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 |
|---|---|---|---|---|---|---|
1,201 | Nested cross validation for model selection | In addition to cebeleites excellent answer (+1), the basic idea is that cross-validation is used to assess the performance of a method for fitting a model, not of the model itself. If you need to perform model selection, then you need to perform that independently in each fold of the cross-validation procedure, as it ... | Nested cross validation for model selection | In addition to cebeleites excellent answer (+1), the basic idea is that cross-validation is used to assess the performance of a method for fitting a model, not of the model itself. If you need to per | Nested cross validation for model selection
In addition to cebeleites excellent answer (+1), the basic idea is that cross-validation is used to assess the performance of a method for fitting a model, not of the model itself. If you need to perform model selection, then you need to perform that independently in each fo... | Nested cross validation for model selection
In addition to cebeleites excellent answer (+1), the basic idea is that cross-validation is used to assess the performance of a method for fitting a model, not of the model itself. If you need to per |
1,202 | Nested cross validation for model selection | I don't think anyone really answered the first question. By "Nested cross-validation" I think he meant combining it with GridSearch. Usually GridSearch has CV built in and takes a parameter on how many folds we wish to test. Combining those two I think its a good practice but the model from GridSearch and CrossValidati... | Nested cross validation for model selection | I don't think anyone really answered the first question. By "Nested cross-validation" I think he meant combining it with GridSearch. Usually GridSearch has CV built in and takes a parameter on how man | Nested cross validation for model selection
I don't think anyone really answered the first question. By "Nested cross-validation" I think he meant combining it with GridSearch. Usually GridSearch has CV built in and takes a parameter on how many folds we wish to test. Combining those two I think its a good practice but... | Nested cross validation for model selection
I don't think anyone really answered the first question. By "Nested cross-validation" I think he meant combining it with GridSearch. Usually GridSearch has CV built in and takes a parameter on how man |
1,203 | Nested cross validation for model selection | As was already pointed out by the answer of cebeleites, inner and outer CV loop have different purposes: the inner CV loop is used to get the best model, the outer CV loop can serve different purposes. It can help you to estimate in a more unbiased way the generalisation error of your top performing model. Additionally... | Nested cross validation for model selection | As was already pointed out by the answer of cebeleites, inner and outer CV loop have different purposes: the inner CV loop is used to get the best model, the outer CV loop can serve different purposes | Nested cross validation for model selection
As was already pointed out by the answer of cebeleites, inner and outer CV loop have different purposes: the inner CV loop is used to get the best model, the outer CV loop can serve different purposes. It can help you to estimate in a more unbiased way the generalisation erro... | Nested cross validation for model selection
As was already pointed out by the answer of cebeleites, inner and outer CV loop have different purposes: the inner CV loop is used to get the best model, the outer CV loop can serve different purposes |
1,204 | What's wrong with XKCD's Frequentists vs. Bayesians comic? | The main issue is that the first experiment (Sun gone nova) is not repeatable, which makes it highly unsuitable for frequentist methodology that interprets probability as estimate of how frequent an event is giving that we can repeat the experiment many times. In contrast, bayesian probability is interpreted as our deg... | What's wrong with XKCD's Frequentists vs. Bayesians comic? | The main issue is that the first experiment (Sun gone nova) is not repeatable, which makes it highly unsuitable for frequentist methodology that interprets probability as estimate of how frequent an e | What's wrong with XKCD's Frequentists vs. Bayesians comic?
The main issue is that the first experiment (Sun gone nova) is not repeatable, which makes it highly unsuitable for frequentist methodology that interprets probability as estimate of how frequent an event is giving that we can repeat the experiment many times. ... | What's wrong with XKCD's Frequentists vs. Bayesians comic?
The main issue is that the first experiment (Sun gone nova) is not repeatable, which makes it highly unsuitable for frequentist methodology that interprets probability as estimate of how frequent an e |
1,205 | What's wrong with XKCD's Frequentists vs. Bayesians comic? | Why does this result seem "wrong?" A Bayesian would say that the result seems counter-intuitive because we have "prior" beliefs about when the sun will explode, and the evidence provided by this machine isn't enough to wash out those beliefs (mostly because of it's uncertainty due to the coin flipping). But a frequent... | What's wrong with XKCD's Frequentists vs. Bayesians comic? | Why does this result seem "wrong?" A Bayesian would say that the result seems counter-intuitive because we have "prior" beliefs about when the sun will explode, and the evidence provided by this mach | What's wrong with XKCD's Frequentists vs. Bayesians comic?
Why does this result seem "wrong?" A Bayesian would say that the result seems counter-intuitive because we have "prior" beliefs about when the sun will explode, and the evidence provided by this machine isn't enough to wash out those beliefs (mostly because of... | What's wrong with XKCD's Frequentists vs. Bayesians comic?
Why does this result seem "wrong?" A Bayesian would say that the result seems counter-intuitive because we have "prior" beliefs about when the sun will explode, and the evidence provided by this mach |
1,206 | What's wrong with XKCD's Frequentists vs. Bayesians comic? | As far as I can see the frequentist bit is reasonable this far:
Let $H_0$ be the hypothesis that the sun has not exploded and $H_1$ be the hypothesis that it has. The p-value is thus the probability of observing the result (the machine saying "yes") under $H_0$. Assuming that the machine correctly detects the presenc... | What's wrong with XKCD's Frequentists vs. Bayesians comic? | As far as I can see the frequentist bit is reasonable this far:
Let $H_0$ be the hypothesis that the sun has not exploded and $H_1$ be the hypothesis that it has. The p-value is thus the probability | What's wrong with XKCD's Frequentists vs. Bayesians comic?
As far as I can see the frequentist bit is reasonable this far:
Let $H_0$ be the hypothesis that the sun has not exploded and $H_1$ be the hypothesis that it has. The p-value is thus the probability of observing the result (the machine saying "yes") under $H_0... | What's wrong with XKCD's Frequentists vs. Bayesians comic?
As far as I can see the frequentist bit is reasonable this far:
Let $H_0$ be the hypothesis that the sun has not exploded and $H_1$ be the hypothesis that it has. The p-value is thus the probability |
1,207 | What's wrong with XKCD's Frequentists vs. Bayesians comic? | The greatest problem that I see is that there is no test statistic derived. $p$-value (with all the criticisms that Bayesian statisticians mount against it) for a value $t$ of a test statistic $T$ is defined as ${\rm Prob}[T \ge t| H_0]$ (assuming that the null is rejected for greater values of $T$, as would be a case ... | What's wrong with XKCD's Frequentists vs. Bayesians comic? | The greatest problem that I see is that there is no test statistic derived. $p$-value (with all the criticisms that Bayesian statisticians mount against it) for a value $t$ of a test statistic $T$ is | What's wrong with XKCD's Frequentists vs. Bayesians comic?
The greatest problem that I see is that there is no test statistic derived. $p$-value (with all the criticisms that Bayesian statisticians mount against it) for a value $t$ of a test statistic $T$ is defined as ${\rm Prob}[T \ge t| H_0]$ (assuming that the null... | What's wrong with XKCD's Frequentists vs. Bayesians comic?
The greatest problem that I see is that there is no test statistic derived. $p$-value (with all the criticisms that Bayesian statisticians mount against it) for a value $t$ of a test statistic $T$ is |
1,208 | What's wrong with XKCD's Frequentists vs. Bayesians comic? | I agree with @GeorgeLewis that it may be premature to conclude the Frequentist approach is wrong - let's just rerun the neutrino detector several more times to collect more data. No need to mess around with priors. | What's wrong with XKCD's Frequentists vs. Bayesians comic? | I agree with @GeorgeLewis that it may be premature to conclude the Frequentist approach is wrong - let's just rerun the neutrino detector several more times to collect more data. No need to mess aroun | What's wrong with XKCD's Frequentists vs. Bayesians comic?
I agree with @GeorgeLewis that it may be premature to conclude the Frequentist approach is wrong - let's just rerun the neutrino detector several more times to collect more data. No need to mess around with priors. | What's wrong with XKCD's Frequentists vs. Bayesians comic?
I agree with @GeorgeLewis that it may be premature to conclude the Frequentist approach is wrong - let's just rerun the neutrino detector several more times to collect more data. No need to mess aroun |
1,209 | What's wrong with XKCD's Frequentists vs. Bayesians comic? | There's nothing wrong with this comic, and the reason has nothing to do with statistics. It's economics. If the frequentist is correct, the Earth will be tantamount to uninhabitable within 48 hours. The value of \$50 will be effectively null. The Bayesian, recognizing this, can make the bet knowing that his benefit ... | What's wrong with XKCD's Frequentists vs. Bayesians comic? | There's nothing wrong with this comic, and the reason has nothing to do with statistics. It's economics. If the frequentist is correct, the Earth will be tantamount to uninhabitable within 48 hours. | What's wrong with XKCD's Frequentists vs. Bayesians comic?
There's nothing wrong with this comic, and the reason has nothing to do with statistics. It's economics. If the frequentist is correct, the Earth will be tantamount to uninhabitable within 48 hours. The value of \$50 will be effectively null. The Bayesian, r... | What's wrong with XKCD's Frequentists vs. Bayesians comic?
There's nothing wrong with this comic, and the reason has nothing to do with statistics. It's economics. If the frequentist is correct, the Earth will be tantamount to uninhabitable within 48 hours. |
1,210 | What's wrong with XKCD's Frequentists vs. Bayesians comic? | Now that CERN has decided that neutrinos are not faster than light - the electromagnetic radiation shock front would hit the earth before the neutrino change was noticed. This would have at the least (in the very short term) spectacular auroral effects. Thus the fact that it is dark would not prevent the skies from ... | What's wrong with XKCD's Frequentists vs. Bayesians comic? | Now that CERN has decided that neutrinos are not faster than light - the electromagnetic radiation shock front would hit the earth before the neutrino change was noticed. This would have at the leas | What's wrong with XKCD's Frequentists vs. Bayesians comic?
Now that CERN has decided that neutrinos are not faster than light - the electromagnetic radiation shock front would hit the earth before the neutrino change was noticed. This would have at the least (in the very short term) spectacular auroral effects. Thus... | What's wrong with XKCD's Frequentists vs. Bayesians comic?
Now that CERN has decided that neutrinos are not faster than light - the electromagnetic radiation shock front would hit the earth before the neutrino change was noticed. This would have at the leas |
1,211 | What's wrong with XKCD's Frequentists vs. Bayesians comic? | The answer for your question: "does he correctly apply the frequentist methodology?" is no, he does not applied precisely the frequentist approach. The p-value for this problem is not exactly 1/36.
We first must note that the involved hypotheses are
H0: The Sun has not exploded,
H1: The Sun has exploded.
Then,
p-value ... | What's wrong with XKCD's Frequentists vs. Bayesians comic? | The answer for your question: "does he correctly apply the frequentist methodology?" is no, he does not applied precisely the frequentist approach. The p-value for this problem is not exactly 1/36.
We | What's wrong with XKCD's Frequentists vs. Bayesians comic?
The answer for your question: "does he correctly apply the frequentist methodology?" is no, he does not applied precisely the frequentist approach. The p-value for this problem is not exactly 1/36.
We first must note that the involved hypotheses are
H0: The Sun... | What's wrong with XKCD's Frequentists vs. Bayesians comic?
The answer for your question: "does he correctly apply the frequentist methodology?" is no, he does not applied precisely the frequentist approach. The p-value for this problem is not exactly 1/36.
We |
1,212 | What's wrong with XKCD's Frequentists vs. Bayesians comic? | A simpler point that may be lost among all the verbose answers here is that the frequentist is depicted drawing his conclusion based upon a single sample. In practice you would never do this.
Reaching a valid conclusion requires a statistically significant sample size (or in other words, science needs to be repeatable... | What's wrong with XKCD's Frequentists vs. Bayesians comic? | A simpler point that may be lost among all the verbose answers here is that the frequentist is depicted drawing his conclusion based upon a single sample. In practice you would never do this.
Reachin | What's wrong with XKCD's Frequentists vs. Bayesians comic?
A simpler point that may be lost among all the verbose answers here is that the frequentist is depicted drawing his conclusion based upon a single sample. In practice you would never do this.
Reaching a valid conclusion requires a statistically significant sam... | What's wrong with XKCD's Frequentists vs. Bayesians comic?
A simpler point that may be lost among all the verbose answers here is that the frequentist is depicted drawing his conclusion based upon a single sample. In practice you would never do this.
Reachin |
1,213 | What's wrong with XKCD's Frequentists vs. Bayesians comic? | This is of course a frequentist 0.05 level test - the null hypothesis is rejected less than 5% of the time under the null hypothesis and even the power under the alternative is great.
On the other hand prior information tells us that the sun going supernova at a by particular point in time is pretty unlikely, but that ... | What's wrong with XKCD's Frequentists vs. Bayesians comic? | This is of course a frequentist 0.05 level test - the null hypothesis is rejected less than 5% of the time under the null hypothesis and even the power under the alternative is great.
On the other han | What's wrong with XKCD's Frequentists vs. Bayesians comic?
This is of course a frequentist 0.05 level test - the null hypothesis is rejected less than 5% of the time under the null hypothesis and even the power under the alternative is great.
On the other hand prior information tells us that the sun going supernova at ... | What's wrong with XKCD's Frequentists vs. Bayesians comic?
This is of course a frequentist 0.05 level test - the null hypothesis is rejected less than 5% of the time under the null hypothesis and even the power under the alternative is great.
On the other han |
1,214 | What's wrong with XKCD's Frequentists vs. Bayesians comic? | I don't see any problem with the frequentist's approach. If the null hypothesis is rejected, the p-value is the probability of a type 1 error. A type 1 error is rejecting a true null hypothesis. In this case we have a p-value of 0.028. This means that among all the hypothesis tests with this p-value ever conducted, rou... | What's wrong with XKCD's Frequentists vs. Bayesians comic? | I don't see any problem with the frequentist's approach. If the null hypothesis is rejected, the p-value is the probability of a type 1 error. A type 1 error is rejecting a true null hypothesis. In th | What's wrong with XKCD's Frequentists vs. Bayesians comic?
I don't see any problem with the frequentist's approach. If the null hypothesis is rejected, the p-value is the probability of a type 1 error. A type 1 error is rejecting a true null hypothesis. In this case we have a p-value of 0.028. This means that among all... | What's wrong with XKCD's Frequentists vs. Bayesians comic?
I don't see any problem with the frequentist's approach. If the null hypothesis is rejected, the p-value is the probability of a type 1 error. A type 1 error is rejecting a true null hypothesis. In th |
1,215 | What's wrong with XKCD's Frequentists vs. Bayesians comic? | How to integrate "prior knowledge" about the sun stability in the
frequentist methodology?
Very interesting topic.
Here are just some thoughts, not a perfect analysis...
Using the Bayesian approach with a noninformative prior typically provides a statistical inference comparable to the frequentist one.
Why does the... | What's wrong with XKCD's Frequentists vs. Bayesians comic? | How to integrate "prior knowledge" about the sun stability in the
frequentist methodology?
Very interesting topic.
Here are just some thoughts, not a perfect analysis...
Using the Bayesian approach | What's wrong with XKCD's Frequentists vs. Bayesians comic?
How to integrate "prior knowledge" about the sun stability in the
frequentist methodology?
Very interesting topic.
Here are just some thoughts, not a perfect analysis...
Using the Bayesian approach with a noninformative prior typically provides a statistical... | What's wrong with XKCD's Frequentists vs. Bayesians comic?
How to integrate "prior knowledge" about the sun stability in the
frequentist methodology?
Very interesting topic.
Here are just some thoughts, not a perfect analysis...
Using the Bayesian approach |
1,216 | What's wrong with XKCD's Frequentists vs. Bayesians comic? | If the frequentist is set on using a p-value to determine whether the sun has exploded, his mistake is that he should be testing at a much lower significance level $\alpha$ than 0.05, since the claim that the sun has gone nova and that the frequentist is still alive despite photons from the nova already reaching Earth ... | What's wrong with XKCD's Frequentists vs. Bayesians comic? | If the frequentist is set on using a p-value to determine whether the sun has exploded, his mistake is that he should be testing at a much lower significance level $\alpha$ than 0.05, since the claim | What's wrong with XKCD's Frequentists vs. Bayesians comic?
If the frequentist is set on using a p-value to determine whether the sun has exploded, his mistake is that he should be testing at a much lower significance level $\alpha$ than 0.05, since the claim that the sun has gone nova and that the frequentist is still ... | What's wrong with XKCD's Frequentists vs. Bayesians comic?
If the frequentist is set on using a p-value to determine whether the sun has exploded, his mistake is that he should be testing at a much lower significance level $\alpha$ than 0.05, since the claim |
1,217 | What's wrong with XKCD's Frequentists vs. Bayesians comic? | In my view, a more correct frequentist analysis would be as follows:
H0: The sun has exploded and the machine is telling the truth.
H1: The sun has not exploded and the machine is lying.
The p value here is = P(sun exploded) . p(machine is telling the truth)
= 0.97 . P(sun exploded)
The statistician can not conclude an... | What's wrong with XKCD's Frequentists vs. Bayesians comic? | In my view, a more correct frequentist analysis would be as follows:
H0: The sun has exploded and the machine is telling the truth.
H1: The sun has not exploded and the machine is lying.
The p value h | What's wrong with XKCD's Frequentists vs. Bayesians comic?
In my view, a more correct frequentist analysis would be as follows:
H0: The sun has exploded and the machine is telling the truth.
H1: The sun has not exploded and the machine is lying.
The p value here is = P(sun exploded) . p(machine is telling the truth)
= ... | What's wrong with XKCD's Frequentists vs. Bayesians comic?
In my view, a more correct frequentist analysis would be as follows:
H0: The sun has exploded and the machine is telling the truth.
H1: The sun has not exploded and the machine is lying.
The p value h |
1,218 | How does a Support Vector Machine (SVM) work? | Support vector machines focus only on the points that are the most difficult to tell apart, whereas other classifiers pay attention to all of the points.
The intuition behind the support vector machine approach is that if a classifier is good at the most challenging comparisons (the points in B and A that are closest ... | How does a Support Vector Machine (SVM) work? | Support vector machines focus only on the points that are the most difficult to tell apart, whereas other classifiers pay attention to all of the points.
The intuition behind the support vector machi | How does a Support Vector Machine (SVM) work?
Support vector machines focus only on the points that are the most difficult to tell apart, whereas other classifiers pay attention to all of the points.
The intuition behind the support vector machine approach is that if a classifier is good at the most challenging compar... | How does a Support Vector Machine (SVM) work?
Support vector machines focus only on the points that are the most difficult to tell apart, whereas other classifiers pay attention to all of the points.
The intuition behind the support vector machi |
1,219 | How does a Support Vector Machine (SVM) work? | Ryan Zotti's answer explains the motivation behind the maximization of the decision boundaries, carlosdc's answer gives some similarities and differences with respect to other classifiers. I'll give in this answer a brief mathematical overview of how SVMs are trained and used.
Notations
In the following, scalars are de... | How does a Support Vector Machine (SVM) work? | Ryan Zotti's answer explains the motivation behind the maximization of the decision boundaries, carlosdc's answer gives some similarities and differences with respect to other classifiers. I'll give i | How does a Support Vector Machine (SVM) work?
Ryan Zotti's answer explains the motivation behind the maximization of the decision boundaries, carlosdc's answer gives some similarities and differences with respect to other classifiers. I'll give in this answer a brief mathematical overview of how SVMs are trained and us... | How does a Support Vector Machine (SVM) work?
Ryan Zotti's answer explains the motivation behind the maximization of the decision boundaries, carlosdc's answer gives some similarities and differences with respect to other classifiers. I'll give i |
1,220 | How does a Support Vector Machine (SVM) work? | The technique is predicated upon drawing a decision boundary line leaving as ample a margin to the first positive and negative examples as possible:
As in the illustration above, if we select an orthogonal vector such that $ \lVert w \rVert=1$ we can establish a decision criterion for any unknown example $\mathbf u$ t... | How does a Support Vector Machine (SVM) work? | The technique is predicated upon drawing a decision boundary line leaving as ample a margin to the first positive and negative examples as possible:
As in the illustration above, if we select an orth | How does a Support Vector Machine (SVM) work?
The technique is predicated upon drawing a decision boundary line leaving as ample a margin to the first positive and negative examples as possible:
As in the illustration above, if we select an orthogonal vector such that $ \lVert w \rVert=1$ we can establish a decision c... | How does a Support Vector Machine (SVM) work?
The technique is predicated upon drawing a decision boundary line leaving as ample a margin to the first positive and negative examples as possible:
As in the illustration above, if we select an orth |
1,221 | How does a Support Vector Machine (SVM) work? | I'm going to focus on the the similarities and differences it from other classifiers:
From a perceptron: SVM uses hinge loss and L2 regularization, the perceptron uses the perceptron loss and could use early stopping (or among other techniques) for regularization, there is really no regularization term in the perceptr... | How does a Support Vector Machine (SVM) work? | I'm going to focus on the the similarities and differences it from other classifiers:
From a perceptron: SVM uses hinge loss and L2 regularization, the perceptron uses the perceptron loss and could u | How does a Support Vector Machine (SVM) work?
I'm going to focus on the the similarities and differences it from other classifiers:
From a perceptron: SVM uses hinge loss and L2 regularization, the perceptron uses the perceptron loss and could use early stopping (or among other techniques) for regularization, there is... | How does a Support Vector Machine (SVM) work?
I'm going to focus on the the similarities and differences it from other classifiers:
From a perceptron: SVM uses hinge loss and L2 regularization, the perceptron uses the perceptron loss and could u |
1,222 | How does a Support Vector Machine (SVM) work? | Some comments on Duality and KTT conditions
Primal problem
Picking up from @Antoni's post in between equations $(4)$ and $(5)$, recall that our original, or primal, optimization problem is of the form:
\begin{aligned}
\min_{w, b} f(w,b) & = \min_{w, b} \ \frac{1}{2} ||w||^2
\\
s.t. \ \ g_i(w,b) &= - y^{(i)} (w^T... | How does a Support Vector Machine (SVM) work? | Some comments on Duality and KTT conditions
Primal problem
Picking up from @Antoni's post in between equations $(4)$ and $(5)$, recall that our original, or primal, optimization problem is of the form | How does a Support Vector Machine (SVM) work?
Some comments on Duality and KTT conditions
Primal problem
Picking up from @Antoni's post in between equations $(4)$ and $(5)$, recall that our original, or primal, optimization problem is of the form:
\begin{aligned}
\min_{w, b} f(w,b) & = \min_{w, b} \ \frac{1}{2} ||w... | How does a Support Vector Machine (SVM) work?
Some comments on Duality and KTT conditions
Primal problem
Picking up from @Antoni's post in between equations $(4)$ and $(5)$, recall that our original, or primal, optimization problem is of the form |
1,223 | Is it possible to have a pair of Gaussian random variables for which the joint distribution is not Gaussian? | The bivariate normal distribution is the exception, not the rule!
It is important to recognize that "almost all" joint distributions with normal marginals are not the bivariate normal distribution. That is, the common viewpoint that joint distributions with normal marginals that are not the bivariate normal are somehow... | Is it possible to have a pair of Gaussian random variables for which the joint distribution is not G | The bivariate normal distribution is the exception, not the rule!
It is important to recognize that "almost all" joint distributions with normal marginals are not the bivariate normal distribution. Th | Is it possible to have a pair of Gaussian random variables for which the joint distribution is not Gaussian?
The bivariate normal distribution is the exception, not the rule!
It is important to recognize that "almost all" joint distributions with normal marginals are not the bivariate normal distribution. That is, the ... | Is it possible to have a pair of Gaussian random variables for which the joint distribution is not G
The bivariate normal distribution is the exception, not the rule!
It is important to recognize that "almost all" joint distributions with normal marginals are not the bivariate normal distribution. Th |
1,224 | Is it possible to have a pair of Gaussian random variables for which the joint distribution is not Gaussian? | It is true that each element of a multivariate normal vector is itself normally distributed, and you can deduce their means and variances. However, it is not true that any two Guassian random variables are jointly normally distributed. Here is an example:
Edit: In response to the consensus that a random variable that i... | Is it possible to have a pair of Gaussian random variables for which the joint distribution is not G | It is true that each element of a multivariate normal vector is itself normally distributed, and you can deduce their means and variances. However, it is not true that any two Guassian random variable | Is it possible to have a pair of Gaussian random variables for which the joint distribution is not Gaussian?
It is true that each element of a multivariate normal vector is itself normally distributed, and you can deduce their means and variances. However, it is not true that any two Guassian random variables are joint... | Is it possible to have a pair of Gaussian random variables for which the joint distribution is not G
It is true that each element of a multivariate normal vector is itself normally distributed, and you can deduce their means and variances. However, it is not true that any two Guassian random variable |
1,225 | Is it possible to have a pair of Gaussian random variables for which the joint distribution is not Gaussian? | The following post contains an outline of a proof, just to give the main ideas and get you started.
Let $z = (Z_1, Z_2)$ be two independent Gaussian random variables and let $x = (X_1, X_2)$ be
$$
x =
\begin{pmatrix}
X_1 \\
X_2
\end{pmatrix}
= \begin{pmatrix}
\alpha_{11} Z_1 + \alpha_{12} Z_2\\
\alpha_{21} Z_1 + \alpha... | Is it possible to have a pair of Gaussian random variables for which the joint distribution is not G | The following post contains an outline of a proof, just to give the main ideas and get you started.
Let $z = (Z_1, Z_2)$ be two independent Gaussian random variables and let $x = (X_1, X_2)$ be
$$
x = | Is it possible to have a pair of Gaussian random variables for which the joint distribution is not Gaussian?
The following post contains an outline of a proof, just to give the main ideas and get you started.
Let $z = (Z_1, Z_2)$ be two independent Gaussian random variables and let $x = (X_1, X_2)$ be
$$
x =
\begin{pma... | Is it possible to have a pair of Gaussian random variables for which the joint distribution is not G
The following post contains an outline of a proof, just to give the main ideas and get you started.
Let $z = (Z_1, Z_2)$ be two independent Gaussian random variables and let $x = (X_1, X_2)$ be
$$
x = |
1,226 | Is it possible to have a pair of Gaussian random variables for which the joint distribution is not Gaussian? | I thought it might be worth pointing out a couple of nice examples; one I've mentioned in a couple of older answers here on Cross Validated (e.g. this one) and one rather pretty one which occurred to me the other day.
Here we have two variables, $Y$ and $Z$, that have (uncorrelated) normal distributions, where $Y$ is ... | Is it possible to have a pair of Gaussian random variables for which the joint distribution is not G | I thought it might be worth pointing out a couple of nice examples; one I've mentioned in a couple of older answers here on Cross Validated (e.g. this one) and one rather pretty one which occurred to | Is it possible to have a pair of Gaussian random variables for which the joint distribution is not Gaussian?
I thought it might be worth pointing out a couple of nice examples; one I've mentioned in a couple of older answers here on Cross Validated (e.g. this one) and one rather pretty one which occurred to me the othe... | Is it possible to have a pair of Gaussian random variables for which the joint distribution is not G
I thought it might be worth pointing out a couple of nice examples; one I've mentioned in a couple of older answers here on Cross Validated (e.g. this one) and one rather pretty one which occurred to |
1,227 | Bias and variance in leave-one-out vs K-fold cross validation | why would models learned with leave-one-out CV have higher variance?
[TL:DR] A summary of recent posts and debates (July 2018)
This topic has been widely discussed both on this site, and in the scientific literature, with conflicting views, intuitions and conclusions. Back in 2013 when this question was first asked, t... | Bias and variance in leave-one-out vs K-fold cross validation | why would models learned with leave-one-out CV have higher variance?
[TL:DR] A summary of recent posts and debates (July 2018)
This topic has been widely discussed both on this site, and in the scien | Bias and variance in leave-one-out vs K-fold cross validation
why would models learned with leave-one-out CV have higher variance?
[TL:DR] A summary of recent posts and debates (July 2018)
This topic has been widely discussed both on this site, and in the scientific literature, with conflicting views, intuitions and c... | Bias and variance in leave-one-out vs K-fold cross validation
why would models learned with leave-one-out CV have higher variance?
[TL:DR] A summary of recent posts and debates (July 2018)
This topic has been widely discussed both on this site, and in the scien |
1,228 | Bias and variance in leave-one-out vs K-fold cross validation | In $k$-fold cross-validation we partition a dataset into $k$ equally sized non-overlapping subsets $S$. For each fold $S_i$, a model is trained on $S \setminus S_i$, which is then evaluated on $S_i$. The cross-validation estimator of, for example the prediction error, is defined as the average of the prediction errors ... | Bias and variance in leave-one-out vs K-fold cross validation | In $k$-fold cross-validation we partition a dataset into $k$ equally sized non-overlapping subsets $S$. For each fold $S_i$, a model is trained on $S \setminus S_i$, which is then evaluated on $S_i$. | Bias and variance in leave-one-out vs K-fold cross validation
In $k$-fold cross-validation we partition a dataset into $k$ equally sized non-overlapping subsets $S$. For each fold $S_i$, a model is trained on $S \setminus S_i$, which is then evaluated on $S_i$. The cross-validation estimator of, for example the predict... | Bias and variance in leave-one-out vs K-fold cross validation
In $k$-fold cross-validation we partition a dataset into $k$ equally sized non-overlapping subsets $S$. For each fold $S_i$, a model is trained on $S \setminus S_i$, which is then evaluated on $S_i$. |
1,229 | Bias and variance in leave-one-out vs K-fold cross validation | [...] my intuition tells me that in leave-one-out CV one should see relatively lower variance between models than in the $K$-fold CV, since
we are only shifting one data point across folds and therefore the
training sets between folds overlap substantially.
I think your intuition is sensible if you are thinking ab... | Bias and variance in leave-one-out vs K-fold cross validation | [...] my intuition tells me that in leave-one-out CV one should see relatively lower variance between models than in the $K$-fold CV, since
we are only shifting one data point across folds and there | Bias and variance in leave-one-out vs K-fold cross validation
[...] my intuition tells me that in leave-one-out CV one should see relatively lower variance between models than in the $K$-fold CV, since
we are only shifting one data point across folds and therefore the
training sets between folds overlap substantial... | Bias and variance in leave-one-out vs K-fold cross validation
[...] my intuition tells me that in leave-one-out CV one should see relatively lower variance between models than in the $K$-fold CV, since
we are only shifting one data point across folds and there |
1,230 | Bias and variance in leave-one-out vs K-fold cross validation | Although this question is rather old, I would like to add an additional answer because I think it is worth clarifying this a bit more.
My question is partly motivated by this thread: Optimal number of
folds in K-fold cross-validation: is leave-one-out CV always the best
choice?. The answer there suggests that mod... | Bias and variance in leave-one-out vs K-fold cross validation | Although this question is rather old, I would like to add an additional answer because I think it is worth clarifying this a bit more.
My question is partly motivated by this thread: Optimal number | Bias and variance in leave-one-out vs K-fold cross validation
Although this question is rather old, I would like to add an additional answer because I think it is worth clarifying this a bit more.
My question is partly motivated by this thread: Optimal number of
folds in K-fold cross-validation: is leave-one-out CV... | Bias and variance in leave-one-out vs K-fold cross validation
Although this question is rather old, I would like to add an additional answer because I think it is worth clarifying this a bit more.
My question is partly motivated by this thread: Optimal number |
1,231 | Bias and variance in leave-one-out vs K-fold cross validation | The issues are indeed subtle. But it is definitely not true that LOOCV has larger variance in general. A recent paper discusses some key aspects and addresses several seemingly widespread misconceptions on cross-validation.
Yongli Zhang and Yuhong Yang (2015). Cross-validation for selecting a model selection procedure.... | Bias and variance in leave-one-out vs K-fold cross validation | The issues are indeed subtle. But it is definitely not true that LOOCV has larger variance in general. A recent paper discusses some key aspects and addresses several seemingly widespread misconceptio | Bias and variance in leave-one-out vs K-fold cross validation
The issues are indeed subtle. But it is definitely not true that LOOCV has larger variance in general. A recent paper discusses some key aspects and addresses several seemingly widespread misconceptions on cross-validation.
Yongli Zhang and Yuhong Yang (2015... | Bias and variance in leave-one-out vs K-fold cross validation
The issues are indeed subtle. But it is definitely not true that LOOCV has larger variance in general. A recent paper discusses some key aspects and addresses several seemingly widespread misconceptio |
1,232 | Bias and variance in leave-one-out vs K-fold cross validation | Before discussing about bias and variance, the first question is:
What is estimated by cross-validation?
In our 2004 JMLR paper, we argue that, without any further assumption, $K$-fold cross-validation estimates the expected generalization error of a training algorithm producing models out of samples of size $n(K-1)/... | Bias and variance in leave-one-out vs K-fold cross validation | Before discussing about bias and variance, the first question is:
What is estimated by cross-validation?
In our 2004 JMLR paper, we argue that, without any further assumption, $K$-fold cross-validat | Bias and variance in leave-one-out vs K-fold cross validation
Before discussing about bias and variance, the first question is:
What is estimated by cross-validation?
In our 2004 JMLR paper, we argue that, without any further assumption, $K$-fold cross-validation estimates the expected generalization error of a train... | Bias and variance in leave-one-out vs K-fold cross validation
Before discussing about bias and variance, the first question is:
What is estimated by cross-validation?
In our 2004 JMLR paper, we argue that, without any further assumption, $K$-fold cross-validat |
1,233 | Bias and variance in leave-one-out vs K-fold cross validation | I think there is a more straightforward answer. If you increase k, the test sets get smaller and smaller. Since the folds are randomly sampled, it can happen with small test sets, but not as likely with bigger ones, that they are not representative of a random shuffle. One test set could contain all the difficult to pr... | Bias and variance in leave-one-out vs K-fold cross validation | I think there is a more straightforward answer. If you increase k, the test sets get smaller and smaller. Since the folds are randomly sampled, it can happen with small test sets, but not as likely wi | Bias and variance in leave-one-out vs K-fold cross validation
I think there is a more straightforward answer. If you increase k, the test sets get smaller and smaller. Since the folds are randomly sampled, it can happen with small test sets, but not as likely with bigger ones, that they are not representative of a rand... | Bias and variance in leave-one-out vs K-fold cross validation
I think there is a more straightforward answer. If you increase k, the test sets get smaller and smaller. Since the folds are randomly sampled, it can happen with small test sets, but not as likely wi |
1,234 | Bias and variance in leave-one-out vs K-fold cross validation | I see in most machine learning courses, that a model is validated on smaller training sets and prediction scores are evaluated to give a measure of prediction power, these models are then discarded and the model fit to the whole dataset for the final model.
I have a couple of bug bears with terminology often used when ... | Bias and variance in leave-one-out vs K-fold cross validation | I see in most machine learning courses, that a model is validated on smaller training sets and prediction scores are evaluated to give a measure of prediction power, these models are then discarded an | Bias and variance in leave-one-out vs K-fold cross validation
I see in most machine learning courses, that a model is validated on smaller training sets and prediction scores are evaluated to give a measure of prediction power, these models are then discarded and the model fit to the whole dataset for the final model.
... | Bias and variance in leave-one-out vs K-fold cross validation
I see in most machine learning courses, that a model is validated on smaller training sets and prediction scores are evaluated to give a measure of prediction power, these models are then discarded an |
1,235 | Bias and variance in leave-one-out vs K-fold cross validation | Lets say you have data set of 100 observations. You choose 80 for training and 20 in test data. You will use dataset of 80 observations to train the model. i.e. further split it into K fold.
Method 1: LOOCV:
The holdout data contains only one data point. All the models across different holdout sets will be quite simila... | Bias and variance in leave-one-out vs K-fold cross validation | Lets say you have data set of 100 observations. You choose 80 for training and 20 in test data. You will use dataset of 80 observations to train the model. i.e. further split it into K fold.
Method 1: | Bias and variance in leave-one-out vs K-fold cross validation
Lets say you have data set of 100 observations. You choose 80 for training and 20 in test data. You will use dataset of 80 observations to train the model. i.e. further split it into K fold.
Method 1: LOOCV:
The holdout data contains only one data point. All... | Bias and variance in leave-one-out vs K-fold cross validation
Lets say you have data set of 100 observations. You choose 80 for training and 20 in test data. You will use dataset of 80 observations to train the model. i.e. further split it into K fold.
Method 1: |
1,236 | Bias and variance in leave-one-out vs K-fold cross validation | I think the standard error that we are talking about here is the standard error of the $MSE$s or $Err$s generated across different cross-validation iterations. But the simulation done by Xavier Bourret Sicotte calculated the standard error of $MSE$ or $Err$ based on repeatedly drawing different sample data from the pop... | Bias and variance in leave-one-out vs K-fold cross validation | I think the standard error that we are talking about here is the standard error of the $MSE$s or $Err$s generated across different cross-validation iterations. But the simulation done by Xavier Bourre | Bias and variance in leave-one-out vs K-fold cross validation
I think the standard error that we are talking about here is the standard error of the $MSE$s or $Err$s generated across different cross-validation iterations. But the simulation done by Xavier Bourret Sicotte calculated the standard error of $MSE$ or $Err$ ... | Bias and variance in leave-one-out vs K-fold cross validation
I think the standard error that we are talking about here is the standard error of the $MSE$s or $Err$s generated across different cross-validation iterations. But the simulation done by Xavier Bourre |
1,237 | How to choose between t-test or non-parametric test e.g. Wilcoxon in small samples | I am going to change the order of questions about.
I've found textbooks and lecture notes frequently disagree, and would like a system to work through the choice that can safely be recommended as best practice, and especially a textbook or paper this can be cited to.
Unfortunately, some discussions of this issue in b... | How to choose between t-test or non-parametric test e.g. Wilcoxon in small samples | I am going to change the order of questions about.
I've found textbooks and lecture notes frequently disagree, and would like a system to work through the choice that can safely be recommended as bes | How to choose between t-test or non-parametric test e.g. Wilcoxon in small samples
I am going to change the order of questions about.
I've found textbooks and lecture notes frequently disagree, and would like a system to work through the choice that can safely be recommended as best practice, and especially a textbook... | How to choose between t-test or non-parametric test e.g. Wilcoxon in small samples
I am going to change the order of questions about.
I've found textbooks and lecture notes frequently disagree, and would like a system to work through the choice that can safely be recommended as bes |
1,238 | How to choose between t-test or non-parametric test e.g. Wilcoxon in small samples | In my view the principled approach recognizes that (1) tests and graphical assessments of normality have insufficient sensitivity and graph interpretation is frequently not objective, (2) multi-step procedures have uncertain operating characteristics, (3) many nonparametric tests have excellent operating characteristic... | How to choose between t-test or non-parametric test e.g. Wilcoxon in small samples | In my view the principled approach recognizes that (1) tests and graphical assessments of normality have insufficient sensitivity and graph interpretation is frequently not objective, (2) multi-step p | How to choose between t-test or non-parametric test e.g. Wilcoxon in small samples
In my view the principled approach recognizes that (1) tests and graphical assessments of normality have insufficient sensitivity and graph interpretation is frequently not objective, (2) multi-step procedures have uncertain operating ch... | How to choose between t-test or non-parametric test e.g. Wilcoxon in small samples
In my view the principled approach recognizes that (1) tests and graphical assessments of normality have insufficient sensitivity and graph interpretation is frequently not objective, (2) multi-step p |
1,239 | How to choose between t-test or non-parametric test e.g. Wilcoxon in small samples | Rand Wilcox in his publications and books make some very important points, many of which were listed by Frank Harrell and Glen_b in earlier posts.
The mean is not necessarily the quantity we want to make inferences about. There maybe other quantities that better exemplifies a typical observation.
For t-tests, power ca... | How to choose between t-test or non-parametric test e.g. Wilcoxon in small samples | Rand Wilcox in his publications and books make some very important points, many of which were listed by Frank Harrell and Glen_b in earlier posts.
The mean is not necessarily the quantity we want to | How to choose between t-test or non-parametric test e.g. Wilcoxon in small samples
Rand Wilcox in his publications and books make some very important points, many of which were listed by Frank Harrell and Glen_b in earlier posts.
The mean is not necessarily the quantity we want to make inferences about. There maybe ot... | How to choose between t-test or non-parametric test e.g. Wilcoxon in small samples
Rand Wilcox in his publications and books make some very important points, many of which were listed by Frank Harrell and Glen_b in earlier posts.
The mean is not necessarily the quantity we want to |
1,240 | How to choose between t-test or non-parametric test e.g. Wilcoxon in small samples | Bradley, in his work Distribution-Free Statistical Tests (1968, pp. 17–24), brings thirteen contrasts between what he calls "classical" and "distribution-free" tests. Note that Bradley differentiates between "non-parametric" and "distribution-free," but for the purposes of your question this difference is not relevant.... | How to choose between t-test or non-parametric test e.g. Wilcoxon in small samples | Bradley, in his work Distribution-Free Statistical Tests (1968, pp. 17–24), brings thirteen contrasts between what he calls "classical" and "distribution-free" tests. Note that Bradley differentiates | How to choose between t-test or non-parametric test e.g. Wilcoxon in small samples
Bradley, in his work Distribution-Free Statistical Tests (1968, pp. 17–24), brings thirteen contrasts between what he calls "classical" and "distribution-free" tests. Note that Bradley differentiates between "non-parametric" and "distrib... | How to choose between t-test or non-parametric test e.g. Wilcoxon in small samples
Bradley, in his work Distribution-Free Statistical Tests (1968, pp. 17–24), brings thirteen contrasts between what he calls "classical" and "distribution-free" tests. Note that Bradley differentiates |
1,241 | How to choose between t-test or non-parametric test e.g. Wilcoxon in small samples | Starting to answer this very interesting question.
For non-paired data:
Performance of five two-sample location tests for skewed distributions with unequal variances by Morten W. Fagerland, Leiv Sandvik
(behind paywall) performs a series of experiments with 5 different tests (t-test, Welch U, Yuen-Welch, Wilcoxon-Man... | How to choose between t-test or non-parametric test e.g. Wilcoxon in small samples | Starting to answer this very interesting question.
For non-paired data:
Performance of five two-sample location tests for skewed distributions with unequal variances by Morten W. Fagerland, Leiv Sand | How to choose between t-test or non-parametric test e.g. Wilcoxon in small samples
Starting to answer this very interesting question.
For non-paired data:
Performance of five two-sample location tests for skewed distributions with unequal variances by Morten W. Fagerland, Leiv Sandvik
(behind paywall) performs a seri... | How to choose between t-test or non-parametric test e.g. Wilcoxon in small samples
Starting to answer this very interesting question.
For non-paired data:
Performance of five two-sample location tests for skewed distributions with unequal variances by Morten W. Fagerland, Leiv Sand |
1,242 | How to choose between t-test or non-parametric test e.g. Wilcoxon in small samples | Considering following links:
Is normality testing 'essentially useless'?
Need and best way to determine normality of data
To simplify things, since non-parametric tests are reasonably good even for normal data, why not use them always for small samples. | How to choose between t-test or non-parametric test e.g. Wilcoxon in small samples | Considering following links:
Is normality testing 'essentially useless'?
Need and best way to determine normality of data
To simplify things, since non-parametric tests are reasonably good even for n | How to choose between t-test or non-parametric test e.g. Wilcoxon in small samples
Considering following links:
Is normality testing 'essentially useless'?
Need and best way to determine normality of data
To simplify things, since non-parametric tests are reasonably good even for normal data, why not use them always f... | How to choose between t-test or non-parametric test e.g. Wilcoxon in small samples
Considering following links:
Is normality testing 'essentially useless'?
Need and best way to determine normality of data
To simplify things, since non-parametric tests are reasonably good even for n |
1,243 | How to choose between t-test or non-parametric test e.g. Wilcoxon in small samples | Simulating the difference of means of Gamma populations
Comparing the t-test and the Mann Whitney test
Summary of results
When the variance of the two populations is the same, the Mann Whitney test has greater true power but also greater true type 1 error than the t-test.
For large sample N = 1000, the minimum true t... | How to choose between t-test or non-parametric test e.g. Wilcoxon in small samples | Simulating the difference of means of Gamma populations
Comparing the t-test and the Mann Whitney test
Summary of results
When the variance of the two populations is the same, the Mann Whitney test h | How to choose between t-test or non-parametric test e.g. Wilcoxon in small samples
Simulating the difference of means of Gamma populations
Comparing the t-test and the Mann Whitney test
Summary of results
When the variance of the two populations is the same, the Mann Whitney test has greater true power but also greate... | How to choose between t-test or non-parametric test e.g. Wilcoxon in small samples
Simulating the difference of means of Gamma populations
Comparing the t-test and the Mann Whitney test
Summary of results
When the variance of the two populations is the same, the Mann Whitney test h |
1,244 | Free statistical textbooks | Online books include
http://davidmlane.com/hyperstat/
http://vassarstats.net/textbook/
https://dwstockburger.com/Multibook/mbk.htm
https://web.archive.org/web/20180122061046/http://bookboon.com/en/statistics-ebooks
http://www.freebookcentre.net/SpecialCat/Free-Statistics-Books-Download.html
Update: I can now add my o... | Free statistical textbooks | Online books include
http://davidmlane.com/hyperstat/
http://vassarstats.net/textbook/
https://dwstockburger.com/Multibook/mbk.htm
https://web.archive.org/web/20180122061046/http://bookboon.com/en/st | Free statistical textbooks
Online books include
http://davidmlane.com/hyperstat/
http://vassarstats.net/textbook/
https://dwstockburger.com/Multibook/mbk.htm
https://web.archive.org/web/20180122061046/http://bookboon.com/en/statistics-ebooks
http://www.freebookcentre.net/SpecialCat/Free-Statistics-Books-Download.html
... | Free statistical textbooks
Online books include
http://davidmlane.com/hyperstat/
http://vassarstats.net/textbook/
https://dwstockburger.com/Multibook/mbk.htm
https://web.archive.org/web/20180122061046/http://bookboon.com/en/st |
1,245 | Free statistical textbooks | The Elements of Statistical Learning by Hastie, Tibshirani, and Friedman is a standard text for statistics and data mining, and is now free:
https://web.stanford.edu/~hastie/ElemStatLearn/
Also Available here. | Free statistical textbooks | The Elements of Statistical Learning by Hastie, Tibshirani, and Friedman is a standard text for statistics and data mining, and is now free:
https://web.stanford.edu/~hastie/ElemStatLearn/
Also Availa | Free statistical textbooks
The Elements of Statistical Learning by Hastie, Tibshirani, and Friedman is a standard text for statistics and data mining, and is now free:
https://web.stanford.edu/~hastie/ElemStatLearn/
Also Available here. | Free statistical textbooks
The Elements of Statistical Learning by Hastie, Tibshirani, and Friedman is a standard text for statistics and data mining, and is now free:
https://web.stanford.edu/~hastie/ElemStatLearn/
Also Availa |
1,246 | Free statistical textbooks | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
Introduction to Statistical Thought | Free statistical textbooks | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
| Free statistical textbooks
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
Introduction to Statistical... | Free statistical textbooks
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
|
1,247 | Free statistical textbooks | There's a superb Probability book here:
https://web.archive.org/web/20100102085337/http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/book.html
which you can also buy in hardcopy.; | Free statistical textbooks | There's a superb Probability book here:
https://web.archive.org/web/20100102085337/http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/book.html
which you can also buy in ha | Free statistical textbooks
There's a superb Probability book here:
https://web.archive.org/web/20100102085337/http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/book.html
which you can also buy in hardcopy.; | Free statistical textbooks
There's a superb Probability book here:
https://web.archive.org/web/20100102085337/http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/book.html
which you can also buy in ha |
1,248 | Free statistical textbooks | I've often found the Engineering Statistics Handbook useful. It can be found here.
Although I've never read it myself, I hear Introduction to Probability and Statistics Using R is very good. It's a full ~400 page ebook (also available as an actual book). As a bonus, it also teaches you R, which of course you want to le... | Free statistical textbooks | I've often found the Engineering Statistics Handbook useful. It can be found here.
Although I've never read it myself, I hear Introduction to Probability and Statistics Using R is very good. It's a fu | Free statistical textbooks
I've often found the Engineering Statistics Handbook useful. It can be found here.
Although I've never read it myself, I hear Introduction to Probability and Statistics Using R is very good. It's a full ~400 page ebook (also available as an actual book). As a bonus, it also teaches you R, whi... | Free statistical textbooks
I've often found the Engineering Statistics Handbook useful. It can be found here.
Although I've never read it myself, I hear Introduction to Probability and Statistics Using R is very good. It's a fu |
1,249 | Free statistical textbooks | Machine Learning
One the most, if not the most, popular textbooks on machine learning is Hastie, Tibshirani, and Friedman, The Elements of Statistical Learning, which is fully available online (currently 10th printing). It is comparable in scope e.g. to Bishop's Pattern Recognition and ML or Murphy's ML, but those bo... | Free statistical textbooks | Machine Learning
One the most, if not the most, popular textbooks on machine learning is Hastie, Tibshirani, and Friedman, The Elements of Statistical Learning, which is fully available online (curr | Free statistical textbooks
Machine Learning
One the most, if not the most, popular textbooks on machine learning is Hastie, Tibshirani, and Friedman, The Elements of Statistical Learning, which is fully available online (currently 10th printing). It is comparable in scope e.g. to Bishop's Pattern Recognition and ML o... | Free statistical textbooks
Machine Learning
One the most, if not the most, popular textbooks on machine learning is Hastie, Tibshirani, and Friedman, The Elements of Statistical Learning, which is fully available online (curr |
1,250 | Free statistical textbooks | I really like The Little Handbook of Statistical Practice by Gerard E. Dallal | Free statistical textbooks | I really like The Little Handbook of Statistical Practice by Gerard E. Dallal | Free statistical textbooks
I really like The Little Handbook of Statistical Practice by Gerard E. Dallal | Free statistical textbooks
I really like The Little Handbook of Statistical Practice by Gerard E. Dallal |
1,251 | Free statistical textbooks | Here's a fresh one: Introduction to Probability and Statistics Using R . It's R-specific, though, but it's a great one. I haven't read it yet, but it seems fine so far... | Free statistical textbooks | Here's a fresh one: Introduction to Probability and Statistics Using R . It's R-specific, though, but it's a great one. I haven't read it yet, but it seems fine so far... | Free statistical textbooks
Here's a fresh one: Introduction to Probability and Statistics Using R . It's R-specific, though, but it's a great one. I haven't read it yet, but it seems fine so far... | Free statistical textbooks
Here's a fresh one: Introduction to Probability and Statistics Using R . It's R-specific, though, but it's a great one. I haven't read it yet, but it seems fine so far... |
1,252 | Free statistical textbooks | Norman Matloff has written a mathematical statistics textbook for computer science students that's free. Kind of a niche market, I suppose. For what it's worth, I haven't read it, but Matloff has a Ph.D. in mathematical statistics, works for a computer science department, and wrote a really good R book, that I recomm... | Free statistical textbooks | Norman Matloff has written a mathematical statistics textbook for computer science students that's free. Kind of a niche market, I suppose. For what it's worth, I haven't read it, but Matloff has a | Free statistical textbooks
Norman Matloff has written a mathematical statistics textbook for computer science students that's free. Kind of a niche market, I suppose. For what it's worth, I haven't read it, but Matloff has a Ph.D. in mathematical statistics, works for a computer science department, and wrote a really... | Free statistical textbooks
Norman Matloff has written a mathematical statistics textbook for computer science students that's free. Kind of a niche market, I suppose. For what it's worth, I haven't read it, but Matloff has a |
1,253 | Free statistical textbooks | OpenIntro Statistics
http://www.openintro.org/stat/textbook.php
Inexpensive paperback copies are also available on Amazon. | Free statistical textbooks | OpenIntro Statistics
http://www.openintro.org/stat/textbook.php
Inexpensive paperback copies are also available on Amazon. | Free statistical textbooks
OpenIntro Statistics
http://www.openintro.org/stat/textbook.php
Inexpensive paperback copies are also available on Amazon. | Free statistical textbooks
OpenIntro Statistics
http://www.openintro.org/stat/textbook.php
Inexpensive paperback copies are also available on Amazon. |
1,254 | Free statistical textbooks | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
A New View of Statistics by Will G. Hopkins is great! ... | Free statistical textbooks | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
| Free statistical textbooks
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
A New View of Statistics by... | Free statistical textbooks
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
|
1,255 | Free statistical textbooks | Not Statistics specific, but a good resource is: http://www.reddit.com/r/mathbooks
Also, George Cain at Georgia Tech maintains a list of freely available maths texts that includes some statistical texts. http://people.math.gatech.edu/~cain/textbooks/onlinebooks.html | Free statistical textbooks | Not Statistics specific, but a good resource is: http://www.reddit.com/r/mathbooks
Also, George Cain at Georgia Tech maintains a list of freely available maths texts that includes some statistical te | Free statistical textbooks
Not Statistics specific, but a good resource is: http://www.reddit.com/r/mathbooks
Also, George Cain at Georgia Tech maintains a list of freely available maths texts that includes some statistical texts. http://people.math.gatech.edu/~cain/textbooks/onlinebooks.html | Free statistical textbooks
Not Statistics specific, but a good resource is: http://www.reddit.com/r/mathbooks
Also, George Cain at Georgia Tech maintains a list of freely available maths texts that includes some statistical te |
1,256 | Free statistical textbooks | "An Introduction to Statistical Learning with Applications in R" https://www.statlearning.com/ by two of the 3 authors of the well-known "The Elements of Statistical Learning" plus 2 other authors. An Introduction to Statistical Learning with Applications in R is written at a more introductory level with less mathemat... | Free statistical textbooks | "An Introduction to Statistical Learning with Applications in R" https://www.statlearning.com/ by two of the 3 authors of the well-known "The Elements of Statistical Learning" plus 2 other authors. A | Free statistical textbooks
"An Introduction to Statistical Learning with Applications in R" https://www.statlearning.com/ by two of the 3 authors of the well-known "The Elements of Statistical Learning" plus 2 other authors. An Introduction to Statistical Learning with Applications in R is written at a more introducto... | Free statistical textbooks
"An Introduction to Statistical Learning with Applications in R" https://www.statlearning.com/ by two of the 3 authors of the well-known "The Elements of Statistical Learning" plus 2 other authors. A |
1,257 | Free statistical textbooks | For getting into stochastic processes and SDEs, Tom Kurtz's lecture notes are hard to beat. It starts with a decent review of probability and some convergence results, and then dives right into continuous time stochastic processes in fairly clear, comprehensible language. In general it's one of the best books on the ... | Free statistical textbooks | For getting into stochastic processes and SDEs, Tom Kurtz's lecture notes are hard to beat. It starts with a decent review of probability and some convergence results, and then dives right into conti | Free statistical textbooks
For getting into stochastic processes and SDEs, Tom Kurtz's lecture notes are hard to beat. It starts with a decent review of probability and some convergence results, and then dives right into continuous time stochastic processes in fairly clear, comprehensible language. In general it's on... | Free statistical textbooks
For getting into stochastic processes and SDEs, Tom Kurtz's lecture notes are hard to beat. It starts with a decent review of probability and some convergence results, and then dives right into conti |
1,258 | Free statistical textbooks | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
I really like these two books by Daniel McFadden of Be... | Free statistical textbooks | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
| Free statistical textbooks
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
I really like these two boo... | Free statistical textbooks
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
|
1,259 | Free statistical textbooks | Cosma Shalizi, CMUs ML guru, occasionally updates a draft of a stats book soon to be published by Cambridge Press titled Advanced Data Analysis from an Elementary Point of View. Can't recommend it highly enough...
Here's the Table of contents:
I. Regression and Its Generalizations
Regression Basics
The Truth about Line... | Free statistical textbooks | Cosma Shalizi, CMUs ML guru, occasionally updates a draft of a stats book soon to be published by Cambridge Press titled Advanced Data Analysis from an Elementary Point of View. Can't recommend it hig | Free statistical textbooks
Cosma Shalizi, CMUs ML guru, occasionally updates a draft of a stats book soon to be published by Cambridge Press titled Advanced Data Analysis from an Elementary Point of View. Can't recommend it highly enough...
Here's the Table of contents:
I. Regression and Its Generalizations
Regression ... | Free statistical textbooks
Cosma Shalizi, CMUs ML guru, occasionally updates a draft of a stats book soon to be published by Cambridge Press titled Advanced Data Analysis from an Elementary Point of View. Can't recommend it hig |
1,260 | Free statistical textbooks | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
Some free Stats textbooks are also available here. | Free statistical textbooks | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
| Free statistical textbooks
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
Some free Stats textbooks a... | Free statistical textbooks
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
|
1,261 | Free statistical textbooks | I know other authors have gone to some trouble to make their books available here on stack exchange ... The printed version of our 2002 edition was printed 3 times and sold out 3 times; Springer and Google recently started selling it (book only) as a PDF eBook (no software) on the Springer and Google sites for $79.
W... | Free statistical textbooks | I know other authors have gone to some trouble to make their books available here on stack exchange ... The printed version of our 2002 edition was printed 3 times and sold out 3 times; Springer and | Free statistical textbooks
I know other authors have gone to some trouble to make their books available here on stack exchange ... The printed version of our 2002 edition was printed 3 times and sold out 3 times; Springer and Google recently started selling it (book only) as a PDF eBook (no software) on the Springer ... | Free statistical textbooks
I know other authors have gone to some trouble to make their books available here on stack exchange ... The printed version of our 2002 edition was printed 3 times and sold out 3 times; Springer and |
1,262 | Free statistical textbooks | It's nice to see academics freely distribute their works. Here is trove of free ML / Stats books in PDF:
Machine Learning
Elements of Statistical Learning Hastie, Tibshirani, Friedman
All of Statistics Larry Wasserman
Machine Learning and Bayesian Reasoning David Barber
Gaussian Processes for Machine Learning Rasmusse... | Free statistical textbooks | It's nice to see academics freely distribute their works. Here is trove of free ML / Stats books in PDF:
Machine Learning
Elements of Statistical Learning Hastie, Tibshirani, Friedman
All of Statisti | Free statistical textbooks
It's nice to see academics freely distribute their works. Here is trove of free ML / Stats books in PDF:
Machine Learning
Elements of Statistical Learning Hastie, Tibshirani, Friedman
All of Statistics Larry Wasserman
Machine Learning and Bayesian Reasoning David Barber
Gaussian Processes fo... | Free statistical textbooks
It's nice to see academics freely distribute their works. Here is trove of free ML / Stats books in PDF:
Machine Learning
Elements of Statistical Learning Hastie, Tibshirani, Friedman
All of Statisti |
1,263 | Free statistical textbooks | Statsoft's Electronic Statistics Handbook ('The only Internet Resource about Statistics Recommended by Encyclopedia Britannica') is worth checking out. | Free statistical textbooks | Statsoft's Electronic Statistics Handbook ('The only Internet Resource about Statistics Recommended by Encyclopedia Britannica') is worth checking out. | Free statistical textbooks
Statsoft's Electronic Statistics Handbook ('The only Internet Resource about Statistics Recommended by Encyclopedia Britannica') is worth checking out. | Free statistical textbooks
Statsoft's Electronic Statistics Handbook ('The only Internet Resource about Statistics Recommended by Encyclopedia Britannica') is worth checking out. |
1,264 | Free statistical textbooks | Not properly an entire textbook, but the part IV of Mathematics for Computer Science is about probability and random variables. | Free statistical textbooks | Not properly an entire textbook, but the part IV of Mathematics for Computer Science is about probability and random variables. | Free statistical textbooks
Not properly an entire textbook, but the part IV of Mathematics for Computer Science is about probability and random variables. | Free statistical textbooks
Not properly an entire textbook, but the part IV of Mathematics for Computer Science is about probability and random variables. |
1,265 | Free statistical textbooks | Some downloadable notes on probability, which seems interesting:
http://www.math.harvard.edu/~knill/teaching/math19b_2011/handouts/chapters1-19.pdf
Applied probability:
http://www.acsu.buffalo.edu/~bialas/EAS305/docs/EAS305%20NOTES%202005.pdf
http://www.ma.huji.ac.il/~razk/Teaching/LectureNotes/LectureNotesProbability.... | Free statistical textbooks | Some downloadable notes on probability, which seems interesting:
http://www.math.harvard.edu/~knill/teaching/math19b_2011/handouts/chapters1-19.pdf
Applied probability:
http://www.acsu.buffalo.edu/~bi | Free statistical textbooks
Some downloadable notes on probability, which seems interesting:
http://www.math.harvard.edu/~knill/teaching/math19b_2011/handouts/chapters1-19.pdf
Applied probability:
http://www.acsu.buffalo.edu/~bialas/EAS305/docs/EAS305%20NOTES%202005.pdf
http://www.ma.huji.ac.il/~razk/Teaching/LectureNot... | Free statistical textbooks
Some downloadable notes on probability, which seems interesting:
http://www.math.harvard.edu/~knill/teaching/math19b_2011/handouts/chapters1-19.pdf
Applied probability:
http://www.acsu.buffalo.edu/~bi |
1,266 | Free statistical textbooks | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
A write up of probability tutorials and related puzzle... | Free statistical textbooks | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
| Free statistical textbooks
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
A write up of probability t... | Free statistical textbooks
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
|
1,267 | Free statistical textbooks | http://www.probabilitycourse.com/ is a website hosting free online-based Probability and Statistics textbook. It also has extra features such as graphing tools and lecture videos | Free statistical textbooks | http://www.probabilitycourse.com/ is a website hosting free online-based Probability and Statistics textbook. It also has extra features such as graphing tools and lecture videos | Free statistical textbooks
http://www.probabilitycourse.com/ is a website hosting free online-based Probability and Statistics textbook. It also has extra features such as graphing tools and lecture videos | Free statistical textbooks
http://www.probabilitycourse.com/ is a website hosting free online-based Probability and Statistics textbook. It also has extra features such as graphing tools and lecture videos |
1,268 | Free statistical textbooks | Here is also a great free book on multivariate statistics by Marden, primarily concerned with the normal linear model linked on this page:
https://people.stat.sc.edu/hansont/stat730/Marden2013.pdf | Free statistical textbooks | Here is also a great free book on multivariate statistics by Marden, primarily concerned with the normal linear model linked on this page:
https://people.stat.sc.edu/hansont/stat730/Marden2013.pdf | Free statistical textbooks
Here is also a great free book on multivariate statistics by Marden, primarily concerned with the normal linear model linked on this page:
https://people.stat.sc.edu/hansont/stat730/Marden2013.pdf | Free statistical textbooks
Here is also a great free book on multivariate statistics by Marden, primarily concerned with the normal linear model linked on this page:
https://people.stat.sc.edu/hansont/stat730/Marden2013.pdf |
1,269 | Free statistical textbooks | Gelman et al. "Bayesian Data Analysis" (3rd edition). | Free statistical textbooks | Gelman et al. "Bayesian Data Analysis" (3rd edition). | Free statistical textbooks
Gelman et al. "Bayesian Data Analysis" (3rd edition). | Free statistical textbooks
Gelman et al. "Bayesian Data Analysis" (3rd edition). |
1,270 | Free statistical textbooks | It's not a textbook but Bayesian Methods in the Search for the MH370 is a great introduction to particle filters. | Free statistical textbooks | It's not a textbook but Bayesian Methods in the Search for the MH370 is a great introduction to particle filters. | Free statistical textbooks
It's not a textbook but Bayesian Methods in the Search for the MH370 is a great introduction to particle filters. | Free statistical textbooks
It's not a textbook but Bayesian Methods in the Search for the MH370 is a great introduction to particle filters. |
1,271 | Free statistical textbooks | A digital textbook on probability and statistics by M. Taboga can be found at https://www.statlect.com The level is intermediate. It has hundreds of solved exercises and examples, as well as step-by-step proofs of all the results presented. | Free statistical textbooks | A digital textbook on probability and statistics by M. Taboga can be found at https://www.statlect.com The level is intermediate. It has hundreds of solved exercises and examples, as well as step-by-s | Free statistical textbooks
A digital textbook on probability and statistics by M. Taboga can be found at https://www.statlect.com The level is intermediate. It has hundreds of solved exercises and examples, as well as step-by-step proofs of all the results presented. | Free statistical textbooks
A digital textbook on probability and statistics by M. Taboga can be found at https://www.statlect.com The level is intermediate. It has hundreds of solved exercises and examples, as well as step-by-s |
1,272 | Is there an intuitive interpretation of $A^TA$ for a data matrix $A$? | Geometrically, matrix $\bf A'A$ is called matrix of scalar products (= dot products, = inner products). Algebraically, it is called sum-of-squares-and-cross-products matrix (SSCP).
Its $i$-th diagonal element is equal to $\sum a_{(i)}^2$, where $a_{(i)}$ denotes values in the $i$-th column of $\bf A$ and $\sum$ is the ... | Is there an intuitive interpretation of $A^TA$ for a data matrix $A$? | Geometrically, matrix $\bf A'A$ is called matrix of scalar products (= dot products, = inner products). Algebraically, it is called sum-of-squares-and-cross-products matrix (SSCP).
Its $i$-th diagonal | Is there an intuitive interpretation of $A^TA$ for a data matrix $A$?
Geometrically, matrix $\bf A'A$ is called matrix of scalar products (= dot products, = inner products). Algebraically, it is called sum-of-squares-and-cross-products matrix (SSCP).
Its $i$-th diagonal element is equal to $\sum a_{(i)}^2$, where $a_{(... | Is there an intuitive interpretation of $A^TA$ for a data matrix $A$?
Geometrically, matrix $\bf A'A$ is called matrix of scalar products (= dot products, = inner products). Algebraically, it is called sum-of-squares-and-cross-products matrix (SSCP).
Its $i$-th diagonal |
1,273 | Is there an intuitive interpretation of $A^TA$ for a data matrix $A$? | The matrix $A^TA$ contains all the inner products of all columns in $A$. The diagonal thus contains the squared norms of columns. If you think about geometry and orthogonal projections onto the column space spanned by the columns in $A$ you may recall that norms and inner products of the vectors spanning this space pla... | Is there an intuitive interpretation of $A^TA$ for a data matrix $A$? | The matrix $A^TA$ contains all the inner products of all columns in $A$. The diagonal thus contains the squared norms of columns. If you think about geometry and orthogonal projections onto the column | Is there an intuitive interpretation of $A^TA$ for a data matrix $A$?
The matrix $A^TA$ contains all the inner products of all columns in $A$. The diagonal thus contains the squared norms of columns. If you think about geometry and orthogonal projections onto the column space spanned by the columns in $A$ you may recal... | Is there an intuitive interpretation of $A^TA$ for a data matrix $A$?
The matrix $A^TA$ contains all the inner products of all columns in $A$. The diagonal thus contains the squared norms of columns. If you think about geometry and orthogonal projections onto the column |
1,274 | Is there an intuitive interpretation of $A^TA$ for a data matrix $A$? | @NRH gave a good technical answer.
If you want something really basic, you can think of $A^TA$ as the matrix equivalent of $A^2$ for a scalar. | Is there an intuitive interpretation of $A^TA$ for a data matrix $A$? | @NRH gave a good technical answer.
If you want something really basic, you can think of $A^TA$ as the matrix equivalent of $A^2$ for a scalar. | Is there an intuitive interpretation of $A^TA$ for a data matrix $A$?
@NRH gave a good technical answer.
If you want something really basic, you can think of $A^TA$ as the matrix equivalent of $A^2$ for a scalar. | Is there an intuitive interpretation of $A^TA$ for a data matrix $A$?
@NRH gave a good technical answer.
If you want something really basic, you can think of $A^TA$ as the matrix equivalent of $A^2$ for a scalar. |
1,275 | Is there an intuitive interpretation of $A^TA$ for a data matrix $A$? | Although it has been already discussed that $\textbf{A}^T\textbf{A}$ has the meaning of taking dot products, I would only add a graphical representation of this multiplication.
Indeed, while rows of the matrix $\textbf{A}^T$ (and columns of the matrix $\textbf{A}$) represent variables, we treat each variable measuremen... | Is there an intuitive interpretation of $A^TA$ for a data matrix $A$? | Although it has been already discussed that $\textbf{A}^T\textbf{A}$ has the meaning of taking dot products, I would only add a graphical representation of this multiplication.
Indeed, while rows of t | Is there an intuitive interpretation of $A^TA$ for a data matrix $A$?
Although it has been already discussed that $\textbf{A}^T\textbf{A}$ has the meaning of taking dot products, I would only add a graphical representation of this multiplication.
Indeed, while rows of the matrix $\textbf{A}^T$ (and columns of the matri... | Is there an intuitive interpretation of $A^TA$ for a data matrix $A$?
Although it has been already discussed that $\textbf{A}^T\textbf{A}$ has the meaning of taking dot products, I would only add a graphical representation of this multiplication.
Indeed, while rows of t |
1,276 | Is there an intuitive interpretation of $A^TA$ for a data matrix $A$? | An important view of the geometry of $A'A$ is this (the viewpoint strongly stressed in Strang's book on "Linear Algebra and Its Applications"): Suppose A is an $m \times n$-matrix of rank k, representing a linear map $A: R^n \rightarrow R^m$. Let Col(A) and Row(A) be the column and row spaces of $A$. Then
(a) As a r... | Is there an intuitive interpretation of $A^TA$ for a data matrix $A$? | An important view of the geometry of $A'A$ is this (the viewpoint strongly stressed in Strang's book on "Linear Algebra and Its Applications"): Suppose A is an $m \times n$-matrix of rank k, represen | Is there an intuitive interpretation of $A^TA$ for a data matrix $A$?
An important view of the geometry of $A'A$ is this (the viewpoint strongly stressed in Strang's book on "Linear Algebra and Its Applications"): Suppose A is an $m \times n$-matrix of rank k, representing a linear map $A: R^n \rightarrow R^m$. Let C... | Is there an intuitive interpretation of $A^TA$ for a data matrix $A$?
An important view of the geometry of $A'A$ is this (the viewpoint strongly stressed in Strang's book on "Linear Algebra and Its Applications"): Suppose A is an $m \times n$-matrix of rank k, represen |
1,277 | Is there an intuitive interpretation of $A^TA$ for a data matrix $A$? | There are levels of intuition. For those familiar with matrix notation instatistics the intuition is to think of it as a square of the random variable: $x\to E[x^2]$ vs $A\to A^TA$
In matrix notation a sample of the random variable $x$ observations $x_i$ or a population are represented by a column vector: $$a=\begin{bm... | Is there an intuitive interpretation of $A^TA$ for a data matrix $A$? | There are levels of intuition. For those familiar with matrix notation instatistics the intuition is to think of it as a square of the random variable: $x\to E[x^2]$ vs $A\to A^TA$
In matrix notation | Is there an intuitive interpretation of $A^TA$ for a data matrix $A$?
There are levels of intuition. For those familiar with matrix notation instatistics the intuition is to think of it as a square of the random variable: $x\to E[x^2]$ vs $A\to A^TA$
In matrix notation a sample of the random variable $x$ observations $... | Is there an intuitive interpretation of $A^TA$ for a data matrix $A$?
There are levels of intuition. For those familiar with matrix notation instatistics the intuition is to think of it as a square of the random variable: $x\to E[x^2]$ vs $A\to A^TA$
In matrix notation |
1,278 | Is it necessary to scale the target value in addition to scaling features for regression analysis? | Let's first analyse why feature scaling is performed. Feature scaling improves the convergence of steepest descent algorithms, which do not possess the property of scale invariance.
In stochastic gradient descent training examples inform the weight updates iteratively like so, $$w_{t+1} = w_t - \gamma\nabla_w \ell(f_w(... | Is it necessary to scale the target value in addition to scaling features for regression analysis? | Let's first analyse why feature scaling is performed. Feature scaling improves the convergence of steepest descent algorithms, which do not possess the property of scale invariance.
In stochastic grad | Is it necessary to scale the target value in addition to scaling features for regression analysis?
Let's first analyse why feature scaling is performed. Feature scaling improves the convergence of steepest descent algorithms, which do not possess the property of scale invariance.
In stochastic gradient descent training... | Is it necessary to scale the target value in addition to scaling features for regression analysis?
Let's first analyse why feature scaling is performed. Feature scaling improves the convergence of steepest descent algorithms, which do not possess the property of scale invariance.
In stochastic grad |
1,279 | Is it necessary to scale the target value in addition to scaling features for regression analysis? | Yes, you do need to scale the target variable. I will quote this reference:
A target variable with a large spread of values, in turn, may result in large error gradient values causing weight values to change dramatically, making the learning process unstable.
In the reference, there's also a demonstration on code whe... | Is it necessary to scale the target value in addition to scaling features for regression analysis? | Yes, you do need to scale the target variable. I will quote this reference:
A target variable with a large spread of values, in turn, may result in large error gradient values causing weight values t | Is it necessary to scale the target value in addition to scaling features for regression analysis?
Yes, you do need to scale the target variable. I will quote this reference:
A target variable with a large spread of values, in turn, may result in large error gradient values causing weight values to change dramatically... | Is it necessary to scale the target value in addition to scaling features for regression analysis?
Yes, you do need to scale the target variable. I will quote this reference:
A target variable with a large spread of values, in turn, may result in large error gradient values causing weight values t |
1,280 | Is it necessary to scale the target value in addition to scaling features for regression analysis? | Generally, It is not necessary. Scaling inputs helps to avoid the situation, when one or several features dominate others in magnitude, as a result, the model hardly picks up the contribution of the smaller scale variables, even if they are strong. But if you scale the target, your mean squared error (MSE) is automatic... | Is it necessary to scale the target value in addition to scaling features for regression analysis? | Generally, It is not necessary. Scaling inputs helps to avoid the situation, when one or several features dominate others in magnitude, as a result, the model hardly picks up the contribution of the s | Is it necessary to scale the target value in addition to scaling features for regression analysis?
Generally, It is not necessary. Scaling inputs helps to avoid the situation, when one or several features dominate others in magnitude, as a result, the model hardly picks up the contribution of the smaller scale variable... | Is it necessary to scale the target value in addition to scaling features for regression analysis?
Generally, It is not necessary. Scaling inputs helps to avoid the situation, when one or several features dominate others in magnitude, as a result, the model hardly picks up the contribution of the s |
1,281 | Is it necessary to scale the target value in addition to scaling features for regression analysis? | No, linear transformations of the response are never necessary. They may, however, be helpful to aid in interpretation of your model. For example, if your response is given in meters but is typically very small, it may be helpful to rescale to i.e. millimeters. Note also that centering and/or scaling the inputs can be ... | Is it necessary to scale the target value in addition to scaling features for regression analysis? | No, linear transformations of the response are never necessary. They may, however, be helpful to aid in interpretation of your model. For example, if your response is given in meters but is typically | Is it necessary to scale the target value in addition to scaling features for regression analysis?
No, linear transformations of the response are never necessary. They may, however, be helpful to aid in interpretation of your model. For example, if your response is given in meters but is typically very small, it may be... | Is it necessary to scale the target value in addition to scaling features for regression analysis?
No, linear transformations of the response are never necessary. They may, however, be helpful to aid in interpretation of your model. For example, if your response is given in meters but is typically |
1,282 | Is it necessary to scale the target value in addition to scaling features for regression analysis? | It may be useful for some cases.
Even though not being a common error function, when L1 error used to calculate loss, a rather slow learning may occur.
Assume that we have a linear regression model, and also have a constant learning rate $n$. Say,
$ y = b_1x + b_0 $
$ n = 0.1 $
$b_1$ and $b_0$ are updated as follows:
$... | Is it necessary to scale the target value in addition to scaling features for regression analysis? | It may be useful for some cases.
Even though not being a common error function, when L1 error used to calculate loss, a rather slow learning may occur.
Assume that we have a linear regression model, a | Is it necessary to scale the target value in addition to scaling features for regression analysis?
It may be useful for some cases.
Even though not being a common error function, when L1 error used to calculate loss, a rather slow learning may occur.
Assume that we have a linear regression model, and also have a consta... | Is it necessary to scale the target value in addition to scaling features for regression analysis?
It may be useful for some cases.
Even though not being a common error function, when L1 error used to calculate loss, a rather slow learning may occur.
Assume that we have a linear regression model, a |
1,283 | Is it necessary to scale the target value in addition to scaling features for regression analysis? | It does affect gradient descent in a bad way.
check the formula for gradient descent:
$$ x_{n+1} = x_{n} - \gamma\Delta F(x_n) $$
lets say that $x_2$ is a feature that is 1000 times greater than $x_1$
for $ F(\vec{x})=\vec{x}^2 $ we have $ \Delta F(\vec{x})=2*\vec{x} $. The optimal way to reach (0,0) which is the glob... | Is it necessary to scale the target value in addition to scaling features for regression analysis? | It does affect gradient descent in a bad way.
check the formula for gradient descent:
$$ x_{n+1} = x_{n} - \gamma\Delta F(x_n) $$
lets say that $x_2$ is a feature that is 1000 times greater than $x_1 | Is it necessary to scale the target value in addition to scaling features for regression analysis?
It does affect gradient descent in a bad way.
check the formula for gradient descent:
$$ x_{n+1} = x_{n} - \gamma\Delta F(x_n) $$
lets say that $x_2$ is a feature that is 1000 times greater than $x_1$
for $ F(\vec{x})=\v... | Is it necessary to scale the target value in addition to scaling features for regression analysis?
It does affect gradient descent in a bad way.
check the formula for gradient descent:
$$ x_{n+1} = x_{n} - \gamma\Delta F(x_n) $$
lets say that $x_2$ is a feature that is 1000 times greater than $x_1 |
1,284 | Is it necessary to scale the target value in addition to scaling features for regression analysis? | I think the best way to know whether we should scale the output is to try both way, using scaler.inverse_transform in sklearn.
Neural network is not robust to transformation, in general. Therefore, if you scale the output variables, train,then the MSE produced is for the scaled version.
However, if you use that model... | Is it necessary to scale the target value in addition to scaling features for regression analysis? | I think the best way to know whether we should scale the output is to try both way, using scaler.inverse_transform in sklearn.
Neural network is not robust to transformation, in general. Therefore, i | Is it necessary to scale the target value in addition to scaling features for regression analysis?
I think the best way to know whether we should scale the output is to try both way, using scaler.inverse_transform in sklearn.
Neural network is not robust to transformation, in general. Therefore, if you scale the outpu... | Is it necessary to scale the target value in addition to scaling features for regression analysis?
I think the best way to know whether we should scale the output is to try both way, using scaler.inverse_transform in sklearn.
Neural network is not robust to transformation, in general. Therefore, i |
1,285 | Differences between cross validation and bootstrapping to estimate the prediction error | It comes down to variance and bias (as usual). CV tends to be less biased but K-fold CV has fairly large variance. On the other hand, bootstrapping tends to drastically reduce the variance but gives more biased results (they tend to be pessimistic). Other bootstrapping methods have been adapted to deal with the bootstr... | Differences between cross validation and bootstrapping to estimate the prediction error | It comes down to variance and bias (as usual). CV tends to be less biased but K-fold CV has fairly large variance. On the other hand, bootstrapping tends to drastically reduce the variance but gives m | Differences between cross validation and bootstrapping to estimate the prediction error
It comes down to variance and bias (as usual). CV tends to be less biased but K-fold CV has fairly large variance. On the other hand, bootstrapping tends to drastically reduce the variance but gives more biased results (they tend to... | Differences between cross validation and bootstrapping to estimate the prediction error
It comes down to variance and bias (as usual). CV tends to be less biased but K-fold CV has fairly large variance. On the other hand, bootstrapping tends to drastically reduce the variance but gives m |
1,286 | Differences between cross validation and bootstrapping to estimate the prediction error | @Frank Harrell has done a lot of work on this question. I don't know of specific references.
But I rather see the two techniques as being for different purposes. Cross validation is a good tool when deciding on the model -- it helps you avoid fooling yourself into thinking that you have a good model when in fact you a... | Differences between cross validation and bootstrapping to estimate the prediction error | @Frank Harrell has done a lot of work on this question. I don't know of specific references.
But I rather see the two techniques as being for different purposes. Cross validation is a good tool when | Differences between cross validation and bootstrapping to estimate the prediction error
@Frank Harrell has done a lot of work on this question. I don't know of specific references.
But I rather see the two techniques as being for different purposes. Cross validation is a good tool when deciding on the model -- it help... | Differences between cross validation and bootstrapping to estimate the prediction error
@Frank Harrell has done a lot of work on this question. I don't know of specific references.
But I rather see the two techniques as being for different purposes. Cross validation is a good tool when |
1,287 | Differences between cross validation and bootstrapping to estimate the prediction error | My understanding is that bootstrapping is a way to quantify the uncertainty in your model while cross validation is used for model selection and measuring predictive accuracy. | Differences between cross validation and bootstrapping to estimate the prediction error | My understanding is that bootstrapping is a way to quantify the uncertainty in your model while cross validation is used for model selection and measuring predictive accuracy. | Differences between cross validation and bootstrapping to estimate the prediction error
My understanding is that bootstrapping is a way to quantify the uncertainty in your model while cross validation is used for model selection and measuring predictive accuracy. | Differences between cross validation and bootstrapping to estimate the prediction error
My understanding is that bootstrapping is a way to quantify the uncertainty in your model while cross validation is used for model selection and measuring predictive accuracy. |
1,288 | Differences between cross validation and bootstrapping to estimate the prediction error | These are two techniques of resampling:
In cross validation we divide the data randomly into kfold and it helps in overfitting, but this approach has its drawback. As it uses random samples so some sample produces major error. In order to minimize CV has techniques but its not so powerful with classification problems. ... | Differences between cross validation and bootstrapping to estimate the prediction error | These are two techniques of resampling:
In cross validation we divide the data randomly into kfold and it helps in overfitting, but this approach has its drawback. As it uses random samples so some sa | Differences between cross validation and bootstrapping to estimate the prediction error
These are two techniques of resampling:
In cross validation we divide the data randomly into kfold and it helps in overfitting, but this approach has its drawback. As it uses random samples so some sample produces major error. In or... | Differences between cross validation and bootstrapping to estimate the prediction error
These are two techniques of resampling:
In cross validation we divide the data randomly into kfold and it helps in overfitting, but this approach has its drawback. As it uses random samples so some sa |
1,289 | Numerical example to understand Expectation-Maximization | This is a recipe to learn EM with a practical and (in my opinion) very intuitive 'Coin-Toss' example:
Read this short EM tutorial paper by Do and Batzoglou. This is the schema where the coin toss example is explained:
You may have question marks in your head, especially regarding where the probabilities in the Expe... | Numerical example to understand Expectation-Maximization | This is a recipe to learn EM with a practical and (in my opinion) very intuitive 'Coin-Toss' example:
Read this short EM tutorial paper by Do and Batzoglou. This is the schema where the coin toss e | Numerical example to understand Expectation-Maximization
This is a recipe to learn EM with a practical and (in my opinion) very intuitive 'Coin-Toss' example:
Read this short EM tutorial paper by Do and Batzoglou. This is the schema where the coin toss example is explained:
You may have question marks in your head,... | Numerical example to understand Expectation-Maximization
This is a recipe to learn EM with a practical and (in my opinion) very intuitive 'Coin-Toss' example:
Read this short EM tutorial paper by Do and Batzoglou. This is the schema where the coin toss e |
1,290 | Numerical example to understand Expectation-Maximization | It sounds like your question has two parts: the underlying idea and a concrete example. I'll start with the underlying idea, then link to an example at the bottom.
EM is useful in Catch-22 situations where it seems like you need to know $A$ before you can calculate $B$ and you need to know $B$ before you can calculat... | Numerical example to understand Expectation-Maximization | It sounds like your question has two parts: the underlying idea and a concrete example. I'll start with the underlying idea, then link to an example at the bottom.
EM is useful in Catch-22 situation | Numerical example to understand Expectation-Maximization
It sounds like your question has two parts: the underlying idea and a concrete example. I'll start with the underlying idea, then link to an example at the bottom.
EM is useful in Catch-22 situations where it seems like you need to know $A$ before you can calcu... | Numerical example to understand Expectation-Maximization
It sounds like your question has two parts: the underlying idea and a concrete example. I'll start with the underlying idea, then link to an example at the bottom.
EM is useful in Catch-22 situation |
1,291 | Numerical example to understand Expectation-Maximization | Here's an example of Expectation Maximisation (EM) used to estimate the mean and standard deviation. The code is in Python, but it should be easy to follow even if you're not familiar with the language.
The motivation for EM
The red and blue points shown below are drawn from two different normal distributions, each wit... | Numerical example to understand Expectation-Maximization | Here's an example of Expectation Maximisation (EM) used to estimate the mean and standard deviation. The code is in Python, but it should be easy to follow even if you're not familiar with the languag | Numerical example to understand Expectation-Maximization
Here's an example of Expectation Maximisation (EM) used to estimate the mean and standard deviation. The code is in Python, but it should be easy to follow even if you're not familiar with the language.
The motivation for EM
The red and blue points shown below ar... | Numerical example to understand Expectation-Maximization
Here's an example of Expectation Maximisation (EM) used to estimate the mean and standard deviation. The code is in Python, but it should be easy to follow even if you're not familiar with the languag |
1,292 | Numerical example to understand Expectation-Maximization | Following Zhubarb's answer, I implemented the Do and Batzoglou "coin tossing" E-M example in GNU R. Note that I use the mle function of the stats4 package - this helped me to understand more clearly how E-M and MLE are related.
require("stats4");
## sample data from Do and Batzoglou
ds<-data.frame(heads=c(5,9,8,4,7),n... | Numerical example to understand Expectation-Maximization | Following Zhubarb's answer, I implemented the Do and Batzoglou "coin tossing" E-M example in GNU R. Note that I use the mle function of the stats4 package - this helped me to understand more clearly h | Numerical example to understand Expectation-Maximization
Following Zhubarb's answer, I implemented the Do and Batzoglou "coin tossing" E-M example in GNU R. Note that I use the mle function of the stats4 package - this helped me to understand more clearly how E-M and MLE are related.
require("stats4");
## sample data ... | Numerical example to understand Expectation-Maximization
Following Zhubarb's answer, I implemented the Do and Batzoglou "coin tossing" E-M example in GNU R. Note that I use the mle function of the stats4 package - this helped me to understand more clearly h |
1,293 | Numerical example to understand Expectation-Maximization | All of the above look like great resources, but I must link to this great example. It presents a very simple explanation for finding the parameters for two lines of a set of points. The tutorial is by Yair Weiss while at MIT.
http://www.cs.huji.ac.il/~yweiss/emTutorial.pdf
http://www.cs.huji.ac.il/~yweiss/tutorials.h... | Numerical example to understand Expectation-Maximization | All of the above look like great resources, but I must link to this great example. It presents a very simple explanation for finding the parameters for two lines of a set of points. The tutorial is | Numerical example to understand Expectation-Maximization
All of the above look like great resources, but I must link to this great example. It presents a very simple explanation for finding the parameters for two lines of a set of points. The tutorial is by Yair Weiss while at MIT.
http://www.cs.huji.ac.il/~yweiss/em... | Numerical example to understand Expectation-Maximization
All of the above look like great resources, but I must link to this great example. It presents a very simple explanation for finding the parameters for two lines of a set of points. The tutorial is |
1,294 | Numerical example to understand Expectation-Maximization | The answer given by Zhubarb is great, but unfortunately it is in Python. Below is a Java implementation of the EM algorithm executed on the same problem (posed in the article by Do and Batzoglou, 2008). I've added some printf's to the standard output to see how the parameters converge.
thetaA = 0.71301, thetaB = 0.5813... | Numerical example to understand Expectation-Maximization | The answer given by Zhubarb is great, but unfortunately it is in Python. Below is a Java implementation of the EM algorithm executed on the same problem (posed in the article by Do and Batzoglou, 2008 | Numerical example to understand Expectation-Maximization
The answer given by Zhubarb is great, but unfortunately it is in Python. Below is a Java implementation of the EM algorithm executed on the same problem (posed in the article by Do and Batzoglou, 2008). I've added some printf's to the standard output to see how t... | Numerical example to understand Expectation-Maximization
The answer given by Zhubarb is great, but unfortunately it is in Python. Below is a Java implementation of the EM algorithm executed on the same problem (posed in the article by Do and Batzoglou, 2008 |
1,295 | Numerical example to understand Expectation-Maximization | % Implementation of the EM (Expectation-Maximization)algorithm example exposed on:
% Motion Segmentation using EM - a short tutorial, Yair Weiss, %http://www.cs.huji.ac.il/~yweiss/emTutorial.pdf
% Juan Andrade, jandrader@yahoo.com
clear all
clc
%% Setup parameters
m1 = 2; % slope line 1
m2 = 6; ... | Numerical example to understand Expectation-Maximization | % Implementation of the EM (Expectation-Maximization)algorithm example exposed on:
% Motion Segmentation using EM - a short tutorial, Yair Weiss, %http://www.cs.huji.ac.il/~yweiss/emTutorial.pdf
% Jua | Numerical example to understand Expectation-Maximization
% Implementation of the EM (Expectation-Maximization)algorithm example exposed on:
% Motion Segmentation using EM - a short tutorial, Yair Weiss, %http://www.cs.huji.ac.il/~yweiss/emTutorial.pdf
% Juan Andrade, jandrader@yahoo.com
clear all
clc
%% Setup paramet... | Numerical example to understand Expectation-Maximization
% Implementation of the EM (Expectation-Maximization)algorithm example exposed on:
% Motion Segmentation using EM - a short tutorial, Yair Weiss, %http://www.cs.huji.ac.il/~yweiss/emTutorial.pdf
% Jua |
1,296 | Numerical example to understand Expectation-Maximization | Well, I would suggest you to go through a book on R by Maria L Rizzo. One of the chapters contain the use of EM algorithm with a numerical example. I remember going through the code for better understanding.
Also, try to view it from a clustering point of view in the beginning. Work out by hand, a clustering problem w... | Numerical example to understand Expectation-Maximization | Well, I would suggest you to go through a book on R by Maria L Rizzo. One of the chapters contain the use of EM algorithm with a numerical example. I remember going through the code for better underst | Numerical example to understand Expectation-Maximization
Well, I would suggest you to go through a book on R by Maria L Rizzo. One of the chapters contain the use of EM algorithm with a numerical example. I remember going through the code for better understanding.
Also, try to view it from a clustering point of view i... | Numerical example to understand Expectation-Maximization
Well, I would suggest you to go through a book on R by Maria L Rizzo. One of the chapters contain the use of EM algorithm with a numerical example. I remember going through the code for better underst |
1,297 | Numerical example to understand Expectation-Maximization | Just in case, I have written a Ruby implementation of the above mentioned coin toss example by Do & Batzoglou and it produces exactly the same numbers as they do w.r.t. the same input parameters $\theta_A = 0.6$ and $\theta_B = 0.5$.
# gem install distribution
require 'distribution'
# error bound
EPS = 10**-6
# num... | Numerical example to understand Expectation-Maximization | Just in case, I have written a Ruby implementation of the above mentioned coin toss example by Do & Batzoglou and it produces exactly the same numbers as they do w.r.t. the same input parameters $\the | Numerical example to understand Expectation-Maximization
Just in case, I have written a Ruby implementation of the above mentioned coin toss example by Do & Batzoglou and it produces exactly the same numbers as they do w.r.t. the same input parameters $\theta_A = 0.6$ and $\theta_B = 0.5$.
# gem install distribution
... | Numerical example to understand Expectation-Maximization
Just in case, I have written a Ruby implementation of the above mentioned coin toss example by Do & Batzoglou and it produces exactly the same numbers as they do w.r.t. the same input parameters $\the |
1,298 | When to use gamma GLMs? | The gamma has a property shared by the lognormal; namely that when the shape parameter is held constant while the scale parameter is varied (as is usually done when using either for models), the variance is proportional to mean-squared (constant coefficient of variation).
Something approximate to this occurs fairly oft... | When to use gamma GLMs? | The gamma has a property shared by the lognormal; namely that when the shape parameter is held constant while the scale parameter is varied (as is usually done when using either for models), the varia | When to use gamma GLMs?
The gamma has a property shared by the lognormal; namely that when the shape parameter is held constant while the scale parameter is varied (as is usually done when using either for models), the variance is proportional to mean-squared (constant coefficient of variation).
Something approximate t... | When to use gamma GLMs?
The gamma has a property shared by the lognormal; namely that when the shape parameter is held constant while the scale parameter is varied (as is usually done when using either for models), the varia |
1,299 | When to use gamma GLMs? | That's a good question. In fact, why don't people use generalised linear models (GLM) more is also a good question.
Warning note: Some people use GLM for general linear model, not what is in mind here.
It does depend where you look. For example, gamma distributions have been popular in several of the environmental s... | When to use gamma GLMs? | That's a good question. In fact, why don't people use generalised linear models (GLM) more is also a good question.
Warning note: Some people use GLM for general linear model, not what is in mind her | When to use gamma GLMs?
That's a good question. In fact, why don't people use generalised linear models (GLM) more is also a good question.
Warning note: Some people use GLM for general linear model, not what is in mind here.
It does depend where you look. For example, gamma distributions have been popular in severa... | When to use gamma GLMs?
That's a good question. In fact, why don't people use generalised linear models (GLM) more is also a good question.
Warning note: Some people use GLM for general linear model, not what is in mind her |
1,300 | When to use gamma GLMs? | Gamma regression is in the GLM and so you can get many useful quantities for diagnostic purposes, such as deviance residuals, leverages, Cook's distance, and so on. They are perhaps not as nice as the corresponding quantities for log-transformed data.
One thing that gamma regression avoids compared to the lognormal is... | When to use gamma GLMs? | Gamma regression is in the GLM and so you can get many useful quantities for diagnostic purposes, such as deviance residuals, leverages, Cook's distance, and so on. They are perhaps not as nice as the | When to use gamma GLMs?
Gamma regression is in the GLM and so you can get many useful quantities for diagnostic purposes, such as deviance residuals, leverages, Cook's distance, and so on. They are perhaps not as nice as the corresponding quantities for log-transformed data.
One thing that gamma regression avoids comp... | When to use gamma GLMs?
Gamma regression is in the GLM and so you can get many useful quantities for diagnostic purposes, such as deviance residuals, leverages, Cook's distance, and so on. They are perhaps not as nice as the |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.