameter $1/n$: th... | Asymptotic normality: do the following convergences hold? | This can be solved from basic principles. At the end I'll explain the underlying idea.
Let $X_n$ be a sequence of iid standard Normal variables and, independently of it, let $Y_n$ also be such a sequ | Asymptotic normality: do the following convergences hold?
This can be solved from basic principles. At the end I'll explain the underlying idea.
Let $X_n$ be a sequence of iid standard Normal variables and, independently of it, let $Y_n$ also be such a sequence. Independently of both of them let $U_n$ be a sequence o... | Asymptotic normality: do the following convergences hold?
This can be solved from basic principles. At the end I'll explain the underlying idea.
Let $X_n$ be a sequence of iid standard Normal variables and, independently of it, let $Y_n$ also be such a sequ |
55,892 | Why do we need to take the transpose of the data for PCA? | We do not need to.
It is a common and long-standing convention in statistics that data matrices have observations in rows and variables in columns. In your case, you indeed have $1000$ observations of $9$ variables. So it would be standard to organize your data in a matrix of $1000\times 9$ size. Most standard PCA impl... | Why do we need to take the transpose of the data for PCA? | We do not need to.
It is a common and long-standing convention in statistics that data matrices have observations in rows and variables in columns. In your case, you indeed have $1000$ observations of | Why do we need to take the transpose of the data for PCA?
We do not need to.
It is a common and long-standing convention in statistics that data matrices have observations in rows and variables in columns. In your case, you indeed have $1000$ observations of $9$ variables. So it would be standard to organize your data ... | Why do we need to take the transpose of the data for PCA?
We do not need to.
It is a common and long-standing convention in statistics that data matrices have observations in rows and variables in columns. In your case, you indeed have $1000$ observations of |
55,893 | Durbin-Watson test and biological (non time-series) data | (1) There is some correlation in the ordering of the observations. In this case, (part of) the reason is that the observations are ordered by Cult (a factor indicating the cultivator of the cabbages). And because the first cultivator is mostly associated with negative residuals and the second cultivator mostly with pos... | Durbin-Watson test and biological (non time-series) data | (1) There is some correlation in the ordering of the observations. In this case, (part of) the reason is that the observations are ordered by Cult (a factor indicating the cultivator of the cabbages). | Durbin-Watson test and biological (non time-series) data
(1) There is some correlation in the ordering of the observations. In this case, (part of) the reason is that the observations are ordered by Cult (a factor indicating the cultivator of the cabbages). And because the first cultivator is mostly associated with neg... | Durbin-Watson test and biological (non time-series) data
(1) There is some correlation in the ordering of the observations. In this case, (part of) the reason is that the observations are ordered by Cult (a factor indicating the cultivator of the cabbages). |
55,894 | How to gain knowledge from dataset using regressions in R [closed] | The most important thing to do is for you to check if the model makes sense. You have fit a linear model to three continuous predictors, you need to make sure that it makes sense to do so You should look at scatterplots of age, height, and weight against y, and adjust the fits of these predictors if needed.
Assuming ... | How to gain knowledge from dataset using regressions in R [closed] | The most important thing to do is for you to check if the model makes sense. You have fit a linear model to three continuous predictors, you need to make sure that it makes sense to do so You should | How to gain knowledge from dataset using regressions in R [closed]
The most important thing to do is for you to check if the model makes sense. You have fit a linear model to three continuous predictors, you need to make sure that it makes sense to do so You should look at scatterplots of age, height, and weight agai... | How to gain knowledge from dataset using regressions in R [closed]
The most important thing to do is for you to check if the model makes sense. You have fit a linear model to three continuous predictors, you need to make sure that it makes sense to do so You should |
55,895 | How to gain knowledge from dataset using regressions in R [closed] | Because there can be dependencies between the predictor variables, it is possible that say X1 looks significant when X2 is left out. But, because X1 and X2 are highly dependent, X1 may appear non-significant when X2 is included in the model. With four predictor variables, there are $2^4 -1$ possible non-empty models. ... | How to gain knowledge from dataset using regressions in R [closed] | Because there can be dependencies between the predictor variables, it is possible that say X1 looks significant when X2 is left out. But, because X1 and X2 are highly dependent, X1 may appear non-sign | How to gain knowledge from dataset using regressions in R [closed]
Because there can be dependencies between the predictor variables, it is possible that say X1 looks significant when X2 is left out. But, because X1 and X2 are highly dependent, X1 may appear non-significant when X2 is included in the model. With four ... | How to gain knowledge from dataset using regressions in R [closed]
Because there can be dependencies between the predictor variables, it is possible that say X1 looks significant when X2 is left out. But, because X1 and X2 are highly dependent, X1 may appear non-sign |
55,896 | How to transform a unit root process to a stationary process? | If a process has a unit root (a stochastic trend) and you want to make it stationary, you need to difference it. In other words, if $x_t\sim I(1)$, then $\Delta x_t:=x_t-x_{t-1} \sim I(0)$.
Without differencing you will not get rid of the unit root. E.g. subtracting a deterministic trend will not help because a unit r... | How to transform a unit root process to a stationary process? | If a process has a unit root (a stochastic trend) and you want to make it stationary, you need to difference it. In other words, if $x_t\sim I(1)$, then $\Delta x_t:=x_t-x_{t-1} \sim I(0)$.
Without d | How to transform a unit root process to a stationary process?
If a process has a unit root (a stochastic trend) and you want to make it stationary, you need to difference it. In other words, if $x_t\sim I(1)$, then $\Delta x_t:=x_t-x_{t-1} \sim I(0)$.
Without differencing you will not get rid of the unit root. E.g. su... | How to transform a unit root process to a stationary process?
If a process has a unit root (a stochastic trend) and you want to make it stationary, you need to difference it. In other words, if $x_t\sim I(1)$, then $\Delta x_t:=x_t-x_{t-1} \sim I(0)$.
Without d |
55,897 | How to transform a unit root process to a stationary process? | taking the difference of the time series is NOT the only way to detrend a time series and to remove the unit root. the cointegration should be able to serve the same purpose. | How to transform a unit root process to a stationary process? | taking the difference of the time series is NOT the only way to detrend a time series and to remove the unit root. the cointegration should be able to serve the same purpose. | How to transform a unit root process to a stationary process?
taking the difference of the time series is NOT the only way to detrend a time series and to remove the unit root. the cointegration should be able to serve the same purpose. | How to transform a unit root process to a stationary process?
taking the difference of the time series is NOT the only way to detrend a time series and to remove the unit root. the cointegration should be able to serve the same purpose. |
55,898 | When to use Bernoulli Naive Bayes? | Bernoulli Naive Bayes is for binary features only. Similarly, multinomial naive Bayes treats features as event probabilities. Your example is given for nonbinary real-valued features $(x,y)$, which do not exclusively lie in the interval $[0,1]$, so the models do not apply to your features.
A typical example (taken fro... | When to use Bernoulli Naive Bayes? | Bernoulli Naive Bayes is for binary features only. Similarly, multinomial naive Bayes treats features as event probabilities. Your example is given for nonbinary real-valued features $(x,y)$, which do | When to use Bernoulli Naive Bayes?
Bernoulli Naive Bayes is for binary features only. Similarly, multinomial naive Bayes treats features as event probabilities. Your example is given for nonbinary real-valued features $(x,y)$, which do not exclusively lie in the interval $[0,1]$, so the models do not apply to your feat... | When to use Bernoulli Naive Bayes?
Bernoulli Naive Bayes is for binary features only. Similarly, multinomial naive Bayes treats features as event probabilities. Your example is given for nonbinary real-valued features $(x,y)$, which do |
55,899 | When to use Bernoulli Naive Bayes? | Bernoulli is well to use for discontinuous variation, most especially features as binary format e.g iris, fingerprint, blood etc. while Gaussian is for normal distribution or continuous variation the likes of age, height, size etc. | When to use Bernoulli Naive Bayes? | Bernoulli is well to use for discontinuous variation, most especially features as binary format e.g iris, fingerprint, blood etc. while Gaussian is for normal distribution or continuous variation the | When to use Bernoulli Naive Bayes?
Bernoulli is well to use for discontinuous variation, most especially features as binary format e.g iris, fingerprint, blood etc. while Gaussian is for normal distribution or continuous variation the likes of age, height, size etc. | When to use Bernoulli Naive Bayes?
Bernoulli is well to use for discontinuous variation, most especially features as binary format e.g iris, fingerprint, blood etc. while Gaussian is for normal distribution or continuous variation the |
55,900 | How to model nested fixed-factor with GLMM | Stream of consciousness:
you might want to consider log-transforming the response (provided there are no zeros) rather than using the log link, i.e. lmer(log(WaterChlA) ~ ...) rather than glmer(WaterChla ~ ..., family=gaussian(link="log")); I say this because log-transforming can take care of heteroscedasticity in the... | How to model nested fixed-factor with GLMM | Stream of consciousness:
you might want to consider log-transforming the response (provided there are no zeros) rather than using the log link, i.e. lmer(log(WaterChlA) ~ ...) rather than glmer(Water | How to model nested fixed-factor with GLMM
Stream of consciousness:
you might want to consider log-transforming the response (provided there are no zeros) rather than using the log link, i.e. lmer(log(WaterChlA) ~ ...) rather than glmer(WaterChla ~ ..., family=gaussian(link="log")); I say this because log-transforming... | How to model nested fixed-factor with GLMM
Stream of consciousness:
you might want to consider log-transforming the response (provided there are no zeros) rather than using the log link, i.e. lmer(log(WaterChlA) ~ ...) rather than glmer(Water |
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