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 |
|---|---|---|---|---|---|---|
47,201 | Why I am getting different $R^2$ from R LM and manual calculation? | I found the problem.
I am not adding the intercept in the model and without intercept SST is calculated differently, where it should be
crossprod(diamonds$price)
but not
crossprod(diamonds$price-mean(diamonds$price))
I think most books are confusing that just give us the formula to SST as
$$
\|y-\bar y\|^2
$$
but no... | Why I am getting different $R^2$ from R LM and manual calculation? | I found the problem.
I am not adding the intercept in the model and without intercept SST is calculated differently, where it should be
crossprod(diamonds$price)
but not
crossprod(diamonds$price-me | Why I am getting different $R^2$ from R LM and manual calculation?
I found the problem.
I am not adding the intercept in the model and without intercept SST is calculated differently, where it should be
crossprod(diamonds$price)
but not
crossprod(diamonds$price-mean(diamonds$price))
I think most books are confusing ... | Why I am getting different $R^2$ from R LM and manual calculation?
I found the problem.
I am not adding the intercept in the model and without intercept SST is calculated differently, where it should be
crossprod(diamonds$price)
but not
crossprod(diamonds$price-me |
47,202 | Something more powerful than Kruskal-Wallis Test? | I think the issue you're having is both one of sample size and the nature of the alternative hypothesis for the particular test you're using. The Kruskal-Wallis test tries to determine if the distributions are equal, or if one stochastically dominates another. This means that the probability that one quantity is larg... | Something more powerful than Kruskal-Wallis Test? | I think the issue you're having is both one of sample size and the nature of the alternative hypothesis for the particular test you're using. The Kruskal-Wallis test tries to determine if the distrib | Something more powerful than Kruskal-Wallis Test?
I think the issue you're having is both one of sample size and the nature of the alternative hypothesis for the particular test you're using. The Kruskal-Wallis test tries to determine if the distributions are equal, or if one stochastically dominates another. This me... | Something more powerful than Kruskal-Wallis Test?
I think the issue you're having is both one of sample size and the nature of the alternative hypothesis for the particular test you're using. The Kruskal-Wallis test tries to determine if the distrib |
47,203 | Something more powerful than Kruskal-Wallis Test? | (A little less formal that dsaxton's analysis... but a quick way to judge in this case)
It's not at all clear to me that these are different:
For a rough pairwise comparison, at sample size 10, the uncertainty in the median (since we're looking at boxplots here) is about the size that if the boxes overlap, the two are... | Something more powerful than Kruskal-Wallis Test? | (A little less formal that dsaxton's analysis... but a quick way to judge in this case)
It's not at all clear to me that these are different:
For a rough pairwise comparison, at sample size 10, the u | Something more powerful than Kruskal-Wallis Test?
(A little less formal that dsaxton's analysis... but a quick way to judge in this case)
It's not at all clear to me that these are different:
For a rough pairwise comparison, at sample size 10, the uncertainty in the median (since we're looking at boxplots here) is abo... | Something more powerful than Kruskal-Wallis Test?
(A little less formal that dsaxton's analysis... but a quick way to judge in this case)
It's not at all clear to me that these are different:
For a rough pairwise comparison, at sample size 10, the u |
47,204 | Causal Markov condition simple explanation | One way to think about the Causal Markov Condition (CMC) is giving a rule for "screening off": once you know the values of $X$'s parents, all other variables in $V$ become irrelevant for predicting $X$, except for $X$'s descendants.
I find examples make the CMC easiest to understand. I did a quick google image search ... | Causal Markov condition simple explanation | One way to think about the Causal Markov Condition (CMC) is giving a rule for "screening off": once you know the values of $X$'s parents, all other variables in $V$ become irrelevant for predicting $X | Causal Markov condition simple explanation
One way to think about the Causal Markov Condition (CMC) is giving a rule for "screening off": once you know the values of $X$'s parents, all other variables in $V$ become irrelevant for predicting $X$, except for $X$'s descendants.
I find examples make the CMC easiest to und... | Causal Markov condition simple explanation
One way to think about the Causal Markov Condition (CMC) is giving a rule for "screening off": once you know the values of $X$'s parents, all other variables in $V$ become irrelevant for predicting $X |
47,205 | R using GLM and manual solve logistic regression have different (close but not exactly the same) results | Short answer: Optimise harder.
Your loss function is fine, no numeric issues there. For instance you can easily check that:
all.equal( lossLogistic(coef(fit)), as.numeric(-logLik(fit)),
check.attributes = FALSE)
[1] TRUE
What happens is that you assume that optim's BFGS implementation can get as good as a... | R using GLM and manual solve logistic regression have different (close but not exactly the same) res | Short answer: Optimise harder.
Your loss function is fine, no numeric issues there. For instance you can easily check that:
all.equal( lossLogistic(coef(fit)), as.numeric(-logLik(fit)),
c | R using GLM and manual solve logistic regression have different (close but not exactly the same) results
Short answer: Optimise harder.
Your loss function is fine, no numeric issues there. For instance you can easily check that:
all.equal( lossLogistic(coef(fit)), as.numeric(-logLik(fit)),
check.attributes... | R using GLM and manual solve logistic regression have different (close but not exactly the same) res
Short answer: Optimise harder.
Your loss function is fine, no numeric issues there. For instance you can easily check that:
all.equal( lossLogistic(coef(fit)), as.numeric(-logLik(fit)),
c |
47,206 | Formulation of states for this RL problem and other questions. | Summary
The state space follows from the problem. "Niceness" depends on the method, as does "too big."
You can alter the reward function to speed learning if you know the optimal policy is invariant to the transformation.
Tractable depends on more than just state space. RL has been applied to much larger problems, tho... | Formulation of states for this RL problem and other questions. | Summary
The state space follows from the problem. "Niceness" depends on the method, as does "too big."
You can alter the reward function to speed learning if you know the optimal policy is invariant | Formulation of states for this RL problem and other questions.
Summary
The state space follows from the problem. "Niceness" depends on the method, as does "too big."
You can alter the reward function to speed learning if you know the optimal policy is invariant to the transformation.
Tractable depends on more than jus... | Formulation of states for this RL problem and other questions.
Summary
The state space follows from the problem. "Niceness" depends on the method, as does "too big."
You can alter the reward function to speed learning if you know the optimal policy is invariant |
47,207 | Improving the speed of XGBoost CV | The "tricks" I am familiar with are :
Sparse matrices, which you already used. However, you need to make sure that the percentage of non zero values in your matrix is low (otherwise, it could actually take longer to run)
Grow the trees one by one and observe the performance after each batch
I once used the following (... | Improving the speed of XGBoost CV | The "tricks" I am familiar with are :
Sparse matrices, which you already used. However, you need to make sure that the percentage of non zero values in your matrix is low (otherwise, it could actually | Improving the speed of XGBoost CV
The "tricks" I am familiar with are :
Sparse matrices, which you already used. However, you need to make sure that the percentage of non zero values in your matrix is low (otherwise, it could actually take longer to run)
Grow the trees one by one and observe the performance after each ... | Improving the speed of XGBoost CV
The "tricks" I am familiar with are :
Sparse matrices, which you already used. However, you need to make sure that the percentage of non zero values in your matrix is low (otherwise, it could actually |
47,208 | perform Random Forest AFTER multiple imputation with MICE | This is not a direct answer to your question, and I don't have enough reputation to comment, but one thing you can do is use the Machine Learning in R package. There are many random forest learner implementations there that can use data with missing values. You can also tune the learners based on what your dataset is.... | perform Random Forest AFTER multiple imputation with MICE | This is not a direct answer to your question, and I don't have enough reputation to comment, but one thing you can do is use the Machine Learning in R package. There are many random forest learner im | perform Random Forest AFTER multiple imputation with MICE
This is not a direct answer to your question, and I don't have enough reputation to comment, but one thing you can do is use the Machine Learning in R package. There are many random forest learner implementations there that can use data with missing values. You... | perform Random Forest AFTER multiple imputation with MICE
This is not a direct answer to your question, and I don't have enough reputation to comment, but one thing you can do is use the Machine Learning in R package. There are many random forest learner im |
47,209 | perform Random Forest AFTER multiple imputation with MICE | The combine function in randomForest makes it possible to combine multiple randomForest objects.
Prepare data:
set.seed(1234)
X1 <- rnorm(100, 120, 16)
X2 <- X1 + rnorm(100, 200, 10)
X3 <- 0.8*X2 + rnorm(100, 140, 12)
Y <- factor(as.numeric(X1 > 125))
dat.test <- data.frame(Y, X1, X2, X3)
# Impose missingness
Y[runi... | perform Random Forest AFTER multiple imputation with MICE | The combine function in randomForest makes it possible to combine multiple randomForest objects.
Prepare data:
set.seed(1234)
X1 <- rnorm(100, 120, 16)
X2 <- X1 + rnorm(100, 200, 10)
X3 <- 0.8*X2 + r | perform Random Forest AFTER multiple imputation with MICE
The combine function in randomForest makes it possible to combine multiple randomForest objects.
Prepare data:
set.seed(1234)
X1 <- rnorm(100, 120, 16)
X2 <- X1 + rnorm(100, 200, 10)
X3 <- 0.8*X2 + rnorm(100, 140, 12)
Y <- factor(as.numeric(X1 > 125))
dat.test... | perform Random Forest AFTER multiple imputation with MICE
The combine function in randomForest makes it possible to combine multiple randomForest objects.
Prepare data:
set.seed(1234)
X1 <- rnorm(100, 120, 16)
X2 <- X1 + rnorm(100, 200, 10)
X3 <- 0.8*X2 + r |
47,210 | Difference between a mixture of distributions and a convolution. Interpretation in a applied setting | The mathematical difference is simple (and you probably got that already). A mixture distribution has a density which is a weighted sum of other probability densities (often from the same class) whereas a convolution is a sum of random variables.
The intuition for a mixture can be illustrated (in line with your exampl... | Difference between a mixture of distributions and a convolution. Interpretation in a applied setting | The mathematical difference is simple (and you probably got that already). A mixture distribution has a density which is a weighted sum of other probability densities (often from the same class) where | Difference between a mixture of distributions and a convolution. Interpretation in a applied setting
The mathematical difference is simple (and you probably got that already). A mixture distribution has a density which is a weighted sum of other probability densities (often from the same class) whereas a convolution is... | Difference between a mixture of distributions and a convolution. Interpretation in a applied setting
The mathematical difference is simple (and you probably got that already). A mixture distribution has a density which is a weighted sum of other probability densities (often from the same class) where |
47,211 | Reversibility in MCMC | I am interpreting your question as much more general in that "Is there any gain to using a reversible Markov chain over a non-reversible Markov chain?". Here are two reasons I can think of off the top of my head:
Standard errors: If the chain is reversible, then a Markov chain CLT can hold for geometrically ergodic Ma... | Reversibility in MCMC | I am interpreting your question as much more general in that "Is there any gain to using a reversible Markov chain over a non-reversible Markov chain?". Here are two reasons I can think of off the top | Reversibility in MCMC
I am interpreting your question as much more general in that "Is there any gain to using a reversible Markov chain over a non-reversible Markov chain?". Here are two reasons I can think of off the top of my head:
Standard errors: If the chain is reversible, then a Markov chain CLT can hold for ge... | Reversibility in MCMC
I am interpreting your question as much more general in that "Is there any gain to using a reversible Markov chain over a non-reversible Markov chain?". Here are two reasons I can think of off the top |
47,212 | Should standardization be done using leave-one-out? | If the goal is to standardize the data set (mean center and measure distance from the mean in standard deviation units), then the leave-one-out (LOO) approach simply is not correct. This can be best seen with a simple data set (with an outlier, to exaggerate the point).
$$\{47.5,50.7,55.7,58,42.1,51.8,40.8,39.9,45.6,9... | Should standardization be done using leave-one-out? | If the goal is to standardize the data set (mean center and measure distance from the mean in standard deviation units), then the leave-one-out (LOO) approach simply is not correct. This can be best | Should standardization be done using leave-one-out?
If the goal is to standardize the data set (mean center and measure distance from the mean in standard deviation units), then the leave-one-out (LOO) approach simply is not correct. This can be best seen with a simple data set (with an outlier, to exaggerate the poin... | Should standardization be done using leave-one-out?
If the goal is to standardize the data set (mean center and measure distance from the mean in standard deviation units), then the leave-one-out (LOO) approach simply is not correct. This can be best |
47,213 | Should standardization be done using leave-one-out? | Given that you used the term leave-one-out, I think what is implied by the question is that you want to do a LOO cross-validation. That is, you want to train on n-1 examples and test your model on the remaining example. In that case, being very methodologically strict, you are correct. The standardization is performed ... | Should standardization be done using leave-one-out? | Given that you used the term leave-one-out, I think what is implied by the question is that you want to do a LOO cross-validation. That is, you want to train on n-1 examples and test your model on the | Should standardization be done using leave-one-out?
Given that you used the term leave-one-out, I think what is implied by the question is that you want to do a LOO cross-validation. That is, you want to train on n-1 examples and test your model on the remaining example. In that case, being very methodologically strict... | Should standardization be done using leave-one-out?
Given that you used the term leave-one-out, I think what is implied by the question is that you want to do a LOO cross-validation. That is, you want to train on n-1 examples and test your model on the |
47,214 | Constrained optimization algorithm in linear regression | The so-called local linear approximation (LLA) algorithm described in One-step sparse estimates in nonconcave penalized likelihood models by Zou and Li solves the optimization problem for certain concave choices of $f$. Specifically, for
$$f(s) = p(|s|)$$
and a concave function $p : [0,\infty) \to [0,\infty)$, which i... | Constrained optimization algorithm in linear regression | The so-called local linear approximation (LLA) algorithm described in One-step sparse estimates in nonconcave penalized likelihood models by Zou and Li solves the optimization problem for certain conc | Constrained optimization algorithm in linear regression
The so-called local linear approximation (LLA) algorithm described in One-step sparse estimates in nonconcave penalized likelihood models by Zou and Li solves the optimization problem for certain concave choices of $f$. Specifically, for
$$f(s) = p(|s|)$$
and a c... | Constrained optimization algorithm in linear regression
The so-called local linear approximation (LLA) algorithm described in One-step sparse estimates in nonconcave penalized likelihood models by Zou and Li solves the optimization problem for certain conc |
47,215 | What's the difference between concordance correlation and intraclass correlation? | The modern definition of intraclass correlation (ICC) is a biased estimate of the fraction of the total variance that is due to variation between groups as pertains to the framework of analysis of variance (ANOVA), and random effects models.
What would we use this for? An intraclass correlation (ICC) can be a useful e... | What's the difference between concordance correlation and intraclass correlation? | The modern definition of intraclass correlation (ICC) is a biased estimate of the fraction of the total variance that is due to variation between groups as pertains to the framework of analysis of var | What's the difference between concordance correlation and intraclass correlation?
The modern definition of intraclass correlation (ICC) is a biased estimate of the fraction of the total variance that is due to variation between groups as pertains to the framework of analysis of variance (ANOVA), and random effects mode... | What's the difference between concordance correlation and intraclass correlation?
The modern definition of intraclass correlation (ICC) is a biased estimate of the fraction of the total variance that is due to variation between groups as pertains to the framework of analysis of var |
47,216 | Is there a non-boostrap way to estimate confidence intervals for Kernel regression predictions? | Under non-fixed-design $x$'s, [Härdle][1] (p136) gives an asymptotic distributional approximation relating to the Nadaraya-Watson estimator $\hat{m}(x_j)$:
$(nh)^\frac12 \frac{\hat{m}_h(x_j)-m(x_j)}{V(x_j)^\frac12} \stackrel{.}{\sim} N(B(x_j),1)$
where $V(x_j) = \sigma^2(x_j)||K||_2^2/f(x_j)$ and $B(x_j) = \mu_2(K)[m''... | Is there a non-boostrap way to estimate confidence intervals for Kernel regression predictions? | Under non-fixed-design $x$'s, [Härdle][1] (p136) gives an asymptotic distributional approximation relating to the Nadaraya-Watson estimator $\hat{m}(x_j)$:
$(nh)^\frac12 \frac{\hat{m}_h(x_j)-m(x_j)}{V | Is there a non-boostrap way to estimate confidence intervals for Kernel regression predictions?
Under non-fixed-design $x$'s, [Härdle][1] (p136) gives an asymptotic distributional approximation relating to the Nadaraya-Watson estimator $\hat{m}(x_j)$:
$(nh)^\frac12 \frac{\hat{m}_h(x_j)-m(x_j)}{V(x_j)^\frac12} \stackrel... | Is there a non-boostrap way to estimate confidence intervals for Kernel regression predictions?
Under non-fixed-design $x$'s, [Härdle][1] (p136) gives an asymptotic distributional approximation relating to the Nadaraya-Watson estimator $\hat{m}(x_j)$:
$(nh)^\frac12 \frac{\hat{m}_h(x_j)-m(x_j)}{V |
47,217 | Time series and instrumental variables | Consider a series $Y_t$ generated as an $ARMA(1,1)$ process
$$
Y_t=\phi Y_{t-1}+\epsilon_t+\theta\epsilon_{t-1}
$$
Suppose our interest centers on estimating $\phi$. We have an endogeneity issue here, as the error term $\epsilon_t+\theta\epsilon_{t-1}$ is correlated with the regressor $Y_{t-1}$, so OLS of $Y_{t}$ on $Y... | Time series and instrumental variables | Consider a series $Y_t$ generated as an $ARMA(1,1)$ process
$$
Y_t=\phi Y_{t-1}+\epsilon_t+\theta\epsilon_{t-1}
$$
Suppose our interest centers on estimating $\phi$. We have an endogeneity issue here, | Time series and instrumental variables
Consider a series $Y_t$ generated as an $ARMA(1,1)$ process
$$
Y_t=\phi Y_{t-1}+\epsilon_t+\theta\epsilon_{t-1}
$$
Suppose our interest centers on estimating $\phi$. We have an endogeneity issue here, as the error term $\epsilon_t+\theta\epsilon_{t-1}$ is correlated with the regre... | Time series and instrumental variables
Consider a series $Y_t$ generated as an $ARMA(1,1)$ process
$$
Y_t=\phi Y_{t-1}+\epsilon_t+\theta\epsilon_{t-1}
$$
Suppose our interest centers on estimating $\phi$. We have an endogeneity issue here, |
47,218 | Optimize starting parameters for Bayesian Linear Regression? | I'll illustrate my answer with a simple example. Imagine that your data $X_1,\dots,X_n$ are counts that follow a Poisson distribution. Poisson distributtion is described using a single parameter $\lambda$ that we want to estimate given the data we have. To set up a Bayesian model we use Bayes theorem
$$ \underbrace{p(\... | Optimize starting parameters for Bayesian Linear Regression? | I'll illustrate my answer with a simple example. Imagine that your data $X_1,\dots,X_n$ are counts that follow a Poisson distribution. Poisson distributtion is described using a single parameter $\lam | Optimize starting parameters for Bayesian Linear Regression?
I'll illustrate my answer with a simple example. Imagine that your data $X_1,\dots,X_n$ are counts that follow a Poisson distribution. Poisson distributtion is described using a single parameter $\lambda$ that we want to estimate given the data we have. To se... | Optimize starting parameters for Bayesian Linear Regression?
I'll illustrate my answer with a simple example. Imagine that your data $X_1,\dots,X_n$ are counts that follow a Poisson distribution. Poisson distributtion is described using a single parameter $\lam |
47,219 | Optimize starting parameters for Bayesian Linear Regression? | Intuitively, the one on the left seems to give you unreasonably large coefficients.
To be more quantitative, you can do model comparison. Cross-validation is one way to compare them, but there exist various other measures that estimate the result you would get in a cross-validation. PyMC3 has various model comparison m... | Optimize starting parameters for Bayesian Linear Regression? | Intuitively, the one on the left seems to give you unreasonably large coefficients.
To be more quantitative, you can do model comparison. Cross-validation is one way to compare them, but there exist v | Optimize starting parameters for Bayesian Linear Regression?
Intuitively, the one on the left seems to give you unreasonably large coefficients.
To be more quantitative, you can do model comparison. Cross-validation is one way to compare them, but there exist various other measures that estimate the result you would ge... | Optimize starting parameters for Bayesian Linear Regression?
Intuitively, the one on the left seems to give you unreasonably large coefficients.
To be more quantitative, you can do model comparison. Cross-validation is one way to compare them, but there exist v |
47,220 | For a Fisher Information matrix $I(\theta)$ of multiple variables, is it true that $I(\theta) = nI_1(\theta)$? | Since the wikipedia article https://en.wikipedia.org/wiki/Fisher_information do not contain a proof, I will write one here. Let $X_1, X_2, \dotsc, X_n$ be independent random variables with density function $f(x;\theta)$ (which might in addition depend on known covariates, so this covers more than the iid case). Then t... | For a Fisher Information matrix $I(\theta)$ of multiple variables, is it true that $I(\theta) = nI_1 | Since the wikipedia article https://en.wikipedia.org/wiki/Fisher_information do not contain a proof, I will write one here. Let $X_1, X_2, \dotsc, X_n$ be independent random variables with density fu | For a Fisher Information matrix $I(\theta)$ of multiple variables, is it true that $I(\theta) = nI_1(\theta)$?
Since the wikipedia article https://en.wikipedia.org/wiki/Fisher_information do not contain a proof, I will write one here. Let $X_1, X_2, \dotsc, X_n$ be independent random variables with density function $f... | For a Fisher Information matrix $I(\theta)$ of multiple variables, is it true that $I(\theta) = nI_1
Since the wikipedia article https://en.wikipedia.org/wiki/Fisher_information do not contain a proof, I will write one here. Let $X_1, X_2, \dotsc, X_n$ be independent random variables with density fu |
47,221 | For a Fisher Information matrix $I(\theta)$ of multiple variables, is it true that $I(\theta) = nI_1(\theta)$? | Let $X$ be a random variable with probability density function
$f(x;\theta)$.
Assume that the observations $x_1,\ldots,x_n$ are independent realizations
of $X$.
Let us prove that the Fisher matrix is:
\begin{align}
I(\theta) = n I_1(\theta)
\end{align}
where $I_1(\theta)$ is the Fisher matrix for one single observation... | For a Fisher Information matrix $I(\theta)$ of multiple variables, is it true that $I(\theta) = nI_1 | Let $X$ be a random variable with probability density function
$f(x;\theta)$.
Assume that the observations $x_1,\ldots,x_n$ are independent realizations
of $X$.
Let us prove that the Fisher matrix is: | For a Fisher Information matrix $I(\theta)$ of multiple variables, is it true that $I(\theta) = nI_1(\theta)$?
Let $X$ be a random variable with probability density function
$f(x;\theta)$.
Assume that the observations $x_1,\ldots,x_n$ are independent realizations
of $X$.
Let us prove that the Fisher matrix is:
\begin{a... | For a Fisher Information matrix $I(\theta)$ of multiple variables, is it true that $I(\theta) = nI_1
Let $X$ be a random variable with probability density function
$f(x;\theta)$.
Assume that the observations $x_1,\ldots,x_n$ are independent realizations
of $X$.
Let us prove that the Fisher matrix is: |
47,222 | For a Fisher Information matrix $I(\theta)$ of multiple variables, is it true that $I(\theta) = nI_1(\theta)$? | The proof by kjetil b halvorsen is incorrect, you missed the cross-terms. The correct equation for the $I(\theta)$ should read something like this:
$$
I(\theta) = \mathbb{E}\left[\left(\sum\limits_i\frac{\partial}{\partial\theta}\log f(X_i;\theta)\right)\left(\sum\limits_j\frac{\partial}{\partial\theta}\log f(X_j;\th... | For a Fisher Information matrix $I(\theta)$ of multiple variables, is it true that $I(\theta) = nI_1 | The proof by kjetil b halvorsen is incorrect, you missed the cross-terms. The correct equation for the $I(\theta)$ should read something like this:
$$
I(\theta) = \mathbb{E}\left[\left(\sum\limits_i | For a Fisher Information matrix $I(\theta)$ of multiple variables, is it true that $I(\theta) = nI_1(\theta)$?
The proof by kjetil b halvorsen is incorrect, you missed the cross-terms. The correct equation for the $I(\theta)$ should read something like this:
$$
I(\theta) = \mathbb{E}\left[\left(\sum\limits_i\frac{\pa... | For a Fisher Information matrix $I(\theta)$ of multiple variables, is it true that $I(\theta) = nI_1
The proof by kjetil b halvorsen is incorrect, you missed the cross-terms. The correct equation for the $I(\theta)$ should read something like this:
$$
I(\theta) = \mathbb{E}\left[\left(\sum\limits_i |
47,223 | Test for whether two data sets are significantly different | This can be approached like a chi square test of homogeneity. You want to see if there are differences from a theoretical uniform distribution across parks in the counts of snails coming from different populations or groups (colors). The margins of the tabulated data are considered random variables, and used to cross m... | Test for whether two data sets are significantly different | This can be approached like a chi square test of homogeneity. You want to see if there are differences from a theoretical uniform distribution across parks in the counts of snails coming from differen | Test for whether two data sets are significantly different
This can be approached like a chi square test of homogeneity. You want to see if there are differences from a theoretical uniform distribution across parks in the counts of snails coming from different populations or groups (colors). The margins of the tabulate... | Test for whether two data sets are significantly different
This can be approached like a chi square test of homogeneity. You want to see if there are differences from a theoretical uniform distribution across parks in the counts of snails coming from differen |
47,224 | Difference between rulefit and random forest | In fact, RuleFit does excessive pruning on a random forest. It tries to find a set of rules generated by random forest to obtain accuracy as close as possible to the accuracy of random forest while reducing the number of rules tremendously. Finally, it builds a model consisting of simple and short rules which are extra... | Difference between rulefit and random forest | In fact, RuleFit does excessive pruning on a random forest. It tries to find a set of rules generated by random forest to obtain accuracy as close as possible to the accuracy of random forest while re | Difference between rulefit and random forest
In fact, RuleFit does excessive pruning on a random forest. It tries to find a set of rules generated by random forest to obtain accuracy as close as possible to the accuracy of random forest while reducing the number of rules tremendously. Finally, it builds a model consist... | Difference between rulefit and random forest
In fact, RuleFit does excessive pruning on a random forest. It tries to find a set of rules generated by random forest to obtain accuracy as close as possible to the accuracy of random forest while re |
47,225 | Difference between rulefit and random forest | They differ in their approaches to tree generation and selection of baselearners to retain for the predictive model:
RuleFit first generates a boosted decision tree ensemble. That is:
It sequentially grows trees on a pseudo response variable, where the pseudo response for each tree is corrected for the predictions of ... | Difference between rulefit and random forest | They differ in their approaches to tree generation and selection of baselearners to retain for the predictive model:
RuleFit first generates a boosted decision tree ensemble. That is:
It sequentially | Difference between rulefit and random forest
They differ in their approaches to tree generation and selection of baselearners to retain for the predictive model:
RuleFit first generates a boosted decision tree ensemble. That is:
It sequentially grows trees on a pseudo response variable, where the pseudo response for e... | Difference between rulefit and random forest
They differ in their approaches to tree generation and selection of baselearners to retain for the predictive model:
RuleFit first generates a boosted decision tree ensemble. That is:
It sequentially |
47,226 | Overview of predictive modelling, machine learning, etc. | I don't understand this phrase:
In these situations, it is not always necessary to think about samples and populations, or to think about a model that expresses a scientific idea.
It doesn't make sense to me, because if I were to build a regression model I would still need to think about my samples and population. I do... | Overview of predictive modelling, machine learning, etc. | I don't understand this phrase:
In these situations, it is not always necessary to think about samples and populations, or to think about a model that expresses a scientific idea.
It doesn't make sens | Overview of predictive modelling, machine learning, etc.
I don't understand this phrase:
In these situations, it is not always necessary to think about samples and populations, or to think about a model that expresses a scientific idea.
It doesn't make sense to me, because if I were to build a regression model I would ... | Overview of predictive modelling, machine learning, etc.
I don't understand this phrase:
In these situations, it is not always necessary to think about samples and populations, or to think about a model that expresses a scientific idea.
It doesn't make sens |
47,227 | Overview of predictive modelling, machine learning, etc. | Are not all (or nearly) all approaches in some sense trying to deduce something that generalizes and thus predicts what will happen? There is not so much of a distinction in this respect and it is not an entirely different goal. The sentence
In these situations, it is not always necessary to think about samples and p... | Overview of predictive modelling, machine learning, etc. | Are not all (or nearly) all approaches in some sense trying to deduce something that generalizes and thus predicts what will happen? There is not so much of a distinction in this respect and it is not | Overview of predictive modelling, machine learning, etc.
Are not all (or nearly) all approaches in some sense trying to deduce something that generalizes and thus predicts what will happen? There is not so much of a distinction in this respect and it is not an entirely different goal. The sentence
In these situations... | Overview of predictive modelling, machine learning, etc.
Are not all (or nearly) all approaches in some sense trying to deduce something that generalizes and thus predicts what will happen? There is not so much of a distinction in this respect and it is not |
47,228 | Overview of predictive modelling, machine learning, etc. | A few thoughts beyond those from @Björn and @StudentT that wouldn't fit into a comment on either of their answers.
It seems that the distinction you are trying to draw is between testing hypotheses on data (traditional statistical inference, the topic of your book) and gleaning relationships from data (machine learning... | Overview of predictive modelling, machine learning, etc. | A few thoughts beyond those from @Björn and @StudentT that wouldn't fit into a comment on either of their answers.
It seems that the distinction you are trying to draw is between testing hypotheses on | Overview of predictive modelling, machine learning, etc.
A few thoughts beyond those from @Björn and @StudentT that wouldn't fit into a comment on either of their answers.
It seems that the distinction you are trying to draw is between testing hypotheses on data (traditional statistical inference, the topic of your boo... | Overview of predictive modelling, machine learning, etc.
A few thoughts beyond those from @Björn and @StudentT that wouldn't fit into a comment on either of their answers.
It seems that the distinction you are trying to draw is between testing hypotheses on |
47,229 | Statistics books for someone who has a conceptual base in introductory statistics but little programming background in R | It is a tall order to get a book that reviews basic statistics, introduces R, and takes you down the path to "advanced pattern recognition." I think that is a lot for one book. :-)
One of the best books on intermediate statistics in R, with discussions of both the statistics (and math) and R is Maindonald and Braun Dat... | Statistics books for someone who has a conceptual base in introductory statistics but little program | It is a tall order to get a book that reviews basic statistics, introduces R, and takes you down the path to "advanced pattern recognition." I think that is a lot for one book. :-)
One of the best boo | Statistics books for someone who has a conceptual base in introductory statistics but little programming background in R
It is a tall order to get a book that reviews basic statistics, introduces R, and takes you down the path to "advanced pattern recognition." I think that is a lot for one book. :-)
One of the best bo... | Statistics books for someone who has a conceptual base in introductory statistics but little program
It is a tall order to get a book that reviews basic statistics, introduces R, and takes you down the path to "advanced pattern recognition." I think that is a lot for one book. :-)
One of the best boo |
47,230 | Statistics books for someone who has a conceptual base in introductory statistics but little programming background in R | These books have a lot of examples that cover basic topics as well as more advanced techniques used in machine learning.
Statistics and Data with R: An Applied Approach Through Examples by
Yosef Cohen, Jeremiah Y. Cohen
Data Mining and Business Analytics with R by Johannes Ledolter
R and Data Mining: Examples and Cas... | Statistics books for someone who has a conceptual base in introductory statistics but little program | These books have a lot of examples that cover basic topics as well as more advanced techniques used in machine learning.
Statistics and Data with R: An Applied Approach Through Examples by
Yosef Coh | Statistics books for someone who has a conceptual base in introductory statistics but little programming background in R
These books have a lot of examples that cover basic topics as well as more advanced techniques used in machine learning.
Statistics and Data with R: An Applied Approach Through Examples by
Yosef Co... | Statistics books for someone who has a conceptual base in introductory statistics but little program
These books have a lot of examples that cover basic topics as well as more advanced techniques used in machine learning.
Statistics and Data with R: An Applied Approach Through Examples by
Yosef Coh |
47,231 | Statistics books for someone who has a conceptual base in introductory statistics but little programming background in R | you may want to check this website, which lists books on R categorised into topics e.g. statistics, machine learning, data science, finance (it also shows required level of statistic and programming knowledge for each book):
https://www.rbookshub.co.uk/ | Statistics books for someone who has a conceptual base in introductory statistics but little program | you may want to check this website, which lists books on R categorised into topics e.g. statistics, machine learning, data science, finance (it also shows required level of statistic and programming k | Statistics books for someone who has a conceptual base in introductory statistics but little programming background in R
you may want to check this website, which lists books on R categorised into topics e.g. statistics, machine learning, data science, finance (it also shows required level of statistic and programming ... | Statistics books for someone who has a conceptual base in introductory statistics but little program
you may want to check this website, which lists books on R categorised into topics e.g. statistics, machine learning, data science, finance (it also shows required level of statistic and programming k |
47,232 | Statistics books for someone who has a conceptual base in introductory statistics but little programming background in R | There's an awesome guy on YouTube who does quick 2 minute videos on R programming to learn the basics very fast. I've learned so much from this playlist, I can really recommend watching that. You'll have a fast introduction on what you can do with R. | Statistics books for someone who has a conceptual base in introductory statistics but little program | There's an awesome guy on YouTube who does quick 2 minute videos on R programming to learn the basics very fast. I've learned so much from this playlist, I can really recommend watching that. You'll h | Statistics books for someone who has a conceptual base in introductory statistics but little programming background in R
There's an awesome guy on YouTube who does quick 2 minute videos on R programming to learn the basics very fast. I've learned so much from this playlist, I can really recommend watching that. You'll ... | Statistics books for someone who has a conceptual base in introductory statistics but little program
There's an awesome guy on YouTube who does quick 2 minute videos on R programming to learn the basics very fast. I've learned so much from this playlist, I can really recommend watching that. You'll h |
47,233 | Repeated Measures ANOVA in python | I also think your best (and probably only) bet is the library Statsmodels. Statsmodels contains a linear mixed effects model routine.
Having said that you can bite the bullet now and look into calling R from within Python. The package rpy2 seems to be the basic computational bed-rock for this. Good luck! | Repeated Measures ANOVA in python | I also think your best (and probably only) bet is the library Statsmodels. Statsmodels contains a linear mixed effects model routine.
Having said that you can bite the bullet now and look into calling | Repeated Measures ANOVA in python
I also think your best (and probably only) bet is the library Statsmodels. Statsmodels contains a linear mixed effects model routine.
Having said that you can bite the bullet now and look into calling R from within Python. The package rpy2 seems to be the basic computational bed-rock f... | Repeated Measures ANOVA in python
I also think your best (and probably only) bet is the library Statsmodels. Statsmodels contains a linear mixed effects model routine.
Having said that you can bite the bullet now and look into calling |
47,234 | Interpreting VAR impulse response | When you conduct VAR all variables should be on the same scale or same variable transformation basis (or as close as possible). It makes perfect sense that when you multiply your original variables by a 100, the IRF graph also reflects responses that are 100 times greater than in the original. The revised graph propo... | Interpreting VAR impulse response | When you conduct VAR all variables should be on the same scale or same variable transformation basis (or as close as possible). It makes perfect sense that when you multiply your original variables b | Interpreting VAR impulse response
When you conduct VAR all variables should be on the same scale or same variable transformation basis (or as close as possible). It makes perfect sense that when you multiply your original variables by a 100, the IRF graph also reflects responses that are 100 times greater than in the ... | Interpreting VAR impulse response
When you conduct VAR all variables should be on the same scale or same variable transformation basis (or as close as possible). It makes perfect sense that when you multiply your original variables b |
47,235 | Calculating MAPE [closed] | From the name Mean Absolute Percentage Error, there needs to be an absolute value in the calculation of MAPE:
rowMeans(abs((actual-predicted)/actual) * 100)
This matches the formula for MAPE at, for instance, https://en.wikipedia.org/wiki/Mean_absolute_percentage_error | Calculating MAPE [closed] | From the name Mean Absolute Percentage Error, there needs to be an absolute value in the calculation of MAPE:
rowMeans(abs((actual-predicted)/actual) * 100)
This matches the formula for MAPE at, for | Calculating MAPE [closed]
From the name Mean Absolute Percentage Error, there needs to be an absolute value in the calculation of MAPE:
rowMeans(abs((actual-predicted)/actual) * 100)
This matches the formula for MAPE at, for instance, https://en.wikipedia.org/wiki/Mean_absolute_percentage_error | Calculating MAPE [closed]
From the name Mean Absolute Percentage Error, there needs to be an absolute value in the calculation of MAPE:
rowMeans(abs((actual-predicted)/actual) * 100)
This matches the formula for MAPE at, for |
47,236 | Probability of n-bit sequence appearing at least twice in m-bit sequence | As @NeilG stated in the comments, the desired probability can still be computed exactly by defining a (2n+1)-state markov chain and computing the probability of having seen 2 copies of $\alpha$ after m iterations. The states in the markov chain will be of the form $(a, b)$, where $a$ is the number of times we have alre... | Probability of n-bit sequence appearing at least twice in m-bit sequence | As @NeilG stated in the comments, the desired probability can still be computed exactly by defining a (2n+1)-state markov chain and computing the probability of having seen 2 copies of $\alpha$ after | Probability of n-bit sequence appearing at least twice in m-bit sequence
As @NeilG stated in the comments, the desired probability can still be computed exactly by defining a (2n+1)-state markov chain and computing the probability of having seen 2 copies of $\alpha$ after m iterations. The states in the markov chain wi... | Probability of n-bit sequence appearing at least twice in m-bit sequence
As @NeilG stated in the comments, the desired probability can still be computed exactly by defining a (2n+1)-state markov chain and computing the probability of having seen 2 copies of $\alpha$ after |
47,237 | Probability of n-bit sequence appearing at least twice in m-bit sequence | Part 1: The occurrences of $\alpha$ are disjoint
First consider the case where the two occurrences of $\alpha$ are non-overlapping. Then we could lay out the m bits as:
******alpha*****alpha****
Basically there are three regions of bits that can take any value -- before the first $\alpha$, between the two occurrences,... | Probability of n-bit sequence appearing at least twice in m-bit sequence | Part 1: The occurrences of $\alpha$ are disjoint
First consider the case where the two occurrences of $\alpha$ are non-overlapping. Then we could lay out the m bits as:
******alpha*****alpha****
Basi | Probability of n-bit sequence appearing at least twice in m-bit sequence
Part 1: The occurrences of $\alpha$ are disjoint
First consider the case where the two occurrences of $\alpha$ are non-overlapping. Then we could lay out the m bits as:
******alpha*****alpha****
Basically there are three regions of bits that can ... | Probability of n-bit sequence appearing at least twice in m-bit sequence
Part 1: The occurrences of $\alpha$ are disjoint
First consider the case where the two occurrences of $\alpha$ are non-overlapping. Then we could lay out the m bits as:
******alpha*****alpha****
Basi |
47,238 | Probability of n-bit sequence appearing at least twice in m-bit sequence | If we assume that the two substrings are disjoint
(i.e. $s_1=s[i,i+n]$ $s_2=s[j,j+n]$ such that $0<i<i+n<j<m$),
Then $\alpha$ doesn't matter, (because $0$ and $1$ have equal chance of being chosen)
So lets assume $\alpha$ is all zeros and rephrase the question as:
Given a random binary string of length $m$, what is th... | Probability of n-bit sequence appearing at least twice in m-bit sequence | If we assume that the two substrings are disjoint
(i.e. $s_1=s[i,i+n]$ $s_2=s[j,j+n]$ such that $0<i<i+n<j<m$),
Then $\alpha$ doesn't matter, (because $0$ and $1$ have equal chance of being chosen)
So | Probability of n-bit sequence appearing at least twice in m-bit sequence
If we assume that the two substrings are disjoint
(i.e. $s_1=s[i,i+n]$ $s_2=s[j,j+n]$ such that $0<i<i+n<j<m$),
Then $\alpha$ doesn't matter, (because $0$ and $1$ have equal chance of being chosen)
So lets assume $\alpha$ is all zeros and rephrase... | Probability of n-bit sequence appearing at least twice in m-bit sequence
If we assume that the two substrings are disjoint
(i.e. $s_1=s[i,i+n]$ $s_2=s[j,j+n]$ such that $0<i<i+n<j<m$),
Then $\alpha$ doesn't matter, (because $0$ and $1$ have equal chance of being chosen)
So |
47,239 | Intuitive example for MLE, MAP and Naive Bayes classifier | You find a coin, and want to check what are the chances (probability) that if you flip it, it would land on the "Heads" side. You flip it 10 times (a sample of 10 observations) and count the number of times if landed on "Heads", e.g. $X=3$.
You assume that what you just done is a sample from a Binomial distribution $B... | Intuitive example for MLE, MAP and Naive Bayes classifier | You find a coin, and want to check what are the chances (probability) that if you flip it, it would land on the "Heads" side. You flip it 10 times (a sample of 10 observations) and count the number of | Intuitive example for MLE, MAP and Naive Bayes classifier
You find a coin, and want to check what are the chances (probability) that if you flip it, it would land on the "Heads" side. You flip it 10 times (a sample of 10 observations) and count the number of times if landed on "Heads", e.g. $X=3$.
You assume that what... | Intuitive example for MLE, MAP and Naive Bayes classifier
You find a coin, and want to check what are the chances (probability) that if you flip it, it would land on the "Heads" side. You flip it 10 times (a sample of 10 observations) and count the number of |
47,240 | Role of Central Limit Theorem in one-way ANOVA | That is not a correct interpretation of the CLT. The CLT is a limiting argument and only helps you with respect to type I error, not type II error. Confidence intervals using the CLT can be horrendously inaccurate for sample sizes in the thousands when the data distribution is very skewed (e.g., lognormal distributio... | Role of Central Limit Theorem in one-way ANOVA | That is not a correct interpretation of the CLT. The CLT is a limiting argument and only helps you with respect to type I error, not type II error. Confidence intervals using the CLT can be horrendo | Role of Central Limit Theorem in one-way ANOVA
That is not a correct interpretation of the CLT. The CLT is a limiting argument and only helps you with respect to type I error, not type II error. Confidence intervals using the CLT can be horrendously inaccurate for sample sizes in the thousands when the data distribut... | Role of Central Limit Theorem in one-way ANOVA
That is not a correct interpretation of the CLT. The CLT is a limiting argument and only helps you with respect to type I error, not type II error. Confidence intervals using the CLT can be horrendo |
47,241 | Role of Central Limit Theorem in one-way ANOVA | The t-statistic has a numerator and a denominator.
For this discussion, assume both numerator and denominator are now divided by $\sigma/\sqrt{n}$. The numerator is then of the standardized form required for the CLT.
The CLT only gives you that (under certain conditions) as $n\to\infty$ a standardized numerator will g... | Role of Central Limit Theorem in one-way ANOVA | The t-statistic has a numerator and a denominator.
For this discussion, assume both numerator and denominator are now divided by $\sigma/\sqrt{n}$. The numerator is then of the standardized form requ | Role of Central Limit Theorem in one-way ANOVA
The t-statistic has a numerator and a denominator.
For this discussion, assume both numerator and denominator are now divided by $\sigma/\sqrt{n}$. The numerator is then of the standardized form required for the CLT.
The CLT only gives you that (under certain conditions) ... | Role of Central Limit Theorem in one-way ANOVA
The t-statistic has a numerator and a denominator.
For this discussion, assume both numerator and denominator are now divided by $\sigma/\sqrt{n}$. The numerator is then of the standardized form requ |
47,242 | Prove that maximum likelihood estimators for Gaussian distribution are a global maximum | You can use a sum-of-squares argument to see this.
$$\sum_i (x_i-\theta)^2 = \sum_i (x_i - \bar{x}+\bar{x}-\theta)^2 = \sum_i (x_i-\bar{x})^2+n(\bar{x}-\theta)^2+\\\color{red}{2(\bar{x}-\theta)\sum_i(x_i-\bar{x})}$$
Now, $\bar{x}$ is defined so that the cross term becomes zero since $\sum_i x_i = \sum_i \bar{x}$.
We ar... | Prove that maximum likelihood estimators for Gaussian distribution are a global maximum | You can use a sum-of-squares argument to see this.
$$\sum_i (x_i-\theta)^2 = \sum_i (x_i - \bar{x}+\bar{x}-\theta)^2 = \sum_i (x_i-\bar{x})^2+n(\bar{x}-\theta)^2+\\\color{red}{2(\bar{x}-\theta)\sum_i( | Prove that maximum likelihood estimators for Gaussian distribution are a global maximum
You can use a sum-of-squares argument to see this.
$$\sum_i (x_i-\theta)^2 = \sum_i (x_i - \bar{x}+\bar{x}-\theta)^2 = \sum_i (x_i-\bar{x})^2+n(\bar{x}-\theta)^2+\\\color{red}{2(\bar{x}-\theta)\sum_i(x_i-\bar{x})}$$
Now, $\bar{x}$ i... | Prove that maximum likelihood estimators for Gaussian distribution are a global maximum
You can use a sum-of-squares argument to see this.
$$\sum_i (x_i-\theta)^2 = \sum_i (x_i - \bar{x}+\bar{x}-\theta)^2 = \sum_i (x_i-\bar{x})^2+n(\bar{x}-\theta)^2+\\\color{red}{2(\bar{x}-\theta)\sum_i( |
47,243 | Prove that maximum likelihood estimators for Gaussian distribution are a global maximum | $\theta\mapsto \sum (x_i-\theta)^2$ is a quadratic function in $\theta$ that opens upwards. It has a unique minimum where its derivative is $0$, that is to say when $2\sum (x_i-\theta)=0$ ie $\theta = \hat x$. | Prove that maximum likelihood estimators for Gaussian distribution are a global maximum | $\theta\mapsto \sum (x_i-\theta)^2$ is a quadratic function in $\theta$ that opens upwards. It has a unique minimum where its derivative is $0$, that is to say when $2\sum (x_i-\theta)=0$ ie $\theta = | Prove that maximum likelihood estimators for Gaussian distribution are a global maximum
$\theta\mapsto \sum (x_i-\theta)^2$ is a quadratic function in $\theta$ that opens upwards. It has a unique minimum where its derivative is $0$, that is to say when $2\sum (x_i-\theta)=0$ ie $\theta = \hat x$. | Prove that maximum likelihood estimators for Gaussian distribution are a global maximum
$\theta\mapsto \sum (x_i-\theta)^2$ is a quadratic function in $\theta$ that opens upwards. It has a unique minimum where its derivative is $0$, that is to say when $2\sum (x_i-\theta)=0$ ie $\theta = |
47,244 | Classifying time-series similarity - what variable should I train on? | hard to say from just two examples.
is the amplitude important? If so, try the area under the curves as a feature.
if not, you need to z-normalize the data.
This paper lists many many possible time series features http://arxiv.org/pdf/1401.3531.pdf
I could help you more, if you showed many more examples.
eamonn keogh | Classifying time-series similarity - what variable should I train on? | hard to say from just two examples.
is the amplitude important? If so, try the area under the curves as a feature.
if not, you need to z-normalize the data.
This paper lists many many possible time se | Classifying time-series similarity - what variable should I train on?
hard to say from just two examples.
is the amplitude important? If so, try the area under the curves as a feature.
if not, you need to z-normalize the data.
This paper lists many many possible time series features http://arxiv.org/pdf/1401.3531.pdf
... | Classifying time-series similarity - what variable should I train on?
hard to say from just two examples.
is the amplitude important? If so, try the area under the curves as a feature.
if not, you need to z-normalize the data.
This paper lists many many possible time se |
47,245 | Classifying time-series similarity - what variable should I train on? | Based on the examples you show, simple Euclidean distance will get you 100% accuracy.
This appears to be VERY easy. | Classifying time-series similarity - what variable should I train on? | Based on the examples you show, simple Euclidean distance will get you 100% accuracy.
This appears to be VERY easy. | Classifying time-series similarity - what variable should I train on?
Based on the examples you show, simple Euclidean distance will get you 100% accuracy.
This appears to be VERY easy. | Classifying time-series similarity - what variable should I train on?
Based on the examples you show, simple Euclidean distance will get you 100% accuracy.
This appears to be VERY easy. |
47,246 | Marginal normality and joint normality | A bivariate normal, centered anywhere in the YZ-plane, must exist over the entire plane...that is, in quadrants I, II, III, and IV because its domain is infinite in both variables.
But for it to exist in Quadrants II and IV, Y and Z must be oppositely-signed. If they cannot be, then the joint distribution cannot be a... | Marginal normality and joint normality | A bivariate normal, centered anywhere in the YZ-plane, must exist over the entire plane...that is, in quadrants I, II, III, and IV because its domain is infinite in both variables.
But for it to exis | Marginal normality and joint normality
A bivariate normal, centered anywhere in the YZ-plane, must exist over the entire plane...that is, in quadrants I, II, III, and IV because its domain is infinite in both variables.
But for it to exist in Quadrants II and IV, Y and Z must be oppositely-signed. If they cannot be, ... | Marginal normality and joint normality
A bivariate normal, centered anywhere in the YZ-plane, must exist over the entire plane...that is, in quadrants I, II, III, and IV because its domain is infinite in both variables.
But for it to exis |
47,247 | RMSE is scale-dependent; is RMSE%? | A function $f(\cdot)$ is scale-invariant if it yields the same result for argument $x$ as it does for argument $cx$, where $c$ is some positive constant. Let us see whether supplying $(cy_i,c\hat{y}_i)$ in place of $(y_i,\hat{y}_i)$ for $i=1,\dotsc,n$ will change the value of $\text{RMSE%}$:
$$
\begin{equation}
\begin{... | RMSE is scale-dependent; is RMSE%? | A function $f(\cdot)$ is scale-invariant if it yields the same result for argument $x$ as it does for argument $cx$, where $c$ is some positive constant. Let us see whether supplying $(cy_i,c\hat{y}_i | RMSE is scale-dependent; is RMSE%?
A function $f(\cdot)$ is scale-invariant if it yields the same result for argument $x$ as it does for argument $cx$, where $c$ is some positive constant. Let us see whether supplying $(cy_i,c\hat{y}_i)$ in place of $(y_i,\hat{y}_i)$ for $i=1,\dotsc,n$ will change the value of $\text{R... | RMSE is scale-dependent; is RMSE%?
A function $f(\cdot)$ is scale-invariant if it yields the same result for argument $x$ as it does for argument $cx$, where $c$ is some positive constant. Let us see whether supplying $(cy_i,c\hat{y}_i |
47,248 | Conditional variance in OLS regression | The title of your question "Conditional variance in OLS regression" gives a clue. The first expression
$$\text{Var}(y_{it})=\beta^{2}\sigma_{x}^{2}+\sigma_{\epsilon}^{2}$$
gives the unconditional variance ($x$ is not "conditioned away" and remains in the expression) while the second one
$$\text{E}\left[y_{it}-\text{... | Conditional variance in OLS regression | The title of your question "Conditional variance in OLS regression" gives a clue. The first expression
$$\text{Var}(y_{it})=\beta^{2}\sigma_{x}^{2}+\sigma_{\epsilon}^{2}$$
gives the unconditional va | Conditional variance in OLS regression
The title of your question "Conditional variance in OLS regression" gives a clue. The first expression
$$\text{Var}(y_{it})=\beta^{2}\sigma_{x}^{2}+\sigma_{\epsilon}^{2}$$
gives the unconditional variance ($x$ is not "conditioned away" and remains in the expression) while the se... | Conditional variance in OLS regression
The title of your question "Conditional variance in OLS regression" gives a clue. The first expression
$$\text{Var}(y_{it})=\beta^{2}\sigma_{x}^{2}+\sigma_{\epsilon}^{2}$$
gives the unconditional va |
47,249 | Conditional variance in OLS regression | But your final equation cannot be right if you are not treating the predictors as fixed. For
$$y_i = \beta x_i + \epsilon_i$$
recalling that
$$E\left(Y \right) = E\left[ E \left(Y|X \right) \right]$$
we have
$$E(y_i) =E\left( E\left(\beta x_i + \epsilon_i|x_i \right) \right) = \beta \mu_x$$
and so
\begin{align} Var(... | Conditional variance in OLS regression | But your final equation cannot be right if you are not treating the predictors as fixed. For
$$y_i = \beta x_i + \epsilon_i$$
recalling that
$$E\left(Y \right) = E\left[ E \left(Y|X \right) \right]$$
| Conditional variance in OLS regression
But your final equation cannot be right if you are not treating the predictors as fixed. For
$$y_i = \beta x_i + \epsilon_i$$
recalling that
$$E\left(Y \right) = E\left[ E \left(Y|X \right) \right]$$
we have
$$E(y_i) =E\left( E\left(\beta x_i + \epsilon_i|x_i \right) \right) = \... | Conditional variance in OLS regression
But your final equation cannot be right if you are not treating the predictors as fixed. For
$$y_i = \beta x_i + \epsilon_i$$
recalling that
$$E\left(Y \right) = E\left[ E \left(Y|X \right) \right]$$
|
47,250 | Does multicollinearity affect performance of a classifier? | There is an important qualifier in the continuation of the first cited quote from Wikipedia: "Multicollinearity does not reduce the predictive power or reliability of the model as a whole, at least within the sample data set" (emphasis added).
Unless there is a singular design matrix, multicollinearity does not prevent... | Does multicollinearity affect performance of a classifier? | There is an important qualifier in the continuation of the first cited quote from Wikipedia: "Multicollinearity does not reduce the predictive power or reliability of the model as a whole, at least wi | Does multicollinearity affect performance of a classifier?
There is an important qualifier in the continuation of the first cited quote from Wikipedia: "Multicollinearity does not reduce the predictive power or reliability of the model as a whole, at least within the sample data set" (emphasis added).
Unless there is a... | Does multicollinearity affect performance of a classifier?
There is an important qualifier in the continuation of the first cited quote from Wikipedia: "Multicollinearity does not reduce the predictive power or reliability of the model as a whole, at least wi |
47,251 | Does multicollinearity affect performance of a classifier? | Contrary to @EdM's answer, based on the answer here, the performance will not degrade if the test set has the same covariance matrix. In different words, if the correlation between the variables in the test set is the same, the combination of the coefficients and the feature vectors will lead to a valid result. Often t... | Does multicollinearity affect performance of a classifier? | Contrary to @EdM's answer, based on the answer here, the performance will not degrade if the test set has the same covariance matrix. In different words, if the correlation between the variables in th | Does multicollinearity affect performance of a classifier?
Contrary to @EdM's answer, based on the answer here, the performance will not degrade if the test set has the same covariance matrix. In different words, if the correlation between the variables in the test set is the same, the combination of the coefficients a... | Does multicollinearity affect performance of a classifier?
Contrary to @EdM's answer, based on the answer here, the performance will not degrade if the test set has the same covariance matrix. In different words, if the correlation between the variables in th |
47,252 | Why do we need to normalize data before applying penalizing methods in the framework of regression? [duplicate] | The reason to normalise your variables beforehand is to ensure that the regularisation term $\lambda$ regularises/affects the variable involved in a (somewhat) similar manner.
A very interesting thread touching on this issue appeared is here where the regularisation was imposed to normalised and unnormalised data and u... | Why do we need to normalize data before applying penalizing methods in the framework of regression? | The reason to normalise your variables beforehand is to ensure that the regularisation term $\lambda$ regularises/affects the variable involved in a (somewhat) similar manner.
A very interesting threa | Why do we need to normalize data before applying penalizing methods in the framework of regression? [duplicate]
The reason to normalise your variables beforehand is to ensure that the regularisation term $\lambda$ regularises/affects the variable involved in a (somewhat) similar manner.
A very interesting thread touchi... | Why do we need to normalize data before applying penalizing methods in the framework of regression?
The reason to normalise your variables beforehand is to ensure that the regularisation term $\lambda$ regularises/affects the variable involved in a (somewhat) similar manner.
A very interesting threa |
47,253 | Exercise on Chebyshev inequality compared to the Central Limit Theorem | Chebyshev's inequality works for any probability distribution (or large enough empirical data) while the CLT has stronger assumptions (independence, existence of moments, etc.). Its a good rule of thumb that if you want to reduce the number of assumptions in your model (or use a parametric model) you'll need more data ... | Exercise on Chebyshev inequality compared to the Central Limit Theorem | Chebyshev's inequality works for any probability distribution (or large enough empirical data) while the CLT has stronger assumptions (independence, existence of moments, etc.). Its a good rule of thu | Exercise on Chebyshev inequality compared to the Central Limit Theorem
Chebyshev's inequality works for any probability distribution (or large enough empirical data) while the CLT has stronger assumptions (independence, existence of moments, etc.). Its a good rule of thumb that if you want to reduce the number of assum... | Exercise on Chebyshev inequality compared to the Central Limit Theorem
Chebyshev's inequality works for any probability distribution (or large enough empirical data) while the CLT has stronger assumptions (independence, existence of moments, etc.). Its a good rule of thu |
47,254 | How to compute expectation of square of Riemann integral of a random variable? | Assuming that $E[W_tW_s]=\sigma^2\min(t,s)$,
\begin{align}
E\left[\left(\int_0^TW_s\,\mathrm ds\right)^2\right]&=E\left[\int_0^TW_t\,\mathrm dt\int_0^TW_s\,\mathrm ds\right]\\
&=E\left[\int_0^T\int_0^TW_t\,W_s\,\mathrm dt\mathrm ds\right]\\
&=\int_0^T\int_0^T E[W_tW_s]\,\mathrm dt\,\mathrm ds\\
&=\int_0^T\int_0^T \sigm... | How to compute expectation of square of Riemann integral of a random variable? | Assuming that $E[W_tW_s]=\sigma^2\min(t,s)$,
\begin{align}
E\left[\left(\int_0^TW_s\,\mathrm ds\right)^2\right]&=E\left[\int_0^TW_t\,\mathrm dt\int_0^TW_s\,\mathrm ds\right]\\
&=E\left[\int_0^T\int_0^ | How to compute expectation of square of Riemann integral of a random variable?
Assuming that $E[W_tW_s]=\sigma^2\min(t,s)$,
\begin{align}
E\left[\left(\int_0^TW_s\,\mathrm ds\right)^2\right]&=E\left[\int_0^TW_t\,\mathrm dt\int_0^TW_s\,\mathrm ds\right]\\
&=E\left[\int_0^T\int_0^TW_t\,W_s\,\mathrm dt\mathrm ds\right]\\
... | How to compute expectation of square of Riemann integral of a random variable?
Assuming that $E[W_tW_s]=\sigma^2\min(t,s)$,
\begin{align}
E\left[\left(\int_0^TW_s\,\mathrm ds\right)^2\right]&=E\left[\int_0^TW_t\,\mathrm dt\int_0^TW_s\,\mathrm ds\right]\\
&=E\left[\int_0^T\int_0^ |
47,255 | Exponentially decaying integral of a Poisson process | The answer may be surprising. Here is a brief sketch of a solution. As with a somewhat related problem, the idea is to obtain a recurrence relation for a quantity related to the asymptotic distribution and then solve that relation.
Since all uniform distributions are symmetric, the sum can equally well be expressed ... | Exponentially decaying integral of a Poisson process | The answer may be surprising. Here is a brief sketch of a solution. As with a somewhat related problem, the idea is to obtain a recurrence relation for a quantity related to the asymptotic distribut | Exponentially decaying integral of a Poisson process
The answer may be surprising. Here is a brief sketch of a solution. As with a somewhat related problem, the idea is to obtain a recurrence relation for a quantity related to the asymptotic distribution and then solve that relation.
Since all uniform distributions ... | Exponentially decaying integral of a Poisson process
The answer may be surprising. Here is a brief sketch of a solution. As with a somewhat related problem, the idea is to obtain a recurrence relation for a quantity related to the asymptotic distribut |
47,256 | How to read the Interaction effect in multiple linear regression with continuous regressors? | There seems to be one single intercept 49.80842, whereas it would make sense to have two different intercepts
No, it usually wouldn't make sense to have two intercepts; that only makes sense when you have a factor with two levels (and even then only if you regard the relationship holding factor levels constant).
The ... | How to read the Interaction effect in multiple linear regression with continuous regressors? | There seems to be one single intercept 49.80842, whereas it would make sense to have two different intercepts
No, it usually wouldn't make sense to have two intercepts; that only makes sense when yo | How to read the Interaction effect in multiple linear regression with continuous regressors?
There seems to be one single intercept 49.80842, whereas it would make sense to have two different intercepts
No, it usually wouldn't make sense to have two intercepts; that only makes sense when you have a factor with two le... | How to read the Interaction effect in multiple linear regression with continuous regressors?
There seems to be one single intercept 49.80842, whereas it would make sense to have two different intercepts
No, it usually wouldn't make sense to have two intercepts; that only makes sense when yo |
47,257 | How to read the Interaction effect in multiple linear regression with continuous regressors? | Output
Coefficients:
(Intercept) wt hp wt:hp
49.80842 -8.21662 -0.12010 0.02785
How do we read this output? ... We have a slope for wt and a slope for hp (-8.21662 -0.12010 = -8.33672, is that right?).
Nope. Some calculus should confirm that the derivative of mpg with ... | How to read the Interaction effect in multiple linear regression with continuous regressors? | Output
Coefficients:
(Intercept) wt hp wt:hp
49.80842 -8.21662 -0.12010 0.02785
How do we read this output? ... We have a slope for wt and a slope for | How to read the Interaction effect in multiple linear regression with continuous regressors?
Output
Coefficients:
(Intercept) wt hp wt:hp
49.80842 -8.21662 -0.12010 0.02785
How do we read this output? ... We have a slope for wt and a slope for hp (-8.21662 -0.12010 = -8.... | How to read the Interaction effect in multiple linear regression with continuous regressors?
Output
Coefficients:
(Intercept) wt hp wt:hp
49.80842 -8.21662 -0.12010 0.02785
How do we read this output? ... We have a slope for wt and a slope for |
47,258 | How to read the Interaction effect in multiple linear regression with continuous regressors? | The easiest way is to have a look at different quantiles of one of your variables of interest, depending on your research question. Assuming that you want to know the effect of one additional unit of horse power on the miles per gallon a car uses, you look at the distribution of the weight and use e.g. the percentiles ... | How to read the Interaction effect in multiple linear regression with continuous regressors? | The easiest way is to have a look at different quantiles of one of your variables of interest, depending on your research question. Assuming that you want to know the effect of one additional unit of | How to read the Interaction effect in multiple linear regression with continuous regressors?
The easiest way is to have a look at different quantiles of one of your variables of interest, depending on your research question. Assuming that you want to know the effect of one additional unit of horse power on the miles pe... | How to read the Interaction effect in multiple linear regression with continuous regressors?
The easiest way is to have a look at different quantiles of one of your variables of interest, depending on your research question. Assuming that you want to know the effect of one additional unit of |
47,259 | Interpret multidimensional scaling plot | Despite having 24 original variables, you can perfectly fit the distances amongst your data with 3 dimensions because you have only 4 points. It is possible that your points lie exactly on a 2D plane through the original 24D space, but that is incredibly unlikely, in my opinion. It is reasonable to imagine that the v... | Interpret multidimensional scaling plot | Despite having 24 original variables, you can perfectly fit the distances amongst your data with 3 dimensions because you have only 4 points. It is possible that your points lie exactly on a 2D plane | Interpret multidimensional scaling plot
Despite having 24 original variables, you can perfectly fit the distances amongst your data with 3 dimensions because you have only 4 points. It is possible that your points lie exactly on a 2D plane through the original 24D space, but that is incredibly unlikely, in my opinion.... | Interpret multidimensional scaling plot
Despite having 24 original variables, you can perfectly fit the distances amongst your data with 3 dimensions because you have only 4 points. It is possible that your points lie exactly on a 2D plane |
47,260 | Interpret multidimensional scaling plot | Sorry to necro, but found this through a search and thought I could help others.
The correct answer is that there is no interpretability to the MDS1 and MDS2 dimensions with respect to your original 24-space points.
This is because MDS performs a nonparametric transformations from the original 24-space into 2-space.
Th... | Interpret multidimensional scaling plot | Sorry to necro, but found this through a search and thought I could help others.
The correct answer is that there is no interpretability to the MDS1 and MDS2 dimensions with respect to your original 2 | Interpret multidimensional scaling plot
Sorry to necro, but found this through a search and thought I could help others.
The correct answer is that there is no interpretability to the MDS1 and MDS2 dimensions with respect to your original 24-space points.
This is because MDS performs a nonparametric transformations fro... | Interpret multidimensional scaling plot
Sorry to necro, but found this through a search and thought I could help others.
The correct answer is that there is no interpretability to the MDS1 and MDS2 dimensions with respect to your original 2 |
47,261 | machine learning for panel data in Python? | If you are considering to apply machine learning to temporal (i.e. panel data) then I recommend to use a recurrent neural network (RNN) for the tasks at hand.
Python offers several excellent neural networks libraries, such as Caffe, Brainstorm and Theano.
Note that when applying neural networks it is of importance tha... | machine learning for panel data in Python? | If you are considering to apply machine learning to temporal (i.e. panel data) then I recommend to use a recurrent neural network (RNN) for the tasks at hand.
Python offers several excellent neural ne | machine learning for panel data in Python?
If you are considering to apply machine learning to temporal (i.e. panel data) then I recommend to use a recurrent neural network (RNN) for the tasks at hand.
Python offers several excellent neural networks libraries, such as Caffe, Brainstorm and Theano.
Note that when apply... | machine learning for panel data in Python?
If you are considering to apply machine learning to temporal (i.e. panel data) then I recommend to use a recurrent neural network (RNN) for the tasks at hand.
Python offers several excellent neural ne |
47,262 | machine learning for panel data in Python? | If you define panel data as 'grouped' data where the intra-group observations are correlated, see sklearn leave P groups out. See my answer here. | machine learning for panel data in Python? | If you define panel data as 'grouped' data where the intra-group observations are correlated, see sklearn leave P groups out. See my answer here. | machine learning for panel data in Python?
If you define panel data as 'grouped' data where the intra-group observations are correlated, see sklearn leave P groups out. See my answer here. | machine learning for panel data in Python?
If you define panel data as 'grouped' data where the intra-group observations are correlated, see sklearn leave P groups out. See my answer here. |
47,263 | multivariate transformation of random variable | I have two suggestions:
Use differential algebra instead of Jacobians. It's a simpler, more reliable way to keep track of the derivatives.
Draw a picture. Often the trickiest part of such calculations is to determine what the domain of the new variables is. Pictures help.
Details and supporting code follow.
Two... | multivariate transformation of random variable | I have two suggestions:
Use differential algebra instead of Jacobians. It's a simpler, more reliable way to keep track of the derivatives.
Draw a picture. Often the trickiest part of such calculat | multivariate transformation of random variable
I have two suggestions:
Use differential algebra instead of Jacobians. It's a simpler, more reliable way to keep track of the derivatives.
Draw a picture. Often the trickiest part of such calculations is to determine what the domain of the new variables is. Pictures h... | multivariate transformation of random variable
I have two suggestions:
Use differential algebra instead of Jacobians. It's a simpler, more reliable way to keep track of the derivatives.
Draw a picture. Often the trickiest part of such calculat |
47,264 | What statistics can I use to combine multiple rankings in order to create a final ranking? | Let $r_{g,i}$ be the rank of gene $g$ in ranking $i$ (out of a total of $k$ rankings). Then a statistic which pools these ranks together is the rank product statistic, which is just the geometric mean of the ranks:
$$RP(g) = \left(\prod_{i=1}^k r_{g,i}\right)^{\frac{1}{k}}$$
The rank product statistic was mainly develo... | What statistics can I use to combine multiple rankings in order to create a final ranking? | Let $r_{g,i}$ be the rank of gene $g$ in ranking $i$ (out of a total of $k$ rankings). Then a statistic which pools these ranks together is the rank product statistic, which is just the geometric mean | What statistics can I use to combine multiple rankings in order to create a final ranking?
Let $r_{g,i}$ be the rank of gene $g$ in ranking $i$ (out of a total of $k$ rankings). Then a statistic which pools these ranks together is the rank product statistic, which is just the geometric mean of the ranks:
$$RP(g) = \lef... | What statistics can I use to combine multiple rankings in order to create a final ranking?
Let $r_{g,i}$ be the rank of gene $g$ in ranking $i$ (out of a total of $k$ rankings). Then a statistic which pools these ranks together is the rank product statistic, which is just the geometric mean |
47,265 | Interpreting logistic regression with an interaction and a quadratic term? | The only model that would really make sense is
$$Y = \beta_{0} + \beta_{1}X + \beta_{2}X^{2} + \beta_{3}(Z=b) + \beta_{4}(Z=c) + \beta_{5}X(Z=b) + \beta_{6}X(Z=c) + \beta_{7}X^{2}(Z=b) + \beta_{8}X^{2}(Z=c)$$
where $(Z=k)$ denotes 1 if $Z=k$ and 0 otherwise.
In this model the test for interaction is $H_{0}: \beta_{5}\... | Interpreting logistic regression with an interaction and a quadratic term? | The only model that would really make sense is
$$Y = \beta_{0} + \beta_{1}X + \beta_{2}X^{2} + \beta_{3}(Z=b) + \beta_{4}(Z=c) + \beta_{5}X(Z=b) + \beta_{6}X(Z=c) + \beta_{7}X^{2}(Z=b) + \beta_{8}X^{ | Interpreting logistic regression with an interaction and a quadratic term?
The only model that would really make sense is
$$Y = \beta_{0} + \beta_{1}X + \beta_{2}X^{2} + \beta_{3}(Z=b) + \beta_{4}(Z=c) + \beta_{5}X(Z=b) + \beta_{6}X(Z=c) + \beta_{7}X^{2}(Z=b) + \beta_{8}X^{2}(Z=c)$$
where $(Z=k)$ denotes 1 if $Z=k$ an... | Interpreting logistic regression with an interaction and a quadratic term?
The only model that would really make sense is
$$Y = \beta_{0} + \beta_{1}X + \beta_{2}X^{2} + \beta_{3}(Z=b) + \beta_{4}(Z=c) + \beta_{5}X(Z=b) + \beta_{6}X(Z=c) + \beta_{7}X^{2}(Z=b) + \beta_{8}X^{ |
47,266 | Sum of Gaussian mixture and Gaussian scale mixture | Let $X$ has the mixture distribution with density $f(x)=\sum \pi_i f_i(x)$ and $Y$ the mixture distribition with density $g(x) = \sum \phi_i g_i(x)$, and suppose $X$ and $Y$ are independent. A useful tool for analyzing distribution of sums of independent random variables is the moment generating function (look it upon ... | Sum of Gaussian mixture and Gaussian scale mixture | Let $X$ has the mixture distribution with density $f(x)=\sum \pi_i f_i(x)$ and $Y$ the mixture distribition with density $g(x) = \sum \phi_i g_i(x)$, and suppose $X$ and $Y$ are independent. A useful | Sum of Gaussian mixture and Gaussian scale mixture
Let $X$ has the mixture distribution with density $f(x)=\sum \pi_i f_i(x)$ and $Y$ the mixture distribition with density $g(x) = \sum \phi_i g_i(x)$, and suppose $X$ and $Y$ are independent. A useful tool for analyzing distribution of sums of independent random variabl... | Sum of Gaussian mixture and Gaussian scale mixture
Let $X$ has the mixture distribution with density $f(x)=\sum \pi_i f_i(x)$ and $Y$ the mixture distribition with density $g(x) = \sum \phi_i g_i(x)$, and suppose $X$ and $Y$ are independent. A useful |
47,267 | Sum of Gaussian mixture and Gaussian scale mixture | If I understand your notation you are asking about the distribution of $Y$ when $Y = X + Z$ where $X \sim \mathcal N(a,b)$, $Z \sim \mathcal N(c,d)$.
In this case $Y$ is Gaussian if $Z$ and $X$ are independent or jointly normal, with mean $a+b$ and a covariance matrix dependent on the relationship between $X$ and $Z$.... | Sum of Gaussian mixture and Gaussian scale mixture | If I understand your notation you are asking about the distribution of $Y$ when $Y = X + Z$ where $X \sim \mathcal N(a,b)$, $Z \sim \mathcal N(c,d)$.
In this case $Y$ is Gaussian if $Z$ and $X$ are i | Sum of Gaussian mixture and Gaussian scale mixture
If I understand your notation you are asking about the distribution of $Y$ when $Y = X + Z$ where $X \sim \mathcal N(a,b)$, $Z \sim \mathcal N(c,d)$.
In this case $Y$ is Gaussian if $Z$ and $X$ are independent or jointly normal, with mean $a+b$ and a covariance matrix... | Sum of Gaussian mixture and Gaussian scale mixture
If I understand your notation you are asking about the distribution of $Y$ when $Y = X + Z$ where $X \sim \mathcal N(a,b)$, $Z \sim \mathcal N(c,d)$.
In this case $Y$ is Gaussian if $Z$ and $X$ are i |
47,268 | Generating a sample from Epanechnikov's kernel | Consider this alternative description of the same algorithm:
Generate iid $X_1, X_2, X_3$ with Uniform$(0,1)$ distributions.
Select one of the two smallest of the $X_i$ at random, with equal probability. Call this value $X$.
Randomly negate $X$ with probability $1/2$.
Parts (1) and (3) reflect the fact that a Unifor... | Generating a sample from Epanechnikov's kernel | Consider this alternative description of the same algorithm:
Generate iid $X_1, X_2, X_3$ with Uniform$(0,1)$ distributions.
Select one of the two smallest of the $X_i$ at random, with equal probabil | Generating a sample from Epanechnikov's kernel
Consider this alternative description of the same algorithm:
Generate iid $X_1, X_2, X_3$ with Uniform$(0,1)$ distributions.
Select one of the two smallest of the $X_i$ at random, with equal probability. Call this value $X$.
Randomly negate $X$ with probability $1/2$.
P... | Generating a sample from Epanechnikov's kernel
Consider this alternative description of the same algorithm:
Generate iid $X_1, X_2, X_3$ with Uniform$(0,1)$ distributions.
Select one of the two smallest of the $X_i$ at random, with equal probabil |
47,269 | Generating a sample from Epanechnikov's kernel | Although it only is a too long comment that comes a day late and a dollar short, my explanation, which is highly related to the more detailed and to the point answer by whuber, is that the outcome of Devroye's algorithm with those three uniforms is indeed distributed from the mixture of the distributions of the first o... | Generating a sample from Epanechnikov's kernel | Although it only is a too long comment that comes a day late and a dollar short, my explanation, which is highly related to the more detailed and to the point answer by whuber, is that the outcome of | Generating a sample from Epanechnikov's kernel
Although it only is a too long comment that comes a day late and a dollar short, my explanation, which is highly related to the more detailed and to the point answer by whuber, is that the outcome of Devroye's algorithm with those three uniforms is indeed distributed from ... | Generating a sample from Epanechnikov's kernel
Although it only is a too long comment that comes a day late and a dollar short, my explanation, which is highly related to the more detailed and to the point answer by whuber, is that the outcome of |
47,270 | How to get the standard error of linear regression parameters? | Hint:
Write $$\widehat{\beta_1}= \frac{\sum_{i=1}^n \left( x_i-\bar{x} \right)}{\sum_{i=1}^n \left(x_i-\bar{x} \right)^2} y_i $$
and you can check that these two expressions are equivalent, as the sum of mean deviations is zero. Since we are treating the predictors as fixed, you can use the properties of the variance t... | How to get the standard error of linear regression parameters? | Hint:
Write $$\widehat{\beta_1}= \frac{\sum_{i=1}^n \left( x_i-\bar{x} \right)}{\sum_{i=1}^n \left(x_i-\bar{x} \right)^2} y_i $$
and you can check that these two expressions are equivalent, as the sum | How to get the standard error of linear regression parameters?
Hint:
Write $$\widehat{\beta_1}= \frac{\sum_{i=1}^n \left( x_i-\bar{x} \right)}{\sum_{i=1}^n \left(x_i-\bar{x} \right)^2} y_i $$
and you can check that these two expressions are equivalent, as the sum of mean deviations is zero. Since we are treating the pr... | How to get the standard error of linear regression parameters?
Hint:
Write $$\widehat{\beta_1}= \frac{\sum_{i=1}^n \left( x_i-\bar{x} \right)}{\sum_{i=1}^n \left(x_i-\bar{x} \right)^2} y_i $$
and you can check that these two expressions are equivalent, as the sum |
47,271 | How to get the standard error of linear regression parameters? | The long algebraic manipulations involved in standard demonstrations are bothersome. There ought to be a demonstration that is simple, direct, and provides insight into what the terms in the formulas mean.
By "simple" I will allow liberal use of substitution in formulas and application of the most straightforward alge... | How to get the standard error of linear regression parameters? | The long algebraic manipulations involved in standard demonstrations are bothersome. There ought to be a demonstration that is simple, direct, and provides insight into what the terms in the formulas | How to get the standard error of linear regression parameters?
The long algebraic manipulations involved in standard demonstrations are bothersome. There ought to be a demonstration that is simple, direct, and provides insight into what the terms in the formulas mean.
By "simple" I will allow liberal use of substituti... | How to get the standard error of linear regression parameters?
The long algebraic manipulations involved in standard demonstrations are bothersome. There ought to be a demonstration that is simple, direct, and provides insight into what the terms in the formulas |
47,272 | How to get the standard error of linear regression parameters? | The principle for derivation below
The estimators $\beta_0$ and $\beta_1$ are linear estimators. That means that you can write it as a weighted sum of the observations $y_i$.
$$\hat\beta_ 0 = \sum b_{0i} y_i\\\hat\beta_ 1 = \sum b_{1i} y_i$$
As a consequence, we see that the sampling distribution of the estimators corr... | How to get the standard error of linear regression parameters? | The principle for derivation below
The estimators $\beta_0$ and $\beta_1$ are linear estimators. That means that you can write it as a weighted sum of the observations $y_i$.
$$\hat\beta_ 0 = \sum b_{ | How to get the standard error of linear regression parameters?
The principle for derivation below
The estimators $\beta_0$ and $\beta_1$ are linear estimators. That means that you can write it as a weighted sum of the observations $y_i$.
$$\hat\beta_ 0 = \sum b_{0i} y_i\\\hat\beta_ 1 = \sum b_{1i} y_i$$
As a consequenc... | How to get the standard error of linear regression parameters?
The principle for derivation below
The estimators $\beta_0$ and $\beta_1$ are linear estimators. That means that you can write it as a weighted sum of the observations $y_i$.
$$\hat\beta_ 0 = \sum b_{ |
47,273 | How to use PCA for prediction? | It seems that you have 418 cases, divided into a training set of 318 cases and a test set of 100 cases. I'll answer your question and suggest a closely related but potentially better approach to your problem.
As noted on the MATLAB help page, for PCR it's best if the predictors are both centered and scaled to unit var... | How to use PCA for prediction? | It seems that you have 418 cases, divided into a training set of 318 cases and a test set of 100 cases. I'll answer your question and suggest a closely related but potentially better approach to your | How to use PCA for prediction?
It seems that you have 418 cases, divided into a training set of 318 cases and a test set of 100 cases. I'll answer your question and suggest a closely related but potentially better approach to your problem.
As noted on the MATLAB help page, for PCR it's best if the predictors are both ... | How to use PCA for prediction?
It seems that you have 418 cases, divided into a training set of 318 cases and a test set of 100 cases. I'll answer your question and suggest a closely related but potentially better approach to your |
47,274 | How to use PCA for prediction? | Here are some ways to test whether your understanding of the calculations is correct:
Take a few of the training cases and calculate the prediction as you think. Then compare with the fitted values from the help page.
If you use the full PCA model (all loadings), the PCA performs only a rotation of the data. The pre... | How to use PCA for prediction? | Here are some ways to test whether your understanding of the calculations is correct:
Take a few of the training cases and calculate the prediction as you think. Then compare with the fitted values | How to use PCA for prediction?
Here are some ways to test whether your understanding of the calculations is correct:
Take a few of the training cases and calculate the prediction as you think. Then compare with the fitted values from the help page.
If you use the full PCA model (all loadings), the PCA performs only ... | How to use PCA for prediction?
Here are some ways to test whether your understanding of the calculations is correct:
Take a few of the training cases and calculate the prediction as you think. Then compare with the fitted values |
47,275 | How to use PCA for prediction? | I am not a Matlab user, but you are approaching the problem from the wrong angle. PCA should not be used to help with overfitting - regularization is a proper tool for it. This way you are not throwing data away, and you will most likely end up with a model that is easier to explain (e.g. feature importance or weights,... | How to use PCA for prediction? | I am not a Matlab user, but you are approaching the problem from the wrong angle. PCA should not be used to help with overfitting - regularization is a proper tool for it. This way you are not throwin | How to use PCA for prediction?
I am not a Matlab user, but you are approaching the problem from the wrong angle. PCA should not be used to help with overfitting - regularization is a proper tool for it. This way you are not throwing data away, and you will most likely end up with a model that is easier to explain (e.g.... | How to use PCA for prediction?
I am not a Matlab user, but you are approaching the problem from the wrong angle. PCA should not be used to help with overfitting - regularization is a proper tool for it. This way you are not throwin |
47,276 | Is the Fisher's exact test "parametric" or "non-parametric"? | tl;dr: Fisher's Exact Test is nonparametric in the sense that it does not assume that the population is based on theoretical probability distributions (normal/geometric/exponential etc.), but that the data itself reflects the parameters, which is why it proceeds with the assumption that the row/col totals are fixed.
Fi... | Is the Fisher's exact test "parametric" or "non-parametric"? | tl;dr: Fisher's Exact Test is nonparametric in the sense that it does not assume that the population is based on theoretical probability distributions (normal/geometric/exponential etc.), but that the | Is the Fisher's exact test "parametric" or "non-parametric"?
tl;dr: Fisher's Exact Test is nonparametric in the sense that it does not assume that the population is based on theoretical probability distributions (normal/geometric/exponential etc.), but that the data itself reflects the parameters, which is why it proce... | Is the Fisher's exact test "parametric" or "non-parametric"?
tl;dr: Fisher's Exact Test is nonparametric in the sense that it does not assume that the population is based on theoretical probability distributions (normal/geometric/exponential etc.), but that the |
47,277 | Is the Fisher's exact test "parametric" or "non-parametric"? | Fisher's exact test is a parametric test, because it does assume an underlying binomial distribution for the $2\times 2$ table. The table probabilities are then calculated conditioning on the total number of successes in an exact fashion. The term parametric refers to whether distributional assumptions are made about ... | Is the Fisher's exact test "parametric" or "non-parametric"? | Fisher's exact test is a parametric test, because it does assume an underlying binomial distribution for the $2\times 2$ table. The table probabilities are then calculated conditioning on the total n | Is the Fisher's exact test "parametric" or "non-parametric"?
Fisher's exact test is a parametric test, because it does assume an underlying binomial distribution for the $2\times 2$ table. The table probabilities are then calculated conditioning on the total number of successes in an exact fashion. The term parametric... | Is the Fisher's exact test "parametric" or "non-parametric"?
Fisher's exact test is a parametric test, because it does assume an underlying binomial distribution for the $2\times 2$ table. The table probabilities are then calculated conditioning on the total n |
47,278 | Is the Fisher's exact test "parametric" or "non-parametric"? | Consider the case of comparing two samples of dichotomous observations ("success" & "failure"), & taking one of the following approaches to defining a test statistic & its sampling distribution:
(1) Assume, under the null hypothesis, all observations are drawn independently from the same distribution & condition on the... | Is the Fisher's exact test "parametric" or "non-parametric"? | Consider the case of comparing two samples of dichotomous observations ("success" & "failure"), & taking one of the following approaches to defining a test statistic & its sampling distribution:
(1) A | Is the Fisher's exact test "parametric" or "non-parametric"?
Consider the case of comparing two samples of dichotomous observations ("success" & "failure"), & taking one of the following approaches to defining a test statistic & its sampling distribution:
(1) Assume, under the null hypothesis, all observations are draw... | Is the Fisher's exact test "parametric" or "non-parametric"?
Consider the case of comparing two samples of dichotomous observations ("success" & "failure"), & taking one of the following approaches to defining a test statistic & its sampling distribution:
(1) A |
47,279 | Is the Fisher's exact test "parametric" or "non-parametric"? | Tests that are used on nonparametric data can be used on any data normal or not normal (it is just in comparison to tests that can only be used on normal data they are less reliable). Fishers test is one of the tests that is actually prefered to use over chi-squared when the data is too small. | Is the Fisher's exact test "parametric" or "non-parametric"? | Tests that are used on nonparametric data can be used on any data normal or not normal (it is just in comparison to tests that can only be used on normal data they are less reliable). Fishers test is | Is the Fisher's exact test "parametric" or "non-parametric"?
Tests that are used on nonparametric data can be used on any data normal or not normal (it is just in comparison to tests that can only be used on normal data they are less reliable). Fishers test is one of the tests that is actually prefered to use over chi-... | Is the Fisher's exact test "parametric" or "non-parametric"?
Tests that are used on nonparametric data can be used on any data normal or not normal (it is just in comparison to tests that can only be used on normal data they are less reliable). Fishers test is |
47,280 | What is the meaning of the term "stable" in relation to predictions? | The book Elements of Statistical Learning does not seem to give a formal definition of the concept of "stability" as it is used in this context. The words stable or stability do not occur in the index. However, the following quote seems to indicate the intended meaning (page 16 of second edition):
The linear decision ... | What is the meaning of the term "stable" in relation to predictions? | The book Elements of Statistical Learning does not seem to give a formal definition of the concept of "stability" as it is used in this context. The words stable or stability do not occur in the index | What is the meaning of the term "stable" in relation to predictions?
The book Elements of Statistical Learning does not seem to give a formal definition of the concept of "stability" as it is used in this context. The words stable or stability do not occur in the index. However, the following quote seems to indicate th... | What is the meaning of the term "stable" in relation to predictions?
The book Elements of Statistical Learning does not seem to give a formal definition of the concept of "stability" as it is used in this context. The words stable or stability do not occur in the index |
47,281 | What is the meaning of the term "stable" in relation to predictions? | I'd like to illustrate these two using the following comparison.
As you can see the higher the variance the more unstable the prediction will be and the higher the bias the mean of the prediction will be more far away from the target. The linear regresson would be stable but its bias sometimes is high(overfitting); wh... | What is the meaning of the term "stable" in relation to predictions? | I'd like to illustrate these two using the following comparison.
As you can see the higher the variance the more unstable the prediction will be and the higher the bias the mean of the prediction wil | What is the meaning of the term "stable" in relation to predictions?
I'd like to illustrate these two using the following comparison.
As you can see the higher the variance the more unstable the prediction will be and the higher the bias the mean of the prediction will be more far away from the target. The linear regr... | What is the meaning of the term "stable" in relation to predictions?
I'd like to illustrate these two using the following comparison.
As you can see the higher the variance the more unstable the prediction will be and the higher the bias the mean of the prediction wil |
47,282 | Why are transitions and emissions in HMM assumed to be independent? | Yes, it's a limitation of the model.
In most dynamical systems that you might care to think about using an HMM, the act of measurement or observation is usually conceived and/or constructed in such a way that it is assumed not to affect the system under observation. We want to imagine the observer as being passive and... | Why are transitions and emissions in HMM assumed to be independent? | Yes, it's a limitation of the model.
In most dynamical systems that you might care to think about using an HMM, the act of measurement or observation is usually conceived and/or constructed in such a | Why are transitions and emissions in HMM assumed to be independent?
Yes, it's a limitation of the model.
In most dynamical systems that you might care to think about using an HMM, the act of measurement or observation is usually conceived and/or constructed in such a way that it is assumed not to affect the system unde... | Why are transitions and emissions in HMM assumed to be independent?
Yes, it's a limitation of the model.
In most dynamical systems that you might care to think about using an HMM, the act of measurement or observation is usually conceived and/or constructed in such a |
47,283 | Why are transitions and emissions in HMM assumed to be independent? | In wikipedia article it is stated that next hidden state $x(t+1)$ conditionally depends from previous hidden state $x(t)$:
But we can't say that observation $y(t)$ and next hidden state $x(t+1)$ are independant. Because if you observe $y(t)$ then you have some knowledge about $x(t)$ probability distribution and the... | Why are transitions and emissions in HMM assumed to be independent? | In wikipedia article it is stated that next hidden state $x(t+1)$ conditionally depends from previous hidden state $x(t)$:
But we can't say that observation $y(t)$ and next hidden state $x(t+1)$ ar | Why are transitions and emissions in HMM assumed to be independent?
In wikipedia article it is stated that next hidden state $x(t+1)$ conditionally depends from previous hidden state $x(t)$:
But we can't say that observation $y(t)$ and next hidden state $x(t+1)$ are independant. Because if you observe $y(t)$ then y... | Why are transitions and emissions in HMM assumed to be independent?
In wikipedia article it is stated that next hidden state $x(t+1)$ conditionally depends from previous hidden state $x(t)$:
But we can't say that observation $y(t)$ and next hidden state $x(t+1)$ ar |
47,284 | How to compare (probability) predictive ability of models developed from logistic regression? | There are many good ways to do it. Here are some examples. These methods are implemented in the R rms package (functions val.prob, calibrate, validate):
loess nonparametric full-resolution calibration curve (no binning)
Spiegelhalter's test
Brier score (a proper accuracy score - quadratic score)
Generalized $R^2$ (a... | How to compare (probability) predictive ability of models developed from logistic regression? | There are many good ways to do it. Here are some examples. These methods are implemented in the R rms package (functions val.prob, calibrate, validate):
loess nonparametric full-resolution calibrat | How to compare (probability) predictive ability of models developed from logistic regression?
There are many good ways to do it. Here are some examples. These methods are implemented in the R rms package (functions val.prob, calibrate, validate):
loess nonparametric full-resolution calibration curve (no binning)
Spi... | How to compare (probability) predictive ability of models developed from logistic regression?
There are many good ways to do it. Here are some examples. These methods are implemented in the R rms package (functions val.prob, calibrate, validate):
loess nonparametric full-resolution calibrat |
47,285 | How to compare (probability) predictive ability of models developed from logistic regression? | The AUROC (which is related to Kolmogorov Smirnov) is not only invariant to a change in coefficient, it is invariant for any order-preserving transformation and consequently it tells how well you predict the ranking of the subjects.
A test for checking whether your probabilities are well predicted is e.g. the Hosmer-... | How to compare (probability) predictive ability of models developed from logistic regression? | The AUROC (which is related to Kolmogorov Smirnov) is not only invariant to a change in coefficient, it is invariant for any order-preserving transformation and consequently it tells how well you pred | How to compare (probability) predictive ability of models developed from logistic regression?
The AUROC (which is related to Kolmogorov Smirnov) is not only invariant to a change in coefficient, it is invariant for any order-preserving transformation and consequently it tells how well you predict the ranking of the sub... | How to compare (probability) predictive ability of models developed from logistic regression?
The AUROC (which is related to Kolmogorov Smirnov) is not only invariant to a change in coefficient, it is invariant for any order-preserving transformation and consequently it tells how well you pred |
47,286 | Why SVM struggles to find good features among garbage? | TL;DR: Garbage in, garbage out. Selecting better features will promote a better model. (Sometimes the answer really is that simple!) What follows is a description of one path forward to selecting higher-quality features in the context of fitting an SVM.
SVM performance can suffer when presented with many garbage featur... | Why SVM struggles to find good features among garbage? | TL;DR: Garbage in, garbage out. Selecting better features will promote a better model. (Sometimes the answer really is that simple!) What follows is a description of one path forward to selecting high | Why SVM struggles to find good features among garbage?
TL;DR: Garbage in, garbage out. Selecting better features will promote a better model. (Sometimes the answer really is that simple!) What follows is a description of one path forward to selecting higher-quality features in the context of fitting an SVM.
SVM perform... | Why SVM struggles to find good features among garbage?
TL;DR: Garbage in, garbage out. Selecting better features will promote a better model. (Sometimes the answer really is that simple!) What follows is a description of one path forward to selecting high |
47,287 | How to identify the seasonality of a timeseries from the Periodogram? | Well, the periodogram after taking first differences doesn't indicate any clear periodicity. However, be aware that taking first differences amplifies high-frequency components, which should appear in the power spectrum as a quadratic trend, and in the log-power spectrum as a log-shaped trend (which is roughly compatib... | How to identify the seasonality of a timeseries from the Periodogram? | Well, the periodogram after taking first differences doesn't indicate any clear periodicity. However, be aware that taking first differences amplifies high-frequency components, which should appear in | How to identify the seasonality of a timeseries from the Periodogram?
Well, the periodogram after taking first differences doesn't indicate any clear periodicity. However, be aware that taking first differences amplifies high-frequency components, which should appear in the power spectrum as a quadratic trend, and in t... | How to identify the seasonality of a timeseries from the Periodogram?
Well, the periodogram after taking first differences doesn't indicate any clear periodicity. However, be aware that taking first differences amplifies high-frequency components, which should appear in |
47,288 | Why is Moran's $I$ coming out greater than $1$? | Comparison of $I$ with correlation coefficients is good, but it has its limits. This answer uncovers what those limits are. It derives a tight upper bound for $|I|$ in terms of the weights matrix $W$ and shows that in ordinary applications, where $W$ is symmetric and row-normalized, this bound is $1$ (or less). For t... | Why is Moran's $I$ coming out greater than $1$? | Comparison of $I$ with correlation coefficients is good, but it has its limits. This answer uncovers what those limits are. It derives a tight upper bound for $|I|$ in terms of the weights matrix $W | Why is Moran's $I$ coming out greater than $1$?
Comparison of $I$ with correlation coefficients is good, but it has its limits. This answer uncovers what those limits are. It derives a tight upper bound for $|I|$ in terms of the weights matrix $W$ and shows that in ordinary applications, where $W$ is symmetric and ro... | Why is Moran's $I$ coming out greater than $1$?
Comparison of $I$ with correlation coefficients is good, but it has its limits. This answer uncovers what those limits are. It derives a tight upper bound for $|I|$ in terms of the weights matrix $W |
47,289 | Why is Moran's $I$ coming out greater than $1$? | That is true because you assume no variation(weight) on$X_i,i=2,\ldots,4$. In your case you have,
\begin{align}
I &=\frac{N}{1} \frac{(X_1-\bar{X})(X_1-\bar{X})}{\sum_i(X_i-\bar{X})^2}\\
&=\frac{(X_1-\bar{X})(X_1-\bar{X})}{\hat{\sigma}_X}\\
&=\frac{(X_1-\bar{X})^2}{\hat{\sigma}_X}
\end{align}
In this case $\mu_x=0$ and... | Why is Moran's $I$ coming out greater than $1$? | That is true because you assume no variation(weight) on$X_i,i=2,\ldots,4$. In your case you have,
\begin{align}
I &=\frac{N}{1} \frac{(X_1-\bar{X})(X_1-\bar{X})}{\sum_i(X_i-\bar{X})^2}\\
&=\frac{(X_1- | Why is Moran's $I$ coming out greater than $1$?
That is true because you assume no variation(weight) on$X_i,i=2,\ldots,4$. In your case you have,
\begin{align}
I &=\frac{N}{1} \frac{(X_1-\bar{X})(X_1-\bar{X})}{\sum_i(X_i-\bar{X})^2}\\
&=\frac{(X_1-\bar{X})(X_1-\bar{X})}{\hat{\sigma}_X}\\
&=\frac{(X_1-\bar{X})^2}{\hat{\... | Why is Moran's $I$ coming out greater than $1$?
That is true because you assume no variation(weight) on$X_i,i=2,\ldots,4$. In your case you have,
\begin{align}
I &=\frac{N}{1} \frac{(X_1-\bar{X})(X_1-\bar{X})}{\sum_i(X_i-\bar{X})^2}\\
&=\frac{(X_1- |
47,290 | Is there something called "mean coding" (like dummy coding & effect coding) in regression models? | Yes, that can be done, and is done occasionally. What you have is called "level means coding". For more on this, it may help you to read my answer here: How can logistic regression have a factorial predictor and no intercept? For an example of a case where I found it convenient to use level means coding, see: Why do... | Is there something called "mean coding" (like dummy coding & effect coding) in regression models? | Yes, that can be done, and is done occasionally. What you have is called "level means coding". For more on this, it may help you to read my answer here: How can logistic regression have a factorial | Is there something called "mean coding" (like dummy coding & effect coding) in regression models?
Yes, that can be done, and is done occasionally. What you have is called "level means coding". For more on this, it may help you to read my answer here: How can logistic regression have a factorial predictor and no inter... | Is there something called "mean coding" (like dummy coding & effect coding) in regression models?
Yes, that can be done, and is done occasionally. What you have is called "level means coding". For more on this, it may help you to read my answer here: How can logistic regression have a factorial |
47,291 | A non parametric clustering algorithm suitable for high dimensional data | The most common clustering technique that meets your requirements would be DBSCAN. This finds points that are continuous by virtue of having shared nearest neighbors. There can be any number of clusters, and they can be of any shape. There are only two parameters to choose / enter: epsilon, a 'reachability' distance... | A non parametric clustering algorithm suitable for high dimensional data | The most common clustering technique that meets your requirements would be DBSCAN. This finds points that are continuous by virtue of having shared nearest neighbors. There can be any number of clus | A non parametric clustering algorithm suitable for high dimensional data
The most common clustering technique that meets your requirements would be DBSCAN. This finds points that are continuous by virtue of having shared nearest neighbors. There can be any number of clusters, and they can be of any shape. There are ... | A non parametric clustering algorithm suitable for high dimensional data
The most common clustering technique that meets your requirements would be DBSCAN. This finds points that are continuous by virtue of having shared nearest neighbors. There can be any number of clus |
47,292 | Fourier transform and the multivariate normal | The multivariate normal has some nice properties. In particular, if $x\sim N(\mu,\Sigma)$, then, for any matrix $A$, $Ax \sim N(A\mu, A\Sigma A^T)$.
Noting that a (discrete) Fourier transform can an be written in matrix form as $FT(x) = Fx$, we see that $FT(x) \sim N(F\mu, F\Sigma F^T)$.
You can prove this by check... | Fourier transform and the multivariate normal | The multivariate normal has some nice properties. In particular, if $x\sim N(\mu,\Sigma)$, then, for any matrix $A$, $Ax \sim N(A\mu, A\Sigma A^T)$.
Noting that a (discrete) Fourier transform can an | Fourier transform and the multivariate normal
The multivariate normal has some nice properties. In particular, if $x\sim N(\mu,\Sigma)$, then, for any matrix $A$, $Ax \sim N(A\mu, A\Sigma A^T)$.
Noting that a (discrete) Fourier transform can an be written in matrix form as $FT(x) = Fx$, we see that $FT(x) \sim N(F\mu... | Fourier transform and the multivariate normal
The multivariate normal has some nice properties. In particular, if $x\sim N(\mu,\Sigma)$, then, for any matrix $A$, $Ax \sim N(A\mu, A\Sigma A^T)$.
Noting that a (discrete) Fourier transform can an |
47,293 | Fourier transform and the multivariate normal | Unfortunately, the definition and conventions for complex Multivariate Normal is not completely standardized. Perhaps "yours" is consistent with equatoion 2 of http://cran.r-project.org/web/packages/cmvnorm/vignettes/complicator.pdf , which is different than https://en.wikipedia.org/wiki/Complex_normal_distribution .
... | Fourier transform and the multivariate normal | Unfortunately, the definition and conventions for complex Multivariate Normal is not completely standardized. Perhaps "yours" is consistent with equatoion 2 of http://cran.r-project.org/web/packages/c | Fourier transform and the multivariate normal
Unfortunately, the definition and conventions for complex Multivariate Normal is not completely standardized. Perhaps "yours" is consistent with equatoion 2 of http://cran.r-project.org/web/packages/cmvnorm/vignettes/complicator.pdf , which is different than https://en.wiki... | Fourier transform and the multivariate normal
Unfortunately, the definition and conventions for complex Multivariate Normal is not completely standardized. Perhaps "yours" is consistent with equatoion 2 of http://cran.r-project.org/web/packages/c |
47,294 | Modeling prices with the Hedonic regression | This type of approach clearly can work (and has evidently been used by tax authorities to set property taxes on my house for many years), so there needs to be some investigation of the sources of this difficulty.
Understanding the nature of this data set is very important. If it is to be used for predicting prices of p... | Modeling prices with the Hedonic regression | This type of approach clearly can work (and has evidently been used by tax authorities to set property taxes on my house for many years), so there needs to be some investigation of the sources of this | Modeling prices with the Hedonic regression
This type of approach clearly can work (and has evidently been used by tax authorities to set property taxes on my house for many years), so there needs to be some investigation of the sources of this difficulty.
Understanding the nature of this data set is very important. If... | Modeling prices with the Hedonic regression
This type of approach clearly can work (and has evidently been used by tax authorities to set property taxes on my house for many years), so there needs to be some investigation of the sources of this |
47,295 | Modeling prices with the Hedonic regression | I know this is an old post; hope the message helps someone reading this thread who might approach the same problem. The logical premise that 0 rooms; and 0 living area = zero value is improper because what the model is ignoring is the underlying value of land. This also affects the "geographic" dispersion characteris... | Modeling prices with the Hedonic regression | I know this is an old post; hope the message helps someone reading this thread who might approach the same problem. The logical premise that 0 rooms; and 0 living area = zero value is improper becaus | Modeling prices with the Hedonic regression
I know this is an old post; hope the message helps someone reading this thread who might approach the same problem. The logical premise that 0 rooms; and 0 living area = zero value is improper because what the model is ignoring is the underlying value of land. This also aff... | Modeling prices with the Hedonic regression
I know this is an old post; hope the message helps someone reading this thread who might approach the same problem. The logical premise that 0 rooms; and 0 living area = zero value is improper becaus |
47,296 | Modeling prices with the Hedonic regression | I think your last remark ("I think that the big number of dummy variables damages a little bit the regression") is spot on. The very anormal values you observe for some regession coefficients clearly points to multicollinearity.
You might want to try ridge regression or principal components regression. | Modeling prices with the Hedonic regression | I think your last remark ("I think that the big number of dummy variables damages a little bit the regression") is spot on. The very anormal values you observe for some regession coefficients clearly | Modeling prices with the Hedonic regression
I think your last remark ("I think that the big number of dummy variables damages a little bit the regression") is spot on. The very anormal values you observe for some regession coefficients clearly points to multicollinearity.
You might want to try ridge regression or princ... | Modeling prices with the Hedonic regression
I think your last remark ("I think that the big number of dummy variables damages a little bit the regression") is spot on. The very anormal values you observe for some regession coefficients clearly |
47,297 | Modeling prices with the Hedonic regression | Use intercept in your model. This is very strong assumption, that when all variables would equal 0, then predicted price should be zero and it is not required, especially, that such a real estate would not appear in a train or test data set. Even if it is true, that real estate with all characteristics equal to zero sh... | Modeling prices with the Hedonic regression | Use intercept in your model. This is very strong assumption, that when all variables would equal 0, then predicted price should be zero and it is not required, especially, that such a real estate woul | Modeling prices with the Hedonic regression
Use intercept in your model. This is very strong assumption, that when all variables would equal 0, then predicted price should be zero and it is not required, especially, that such a real estate would not appear in a train or test data set. Even if it is true, that real esta... | Modeling prices with the Hedonic regression
Use intercept in your model. This is very strong assumption, that when all variables would equal 0, then predicted price should be zero and it is not required, especially, that such a real estate woul |
47,298 | Calculate prediction values for linear curve estimation for next 5 intervals | You can do this in R using the predict function. For ease I used Month as predictor and Value as outcome. In the vector new are the predicted values as a function of Month. Please see also the plot that shows the projected values on the regression line.
data=data.frame(Month=c(21:33), Value=c(6591.69, 6579.62, 7133.84... | Calculate prediction values for linear curve estimation for next 5 intervals | You can do this in R using the predict function. For ease I used Month as predictor and Value as outcome. In the vector new are the predicted values as a function of Month. Please see also the plot th | Calculate prediction values for linear curve estimation for next 5 intervals
You can do this in R using the predict function. For ease I used Month as predictor and Value as outcome. In the vector new are the predicted values as a function of Month. Please see also the plot that shows the projected values on the regres... | Calculate prediction values for linear curve estimation for next 5 intervals
You can do this in R using the predict function. For ease I used Month as predictor and Value as outcome. In the vector new are the predicted values as a function of Month. Please see also the plot th |
47,299 | Foundational sufficient statistics | It's just a matter of understanding the notation.
Preliminaries
A random variable, such as $\boldsymbol X$, is a measurable function on a probability space,
$$\boldsymbol X: \Omega \to \mathbb{R}^n.$$
A statistic $T$ is a measurable function
$$T: \mathbb{R}^n \to \mathbb{R}.$$
The composite function
$$T\circ \boldsymbo... | Foundational sufficient statistics | It's just a matter of understanding the notation.
Preliminaries
A random variable, such as $\boldsymbol X$, is a measurable function on a probability space,
$$\boldsymbol X: \Omega \to \mathbb{R}^n.$$ | Foundational sufficient statistics
It's just a matter of understanding the notation.
Preliminaries
A random variable, such as $\boldsymbol X$, is a measurable function on a probability space,
$$\boldsymbol X: \Omega \to \mathbb{R}^n.$$
A statistic $T$ is a measurable function
$$T: \mathbb{R}^n \to \mathbb{R}.$$
The com... | Foundational sufficient statistics
It's just a matter of understanding the notation.
Preliminaries
A random variable, such as $\boldsymbol X$, is a measurable function on a probability space,
$$\boldsymbol X: \Omega \to \mathbb{R}^n.$$ |
47,300 | When should I use k-means instead of Spectral Clustering? | k-means is much much much faster.
K-means is hard to beat performance wise, so it will work on larger data sets. That is probably the key factor.
K-means is $O(n.k.d.i)$, i.e. linear.
For large data sets, anything of $O(n^2)$ or worse is prohibitive.
Spectral clustering is in $O(n^3)$.
Which means it won't work for any... | When should I use k-means instead of Spectral Clustering? | k-means is much much much faster.
K-means is hard to beat performance wise, so it will work on larger data sets. That is probably the key factor.
K-means is $O(n.k.d.i)$, i.e. linear.
For large data s | When should I use k-means instead of Spectral Clustering?
k-means is much much much faster.
K-means is hard to beat performance wise, so it will work on larger data sets. That is probably the key factor.
K-means is $O(n.k.d.i)$, i.e. linear.
For large data sets, anything of $O(n^2)$ or worse is prohibitive.
Spectral cl... | When should I use k-means instead of Spectral Clustering?
k-means is much much much faster.
K-means is hard to beat performance wise, so it will work on larger data sets. That is probably the key factor.
K-means is $O(n.k.d.i)$, i.e. linear.
For large data s |
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