idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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14,801 | Logit with ordinal independent variables | it's perfectly fine to use a categorical predictor in a logit (or OLS) regression model if the levels are ordinal. But if you have a reason to treat each level as discrete (or if in fact your categorical variable is nominal rather than ordinal), then, as alternative to dummy coding, you can also use orthogonal contrast... | Logit with ordinal independent variables | it's perfectly fine to use a categorical predictor in a logit (or OLS) regression model if the levels are ordinal. But if you have a reason to treat each level as discrete (or if in fact your categori | Logit with ordinal independent variables
it's perfectly fine to use a categorical predictor in a logit (or OLS) regression model if the levels are ordinal. But if you have a reason to treat each level as discrete (or if in fact your categorical variable is nominal rather than ordinal), then, as alternative to dummy cod... | Logit with ordinal independent variables
it's perfectly fine to use a categorical predictor in a logit (or OLS) regression model if the levels are ordinal. But if you have a reason to treat each level as discrete (or if in fact your categori |
14,802 | Why does a bagged tree / random forest tree have higher bias than a single decision tree? | I will accept the answer on 1) from Kunlun, but just to close this case, I will here give the conclusions on the two questions that I reached in my thesis (which were both accepted by my Supervisor):
1) More data produces better models, and since we only use part of the whole training data to train the model (bootstrap... | Why does a bagged tree / random forest tree have higher bias than a single decision tree? | I will accept the answer on 1) from Kunlun, but just to close this case, I will here give the conclusions on the two questions that I reached in my thesis (which were both accepted by my Supervisor):
| Why does a bagged tree / random forest tree have higher bias than a single decision tree?
I will accept the answer on 1) from Kunlun, but just to close this case, I will here give the conclusions on the two questions that I reached in my thesis (which were both accepted by my Supervisor):
1) More data produces better m... | Why does a bagged tree / random forest tree have higher bias than a single decision tree?
I will accept the answer on 1) from Kunlun, but just to close this case, I will here give the conclusions on the two questions that I reached in my thesis (which were both accepted by my Supervisor):
|
14,803 | Why does a bagged tree / random forest tree have higher bias than a single decision tree? | According to the authors of "Elements of Statistical Learning" (see proof below):
As in bagging, the bias of a random forest is the same as the bias of
any of the individual sampled trees.
Taken from 2008. Elements of Statistical Learning 2nd Ed, Chapter 9.2.3. Hastie, Tibshirani, Friedman:
Your answer however seem... | Why does a bagged tree / random forest tree have higher bias than a single decision tree? | According to the authors of "Elements of Statistical Learning" (see proof below):
As in bagging, the bias of a random forest is the same as the bias of
any of the individual sampled trees.
Taken fro | Why does a bagged tree / random forest tree have higher bias than a single decision tree?
According to the authors of "Elements of Statistical Learning" (see proof below):
As in bagging, the bias of a random forest is the same as the bias of
any of the individual sampled trees.
Taken from 2008. Elements of Statistica... | Why does a bagged tree / random forest tree have higher bias than a single decision tree?
According to the authors of "Elements of Statistical Learning" (see proof below):
As in bagging, the bias of a random forest is the same as the bias of
any of the individual sampled trees.
Taken fro |
14,804 | Why does a bagged tree / random forest tree have higher bias than a single decision tree? | Your questions are pretty straightforward. 1) More data produces better model, since you only use part of the whole training data to train your model (bootstrap), higher bias is reasonable. 2) More splits means deeper trees, or purer nodes. This typically leads to high variance and low bias. If you limit the split, low... | Why does a bagged tree / random forest tree have higher bias than a single decision tree? | Your questions are pretty straightforward. 1) More data produces better model, since you only use part of the whole training data to train your model (bootstrap), higher bias is reasonable. 2) More sp | Why does a bagged tree / random forest tree have higher bias than a single decision tree?
Your questions are pretty straightforward. 1) More data produces better model, since you only use part of the whole training data to train your model (bootstrap), higher bias is reasonable. 2) More splits means deeper trees, or pu... | Why does a bagged tree / random forest tree have higher bias than a single decision tree?
Your questions are pretty straightforward. 1) More data produces better model, since you only use part of the whole training data to train your model (bootstrap), higher bias is reasonable. 2) More sp |
14,805 | Iconic (toy) models of neural networks | One of the most classical is the Perceptron in 2 dimensions, which goes back to the 1950s. This is a good example because it is a launching pad for more modern techniques:
1) Not everything is linearly separable (hence the need for nonlinear activations or kernel methods, multiple layers, etc.).
2) The Perceptron won't... | Iconic (toy) models of neural networks | One of the most classical is the Perceptron in 2 dimensions, which goes back to the 1950s. This is a good example because it is a launching pad for more modern techniques:
1) Not everything is linearl | Iconic (toy) models of neural networks
One of the most classical is the Perceptron in 2 dimensions, which goes back to the 1950s. This is a good example because it is a launching pad for more modern techniques:
1) Not everything is linearly separable (hence the need for nonlinear activations or kernel methods, multiple... | Iconic (toy) models of neural networks
One of the most classical is the Perceptron in 2 dimensions, which goes back to the 1950s. This is a good example because it is a launching pad for more modern techniques:
1) Not everything is linearl |
14,806 | Iconic (toy) models of neural networks | The XOR problem is probably the canonical ANN toy problem.
Richard Bland June 1998 University of Stirling, Department of Computing Science and Mathematics Computing Science Technical Report
"Learning XOR: exploring the space of a classic problem"
The TensorFlow Playground is an interactive interface to several toy neu... | Iconic (toy) models of neural networks | The XOR problem is probably the canonical ANN toy problem.
Richard Bland June 1998 University of Stirling, Department of Computing Science and Mathematics Computing Science Technical Report
"Learning | Iconic (toy) models of neural networks
The XOR problem is probably the canonical ANN toy problem.
Richard Bland June 1998 University of Stirling, Department of Computing Science and Mathematics Computing Science Technical Report
"Learning XOR: exploring the space of a classic problem"
The TensorFlow Playground is an i... | Iconic (toy) models of neural networks
The XOR problem is probably the canonical ANN toy problem.
Richard Bland June 1998 University of Stirling, Department of Computing Science and Mathematics Computing Science Technical Report
"Learning |
14,807 | What is the Method of Moments and how is it different from MLE? | What is the method of moments?
There is a nice article about this on Wikipedia.
https://en.m.wikipedia.org/wiki/Method_of_moments_(statistics)
It means that you are estimating the population parameters by selecting the parameters such that the population distribution has the moments that are equivalent to the observe... | What is the Method of Moments and how is it different from MLE? | What is the method of moments?
There is a nice article about this on Wikipedia.
https://en.m.wikipedia.org/wiki/Method_of_moments_(statistics)
It means that you are estimating the population paramet | What is the Method of Moments and how is it different from MLE?
What is the method of moments?
There is a nice article about this on Wikipedia.
https://en.m.wikipedia.org/wiki/Method_of_moments_(statistics)
It means that you are estimating the population parameters by selecting the parameters such that the population... | What is the Method of Moments and how is it different from MLE?
What is the method of moments?
There is a nice article about this on Wikipedia.
https://en.m.wikipedia.org/wiki/Method_of_moments_(statistics)
It means that you are estimating the population paramet |
14,808 | What is the Method of Moments and how is it different from MLE? | In MoM, the estimator is chosen so that some function has conditional expectation equal to zero. E.g. $E[g(y,x,\theta)] = 0$. Often the expectation is conditional on $x$. Typically, this is converted to a problem of minimizing a quadratic form in this expectations with a weight matrix.
In MLE, the estimator maximizes ... | What is the Method of Moments and how is it different from MLE? | In MoM, the estimator is chosen so that some function has conditional expectation equal to zero. E.g. $E[g(y,x,\theta)] = 0$. Often the expectation is conditional on $x$. Typically, this is converted | What is the Method of Moments and how is it different from MLE?
In MoM, the estimator is chosen so that some function has conditional expectation equal to zero. E.g. $E[g(y,x,\theta)] = 0$. Often the expectation is conditional on $x$. Typically, this is converted to a problem of minimizing a quadratic form in this expe... | What is the Method of Moments and how is it different from MLE?
In MoM, the estimator is chosen so that some function has conditional expectation equal to zero. E.g. $E[g(y,x,\theta)] = 0$. Often the expectation is conditional on $x$. Typically, this is converted |
14,809 | What is the Method of Moments and how is it different from MLE? | Soorry, I can't past comments..
MLE makes stricter assumptions (the full density) and is thus
typically less robust but more efficient if the assumptions are met
Actually at MITx "Fundamentals of Statistics" we are teached the opposite, that MoM relies on specific equation of the moments, and if we pick up the wron... | What is the Method of Moments and how is it different from MLE? | Soorry, I can't past comments..
MLE makes stricter assumptions (the full density) and is thus
typically less robust but more efficient if the assumptions are met
Actually at MITx "Fundamentals of | What is the Method of Moments and how is it different from MLE?
Soorry, I can't past comments..
MLE makes stricter assumptions (the full density) and is thus
typically less robust but more efficient if the assumptions are met
Actually at MITx "Fundamentals of Statistics" we are teached the opposite, that MoM relies... | What is the Method of Moments and how is it different from MLE?
Soorry, I can't past comments..
MLE makes stricter assumptions (the full density) and is thus
typically less robust but more efficient if the assumptions are met
Actually at MITx "Fundamentals of |
14,810 | Why are p-values often higher in a Cox proportional hazard model than in logistic regression? | The logistic regression model assumes the response is a Bernoulli trial (or more generally a binomial, but for simplicity, we'll keep it 0-1). A survival model assumes the response is typically a time to event (again, there are generalizations of this that we'll skip). Another way to put that is that units are passin... | Why are p-values often higher in a Cox proportional hazard model than in logistic regression? | The logistic regression model assumes the response is a Bernoulli trial (or more generally a binomial, but for simplicity, we'll keep it 0-1). A survival model assumes the response is typically a tim | Why are p-values often higher in a Cox proportional hazard model than in logistic regression?
The logistic regression model assumes the response is a Bernoulli trial (or more generally a binomial, but for simplicity, we'll keep it 0-1). A survival model assumes the response is typically a time to event (again, there a... | Why are p-values often higher in a Cox proportional hazard model than in logistic regression?
The logistic regression model assumes the response is a Bernoulli trial (or more generally a binomial, but for simplicity, we'll keep it 0-1). A survival model assumes the response is typically a tim |
14,811 | What is Thompson Sampling in layman's terms? | I am going to try to give an explanation without any mathematics. Part of this answer is repeated from some points I made in an answer to another question on MAB problems.
The strategic trade-off in multi-arm bandit problems: In multi-arm bandit problems the gambler plays one "bandit" each round and attempts to maxim... | What is Thompson Sampling in layman's terms? | I am going to try to give an explanation without any mathematics. Part of this answer is repeated from some points I made in an answer to another question on MAB problems.
The strategic trade-off in | What is Thompson Sampling in layman's terms?
I am going to try to give an explanation without any mathematics. Part of this answer is repeated from some points I made in an answer to another question on MAB problems.
The strategic trade-off in multi-arm bandit problems: In multi-arm bandit problems the gambler plays ... | What is Thompson Sampling in layman's terms?
I am going to try to give an explanation without any mathematics. Part of this answer is repeated from some points I made in an answer to another question on MAB problems.
The strategic trade-off in |
14,812 | What is Thompson Sampling in layman's terms? | I will give it a shot and I hope you like it! There are some formulas below which might scare you of. I don't hope so, because I will do my best to explain them in the most simple way I can.
These are the two formulas:
The likelihood: $P(r|\theta,a,x)$
And the posterior: $P(\theta|D)$
TL;DR
Thompson Sampling lets yo... | What is Thompson Sampling in layman's terms? | I will give it a shot and I hope you like it! There are some formulas below which might scare you of. I don't hope so, because I will do my best to explain them in the most simple way I can.
These ar | What is Thompson Sampling in layman's terms?
I will give it a shot and I hope you like it! There are some formulas below which might scare you of. I don't hope so, because I will do my best to explain them in the most simple way I can.
These are the two formulas:
The likelihood: $P(r|\theta,a,x)$
And the posterior: $... | What is Thompson Sampling in layman's terms?
I will give it a shot and I hope you like it! There are some formulas below which might scare you of. I don't hope so, because I will do my best to explain them in the most simple way I can.
These ar |
14,813 | What is the difference between feature selection and dimensionality reduction? | The difference is that the set of features made by feature selection must be a subset of the original set of features, and the set made by dimensionality reduction doesn't have to (for instance PCA reduces dimensionality by making new synthetic features from linear combination of the original ones, and then discarding ... | What is the difference between feature selection and dimensionality reduction? | The difference is that the set of features made by feature selection must be a subset of the original set of features, and the set made by dimensionality reduction doesn't have to (for instance PCA re | What is the difference between feature selection and dimensionality reduction?
The difference is that the set of features made by feature selection must be a subset of the original set of features, and the set made by dimensionality reduction doesn't have to (for instance PCA reduces dimensionality by making new synthe... | What is the difference between feature selection and dimensionality reduction?
The difference is that the set of features made by feature selection must be a subset of the original set of features, and the set made by dimensionality reduction doesn't have to (for instance PCA re |
14,814 | Do coefficients of logistic regression have a meaning? | The coefficients from the output do have a meaning, although it isn't very intuitive to most people and certainly not to me. That is why people change them to odds ratios. However, the log of the odds ratio is the coefficient; equivalently, the exponentiated coefficients are the odds ratios.
The coefficients are most ... | Do coefficients of logistic regression have a meaning? | The coefficients from the output do have a meaning, although it isn't very intuitive to most people and certainly not to me. That is why people change them to odds ratios. However, the log of the odds | Do coefficients of logistic regression have a meaning?
The coefficients from the output do have a meaning, although it isn't very intuitive to most people and certainly not to me. That is why people change them to odds ratios. However, the log of the odds ratio is the coefficient; equivalently, the exponentiated coeffi... | Do coefficients of logistic regression have a meaning?
The coefficients from the output do have a meaning, although it isn't very intuitive to most people and certainly not to me. That is why people change them to odds ratios. However, the log of the odds |
14,815 | Do coefficients of logistic regression have a meaning? | Interpreting directly the coefficients is difficult and can be misleading. You have no guarantees on how weights are assigned among the variables.
Quick example, similar to the situation you describe: I have worked on a model of the interaction of users to a website. That model included two variables that represent the... | Do coefficients of logistic regression have a meaning? | Interpreting directly the coefficients is difficult and can be misleading. You have no guarantees on how weights are assigned among the variables.
Quick example, similar to the situation you describe: | Do coefficients of logistic regression have a meaning?
Interpreting directly the coefficients is difficult and can be misleading. You have no guarantees on how weights are assigned among the variables.
Quick example, similar to the situation you describe: I have worked on a model of the interaction of users to a websit... | Do coefficients of logistic regression have a meaning?
Interpreting directly the coefficients is difficult and can be misleading. You have no guarantees on how weights are assigned among the variables.
Quick example, similar to the situation you describe: |
14,816 | Do coefficients of logistic regression have a meaning? | The coefficients most certainly have a meaning. In some software packages the model can be directed in either of two ways to produce either of two types of coefficients. For example, in Stata, one can use either the Logistic command or the logit command; in using one, the model gives traditional coefficients, while i... | Do coefficients of logistic regression have a meaning? | The coefficients most certainly have a meaning. In some software packages the model can be directed in either of two ways to produce either of two types of coefficients. For example, in Stata, one c | Do coefficients of logistic regression have a meaning?
The coefficients most certainly have a meaning. In some software packages the model can be directed in either of two ways to produce either of two types of coefficients. For example, in Stata, one can use either the Logistic command or the logit command; in using... | Do coefficients of logistic regression have a meaning?
The coefficients most certainly have a meaning. In some software packages the model can be directed in either of two ways to produce either of two types of coefficients. For example, in Stata, one c |
14,817 | Does log likelihood in GLM have guaranteed convergence to global maxima? | The definition of exponential family is:
$$
p(x|\theta) = h(x)\exp(\theta^T\phi(x) - A(\theta)),
$$
where $A(\theta)$ is the log partition function. Now one can prove that the following three things hold for 1D case (and they generalize to higher dimensions--you can look into properties of exponential families or log p... | Does log likelihood in GLM have guaranteed convergence to global maxima? | The definition of exponential family is:
$$
p(x|\theta) = h(x)\exp(\theta^T\phi(x) - A(\theta)),
$$
where $A(\theta)$ is the log partition function. Now one can prove that the following three things h | Does log likelihood in GLM have guaranteed convergence to global maxima?
The definition of exponential family is:
$$
p(x|\theta) = h(x)\exp(\theta^T\phi(x) - A(\theta)),
$$
where $A(\theta)$ is the log partition function. Now one can prove that the following three things hold for 1D case (and they generalize to higher ... | Does log likelihood in GLM have guaranteed convergence to global maxima?
The definition of exponential family is:
$$
p(x|\theta) = h(x)\exp(\theta^T\phi(x) - A(\theta)),
$$
where $A(\theta)$ is the log partition function. Now one can prove that the following three things h |
14,818 | Does log likelihood in GLM have guaranteed convergence to global maxima? | I was investigating this heavily during my thesis. The answer is that the GLM likelihood is not always convex, it is only convex under the right assumptions. A very good investigation of this was made by Nelder and Wedderburn in their paper "On the Existence and Uniqueness of the Maximum Likelihood Estimates for Certai... | Does log likelihood in GLM have guaranteed convergence to global maxima? | I was investigating this heavily during my thesis. The answer is that the GLM likelihood is not always convex, it is only convex under the right assumptions. A very good investigation of this was made | Does log likelihood in GLM have guaranteed convergence to global maxima?
I was investigating this heavily during my thesis. The answer is that the GLM likelihood is not always convex, it is only convex under the right assumptions. A very good investigation of this was made by Nelder and Wedderburn in their paper "On th... | Does log likelihood in GLM have guaranteed convergence to global maxima?
I was investigating this heavily during my thesis. The answer is that the GLM likelihood is not always convex, it is only convex under the right assumptions. A very good investigation of this was made |
14,819 | When someone says residual deviance/df should ~ 1 for a Poisson model, how approximate is approximate? | 10 is large... 1.01 is not. Since the variance of a $\chi^2_k$ is $2k$ (see Wikipedia), the standard deviation of a $\chi^2_k$ is $\sqrt{2k}$, and that of $\chi^2_k/k$ is $\sqrt{2/k}$. That's your measuring stick: for $\chi^2_{100}$, 1.01 is not large, but 2 is large (7 s.d.s away). For $\chi^2_{10,000}$, 1.01 is OK, b... | When someone says residual deviance/df should ~ 1 for a Poisson model, how approximate is approximat | 10 is large... 1.01 is not. Since the variance of a $\chi^2_k$ is $2k$ (see Wikipedia), the standard deviation of a $\chi^2_k$ is $\sqrt{2k}$, and that of $\chi^2_k/k$ is $\sqrt{2/k}$. That's your mea | When someone says residual deviance/df should ~ 1 for a Poisson model, how approximate is approximate?
10 is large... 1.01 is not. Since the variance of a $\chi^2_k$ is $2k$ (see Wikipedia), the standard deviation of a $\chi^2_k$ is $\sqrt{2k}$, and that of $\chi^2_k/k$ is $\sqrt{2/k}$. That's your measuring stick: for... | When someone says residual deviance/df should ~ 1 for a Poisson model, how approximate is approximat
10 is large... 1.01 is not. Since the variance of a $\chi^2_k$ is $2k$ (see Wikipedia), the standard deviation of a $\chi^2_k$ is $\sqrt{2k}$, and that of $\chi^2_k/k$ is $\sqrt{2/k}$. That's your mea |
14,820 | When someone says residual deviance/df should ~ 1 for a Poisson model, how approximate is approximate? | Asymptotically the deviance should be chi-square distributed with mean equal to the degrees of freedom. So divide it by its degrees of freedom & you should get about 1 if the data is not over-dispersed. To get a proper test just look up the deviance in chi-square tables - but note (a) that the chi square distribution ... | When someone says residual deviance/df should ~ 1 for a Poisson model, how approximate is approximat | Asymptotically the deviance should be chi-square distributed with mean equal to the degrees of freedom. So divide it by its degrees of freedom & you should get about 1 if the data is not over-dispers | When someone says residual deviance/df should ~ 1 for a Poisson model, how approximate is approximate?
Asymptotically the deviance should be chi-square distributed with mean equal to the degrees of freedom. So divide it by its degrees of freedom & you should get about 1 if the data is not over-dispersed. To get a prop... | When someone says residual deviance/df should ~ 1 for a Poisson model, how approximate is approximat
Asymptotically the deviance should be chi-square distributed with mean equal to the degrees of freedom. So divide it by its degrees of freedom & you should get about 1 if the data is not over-dispers |
14,821 | How to run two-way ANOVA on data with neither normality nor equality of variance in R? | This may be more of a comment than an answer, but it won't fit as a comment. We may be able to help you here, but this may take a few iterations; we need more information.
First, what is your response variable?
Second, note that the marginal distribution of your response does not have to be normal, rather the dist... | How to run two-way ANOVA on data with neither normality nor equality of variance in R? | This may be more of a comment than an answer, but it won't fit as a comment. We may be able to help you here, but this may take a few iterations; we need more information.
First, what is your respo | How to run two-way ANOVA on data with neither normality nor equality of variance in R?
This may be more of a comment than an answer, but it won't fit as a comment. We may be able to help you here, but this may take a few iterations; we need more information.
First, what is your response variable?
Second, note that... | How to run two-way ANOVA on data with neither normality nor equality of variance in R?
This may be more of a comment than an answer, but it won't fit as a comment. We may be able to help you here, but this may take a few iterations; we need more information.
First, what is your respo |
14,822 | How to run two-way ANOVA on data with neither normality nor equality of variance in R? | (note: this answer was posted before the question was migrated and merged from SO, so details have been added to the question that are not addressed here. Many are addressed in the comments and the answer by @gung).
There are many different approaches, and this question has been covered elsewhere on this site. Here is... | How to run two-way ANOVA on data with neither normality nor equality of variance in R? | (note: this answer was posted before the question was migrated and merged from SO, so details have been added to the question that are not addressed here. Many are addressed in the comments and the an | How to run two-way ANOVA on data with neither normality nor equality of variance in R?
(note: this answer was posted before the question was migrated and merged from SO, so details have been added to the question that are not addressed here. Many are addressed in the comments and the answer by @gung).
There are many d... | How to run two-way ANOVA on data with neither normality nor equality of variance in R?
(note: this answer was posted before the question was migrated and merged from SO, so details have been added to the question that are not addressed here. Many are addressed in the comments and the an |
14,823 | Why squaring $R$ gives explained variance? | Hand-wavingly, the correlation $R$ can be thought of as a measure of the angle between two vectors, the dependent vector $Y$ and the independent vector $X$.
If the angle between the vectors is $\theta$, the correlation $R$ is $\cos(\theta)$.
The part of $Y$ that is explained by $X$ is of length $\Vert Y\Vert\cos(\theta... | Why squaring $R$ gives explained variance? | Hand-wavingly, the correlation $R$ can be thought of as a measure of the angle between two vectors, the dependent vector $Y$ and the independent vector $X$.
If the angle between the vectors is $\theta | Why squaring $R$ gives explained variance?
Hand-wavingly, the correlation $R$ can be thought of as a measure of the angle between two vectors, the dependent vector $Y$ and the independent vector $X$.
If the angle between the vectors is $\theta$, the correlation $R$ is $\cos(\theta)$.
The part of $Y$ that is explained b... | Why squaring $R$ gives explained variance?
Hand-wavingly, the correlation $R$ can be thought of as a measure of the angle between two vectors, the dependent vector $Y$ and the independent vector $X$.
If the angle between the vectors is $\theta |
14,824 | Why squaring $R$ gives explained variance? | You can do this a long way and show that the total variance of the dependent variable is a sum of the variance of predicted and the error variance. The ratio of the variance or predicted to the variance of dependent variable is called $R^2$, and it's between 0 and 1 in OLS. It happens so that when you have only one ind... | Why squaring $R$ gives explained variance? | You can do this a long way and show that the total variance of the dependent variable is a sum of the variance of predicted and the error variance. The ratio of the variance or predicted to the varian | Why squaring $R$ gives explained variance?
You can do this a long way and show that the total variance of the dependent variable is a sum of the variance of predicted and the error variance. The ratio of the variance or predicted to the variance of dependent variable is called $R^2$, and it's between 0 and 1 in OLS. It... | Why squaring $R$ gives explained variance?
You can do this a long way and show that the total variance of the dependent variable is a sum of the variance of predicted and the error variance. The ratio of the variance or predicted to the varian |
14,825 | When to use bootstrap vs. bayesian technique? | To my thinking, your problem description points to two main issues. First:
I have a rather complicated decision analysis...
Assuming you've got a loss function in hand, you need to decide whether you care about frequentist risk or posterior expected loss. The bootstrap lets you approximate functionals of the data dis... | When to use bootstrap vs. bayesian technique? | To my thinking, your problem description points to two main issues. First:
I have a rather complicated decision analysis...
Assuming you've got a loss function in hand, you need to decide whether yo | When to use bootstrap vs. bayesian technique?
To my thinking, your problem description points to two main issues. First:
I have a rather complicated decision analysis...
Assuming you've got a loss function in hand, you need to decide whether you care about frequentist risk or posterior expected loss. The bootstrap le... | When to use bootstrap vs. bayesian technique?
To my thinking, your problem description points to two main issues. First:
I have a rather complicated decision analysis...
Assuming you've got a loss function in hand, you need to decide whether yo |
14,826 | When to use bootstrap vs. bayesian technique? | I've read that the non-parametric bootstrap can be seen as a special case of a Bayesian model with a discrete (very)non informative prior, where the assumptions being made in the model is that the data is discrete, and the domain of your target distribution is completely observed in your sample.
Here are two reference... | When to use bootstrap vs. bayesian technique? | I've read that the non-parametric bootstrap can be seen as a special case of a Bayesian model with a discrete (very)non informative prior, where the assumptions being made in the model is that the da | When to use bootstrap vs. bayesian technique?
I've read that the non-parametric bootstrap can be seen as a special case of a Bayesian model with a discrete (very)non informative prior, where the assumptions being made in the model is that the data is discrete, and the domain of your target distribution is completely o... | When to use bootstrap vs. bayesian technique?
I've read that the non-parametric bootstrap can be seen as a special case of a Bayesian model with a discrete (very)non informative prior, where the assumptions being made in the model is that the da |
14,827 | Measuring individual player effectiveness in 2-player per team sports | Below are a couple very simple models. They are both deficient in at least one way, but maybe they'll provide something to build on. The second model actually does not (quite) address the OP's scenario (see remarks below), but I am leaving it in case it helps in some way.
Model 1: A variant of the Bradley–Terry model
S... | Measuring individual player effectiveness in 2-player per team sports | Below are a couple very simple models. They are both deficient in at least one way, but maybe they'll provide something to build on. The second model actually does not (quite) address the OP's scenari | Measuring individual player effectiveness in 2-player per team sports
Below are a couple very simple models. They are both deficient in at least one way, but maybe they'll provide something to build on. The second model actually does not (quite) address the OP's scenario (see remarks below), but I am leaving it in case... | Measuring individual player effectiveness in 2-player per team sports
Below are a couple very simple models. They are both deficient in at least one way, but maybe they'll provide something to build on. The second model actually does not (quite) address the OP's scenari |
14,828 | Measuring individual player effectiveness in 2-player per team sports | Microsoft's TrueSkill algorithm, as used to rank players on XBox Live, can deal with team matches, but does not incorporate margin of victory. It may still be of some use to you. | Measuring individual player effectiveness in 2-player per team sports | Microsoft's TrueSkill algorithm, as used to rank players on XBox Live, can deal with team matches, but does not incorporate margin of victory. It may still be of some use to you. | Measuring individual player effectiveness in 2-player per team sports
Microsoft's TrueSkill algorithm, as used to rank players on XBox Live, can deal with team matches, but does not incorporate margin of victory. It may still be of some use to you. | Measuring individual player effectiveness in 2-player per team sports
Microsoft's TrueSkill algorithm, as used to rank players on XBox Live, can deal with team matches, but does not incorporate margin of victory. It may still be of some use to you. |
14,829 | Measuring individual player effectiveness in 2-player per team sports | Yes.
You could look at each players win/loss record, and point differential. I realize that's a simple answer, but, those stats would still be meaningful. | Measuring individual player effectiveness in 2-player per team sports | Yes.
You could look at each players win/loss record, and point differential. I realize that's a simple answer, but, those stats would still be meaningful. | Measuring individual player effectiveness in 2-player per team sports
Yes.
You could look at each players win/loss record, and point differential. I realize that's a simple answer, but, those stats would still be meaningful. | Measuring individual player effectiveness in 2-player per team sports
Yes.
You could look at each players win/loss record, and point differential. I realize that's a simple answer, but, those stats would still be meaningful. |
14,830 | Measuring individual player effectiveness in 2-player per team sports | (I'd like to add this as a comment for a previous answer, but my reputation was not enough, for the time being)
Martin O'Leary linked TrueSkill algorithm, and it's a good option.
If you're interested in use (more than in development), you should give a try to rankade, our ranking system. Like TrueSkill it can manage t... | Measuring individual player effectiveness in 2-player per team sports | (I'd like to add this as a comment for a previous answer, but my reputation was not enough, for the time being)
Martin O'Leary linked TrueSkill algorithm, and it's a good option.
If you're interested | Measuring individual player effectiveness in 2-player per team sports
(I'd like to add this as a comment for a previous answer, but my reputation was not enough, for the time being)
Martin O'Leary linked TrueSkill algorithm, and it's a good option.
If you're interested in use (more than in development), you should giv... | Measuring individual player effectiveness in 2-player per team sports
(I'd like to add this as a comment for a previous answer, but my reputation was not enough, for the time being)
Martin O'Leary linked TrueSkill algorithm, and it's a good option.
If you're interested |
14,831 | Topic prediction using latent Dirichlet allocation | I'd try 'folding in'. This refers to taking one new document, adding it to the corpus, and then running Gibbs sampling just on the words in that new document, keeping the topic assignments of the old documents the same. This usually converges fast (maybe 5-10-20 iterations), and you don't need to sample your old corpus... | Topic prediction using latent Dirichlet allocation | I'd try 'folding in'. This refers to taking one new document, adding it to the corpus, and then running Gibbs sampling just on the words in that new document, keeping the topic assignments of the old | Topic prediction using latent Dirichlet allocation
I'd try 'folding in'. This refers to taking one new document, adding it to the corpus, and then running Gibbs sampling just on the words in that new document, keeping the topic assignments of the old documents the same. This usually converges fast (maybe 5-10-20 iterat... | Topic prediction using latent Dirichlet allocation
I'd try 'folding in'. This refers to taking one new document, adding it to the corpus, and then running Gibbs sampling just on the words in that new document, keeping the topic assignments of the old |
14,832 | Robust t-test for mean | Why are you looking at non-parametric tests? Are the assumptions of the t-test violated? Namely, ordinal or non-normal data and inconstant variances? Of course, if your sample is large enough you can justify the parametric t-test with its greater power despite the lack of normality in the sample. Likewise if your c... | Robust t-test for mean | Why are you looking at non-parametric tests? Are the assumptions of the t-test violated? Namely, ordinal or non-normal data and inconstant variances? Of course, if your sample is large enough you c | Robust t-test for mean
Why are you looking at non-parametric tests? Are the assumptions of the t-test violated? Namely, ordinal or non-normal data and inconstant variances? Of course, if your sample is large enough you can justify the parametric t-test with its greater power despite the lack of normality in the sam... | Robust t-test for mean
Why are you looking at non-parametric tests? Are the assumptions of the t-test violated? Namely, ordinal or non-normal data and inconstant variances? Of course, if your sample is large enough you c |
14,833 | Robust t-test for mean | I agree that if you want to actually test whether the group means are different (as opposed to testing differences between group medians or trimmed means, etc.), then you don't want to use a nonparametric test that tests a different hypothesis.
In general p-values from a t-test tend to be fairly accurate given moderat... | Robust t-test for mean | I agree that if you want to actually test whether the group means are different (as opposed to testing differences between group medians or trimmed means, etc.), then you don't want to use a nonparame | Robust t-test for mean
I agree that if you want to actually test whether the group means are different (as opposed to testing differences between group medians or trimmed means, etc.), then you don't want to use a nonparametric test that tests a different hypothesis.
In general p-values from a t-test tend to be fairl... | Robust t-test for mean
I agree that if you want to actually test whether the group means are different (as opposed to testing differences between group medians or trimmed means, etc.), then you don't want to use a nonparame |
14,834 | Robust t-test for mean | Johnson (1978) gives a modification for the $t$-statistic and confidence intervals which is a good starting point for my problem. The correction is based on a Cornish-Fisher expansion, and uses sample skew.
The 'latest and greatest' is due to Ogaswara, with references therein to Hall and others. | Robust t-test for mean | Johnson (1978) gives a modification for the $t$-statistic and confidence intervals which is a good starting point for my problem. The correction is based on a Cornish-Fisher expansion, and uses sample | Robust t-test for mean
Johnson (1978) gives a modification for the $t$-statistic and confidence intervals which is a good starting point for my problem. The correction is based on a Cornish-Fisher expansion, and uses sample skew.
The 'latest and greatest' is due to Ogaswara, with references therein to Hall and others... | Robust t-test for mean
Johnson (1978) gives a modification for the $t$-statistic and confidence intervals which is a good starting point for my problem. The correction is based on a Cornish-Fisher expansion, and uses sample |
14,835 | Robust t-test for mean | Yes, there is, the Yuen test for paired and un-paired data, which is nothing but the t-test based on trimmed means. When there are unequal variances in both samples, the Yuen-Welch test is the replacement of the classic Welch t-test. It is implemented in various statistical software. | Robust t-test for mean | Yes, there is, the Yuen test for paired and un-paired data, which is nothing but the t-test based on trimmed means. When there are unequal variances in both samples, the Yuen-Welch test is the replace | Robust t-test for mean
Yes, there is, the Yuen test for paired and un-paired data, which is nothing but the t-test based on trimmed means. When there are unequal variances in both samples, the Yuen-Welch test is the replacement of the classic Welch t-test. It is implemented in various statistical software. | Robust t-test for mean
Yes, there is, the Yuen test for paired and un-paired data, which is nothing but the t-test based on trimmed means. When there are unequal variances in both samples, the Yuen-Welch test is the replace |
14,836 | Robust t-test for mean | I don't have enough reputation for a comment, thus as an answer: Have a look at this calcuation. I think this provides an excellent answer. In brief:
The asymptotic performance is much more sensitive to deviations from
normality in the form of skewness than in the form of kurtosis ...
Thus Student's t-test is sens... | Robust t-test for mean | I don't have enough reputation for a comment, thus as an answer: Have a look at this calcuation. I think this provides an excellent answer. In brief:
The asymptotic performance is much more sensitive | Robust t-test for mean
I don't have enough reputation for a comment, thus as an answer: Have a look at this calcuation. I think this provides an excellent answer. In brief:
The asymptotic performance is much more sensitive to deviations from
normality in the form of skewness than in the form of kurtosis ...
Thus ... | Robust t-test for mean
I don't have enough reputation for a comment, thus as an answer: Have a look at this calcuation. I think this provides an excellent answer. In brief:
The asymptotic performance is much more sensitive |
14,837 | Why are mean 0 and standard deviation 1 distributions always used? | At the beginning the most useful answer is probably that mean of 0 and sd of 1 are mathematically convenient. If you can work out the probabilities for a distribution with a mean of 0 and standard deviation of 1 you can work them out for any similar distribution of scores with a very simple equation.
I'm not following... | Why are mean 0 and standard deviation 1 distributions always used? | At the beginning the most useful answer is probably that mean of 0 and sd of 1 are mathematically convenient. If you can work out the probabilities for a distribution with a mean of 0 and standard de | Why are mean 0 and standard deviation 1 distributions always used?
At the beginning the most useful answer is probably that mean of 0 and sd of 1 are mathematically convenient. If you can work out the probabilities for a distribution with a mean of 0 and standard deviation of 1 you can work them out for any similar di... | Why are mean 0 and standard deviation 1 distributions always used?
At the beginning the most useful answer is probably that mean of 0 and sd of 1 are mathematically convenient. If you can work out the probabilities for a distribution with a mean of 0 and standard de |
14,838 | Why are mean 0 and standard deviation 1 distributions always used? | To start with what we're talking about here is the standard normal distribution, a normal distribution with a mean of 0 and a standard deviation of 1. The short-hand for a variable which is distributed as a standard normal distribution is Z.
Here are my answers to your questions.
(1) I think there are two key reasons ... | Why are mean 0 and standard deviation 1 distributions always used? | To start with what we're talking about here is the standard normal distribution, a normal distribution with a mean of 0 and a standard deviation of 1. The short-hand for a variable which is distribute | Why are mean 0 and standard deviation 1 distributions always used?
To start with what we're talking about here is the standard normal distribution, a normal distribution with a mean of 0 and a standard deviation of 1. The short-hand for a variable which is distributed as a standard normal distribution is Z.
Here are m... | Why are mean 0 and standard deviation 1 distributions always used?
To start with what we're talking about here is the standard normal distribution, a normal distribution with a mean of 0 and a standard deviation of 1. The short-hand for a variable which is distribute |
14,839 | Why are mean 0 and standard deviation 1 distributions always used? | Since you received excellent explanations from Graham and John, I'm just going to answer your last question:
When people talk about Z Scores what do they actually mean here?
Best way to answer this is to think about this question: The grades in class CS 101 is normally distributed with $\mu$ = 80 and $\sigma$ = 5. W... | Why are mean 0 and standard deviation 1 distributions always used? | Since you received excellent explanations from Graham and John, I'm just going to answer your last question:
When people talk about Z Scores what do they actually mean here?
Best way to answer this | Why are mean 0 and standard deviation 1 distributions always used?
Since you received excellent explanations from Graham and John, I'm just going to answer your last question:
When people talk about Z Scores what do they actually mean here?
Best way to answer this is to think about this question: The grades in class ... | Why are mean 0 and standard deviation 1 distributions always used?
Since you received excellent explanations from Graham and John, I'm just going to answer your last question:
When people talk about Z Scores what do they actually mean here?
Best way to answer this |
14,840 | Different ways of modelling interactions between continuous and categorical predictors in GAM | gam1 and gam2 are fine; they are different models, although they are trying to do the same thing, which is model group-specific smooths.
The gam1 form
y ~ f + s(x, by = f)
does this by estimating a separate smoother for each level of f (assuming that f is a standard factor), and indeed, a separate smoothness parameter... | Different ways of modelling interactions between continuous and categorical predictors in GAM | gam1 and gam2 are fine; they are different models, although they are trying to do the same thing, which is model group-specific smooths.
The gam1 form
y ~ f + s(x, by = f)
does this by estimating a s | Different ways of modelling interactions between continuous and categorical predictors in GAM
gam1 and gam2 are fine; they are different models, although they are trying to do the same thing, which is model group-specific smooths.
The gam1 form
y ~ f + s(x, by = f)
does this by estimating a separate smoother for each ... | Different ways of modelling interactions between continuous and categorical predictors in GAM
gam1 and gam2 are fine; they are different models, although they are trying to do the same thing, which is model group-specific smooths.
The gam1 form
y ~ f + s(x, by = f)
does this by estimating a s |
14,841 | Different ways of modelling interactions between continuous and categorical predictors in GAM | This is what Jacolien van Rij writes in her tutorial page:
How to set up the interaction depends on the type of grouping
predictor:
with factor include intercept difference: Group + s(Time, by=Group)
with ordered factor include intercept difference and
reference smooth: Group + s(Time) + s(Time, by=Group)
with bina... | Different ways of modelling interactions between continuous and categorical predictors in GAM | This is what Jacolien van Rij writes in her tutorial page:
How to set up the interaction depends on the type of grouping
predictor:
with factor include intercept difference: Group + s(Time, by=Gro | Different ways of modelling interactions between continuous and categorical predictors in GAM
This is what Jacolien van Rij writes in her tutorial page:
How to set up the interaction depends on the type of grouping
predictor:
with factor include intercept difference: Group + s(Time, by=Group)
with ordered factor in... | Different ways of modelling interactions between continuous and categorical predictors in GAM
This is what Jacolien van Rij writes in her tutorial page:
How to set up the interaction depends on the type of grouping
predictor:
with factor include intercept difference: Group + s(Time, by=Gro |
14,842 | Why in Variational Auto Encoder (Gaussian variational family) we model $\log\sigma^2$ and not $\sigma^2$ (or $\sigma$) itself? | it brings stability and ease of training.
by definition sigma has to be a positive real number. one way to enforce this would be to use a ReLU funtion to obtain its value, but the gradient is not well defined around zero. in addition, the standard deviation values are usually very small 1>>sigma>0. the optimization ha... | Why in Variational Auto Encoder (Gaussian variational family) we model $\log\sigma^2$ and not $\sigm | it brings stability and ease of training.
by definition sigma has to be a positive real number. one way to enforce this would be to use a ReLU funtion to obtain its value, but the gradient is not wel | Why in Variational Auto Encoder (Gaussian variational family) we model $\log\sigma^2$ and not $\sigma^2$ (or $\sigma$) itself?
it brings stability and ease of training.
by definition sigma has to be a positive real number. one way to enforce this would be to use a ReLU funtion to obtain its value, but the gradient is ... | Why in Variational Auto Encoder (Gaussian variational family) we model $\log\sigma^2$ and not $\sigm
it brings stability and ease of training.
by definition sigma has to be a positive real number. one way to enforce this would be to use a ReLU funtion to obtain its value, but the gradient is not wel |
14,843 | Interpreting ROUGE scores | As a user of these methods I need to gauge how far I can rely on the algorithms and how far I need to use humans to do some post-processing on the summarisations.
How "good" is a particular absolute ROUGE score? I'm defining "good" as "minimises the need for human post-processing".
There are two aspects that may impac... | Interpreting ROUGE scores | As a user of these methods I need to gauge how far I can rely on the algorithms and how far I need to use humans to do some post-processing on the summarisations.
How "good" is a particular absolute R | Interpreting ROUGE scores
As a user of these methods I need to gauge how far I can rely on the algorithms and how far I need to use humans to do some post-processing on the summarisations.
How "good" is a particular absolute ROUGE score? I'm defining "good" as "minimises the need for human post-processing".
There are ... | Interpreting ROUGE scores
As a user of these methods I need to gauge how far I can rely on the algorithms and how far I need to use humans to do some post-processing on the summarisations.
How "good" is a particular absolute R |
14,844 | Interpreting ROUGE scores | You should read the original ROUGE paper by Chin-Yew Lin which goes in depth about the various definitions.
ROUGE is a score of overlapping words. ROUGE-N refers to overlapping n-grams. Specifically:
$$
\frac{\sum_{r}\sum_s\text{match}(\text{gram}_{s,c})}{\sum_{r}\sum_s\text{count}(\text{gram}_s)}
$$
I tried to simplif... | Interpreting ROUGE scores | You should read the original ROUGE paper by Chin-Yew Lin which goes in depth about the various definitions.
ROUGE is a score of overlapping words. ROUGE-N refers to overlapping n-grams. Specifically:
| Interpreting ROUGE scores
You should read the original ROUGE paper by Chin-Yew Lin which goes in depth about the various definitions.
ROUGE is a score of overlapping words. ROUGE-N refers to overlapping n-grams. Specifically:
$$
\frac{\sum_{r}\sum_s\text{match}(\text{gram}_{s,c})}{\sum_{r}\sum_s\text{count}(\text{gram}... | Interpreting ROUGE scores
You should read the original ROUGE paper by Chin-Yew Lin which goes in depth about the various definitions.
ROUGE is a score of overlapping words. ROUGE-N refers to overlapping n-grams. Specifically:
|
14,845 | How to interpret differential entropy? | There is no interpretation of differential entropy which would be as meaningful or useful as that of entropy. The problem with continuous random variables is that their values typically have 0 probability, and therefore would require an infinite number of bits to encode.
If you look at the limit of discrete entropy by... | How to interpret differential entropy? | There is no interpretation of differential entropy which would be as meaningful or useful as that of entropy. The problem with continuous random variables is that their values typically have 0 probabi | How to interpret differential entropy?
There is no interpretation of differential entropy which would be as meaningful or useful as that of entropy. The problem with continuous random variables is that their values typically have 0 probability, and therefore would require an infinite number of bits to encode.
If you l... | How to interpret differential entropy?
There is no interpretation of differential entropy which would be as meaningful or useful as that of entropy. The problem with continuous random variables is that their values typically have 0 probabi |
14,846 | How to interpret differential entropy? | For the differential entropy there also exists another, more mathematical interpretation, which is closely related to the bit-interpretation for the entropy.
The differential entropy describes the equivalent side length (in logs) of the set that contains most of the probability of the distribution.
This is nicely illus... | How to interpret differential entropy? | For the differential entropy there also exists another, more mathematical interpretation, which is closely related to the bit-interpretation for the entropy.
The differential entropy describes the equ | How to interpret differential entropy?
For the differential entropy there also exists another, more mathematical interpretation, which is closely related to the bit-interpretation for the entropy.
The differential entropy describes the equivalent side length (in logs) of the set that contains most of the probability of... | How to interpret differential entropy?
For the differential entropy there also exists another, more mathematical interpretation, which is closely related to the bit-interpretation for the entropy.
The differential entropy describes the equ |
14,847 | "Ties should not be present" in one-sample Kolmgorov-Smirnov test in R | You have two problems here:
The K-S test is for a continuous distribution and so MYDATA should not contain any ties (repeated values).
The theory underlying the K-S test does not let you estimate the parameters of the distribution from the data as you have done. The help for ks.test explains this. | "Ties should not be present" in one-sample Kolmgorov-Smirnov test in R | You have two problems here:
The K-S test is for a continuous distribution and so MYDATA should not contain any ties (repeated values).
The theory underlying the K-S test does not let you estimate the | "Ties should not be present" in one-sample Kolmgorov-Smirnov test in R
You have two problems here:
The K-S test is for a continuous distribution and so MYDATA should not contain any ties (repeated values).
The theory underlying the K-S test does not let you estimate the parameters of the distribution from the data as y... | "Ties should not be present" in one-sample Kolmgorov-Smirnov test in R
You have two problems here:
The K-S test is for a continuous distribution and so MYDATA should not contain any ties (repeated values).
The theory underlying the K-S test does not let you estimate the |
14,848 | "Ties should not be present" in one-sample Kolmgorov-Smirnov test in R | As explained by @mdewey, The K-S test is not suitable when estimating the parameters from the data.
You can use the following code, which relies on the Anderson-Darling test for normality, and does not require you to supply the mean and the stddev. This test is stronger in accuracy than the Lilliefors test.
install.pac... | "Ties should not be present" in one-sample Kolmgorov-Smirnov test in R | As explained by @mdewey, The K-S test is not suitable when estimating the parameters from the data.
You can use the following code, which relies on the Anderson-Darling test for normality, and does no | "Ties should not be present" in one-sample Kolmgorov-Smirnov test in R
As explained by @mdewey, The K-S test is not suitable when estimating the parameters from the data.
You can use the following code, which relies on the Anderson-Darling test for normality, and does not require you to supply the mean and the stddev. ... | "Ties should not be present" in one-sample Kolmgorov-Smirnov test in R
As explained by @mdewey, The K-S test is not suitable when estimating the parameters from the data.
You can use the following code, which relies on the Anderson-Darling test for normality, and does no |
14,849 | Kullback-Leibler Divergence for two samples | The Kullback-Leibler divergence is defined as
$$
\DeclareMathOperator{\KL}{KL}
\KL(P || Q) = \int_{-\infty}^\infty p(x) \log \frac{p(x)}{q(x)} \; dx
$$
so to calculate (estimate) this from empirical data we would need, maybe, some estimates of the density functions $p(x), q(x)$. So a natural starting point could... | Kullback-Leibler Divergence for two samples | The Kullback-Leibler divergence is defined as
$$
\DeclareMathOperator{\KL}{KL}
\KL(P || Q) = \int_{-\infty}^\infty p(x) \log \frac{p(x)}{q(x)} \; dx
$$
so to calculate (estimate) this from empir | Kullback-Leibler Divergence for two samples
The Kullback-Leibler divergence is defined as
$$
\DeclareMathOperator{\KL}{KL}
\KL(P || Q) = \int_{-\infty}^\infty p(x) \log \frac{p(x)}{q(x)} \; dx
$$
so to calculate (estimate) this from empirical data we would need, maybe, some estimates of the density functions $p(x... | Kullback-Leibler Divergence for two samples
The Kullback-Leibler divergence is defined as
$$
\DeclareMathOperator{\KL}{KL}
\KL(P || Q) = \int_{-\infty}^\infty p(x) \log \frac{p(x)}{q(x)} \; dx
$$
so to calculate (estimate) this from empir |
14,850 | Kullback-Leibler Divergence for two samples | Expanding a little bit on kjetil-b-halvorsen's answer, and sorry for not commenting, I don't have the reputation:
I have the feeling that the analytical computation should be (without multiplication by 100):
LR <- function(x) dnorm(x,log=TRUE)-dt(x,5,log=TRUE)
integrate(function(x) dnorm(x)*LR(x),lower=-Inf,upper=... | Kullback-Leibler Divergence for two samples | Expanding a little bit on kjetil-b-halvorsen's answer, and sorry for not commenting, I don't have the reputation:
I have the feeling that the analytical computation should be (without multiplication | Kullback-Leibler Divergence for two samples
Expanding a little bit on kjetil-b-halvorsen's answer, and sorry for not commenting, I don't have the reputation:
I have the feeling that the analytical computation should be (without multiplication by 100):
LR <- function(x) dnorm(x,log=TRUE)-dt(x,5,log=TRUE)
integrate(... | Kullback-Leibler Divergence for two samples
Expanding a little bit on kjetil-b-halvorsen's answer, and sorry for not commenting, I don't have the reputation:
I have the feeling that the analytical computation should be (without multiplication |
14,851 | What is the difference between GINI and AUC curve interpretation? | The Gini Coefficient is the summary statistic of the Cumulative Accuracy Profile (CAP) chart. It is calculated as the quotient of the area which the CAP curve and diagonal enclose and the corresponding area in an ideal rating procedure.
Area Under Receiver Operating Characteristic curve (or AUROC for short) is the summ... | What is the difference between GINI and AUC curve interpretation? | The Gini Coefficient is the summary statistic of the Cumulative Accuracy Profile (CAP) chart. It is calculated as the quotient of the area which the CAP curve and diagonal enclose and the correspondin | What is the difference between GINI and AUC curve interpretation?
The Gini Coefficient is the summary statistic of the Cumulative Accuracy Profile (CAP) chart. It is calculated as the quotient of the area which the CAP curve and diagonal enclose and the corresponding area in an ideal rating procedure.
Area Under Receiv... | What is the difference between GINI and AUC curve interpretation?
The Gini Coefficient is the summary statistic of the Cumulative Accuracy Profile (CAP) chart. It is calculated as the quotient of the area which the CAP curve and diagonal enclose and the correspondin |
14,852 | Is using correlation matrix to select predictors for regression correct? | If, for some reason, you are going to include only one variable in your model, then selecting the predictor which has the highest correlation with $y$ has several advantages. Out of the possible regression models with only one predictor, then this model is the one with the highest standardized regression coefficient an... | Is using correlation matrix to select predictors for regression correct? | If, for some reason, you are going to include only one variable in your model, then selecting the predictor which has the highest correlation with $y$ has several advantages. Out of the possible regre | Is using correlation matrix to select predictors for regression correct?
If, for some reason, you are going to include only one variable in your model, then selecting the predictor which has the highest correlation with $y$ has several advantages. Out of the possible regression models with only one predictor, then this... | Is using correlation matrix to select predictors for regression correct?
If, for some reason, you are going to include only one variable in your model, then selecting the predictor which has the highest correlation with $y$ has several advantages. Out of the possible regre |
14,853 | Is using correlation matrix to select predictors for regression correct? | You could run a step-wise regression analysis and let the software choose the variables based on F values. You could also look at Adjusted R^2 value when you run the regression each time, to see if adding any new variable contributing to your model. Your model may have the problem of multicollinearity if you just go by... | Is using correlation matrix to select predictors for regression correct? | You could run a step-wise regression analysis and let the software choose the variables based on F values. You could also look at Adjusted R^2 value when you run the regression each time, to see if ad | Is using correlation matrix to select predictors for regression correct?
You could run a step-wise regression analysis and let the software choose the variables based on F values. You could also look at Adjusted R^2 value when you run the regression each time, to see if adding any new variable contributing to your mode... | Is using correlation matrix to select predictors for regression correct?
You could run a step-wise regression analysis and let the software choose the variables based on F values. You could also look at Adjusted R^2 value when you run the regression each time, to see if ad |
14,854 | Is using correlation matrix to select predictors for regression correct? | Theres nothing wrong with this method, particularly if you know about multicollinearity. Avoiding multicollinearity is very easy.
Simply steer clear of adding independent variables that correlate with one another, since using only one of said variables is necessary. If x1 and x2 both correlate with y and correlate with... | Is using correlation matrix to select predictors for regression correct? | Theres nothing wrong with this method, particularly if you know about multicollinearity. Avoiding multicollinearity is very easy.
Simply steer clear of adding independent variables that correlate with | Is using correlation matrix to select predictors for regression correct?
Theres nothing wrong with this method, particularly if you know about multicollinearity. Avoiding multicollinearity is very easy.
Simply steer clear of adding independent variables that correlate with one another, since using only one of said vari... | Is using correlation matrix to select predictors for regression correct?
Theres nothing wrong with this method, particularly if you know about multicollinearity. Avoiding multicollinearity is very easy.
Simply steer clear of adding independent variables that correlate with |
14,855 | A routine to choose eps and minPts for DBSCAN | There are plenty of publications that propose methods to choose these parameters.
The most notable is OPTICS, a DBSCAN variation that does away with the epsilon parameter; it produces a hierarchical result that can roughly be seen as "running DBSCAN with every possible epsilon".
For minPts, I do suggest to not rely on ... | A routine to choose eps and minPts for DBSCAN | There are plenty of publications that propose methods to choose these parameters.
The most notable is OPTICS, a DBSCAN variation that does away with the epsilon parameter; it produces a hierarchical r | A routine to choose eps and minPts for DBSCAN
There are plenty of publications that propose methods to choose these parameters.
The most notable is OPTICS, a DBSCAN variation that does away with the epsilon parameter; it produces a hierarchical result that can roughly be seen as "running DBSCAN with every possible epsi... | A routine to choose eps and minPts for DBSCAN
There are plenty of publications that propose methods to choose these parameters.
The most notable is OPTICS, a DBSCAN variation that does away with the epsilon parameter; it produces a hierarchical r |
14,856 | A routine to choose eps and minPts for DBSCAN | minPts is selected based on the domain knowledge. If you do not have domain understanding, a rule of thumb is to derive minPts from the number of dimensions D in the data set. minPts >= D + 1. For 2D data, take minPts = 4. For larger datasets, with much noise, it suggested to go with minPts = 2 * D.
Once you have the a... | A routine to choose eps and minPts for DBSCAN | minPts is selected based on the domain knowledge. If you do not have domain understanding, a rule of thumb is to derive minPts from the number of dimensions D in the data set. minPts >= D + 1. For 2D | A routine to choose eps and minPts for DBSCAN
minPts is selected based on the domain knowledge. If you do not have domain understanding, a rule of thumb is to derive minPts from the number of dimensions D in the data set. minPts >= D + 1. For 2D data, take minPts = 4. For larger datasets, with much noise, it suggested ... | A routine to choose eps and minPts for DBSCAN
minPts is selected based on the domain knowledge. If you do not have domain understanding, a rule of thumb is to derive minPts from the number of dimensions D in the data set. minPts >= D + 1. For 2D |
14,857 | A routine to choose eps and minPts for DBSCAN | Maybe a bit late, but I would like to add an answer here for future knowledge.
One way to find the best $\epsilon$ for DBSCAN is to compute the knn, then sort the distances and see where the "knee" is located.
Example in python, because is the language I manage.:
from sklearn.neighbors import NearestNeighbors
import pl... | A routine to choose eps and minPts for DBSCAN | Maybe a bit late, but I would like to add an answer here for future knowledge.
One way to find the best $\epsilon$ for DBSCAN is to compute the knn, then sort the distances and see where the "knee" is | A routine to choose eps and minPts for DBSCAN
Maybe a bit late, but I would like to add an answer here for future knowledge.
One way to find the best $\epsilon$ for DBSCAN is to compute the knn, then sort the distances and see where the "knee" is located.
Example in python, because is the language I manage.:
from sklea... | A routine to choose eps and minPts for DBSCAN
Maybe a bit late, but I would like to add an answer here for future knowledge.
One way to find the best $\epsilon$ for DBSCAN is to compute the knn, then sort the distances and see where the "knee" is |
14,858 | Why do odds ratios from formula and R's fisher.test differ? Which one should one choose? | From the help page for fisher.test():
Note that the conditional Maximum Likelihood Estimate (MLE) rather
than the unconditional MLE (the sample odds ratio) is used. | Why do odds ratios from formula and R's fisher.test differ? Which one should one choose? | From the help page for fisher.test():
Note that the conditional Maximum Likelihood Estimate (MLE) rather
than the unconditional MLE (the sample odds ratio) is used. | Why do odds ratios from formula and R's fisher.test differ? Which one should one choose?
From the help page for fisher.test():
Note that the conditional Maximum Likelihood Estimate (MLE) rather
than the unconditional MLE (the sample odds ratio) is used. | Why do odds ratios from formula and R's fisher.test differ? Which one should one choose?
From the help page for fisher.test():
Note that the conditional Maximum Likelihood Estimate (MLE) rather
than the unconditional MLE (the sample odds ratio) is used. |
14,859 | Why do odds ratios from formula and R's fisher.test differ? Which one should one choose? | To add to the discussion here, it is useful to ask what exactly is conditioned on in this "conditional" likelihood. The Fisher test differs from other categorical analyses in that it considers all margins of the table to be fixed whereas the logistic regression model (and corresponding Pearson chi-square test which is ... | Why do odds ratios from formula and R's fisher.test differ? Which one should one choose? | To add to the discussion here, it is useful to ask what exactly is conditioned on in this "conditional" likelihood. The Fisher test differs from other categorical analyses in that it considers all mar | Why do odds ratios from formula and R's fisher.test differ? Which one should one choose?
To add to the discussion here, it is useful to ask what exactly is conditioned on in this "conditional" likelihood. The Fisher test differs from other categorical analyses in that it considers all margins of the table to be fixed w... | Why do odds ratios from formula and R's fisher.test differ? Which one should one choose?
To add to the discussion here, it is useful to ask what exactly is conditioned on in this "conditional" likelihood. The Fisher test differs from other categorical analyses in that it considers all mar |
14,860 | Why do odds ratios from formula and R's fisher.test differ? Which one should one choose? | To answer your second question, biostats isn't my forte but I believe the reason for multiple odds ratio statistics is to account for sampling design and design of experiments.
I've found three references here that will give you a bit of understanding as to why there is a difference between conditional MLE vs uncondit... | Why do odds ratios from formula and R's fisher.test differ? Which one should one choose? | To answer your second question, biostats isn't my forte but I believe the reason for multiple odds ratio statistics is to account for sampling design and design of experiments.
I've found three refer | Why do odds ratios from formula and R's fisher.test differ? Which one should one choose?
To answer your second question, biostats isn't my forte but I believe the reason for multiple odds ratio statistics is to account for sampling design and design of experiments.
I've found three references here that will give you a... | Why do odds ratios from formula and R's fisher.test differ? Which one should one choose?
To answer your second question, biostats isn't my forte but I believe the reason for multiple odds ratio statistics is to account for sampling design and design of experiments.
I've found three refer |
14,861 | Why do odds ratios from formula and R's fisher.test differ? Which one should one choose? | I am stuck with the same problem. I searched and searched in stackExchange and Google, and I did not find anything explicitly explaining how the odds ratio in fisher.test() is calculated. This is not a complete answer, but it provides something useful to the discussion.
One thing is clear, fisher.test() calculates a co... | Why do odds ratios from formula and R's fisher.test differ? Which one should one choose? | I am stuck with the same problem. I searched and searched in stackExchange and Google, and I did not find anything explicitly explaining how the odds ratio in fisher.test() is calculated. This is not | Why do odds ratios from formula and R's fisher.test differ? Which one should one choose?
I am stuck with the same problem. I searched and searched in stackExchange and Google, and I did not find anything explicitly explaining how the odds ratio in fisher.test() is calculated. This is not a complete answer, but it provi... | Why do odds ratios from formula and R's fisher.test differ? Which one should one choose?
I am stuck with the same problem. I searched and searched in stackExchange and Google, and I did not find anything explicitly explaining how the odds ratio in fisher.test() is calculated. This is not |
14,862 | Programmer looking to break into machine learning field | Everytime I have talked to someone about learning more machine learning they always point me to the Elements of Statistical Learning by Hastie and Tibshirani. This book has the good fortune of being available online for free (a hard copy does have a certain appeal, but is not required) and it is a really great introduc... | Programmer looking to break into machine learning field | Everytime I have talked to someone about learning more machine learning they always point me to the Elements of Statistical Learning by Hastie and Tibshirani. This book has the good fortune of being a | Programmer looking to break into machine learning field
Everytime I have talked to someone about learning more machine learning they always point me to the Elements of Statistical Learning by Hastie and Tibshirani. This book has the good fortune of being available online for free (a hard copy does have a certain appeal... | Programmer looking to break into machine learning field
Everytime I have talked to someone about learning more machine learning they always point me to the Elements of Statistical Learning by Hastie and Tibshirani. This book has the good fortune of being a |
14,863 | Programmer looking to break into machine learning field | In addition to all the other great advices I suggest to get your hands dirty by participating in online competitions, see Sites for predictive modeling competitions
Regarding books etc. you should take a look at:
Machine learning self-learning book?
Can you recommend a book to read before Elements of Statistical Learn... | Programmer looking to break into machine learning field | In addition to all the other great advices I suggest to get your hands dirty by participating in online competitions, see Sites for predictive modeling competitions
Regarding books etc. you should tak | Programmer looking to break into machine learning field
In addition to all the other great advices I suggest to get your hands dirty by participating in online competitions, see Sites for predictive modeling competitions
Regarding books etc. you should take a look at:
Machine learning self-learning book?
Can you recom... | Programmer looking to break into machine learning field
In addition to all the other great advices I suggest to get your hands dirty by participating in online competitions, see Sites for predictive modeling competitions
Regarding books etc. you should tak |
14,864 | Programmer looking to break into machine learning field | Read Tom Mitchell's Machine Learning. That is a good book that should get you started in the field of Machine Learning.
One thing to be aware of: please note that the same algorithm may sometimes perform better or worse according to the scenario and parameters supplied and random chance. Do not get drawn into optimis... | Programmer looking to break into machine learning field | Read Tom Mitchell's Machine Learning. That is a good book that should get you started in the field of Machine Learning.
One thing to be aware of: please note that the same algorithm may sometimes per | Programmer looking to break into machine learning field
Read Tom Mitchell's Machine Learning. That is a good book that should get you started in the field of Machine Learning.
One thing to be aware of: please note that the same algorithm may sometimes perform better or worse according to the scenario and parameters su... | Programmer looking to break into machine learning field
Read Tom Mitchell's Machine Learning. That is a good book that should get you started in the field of Machine Learning.
One thing to be aware of: please note that the same algorithm may sometimes per |
14,865 | Programmer looking to break into machine learning field | There are a large number of good books about machine learning, including several in the O'Reilly series that make use of Python. Working through one, or several of these might might be a good starting point.
I'd also suggest getting some knowledge of statistics - through a course or two, or self study, doesn't really m... | Programmer looking to break into machine learning field | There are a large number of good books about machine learning, including several in the O'Reilly series that make use of Python. Working through one, or several of these might might be a good starting | Programmer looking to break into machine learning field
There are a large number of good books about machine learning, including several in the O'Reilly series that make use of Python. Working through one, or several of these might might be a good starting point.
I'd also suggest getting some knowledge of statistics - ... | Programmer looking to break into machine learning field
There are a large number of good books about machine learning, including several in the O'Reilly series that make use of Python. Working through one, or several of these might might be a good starting |
14,866 | Programmer looking to break into machine learning field | Very nice question. A thing to realize upfront is that machine learning is both an art and science and involves meticulously cleaning out data, visualizing it and eventually build models that suite the business in question, while simultaneously keeping it scalable & tractable.
Skills wise, more important than anything ... | Programmer looking to break into machine learning field | Very nice question. A thing to realize upfront is that machine learning is both an art and science and involves meticulously cleaning out data, visualizing it and eventually build models that suite th | Programmer looking to break into machine learning field
Very nice question. A thing to realize upfront is that machine learning is both an art and science and involves meticulously cleaning out data, visualizing it and eventually build models that suite the business in question, while simultaneously keeping it scalable... | Programmer looking to break into machine learning field
Very nice question. A thing to realize upfront is that machine learning is both an art and science and involves meticulously cleaning out data, visualizing it and eventually build models that suite th |
14,867 | Programmer looking to break into machine learning field | I know its a bit of an old question but given the fact that I saw a lot of programmers still don’t know how to get started.
Thus, I created "A complete daily plan for studying to become a machine learning engineer" repository.
This is my multi-month study plan for going from mobile developer (self-taught, no CS degree)... | Programmer looking to break into machine learning field | I know its a bit of an old question but given the fact that I saw a lot of programmers still don’t know how to get started.
Thus, I created "A complete daily plan for studying to become a machine lear | Programmer looking to break into machine learning field
I know its a bit of an old question but given the fact that I saw a lot of programmers still don’t know how to get started.
Thus, I created "A complete daily plan for studying to become a machine learning engineer" repository.
This is my multi-month study plan for... | Programmer looking to break into machine learning field
I know its a bit of an old question but given the fact that I saw a lot of programmers still don’t know how to get started.
Thus, I created "A complete daily plan for studying to become a machine lear |
14,868 | Can I do a PCA on repeated measures for data reduction? | You could look into Multiple Factor Analysis. This can be implemented in R with FactoMineR.
UPDATE:
To elaborate, Leann was proposing – however long ago – to conduct a PCA on a dataset with repeated measures. If I understand the structure of her dataset correctly, for a given 'context' she had an animal x 'specific mea... | Can I do a PCA on repeated measures for data reduction? | You could look into Multiple Factor Analysis. This can be implemented in R with FactoMineR.
UPDATE:
To elaborate, Leann was proposing – however long ago – to conduct a PCA on a dataset with repeated m | Can I do a PCA on repeated measures for data reduction?
You could look into Multiple Factor Analysis. This can be implemented in R with FactoMineR.
UPDATE:
To elaborate, Leann was proposing – however long ago – to conduct a PCA on a dataset with repeated measures. If I understand the structure of her dataset correctly,... | Can I do a PCA on repeated measures for data reduction?
You could look into Multiple Factor Analysis. This can be implemented in R with FactoMineR.
UPDATE:
To elaborate, Leann was proposing – however long ago – to conduct a PCA on a dataset with repeated m |
14,869 | Can I do a PCA on repeated measures for data reduction? | It is commonplace to use PCA when analyzing repeated measures (e.g., it is used for analyzing sales data, stock prices and exchange rates) The logic is as you articulate (i.e., the justification is that PCA is a data reduction tool not an inferential tool).
One publication by a pretty good statistician is:
Bradlow, E.... | Can I do a PCA on repeated measures for data reduction? | It is commonplace to use PCA when analyzing repeated measures (e.g., it is used for analyzing sales data, stock prices and exchange rates) The logic is as you articulate (i.e., the justification is t | Can I do a PCA on repeated measures for data reduction?
It is commonplace to use PCA when analyzing repeated measures (e.g., it is used for analyzing sales data, stock prices and exchange rates) The logic is as you articulate (i.e., the justification is that PCA is a data reduction tool not an inferential tool).
One p... | Can I do a PCA on repeated measures for data reduction?
It is commonplace to use PCA when analyzing repeated measures (e.g., it is used for analyzing sales data, stock prices and exchange rates) The logic is as you articulate (i.e., the justification is t |
14,870 | Why is a projection matrix of an orthogonal projection symmetric? | This is a fundamental results from linear algebra on orthogonal projections. A relatively simple approach is as follows. If $u_1, \ldots, u_m$ are orthonormal vectors spanning an $m$-dimensional subspace $A$, and $\mathbf{U}$ is the $n \times p$ matrix with the $u_i$'s as the columns, then
$$\mathbf{P} = \mathbf{U}\ma... | Why is a projection matrix of an orthogonal projection symmetric? | This is a fundamental results from linear algebra on orthogonal projections. A relatively simple approach is as follows. If $u_1, \ldots, u_m$ are orthonormal vectors spanning an $m$-dimensional subsp | Why is a projection matrix of an orthogonal projection symmetric?
This is a fundamental results from linear algebra on orthogonal projections. A relatively simple approach is as follows. If $u_1, \ldots, u_m$ are orthonormal vectors spanning an $m$-dimensional subspace $A$, and $\mathbf{U}$ is the $n \times p$ matrix w... | Why is a projection matrix of an orthogonal projection symmetric?
This is a fundamental results from linear algebra on orthogonal projections. A relatively simple approach is as follows. If $u_1, \ldots, u_m$ are orthonormal vectors spanning an $m$-dimensional subsp |
14,871 | Why is a projection matrix of an orthogonal projection symmetric? | An attempt at geometrical intuition...
Recall that:
A symmetric matrix is self adjoint.
A scalar product is determined only by the components in the mutual linear space (and independent of the orthogonal components of any of the vectors).
What you want to "see" is that a projection is self adjoint thus symmetric-- ... | Why is a projection matrix of an orthogonal projection symmetric? | An attempt at geometrical intuition...
Recall that:
A symmetric matrix is self adjoint.
A scalar product is determined only by the components in the mutual linear space (and independent of the ortho | Why is a projection matrix of an orthogonal projection symmetric?
An attempt at geometrical intuition...
Recall that:
A symmetric matrix is self adjoint.
A scalar product is determined only by the components in the mutual linear space (and independent of the orthogonal components of any of the vectors).
What you wa... | Why is a projection matrix of an orthogonal projection symmetric?
An attempt at geometrical intuition...
Recall that:
A symmetric matrix is self adjoint.
A scalar product is determined only by the components in the mutual linear space (and independent of the ortho |
14,872 | Is it ok to use Manhattan distance with Ward's inter-cluster linkage in hierarchical clustering? | The Ward clustering algorithm is a hierarchical clustering method that minimizes an 'inertia' criteria at each step. This inertia quantifies the sum of squared residuals between the reduced signal and the initial signal: it is a measure of the variance of the error in an l2 (Euclidean) sens. Actually, you even mention ... | Is it ok to use Manhattan distance with Ward's inter-cluster linkage in hierarchical clustering? | The Ward clustering algorithm is a hierarchical clustering method that minimizes an 'inertia' criteria at each step. This inertia quantifies the sum of squared residuals between the reduced signal and | Is it ok to use Manhattan distance with Ward's inter-cluster linkage in hierarchical clustering?
The Ward clustering algorithm is a hierarchical clustering method that minimizes an 'inertia' criteria at each step. This inertia quantifies the sum of squared residuals between the reduced signal and the initial signal: it... | Is it ok to use Manhattan distance with Ward's inter-cluster linkage in hierarchical clustering?
The Ward clustering algorithm is a hierarchical clustering method that minimizes an 'inertia' criteria at each step. This inertia quantifies the sum of squared residuals between the reduced signal and |
14,873 | Is it ok to use Manhattan distance with Ward's inter-cluster linkage in hierarchical clustering? | I can't think of any reason why Ward should favor any metric. Ward's method is just another option to decide which clusters to fusion next during agglomeration. This is achieved by finding the two clusters whose fusion will minimize a certain error (examplary source for the formula).
Hence it relies on two concepts:
... | Is it ok to use Manhattan distance with Ward's inter-cluster linkage in hierarchical clustering? | I can't think of any reason why Ward should favor any metric. Ward's method is just another option to decide which clusters to fusion next during agglomeration. This is achieved by finding the two clu | Is it ok to use Manhattan distance with Ward's inter-cluster linkage in hierarchical clustering?
I can't think of any reason why Ward should favor any metric. Ward's method is just another option to decide which clusters to fusion next during agglomeration. This is achieved by finding the two clusters whose fusion will... | Is it ok to use Manhattan distance with Ward's inter-cluster linkage in hierarchical clustering?
I can't think of any reason why Ward should favor any metric. Ward's method is just another option to decide which clusters to fusion next during agglomeration. This is achieved by finding the two clu |
14,874 | Is it ok to use Manhattan distance with Ward's inter-cluster linkage in hierarchical clustering? | Another way of thinking about this, which might lend itself to an adaptation for $\ell_1$ is that choice of the mean comes from the fact that the mean is the point that minimizes the sum of squared Euclidean distances. If you're using $\ell_1$ to measure the distance between time series, then you should be using a cent... | Is it ok to use Manhattan distance with Ward's inter-cluster linkage in hierarchical clustering? | Another way of thinking about this, which might lend itself to an adaptation for $\ell_1$ is that choice of the mean comes from the fact that the mean is the point that minimizes the sum of squared Eu | Is it ok to use Manhattan distance with Ward's inter-cluster linkage in hierarchical clustering?
Another way of thinking about this, which might lend itself to an adaptation for $\ell_1$ is that choice of the mean comes from the fact that the mean is the point that minimizes the sum of squared Euclidean distances. If y... | Is it ok to use Manhattan distance with Ward's inter-cluster linkage in hierarchical clustering?
Another way of thinking about this, which might lend itself to an adaptation for $\ell_1$ is that choice of the mean comes from the fact that the mean is the point that minimizes the sum of squared Eu |
14,875 | Is it ok to use Manhattan distance with Ward's inter-cluster linkage in hierarchical clustering? | Although Ward is meant to be used with Euclidean distances, this paper suggests that the clustering results using Ward and non-euclidean distances are essentially the same as if they had been used with Euclidean distances as it is meant to be.
It is shown that the result from the Ward method to a non positive-definite... | Is it ok to use Manhattan distance with Ward's inter-cluster linkage in hierarchical clustering? | Although Ward is meant to be used with Euclidean distances, this paper suggests that the clustering results using Ward and non-euclidean distances are essentially the same as if they had been used wit | Is it ok to use Manhattan distance with Ward's inter-cluster linkage in hierarchical clustering?
Although Ward is meant to be used with Euclidean distances, this paper suggests that the clustering results using Ward and non-euclidean distances are essentially the same as if they had been used with Euclidean distances a... | Is it ok to use Manhattan distance with Ward's inter-cluster linkage in hierarchical clustering?
Although Ward is meant to be used with Euclidean distances, this paper suggests that the clustering results using Ward and non-euclidean distances are essentially the same as if they had been used wit |
14,876 | Why is the squared difference so commonly used? | A decision-theoretic approach to statistics provides a deep explanation. It says that squaring differences is a proxy for a wide range of loss functions which (whenever they might be justifiably adopted) lead to considerable simplification in the possible statistical procedures one has to consider.
Unfortunately, expl... | Why is the squared difference so commonly used? | A decision-theoretic approach to statistics provides a deep explanation. It says that squaring differences is a proxy for a wide range of loss functions which (whenever they might be justifiably adop | Why is the squared difference so commonly used?
A decision-theoretic approach to statistics provides a deep explanation. It says that squaring differences is a proxy for a wide range of loss functions which (whenever they might be justifiably adopted) lead to considerable simplification in the possible statistical pro... | Why is the squared difference so commonly used?
A decision-theoretic approach to statistics provides a deep explanation. It says that squaring differences is a proxy for a wide range of loss functions which (whenever they might be justifiably adop |
14,877 | Meaning of latent features? | Latent means not directly observable. The common use of the term in PCA and Factor Analysis is to reduce dimension of a large number of directly observable features into a smaller set of indirectly observable features. | Meaning of latent features? | Latent means not directly observable. The common use of the term in PCA and Factor Analysis is to reduce dimension of a large number of directly observable features into a smaller set of indirectly ob | Meaning of latent features?
Latent means not directly observable. The common use of the term in PCA and Factor Analysis is to reduce dimension of a large number of directly observable features into a smaller set of indirectly observable features. | Meaning of latent features?
Latent means not directly observable. The common use of the term in PCA and Factor Analysis is to reduce dimension of a large number of directly observable features into a smaller set of indirectly ob |
14,878 | Meaning of latent features? | In the context of Factorization Method latent features are usually meant to characterize items along each dimension. Let me explain by example.
Suppose we have a matrix of item-users interactions $R$. The model assumption in Matrix Factorization methods is that each cell $R_{ui}$ of this matrix is generated by, for exa... | Meaning of latent features? | In the context of Factorization Method latent features are usually meant to characterize items along each dimension. Let me explain by example.
Suppose we have a matrix of item-users interactions $R$. | Meaning of latent features?
In the context of Factorization Method latent features are usually meant to characterize items along each dimension. Let me explain by example.
Suppose we have a matrix of item-users interactions $R$. The model assumption in Matrix Factorization methods is that each cell $R_{ui}$ of this mat... | Meaning of latent features?
In the context of Factorization Method latent features are usually meant to characterize items along each dimension. Let me explain by example.
Suppose we have a matrix of item-users interactions $R$. |
14,879 | Meaning of latent features? | Here your data is ratings given by various users to various movies. As others have pointed out, latent means not directly observable.
For a movie, its latent features determine the amount of action, romance, story-line, a famous actor, etc. Similarly, for another dataset consisting of handwritten digits, the latent v... | Meaning of latent features? | Here your data is ratings given by various users to various movies. As others have pointed out, latent means not directly observable.
For a movie, its latent features determine the amount of action, | Meaning of latent features?
Here your data is ratings given by various users to various movies. As others have pointed out, latent means not directly observable.
For a movie, its latent features determine the amount of action, romance, story-line, a famous actor, etc. Similarly, for another dataset consisting of hand... | Meaning of latent features?
Here your data is ratings given by various users to various movies. As others have pointed out, latent means not directly observable.
For a movie, its latent features determine the amount of action, |
14,880 | Meaning of latent features? | I would say that factors are more representative than principal components to get a perception of 'latency'/hiddenness of a variable. Latency is one of the reasons why behavioral scientists measure perceptual constructs like feeling, sadness in terms of multiple items/measures and derive a number for such hidden variab... | Meaning of latent features? | I would say that factors are more representative than principal components to get a perception of 'latency'/hiddenness of a variable. Latency is one of the reasons why behavioral scientists measure pe | Meaning of latent features?
I would say that factors are more representative than principal components to get a perception of 'latency'/hiddenness of a variable. Latency is one of the reasons why behavioral scientists measure perceptual constructs like feeling, sadness in terms of multiple items/measures and derive a n... | Meaning of latent features?
I would say that factors are more representative than principal components to get a perception of 'latency'/hiddenness of a variable. Latency is one of the reasons why behavioral scientists measure pe |
14,881 | Under which conditions do gradient boosting machines outperform random forests? | The following provides an explanation as per why Boosting generally outperforms Random Forest in practice, but I would be very interested to know which other different factors may explain Boosting's edge over RF in specific settings.
Basically, within the $error=bias+variance$ framework, RF can only reduce error throug... | Under which conditions do gradient boosting machines outperform random forests? | The following provides an explanation as per why Boosting generally outperforms Random Forest in practice, but I would be very interested to know which other different factors may explain Boosting's e | Under which conditions do gradient boosting machines outperform random forests?
The following provides an explanation as per why Boosting generally outperforms Random Forest in practice, but I would be very interested to know which other different factors may explain Boosting's edge over RF in specific settings.
Basica... | Under which conditions do gradient boosting machines outperform random forests?
The following provides an explanation as per why Boosting generally outperforms Random Forest in practice, but I would be very interested to know which other different factors may explain Boosting's e |
14,882 | Under which conditions do gradient boosting machines outperform random forests? | As bayerj said it, there is no way to know a priori !
Random Forests are relatively easy to calibrate: default parameters of most implementations (R or Python, per example) achieve great results.
On the other hand, GBMs are hard to tune (a too large number of tree leads to overfit, maximum depth is critical, the lear... | Under which conditions do gradient boosting machines outperform random forests? | As bayerj said it, there is no way to know a priori !
Random Forests are relatively easy to calibrate: default parameters of most implementations (R or Python, per example) achieve great results.
On | Under which conditions do gradient boosting machines outperform random forests?
As bayerj said it, there is no way to know a priori !
Random Forests are relatively easy to calibrate: default parameters of most implementations (R or Python, per example) achieve great results.
On the other hand, GBMs are hard to tune (... | Under which conditions do gradient boosting machines outperform random forests?
As bayerj said it, there is no way to know a priori !
Random Forests are relatively easy to calibrate: default parameters of most implementations (R or Python, per example) achieve great results.
On |
14,883 | What is ridge regression? [duplicate] | Ridge Regression is a remedial measure taken to alleviate multicollinearity amongst regression predictor variables in a model. Often predictor variables used in a regression are highly correlated. When they are, the regression coefficient of any one variable depend on which other predictor variables are included in t... | What is ridge regression? [duplicate] | Ridge Regression is a remedial measure taken to alleviate multicollinearity amongst regression predictor variables in a model. Often predictor variables used in a regression are highly correlated. W | What is ridge regression? [duplicate]
Ridge Regression is a remedial measure taken to alleviate multicollinearity amongst regression predictor variables in a model. Often predictor variables used in a regression are highly correlated. When they are, the regression coefficient of any one variable depend on which other... | What is ridge regression? [duplicate]
Ridge Regression is a remedial measure taken to alleviate multicollinearity amongst regression predictor variables in a model. Often predictor variables used in a regression are highly correlated. W |
14,884 | What is ridge regression? [duplicate] | The posts above nicely describe ridge regression and its mathematical underpinning. However, they don't address the issue of where ridge regression should be used, compared to other shrinkage methods. It might be so because there are no specific situation where one shrinkage method has been shown to perform better than... | What is ridge regression? [duplicate] | The posts above nicely describe ridge regression and its mathematical underpinning. However, they don't address the issue of where ridge regression should be used, compared to other shrinkage methods. | What is ridge regression? [duplicate]
The posts above nicely describe ridge regression and its mathematical underpinning. However, they don't address the issue of where ridge regression should be used, compared to other shrinkage methods. It might be so because there are no specific situation where one shrinkage method... | What is ridge regression? [duplicate]
The posts above nicely describe ridge regression and its mathematical underpinning. However, they don't address the issue of where ridge regression should be used, compared to other shrinkage methods. |
14,885 | How does extreme random forest differ from random forest? | This is pretty simple -- RF optimizes splits on trees (i.e. select those which give best information gain with respect to decision) and ERF makes them at random. Now,
optimisation costs (not much, but still), so ERF is usually faster.
optimisation may contribute to correlation of trees in ensemble or overall overfitti... | How does extreme random forest differ from random forest? | This is pretty simple -- RF optimizes splits on trees (i.e. select those which give best information gain with respect to decision) and ERF makes them at random. Now,
optimisation costs (not much, bu | How does extreme random forest differ from random forest?
This is pretty simple -- RF optimizes splits on trees (i.e. select those which give best information gain with respect to decision) and ERF makes them at random. Now,
optimisation costs (not much, but still), so ERF is usually faster.
optimisation may contribut... | How does extreme random forest differ from random forest?
This is pretty simple -- RF optimizes splits on trees (i.e. select those which give best information gain with respect to decision) and ERF makes them at random. Now,
optimisation costs (not much, bu |
14,886 | What summary statistics to use with categorical or qualitative variables? | In general, the answer is no. However, one could argue that you can take the median of ordinal data, but you will, of course, have a category as the median, not a number. The median divides the data equally: Half above, half below. Ordinal data depends only on order.
Further, in some cases, the ordinality can be made i... | What summary statistics to use with categorical or qualitative variables? | In general, the answer is no. However, one could argue that you can take the median of ordinal data, but you will, of course, have a category as the median, not a number. The median divides the data e | What summary statistics to use with categorical or qualitative variables?
In general, the answer is no. However, one could argue that you can take the median of ordinal data, but you will, of course, have a category as the median, not a number. The median divides the data equally: Half above, half below. Ordinal data d... | What summary statistics to use with categorical or qualitative variables?
In general, the answer is no. However, one could argue that you can take the median of ordinal data, but you will, of course, have a category as the median, not a number. The median divides the data e |
14,887 | What summary statistics to use with categorical or qualitative variables? | As has been mentioned, means, SDs and hinge points are not meaningful for categorical data. Hinge points (e.g., median and quartiles) may be meaningful for ordinal data. Your title also asks what summary statistics should be used to describe categorical data. It is standard to characterize categorical data by counts... | What summary statistics to use with categorical or qualitative variables? | As has been mentioned, means, SDs and hinge points are not meaningful for categorical data. Hinge points (e.g., median and quartiles) may be meaningful for ordinal data. Your title also asks what su | What summary statistics to use with categorical or qualitative variables?
As has been mentioned, means, SDs and hinge points are not meaningful for categorical data. Hinge points (e.g., median and quartiles) may be meaningful for ordinal data. Your title also asks what summary statistics should be used to describe ca... | What summary statistics to use with categorical or qualitative variables?
As has been mentioned, means, SDs and hinge points are not meaningful for categorical data. Hinge points (e.g., median and quartiles) may be meaningful for ordinal data. Your title also asks what su |
14,888 | What summary statistics to use with categorical or qualitative variables? | If you have nominal variables there is no ordering or distance function. So how could you define any of the summary statistics that you mention? I don't think you can. Quartiles and range at least require ordering and means and variance require numerical data. I think bar graphs and pie chart are typical examples of t... | What summary statistics to use with categorical or qualitative variables? | If you have nominal variables there is no ordering or distance function. So how could you define any of the summary statistics that you mention? I don't think you can. Quartiles and range at least re | What summary statistics to use with categorical or qualitative variables?
If you have nominal variables there is no ordering or distance function. So how could you define any of the summary statistics that you mention? I don't think you can. Quartiles and range at least require ordering and means and variance require ... | What summary statistics to use with categorical or qualitative variables?
If you have nominal variables there is no ordering or distance function. So how could you define any of the summary statistics that you mention? I don't think you can. Quartiles and range at least re |
14,889 | What summary statistics to use with categorical or qualitative variables? | Mode still works! Is that not an important summary statistic? (What's the most common category?) I think the median suggestion has little to no value as a statistic, but the mode does.
Also count distinct would be valuable. (How many categories do you have?)
You might create ratios, like (most common category) / (l... | What summary statistics to use with categorical or qualitative variables? | Mode still works! Is that not an important summary statistic? (What's the most common category?) I think the median suggestion has little to no value as a statistic, but the mode does.
Also count d | What summary statistics to use with categorical or qualitative variables?
Mode still works! Is that not an important summary statistic? (What's the most common category?) I think the median suggestion has little to no value as a statistic, but the mode does.
Also count distinct would be valuable. (How many categori... | What summary statistics to use with categorical or qualitative variables?
Mode still works! Is that not an important summary statistic? (What's the most common category?) I think the median suggestion has little to no value as a statistic, but the mode does.
Also count d |
14,890 | What summary statistics to use with categorical or qualitative variables? | I do appreciate the other answers, but it seems to me that some topological background would give a much-needed structure to the responses.
Definitions
Let's start with establishing the definitions of the domains:
categorical variable is one whose domain contains elements, but there's no known relationship between the... | What summary statistics to use with categorical or qualitative variables? | I do appreciate the other answers, but it seems to me that some topological background would give a much-needed structure to the responses.
Definitions
Let's start with establishing the definitions of | What summary statistics to use with categorical or qualitative variables?
I do appreciate the other answers, but it seems to me that some topological background would give a much-needed structure to the responses.
Definitions
Let's start with establishing the definitions of the domains:
categorical variable is one who... | What summary statistics to use with categorical or qualitative variables?
I do appreciate the other answers, but it seems to me that some topological background would give a much-needed structure to the responses.
Definitions
Let's start with establishing the definitions of |
14,891 | Distribution that describes the difference between negative binomial distributed variables? | I don't know the name of this distribution but you can just derive it from the law of total probability. Suppose $X, Y$ each have negative binomial distributions with parameters $(r_{1}, p_{1})$ and $(r_{2}, p_{2})$, respectively. I'm using the parameterization where $X,Y$ represent the number of successes before the $... | Distribution that describes the difference between negative binomial distributed variables? | I don't know the name of this distribution but you can just derive it from the law of total probability. Suppose $X, Y$ each have negative binomial distributions with parameters $(r_{1}, p_{1})$ and $ | Distribution that describes the difference between negative binomial distributed variables?
I don't know the name of this distribution but you can just derive it from the law of total probability. Suppose $X, Y$ each have negative binomial distributions with parameters $(r_{1}, p_{1})$ and $(r_{2}, p_{2})$, respectivel... | Distribution that describes the difference between negative binomial distributed variables?
I don't know the name of this distribution but you can just derive it from the law of total probability. Suppose $X, Y$ each have negative binomial distributions with parameters $(r_{1}, p_{1})$ and $ |
14,892 | Distribution that describes the difference between negative binomial distributed variables? | 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.
Yes. skewed generalized discrete Laplace distribution... | Distribution that describes the difference between negative binomial distributed variables? | 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.
| Distribution that describes the difference between negative binomial distributed variables?
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.
... | Distribution that describes the difference between negative binomial distributed variables?
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.
|
14,893 | Why do the ANOVA assumptions (equality of variance, normality of residuals) matter? | The assumptions matter insofar as they affect the properties of the hypothesis tests (and intervals) you might use whose distributional properties under the null are calculated relying on those assumptions.
In particular, for hypothesis tests, the things we might care about are how far the true significance level might... | Why do the ANOVA assumptions (equality of variance, normality of residuals) matter? | The assumptions matter insofar as they affect the properties of the hypothesis tests (and intervals) you might use whose distributional properties under the null are calculated relying on those assump | Why do the ANOVA assumptions (equality of variance, normality of residuals) matter?
The assumptions matter insofar as they affect the properties of the hypothesis tests (and intervals) you might use whose distributional properties under the null are calculated relying on those assumptions.
In particular, for hypothesis... | Why do the ANOVA assumptions (equality of variance, normality of residuals) matter?
The assumptions matter insofar as they affect the properties of the hypothesis tests (and intervals) you might use whose distributional properties under the null are calculated relying on those assump |
14,894 | Why do the ANOVA assumptions (equality of variance, normality of residuals) matter? | In a nutshell, ANOVA is adding, squaring and averaging residuals. Residuals tell you how well your model fits the data. For this example, I used the PlantGrowth dataset in R:
Results from an experiment to compare yields (as measured by dried weight of plants) obtained under a control and two different treatment condit... | Why do the ANOVA assumptions (equality of variance, normality of residuals) matter? | In a nutshell, ANOVA is adding, squaring and averaging residuals. Residuals tell you how well your model fits the data. For this example, I used the PlantGrowth dataset in R:
Results from an experime | Why do the ANOVA assumptions (equality of variance, normality of residuals) matter?
In a nutshell, ANOVA is adding, squaring and averaging residuals. Residuals tell you how well your model fits the data. For this example, I used the PlantGrowth dataset in R:
Results from an experiment to compare yields (as measured by... | Why do the ANOVA assumptions (equality of variance, normality of residuals) matter?
In a nutshell, ANOVA is adding, squaring and averaging residuals. Residuals tell you how well your model fits the data. For this example, I used the PlantGrowth dataset in R:
Results from an experime |
14,895 | Why do the ANOVA assumptions (equality of variance, normality of residuals) matter? | ANOVA it's just a method, it calculates the F-test from your samples and it compares it to the F-distribution.
You need some assumptions to decide what you want to compare and to calculate the p-values.
If you don't meet that assumptions you could calculate other things but it won't be an ANOVA.
The most useful distrib... | Why do the ANOVA assumptions (equality of variance, normality of residuals) matter? | ANOVA it's just a method, it calculates the F-test from your samples and it compares it to the F-distribution.
You need some assumptions to decide what you want to compare and to calculate the p-value | Why do the ANOVA assumptions (equality of variance, normality of residuals) matter?
ANOVA it's just a method, it calculates the F-test from your samples and it compares it to the F-distribution.
You need some assumptions to decide what you want to compare and to calculate the p-values.
If you don't meet that assumption... | Why do the ANOVA assumptions (equality of variance, normality of residuals) matter?
ANOVA it's just a method, it calculates the F-test from your samples and it compares it to the F-distribution.
You need some assumptions to decide what you want to compare and to calculate the p-value |
14,896 | What loss function should one use to get a high precision or high recall binary classifier? | Artificially constructing a balanced training set is debatable, quite controversial actually. If you do it, you should empirically verify that it really works better than leaving the training set unbalanced. Artificially balancing the test-set is almost never a good idea. The test-set should represent new data points a... | What loss function should one use to get a high precision or high recall binary classifier? | Artificially constructing a balanced training set is debatable, quite controversial actually. If you do it, you should empirically verify that it really works better than leaving the training set unba | What loss function should one use to get a high precision or high recall binary classifier?
Artificially constructing a balanced training set is debatable, quite controversial actually. If you do it, you should empirically verify that it really works better than leaving the training set unbalanced. Artificially balanci... | What loss function should one use to get a high precision or high recall binary classifier?
Artificially constructing a balanced training set is debatable, quite controversial actually. If you do it, you should empirically verify that it really works better than leaving the training set unba |
14,897 | What loss function should one use to get a high precision or high recall binary classifier? | You are making several assumptions. It is best to think of the ultimate goal in general terms, then formulate a strategy that meets that goal. For example do you really need forced-choice classification and is the signal:noise ratio large enough to support that (good examples: sound and image recognition)? Or is the... | What loss function should one use to get a high precision or high recall binary classifier? | You are making several assumptions. It is best to think of the ultimate goal in general terms, then formulate a strategy that meets that goal. For example do you really need forced-choice classifica | What loss function should one use to get a high precision or high recall binary classifier?
You are making several assumptions. It is best to think of the ultimate goal in general terms, then formulate a strategy that meets that goal. For example do you really need forced-choice classification and is the signal:noise... | What loss function should one use to get a high precision or high recall binary classifier?
You are making several assumptions. It is best to think of the ultimate goal in general terms, then formulate a strategy that meets that goal. For example do you really need forced-choice classifica |
14,898 | What loss function should one use to get a high precision or high recall binary classifier? | Not too long after you asked this question, there was an interesting research paper entitled Scalable Learning of Non-Decomposable Objectives that I stumbled across from a StackOverflow question that finds ways to build several interesting loss functions:
Precision at fixed recall
Recall at fixed precision
AUCROC maxi... | What loss function should one use to get a high precision or high recall binary classifier? | Not too long after you asked this question, there was an interesting research paper entitled Scalable Learning of Non-Decomposable Objectives that I stumbled across from a StackOverflow question that | What loss function should one use to get a high precision or high recall binary classifier?
Not too long after you asked this question, there was an interesting research paper entitled Scalable Learning of Non-Decomposable Objectives that I stumbled across from a StackOverflow question that finds ways to build several ... | What loss function should one use to get a high precision or high recall binary classifier?
Not too long after you asked this question, there was an interesting research paper entitled Scalable Learning of Non-Decomposable Objectives that I stumbled across from a StackOverflow question that |
14,899 | What loss function should one use to get a high precision or high recall binary classifier? | Regarding your question about whether reweighting training samples is equivalent to multiplying the loss in one of the two cases by a constant: yes, it is. One way to write the logistic regression loss function is
$$\sum_{j=1}^J\log\left\{1+\exp\left[-f\left(x_j\right)\right]\right\}+\sum_{k=1}^K\log\left\{1+\exp\left... | What loss function should one use to get a high precision or high recall binary classifier? | Regarding your question about whether reweighting training samples is equivalent to multiplying the loss in one of the two cases by a constant: yes, it is. One way to write the logistic regression los | What loss function should one use to get a high precision or high recall binary classifier?
Regarding your question about whether reweighting training samples is equivalent to multiplying the loss in one of the two cases by a constant: yes, it is. One way to write the logistic regression loss function is
$$\sum_{j=1}^... | What loss function should one use to get a high precision or high recall binary classifier?
Regarding your question about whether reweighting training samples is equivalent to multiplying the loss in one of the two cases by a constant: yes, it is. One way to write the logistic regression los |
14,900 | What is meant by proximity in random forests? | The term "proximity" means the "closeness" or "nearness" between pairs of cases.
Proximities are calculated for each pair of cases/observations/sample points. If two cases occupy the same terminal node through one tree, their proximity is increased by one. At the end of the run of all trees, the proximities are norma... | What is meant by proximity in random forests? | The term "proximity" means the "closeness" or "nearness" between pairs of cases.
Proximities are calculated for each pair of cases/observations/sample points. If two cases occupy the same terminal n | What is meant by proximity in random forests?
The term "proximity" means the "closeness" or "nearness" between pairs of cases.
Proximities are calculated for each pair of cases/observations/sample points. If two cases occupy the same terminal node through one tree, their proximity is increased by one. At the end of t... | What is meant by proximity in random forests?
The term "proximity" means the "closeness" or "nearness" between pairs of cases.
Proximities are calculated for each pair of cases/observations/sample points. If two cases occupy the same terminal n |
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