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 |
|---|---|---|---|---|---|---|
14,901 | What is meant by proximity in random forests? | Note that the authors of Elements of Statistical Learning state that "Proximity plots for random forests often look very similar, irrespective of
the data, which casts doubt on their utility. They tend to have a star shape,
one arm per class, which is more pronounced the better the classification
performance." (p 595)
... | What is meant by proximity in random forests? | Note that the authors of Elements of Statistical Learning state that "Proximity plots for random forests often look very similar, irrespective of
the data, which casts doubt on their utility. They ten | What is meant by proximity in random forests?
Note that the authors of Elements of Statistical Learning state that "Proximity plots for random forests often look very similar, irrespective of
the data, which casts doubt on their utility. They tend to have a star shape,
one arm per class, which is more pronounced the be... | What is meant by proximity in random forests?
Note that the authors of Elements of Statistical Learning state that "Proximity plots for random forests often look very similar, irrespective of
the data, which casts doubt on their utility. They ten |
14,902 | How to do exploratory data analysis to choose appropriate machine learning algorithm | This is a broad question without a simple answer. At CMU I taught a 3-month course on this topic. It covered issues such as:
Using projections to understand correlation between variables and overall distributional structure.
How to build up a regression model by successively modelling residuals.
Determining when to ... | How to do exploratory data analysis to choose appropriate machine learning algorithm | This is a broad question without a simple answer. At CMU I taught a 3-month course on this topic. It covered issues such as:
Using projections to understand correlation between variables and overal | How to do exploratory data analysis to choose appropriate machine learning algorithm
This is a broad question without a simple answer. At CMU I taught a 3-month course on this topic. It covered issues such as:
Using projections to understand correlation between variables and overall distributional structure.
How to ... | How to do exploratory data analysis to choose appropriate machine learning algorithm
This is a broad question without a simple answer. At CMU I taught a 3-month course on this topic. It covered issues such as:
Using projections to understand correlation between variables and overal |
14,903 | How to do exploratory data analysis to choose appropriate machine learning algorithm | There are some things that you can check in your data.
1 - correlation between variables
2 - categorical variables or continuous variables?
3 - relation between number of samples and number of variables
4 - are the samples independent or is it a time series?
According to these points and to the kind of information y... | How to do exploratory data analysis to choose appropriate machine learning algorithm | There are some things that you can check in your data.
1 - correlation between variables
2 - categorical variables or continuous variables?
3 - relation between number of samples and number of variab | How to do exploratory data analysis to choose appropriate machine learning algorithm
There are some things that you can check in your data.
1 - correlation between variables
2 - categorical variables or continuous variables?
3 - relation between number of samples and number of variables
4 - are the samples independent... | How to do exploratory data analysis to choose appropriate machine learning algorithm
There are some things that you can check in your data.
1 - correlation between variables
2 - categorical variables or continuous variables?
3 - relation between number of samples and number of variab |
14,904 | What is the relationship between profile likelihood and confidence intervals? | I will not give a complete answer (I have a hard time trying to understand what you are doing exactly), but I will try to clarify how profile likelihood is built. I may complete my answer later.
The full likelihood for a normal sample of size $n$ is
$$L(\mu, \sigma^2) = \left( \sigma^2 \right)^{-n/2} \exp\left( - \sum_... | What is the relationship between profile likelihood and confidence intervals? | I will not give a complete answer (I have a hard time trying to understand what you are doing exactly), but I will try to clarify how profile likelihood is built. I may complete my answer later.
The f | What is the relationship between profile likelihood and confidence intervals?
I will not give a complete answer (I have a hard time trying to understand what you are doing exactly), but I will try to clarify how profile likelihood is built. I may complete my answer later.
The full likelihood for a normal sample of size... | What is the relationship between profile likelihood and confidence intervals?
I will not give a complete answer (I have a hard time trying to understand what you are doing exactly), but I will try to clarify how profile likelihood is built. I may complete my answer later.
The f |
14,905 | What is the relationship between profile likelihood and confidence intervals? | In a general framework, profile likelihood intervals are approximate confidence intervals. The proof of this result is essentially the same as proving that the likelihood ratio statistic is (asymptotically) approximately distributed as a $\chi^2_k$ distribution. The idea consists of inverting the hypothesis test obtain... | What is the relationship between profile likelihood and confidence intervals? | In a general framework, profile likelihood intervals are approximate confidence intervals. The proof of this result is essentially the same as proving that the likelihood ratio statistic is (asymptoti | What is the relationship between profile likelihood and confidence intervals?
In a general framework, profile likelihood intervals are approximate confidence intervals. The proof of this result is essentially the same as proving that the likelihood ratio statistic is (asymptotically) approximately distributed as a $\ch... | What is the relationship between profile likelihood and confidence intervals?
In a general framework, profile likelihood intervals are approximate confidence intervals. The proof of this result is essentially the same as proving that the likelihood ratio statistic is (asymptoti |
14,906 | What is the relationship between profile likelihood and confidence intervals? | I will not give an overly mathematical answer, but I would like to address your central question about the relationship between CI's and profile likelihood intervals. As the other respondents have pointed out, CI's can be constructed from a profile likelihood by using the $\chi^2$ approximation to the $normalized$ like... | What is the relationship between profile likelihood and confidence intervals? | I will not give an overly mathematical answer, but I would like to address your central question about the relationship between CI's and profile likelihood intervals. As the other respondents have poi | What is the relationship between profile likelihood and confidence intervals?
I will not give an overly mathematical answer, but I would like to address your central question about the relationship between CI's and profile likelihood intervals. As the other respondents have pointed out, CI's can be constructed from a p... | What is the relationship between profile likelihood and confidence intervals?
I will not give an overly mathematical answer, but I would like to address your central question about the relationship between CI's and profile likelihood intervals. As the other respondents have poi |
14,907 | Feature selection with Random Forests | For feature selection, we need a scoring function as well as a search method to optimize the scoring function.
You may use RF as a feature ranking method if you define some relevant importance score. RF will select features based on random with replacement method and group every subset in a separate subspace (called ra... | Feature selection with Random Forests | For feature selection, we need a scoring function as well as a search method to optimize the scoring function.
You may use RF as a feature ranking method if you define some relevant importance score. | Feature selection with Random Forests
For feature selection, we need a scoring function as well as a search method to optimize the scoring function.
You may use RF as a feature ranking method if you define some relevant importance score. RF will select features based on random with replacement method and group every su... | Feature selection with Random Forests
For feature selection, we need a scoring function as well as a search method to optimize the scoring function.
You may use RF as a feature ranking method if you define some relevant importance score. |
14,908 | Feature selection with Random Forests | I have a dataset with mostly financial variables (120 features, 4k
examples) which are mostly highly correlated and very noisy (technical
indicators, for example) so I would like to select about max 20-30 for
later use with model training (binary classification - increase /
decrease).
4k examples is really not... | Feature selection with Random Forests | I have a dataset with mostly financial variables (120 features, 4k
examples) which are mostly highly correlated and very noisy (technical
indicators, for example) so I would like to select about m | Feature selection with Random Forests
I have a dataset with mostly financial variables (120 features, 4k
examples) which are mostly highly correlated and very noisy (technical
indicators, for example) so I would like to select about max 20-30 for
later use with model training (binary classification - increase /
... | Feature selection with Random Forests
I have a dataset with mostly financial variables (120 features, 4k
examples) which are mostly highly correlated and very noisy (technical
indicators, for example) so I would like to select about m |
14,909 | How do you write up Tukey post-hoc findings? | General strategy of article deconstruction
A general strategy for learning how to write up results involves finding and deconstructing an example publication. I like to call this article deconstruction. A simple way of doing this involves searching Google Scholar to find a few examples. You may want to limit your searc... | How do you write up Tukey post-hoc findings? | General strategy of article deconstruction
A general strategy for learning how to write up results involves finding and deconstructing an example publication. I like to call this article deconstructio | How do you write up Tukey post-hoc findings?
General strategy of article deconstruction
A general strategy for learning how to write up results involves finding and deconstructing an example publication. I like to call this article deconstruction. A simple way of doing this involves searching Google Scholar to find a f... | How do you write up Tukey post-hoc findings?
General strategy of article deconstruction
A general strategy for learning how to write up results involves finding and deconstructing an example publication. I like to call this article deconstructio |
14,910 | How do you write up Tukey post-hoc findings? | It's a tough one to visualize, especially considering the potential audience. But you should also show the homogenous subsets so it's easy to identify those elements that are truly differentiated from each other. Depending on the audience, I don't even bother showing SE or L/U B nor p-values. I had to cut the row label... | How do you write up Tukey post-hoc findings? | It's a tough one to visualize, especially considering the potential audience. But you should also show the homogenous subsets so it's easy to identify those elements that are truly differentiated from | How do you write up Tukey post-hoc findings?
It's a tough one to visualize, especially considering the potential audience. But you should also show the homogenous subsets so it's easy to identify those elements that are truly differentiated from each other. Depending on the audience, I don't even bother showing SE or L... | How do you write up Tukey post-hoc findings?
It's a tough one to visualize, especially considering the potential audience. But you should also show the homogenous subsets so it's easy to identify those elements that are truly differentiated from |
14,911 | Notation: What does the tilde below of the expectation mean? [duplicate] | $z\sim q$ means that RV $Z$ is distributed with respect to $q$ function, i.e. $q(z)$, where $q(z)$ is a valid PDF/PMF. So, the expectation can be unfold as (assuming $z$ being continuous)
$$\mathbb{E}_{z\sim q}[\log_{\phi}(x_i|z)]=\int_{-\infty}^\infty \log_\phi (x_i|z) q(z) dz$$ | Notation: What does the tilde below of the expectation mean? [duplicate] | $z\sim q$ means that RV $Z$ is distributed with respect to $q$ function, i.e. $q(z)$, where $q(z)$ is a valid PDF/PMF. So, the expectation can be unfold as (assuming $z$ being continuous)
$$\mathbb{E} | Notation: What does the tilde below of the expectation mean? [duplicate]
$z\sim q$ means that RV $Z$ is distributed with respect to $q$ function, i.e. $q(z)$, where $q(z)$ is a valid PDF/PMF. So, the expectation can be unfold as (assuming $z$ being continuous)
$$\mathbb{E}_{z\sim q}[\log_{\phi}(x_i|z)]=\int_{-\infty}^\... | Notation: What does the tilde below of the expectation mean? [duplicate]
$z\sim q$ means that RV $Z$ is distributed with respect to $q$ function, i.e. $q(z)$, where $q(z)$ is a valid PDF/PMF. So, the expectation can be unfold as (assuming $z$ being continuous)
$$\mathbb{E} |
14,912 | Using a Random Forest for Time Series Data | It works well but only if the features are properly prepared so that the order of the lines is not important anymore.
E.g. for a univariate time series $y_i$, you would use $y_i$ as response and e.g. the following features:
Lagged versions $y_{i-1}$, $y_{i-2}$, $y_{i-3}$ etc.
Differences of appropriate order, e.g. $y... | Using a Random Forest for Time Series Data | It works well but only if the features are properly prepared so that the order of the lines is not important anymore.
E.g. for a univariate time series $y_i$, you would use $y_i$ as response and e.g. | Using a Random Forest for Time Series Data
It works well but only if the features are properly prepared so that the order of the lines is not important anymore.
E.g. for a univariate time series $y_i$, you would use $y_i$ as response and e.g. the following features:
Lagged versions $y_{i-1}$, $y_{i-2}$, $y_{i-3}$ etc.... | Using a Random Forest for Time Series Data
It works well but only if the features are properly prepared so that the order of the lines is not important anymore.
E.g. for a univariate time series $y_i$, you would use $y_i$ as response and e.g. |
14,913 | Using a Random Forest for Time Series Data | A random forest would not be expected to perform well on time series data for a variety of reasons. In my view the greatest pitfalls are unrelated to the bootstrapping, however, and are not unique to random forests:
Time series have an interdependence between observations, which the model will ignore.
The underlying... | Using a Random Forest for Time Series Data | A random forest would not be expected to perform well on time series data for a variety of reasons. In my view the greatest pitfalls are unrelated to the bootstrapping, however, and are not unique to | Using a Random Forest for Time Series Data
A random forest would not be expected to perform well on time series data for a variety of reasons. In my view the greatest pitfalls are unrelated to the bootstrapping, however, and are not unique to random forests:
Time series have an interdependence between observations, w... | Using a Random Forest for Time Series Data
A random forest would not be expected to perform well on time series data for a variety of reasons. In my view the greatest pitfalls are unrelated to the bootstrapping, however, and are not unique to |
14,914 | Is it wrong to choose features based on p-value? | The t-statistic can have next to nothing to say about the predictive ability of a feature, and they should not be used to screen predictor out of, or allow predictors into a predictive model.
P-values say spurious features are important
Consider the following scenario setup in R. Let's create two vectors, the first ... | Is it wrong to choose features based on p-value? | The t-statistic can have next to nothing to say about the predictive ability of a feature, and they should not be used to screen predictor out of, or allow predictors into a predictive model.
P-valu | Is it wrong to choose features based on p-value?
The t-statistic can have next to nothing to say about the predictive ability of a feature, and they should not be used to screen predictor out of, or allow predictors into a predictive model.
P-values say spurious features are important
Consider the following scenario ... | Is it wrong to choose features based on p-value?
The t-statistic can have next to nothing to say about the predictive ability of a feature, and they should not be used to screen predictor out of, or allow predictors into a predictive model.
P-valu |
14,915 | Is it wrong to choose features based on p-value? | The t-statistic is influenced by the effect size and the sample size. It might be the case that the effect size is non-zero but the sample size is not big enough to make it significant.
In a simple T-test for zero mean (which is analogous to testing if a feature's influence is zero) the T statistic is $t=\left(\frac{\o... | Is it wrong to choose features based on p-value? | The t-statistic is influenced by the effect size and the sample size. It might be the case that the effect size is non-zero but the sample size is not big enough to make it significant.
In a simple T- | Is it wrong to choose features based on p-value?
The t-statistic is influenced by the effect size and the sample size. It might be the case that the effect size is non-zero but the sample size is not big enough to make it significant.
In a simple T-test for zero mean (which is analogous to testing if a feature's influe... | Is it wrong to choose features based on p-value?
The t-statistic is influenced by the effect size and the sample size. It might be the case that the effect size is non-zero but the sample size is not big enough to make it significant.
In a simple T- |
14,916 | Fitting multivariate, natural cubic spline | This paper presented at UseR! 2009 seems to address a similar problem
http://www.r-project.org/conferences/useR-2009/slides/Roustant+Ginsbourger+Deville.pdf
It suggests the DiceKriging package http://cran.r-project.org/web/packages/DiceKriging/index.html
In particular, check the functions km and predict.
Here is a an ... | Fitting multivariate, natural cubic spline | This paper presented at UseR! 2009 seems to address a similar problem
http://www.r-project.org/conferences/useR-2009/slides/Roustant+Ginsbourger+Deville.pdf
It suggests the DiceKriging package http:// | Fitting multivariate, natural cubic spline
This paper presented at UseR! 2009 seems to address a similar problem
http://www.r-project.org/conferences/useR-2009/slides/Roustant+Ginsbourger+Deville.pdf
It suggests the DiceKriging package http://cran.r-project.org/web/packages/DiceKriging/index.html
In particular, check ... | Fitting multivariate, natural cubic spline
This paper presented at UseR! 2009 seems to address a similar problem
http://www.r-project.org/conferences/useR-2009/slides/Roustant+Ginsbourger+Deville.pdf
It suggests the DiceKriging package http:// |
14,917 | Fitting multivariate, natural cubic spline | You need more data for a spline fit. mgcv indeed is a good choice. For your specific request you need to set the cubic spline as the basis function bs='cr' and also not have it penalized with fx=TRUE. Both options are set for a smooth term that is set with s(). Predict works as expected.
library(mgcv)
x <- data.frame(a... | Fitting multivariate, natural cubic spline | You need more data for a spline fit. mgcv indeed is a good choice. For your specific request you need to set the cubic spline as the basis function bs='cr' and also not have it penalized with fx=TRUE. | Fitting multivariate, natural cubic spline
You need more data for a spline fit. mgcv indeed is a good choice. For your specific request you need to set the cubic spline as the basis function bs='cr' and also not have it penalized with fx=TRUE. Both options are set for a smooth term that is set with s(). Predict works a... | Fitting multivariate, natural cubic spline
You need more data for a spline fit. mgcv indeed is a good choice. For your specific request you need to set the cubic spline as the basis function bs='cr' and also not have it penalized with fx=TRUE. |
14,918 | Fitting multivariate, natural cubic spline | You give no details as to the form of the function $f(X)$; it might be that a piecewise constant function is a sufficiently good approximation, in which case you might want to fit a regression tree (with package rpart for instance). Otherwise, you might want to look at package earth, in addition to what has been sugges... | Fitting multivariate, natural cubic spline | You give no details as to the form of the function $f(X)$; it might be that a piecewise constant function is a sufficiently good approximation, in which case you might want to fit a regression tree (w | Fitting multivariate, natural cubic spline
You give no details as to the form of the function $f(X)$; it might be that a piecewise constant function is a sufficiently good approximation, in which case you might want to fit a regression tree (with package rpart for instance). Otherwise, you might want to look at package... | Fitting multivariate, natural cubic spline
You give no details as to the form of the function $f(X)$; it might be that a piecewise constant function is a sufficiently good approximation, in which case you might want to fit a regression tree (w |
14,919 | Persistence in time series | Roughly speaking, the term persistence in time series context is often related to the notion of memory properties of time series. To put it another way, you have a persistent time series process if the effect of infinitesimally (very) small shock will be influencing the future predictions of your time series for a very... | Persistence in time series | Roughly speaking, the term persistence in time series context is often related to the notion of memory properties of time series. To put it another way, you have a persistent time series process if th | Persistence in time series
Roughly speaking, the term persistence in time series context is often related to the notion of memory properties of time series. To put it another way, you have a persistent time series process if the effect of infinitesimally (very) small shock will be influencing the future predictions of ... | Persistence in time series
Roughly speaking, the term persistence in time series context is often related to the notion of memory properties of time series. To put it another way, you have a persistent time series process if th |
14,920 | Persistence in time series | A persistent series is one where the value of the variable at a certain date is closely related to the previous value. The two basic measures of persistence are the autocovariance and the autocorrelation coefficient. | Persistence in time series | A persistent series is one where the value of the variable at a certain date is closely related to the previous value. The two basic measures of persistence are the autocovariance and the autocorrelat | Persistence in time series
A persistent series is one where the value of the variable at a certain date is closely related to the previous value. The two basic measures of persistence are the autocovariance and the autocorrelation coefficient. | Persistence in time series
A persistent series is one where the value of the variable at a certain date is closely related to the previous value. The two basic measures of persistence are the autocovariance and the autocorrelat |
14,921 | Analysis of Danish mask study data by Nassim Nicholas Taleb (binomial GLM with complete separation) | Your 2-sided test implicitly allots exactly half of your 5% significance level to "masks are harmful" ($M_-$) and the other half to "masks are beneficial" ($M_+$). To a Bayesian like Taleb that might suggest that you aren't properly thinking about your prior, because it implies that the amount of evidence it would take... | Analysis of Danish mask study data by Nassim Nicholas Taleb (binomial GLM with complete separation) | Your 2-sided test implicitly allots exactly half of your 5% significance level to "masks are harmful" ($M_-$) and the other half to "masks are beneficial" ($M_+$). To a Bayesian like Taleb that might | Analysis of Danish mask study data by Nassim Nicholas Taleb (binomial GLM with complete separation)
Your 2-sided test implicitly allots exactly half of your 5% significance level to "masks are harmful" ($M_-$) and the other half to "masks are beneficial" ($M_+$). To a Bayesian like Taleb that might suggest that you are... | Analysis of Danish mask study data by Nassim Nicholas Taleb (binomial GLM with complete separation)
Your 2-sided test implicitly allots exactly half of your 5% significance level to "masks are harmful" ($M_-$) and the other half to "masks are beneficial" ($M_+$). To a Bayesian like Taleb that might |
14,922 | Analysis of Danish mask study data by Nassim Nicholas Taleb (binomial GLM with complete separation) | This simulation is an attempt to estimate the result of an exact test in which the chance of observing such an extreme disparity is
$$\begin{aligned}
\Pr(\text{all positive results in one group}) &= \frac{\binom{2470}{5} + \binom{2392}{5}}{\binom{2470+2392}{5}} \\&= 0.03377 + 0.02876 = 0.06253.
\end{aligned}$$
This cal... | Analysis of Danish mask study data by Nassim Nicholas Taleb (binomial GLM with complete separation) | This simulation is an attempt to estimate the result of an exact test in which the chance of observing such an extreme disparity is
$$\begin{aligned}
\Pr(\text{all positive results in one group}) &= \ | Analysis of Danish mask study data by Nassim Nicholas Taleb (binomial GLM with complete separation)
This simulation is an attempt to estimate the result of an exact test in which the chance of observing such an extreme disparity is
$$\begin{aligned}
\Pr(\text{all positive results in one group}) &= \frac{\binom{2470}{5}... | Analysis of Danish mask study data by Nassim Nicholas Taleb (binomial GLM with complete separation)
This simulation is an attempt to estimate the result of an exact test in which the chance of observing such an extreme disparity is
$$\begin{aligned}
\Pr(\text{all positive results in one group}) &= \ |
14,923 | Analysis of Danish mask study data by Nassim Nicholas Taleb (binomial GLM with complete separation) | If you want to acquiesce to
(i) avoiding methods that do p-values
(ii) producing a more "bespoke" test for this problem
(objectives mentioned by Taleb, not necessarilly something you agree with)
One solution would be to simulate and find parameters by rejection sampling (actually approximate Bayesian computation).
So l... | Analysis of Danish mask study data by Nassim Nicholas Taleb (binomial GLM with complete separation) | If you want to acquiesce to
(i) avoiding methods that do p-values
(ii) producing a more "bespoke" test for this problem
(objectives mentioned by Taleb, not necessarilly something you agree with)
One s | Analysis of Danish mask study data by Nassim Nicholas Taleb (binomial GLM with complete separation)
If you want to acquiesce to
(i) avoiding methods that do p-values
(ii) producing a more "bespoke" test for this problem
(objectives mentioned by Taleb, not necessarilly something you agree with)
One solution would be to ... | Analysis of Danish mask study data by Nassim Nicholas Taleb (binomial GLM with complete separation)
If you want to acquiesce to
(i) avoiding methods that do p-values
(ii) producing a more "bespoke" test for this problem
(objectives mentioned by Taleb, not necessarilly something you agree with)
One s |
14,924 | What is the difference between 'regular' linear regression and deep learning linear regression? | Assuming that by deep learning you meant more precisely neural networks: a vanilla fully connected feedforward neural network with only linear activation functions will perform linear regression, regardless of how many layers it has. One difference is that with a neural network one typically uses gradient descent, whe... | What is the difference between 'regular' linear regression and deep learning linear regression? | Assuming that by deep learning you meant more precisely neural networks: a vanilla fully connected feedforward neural network with only linear activation functions will perform linear regression, reg | What is the difference between 'regular' linear regression and deep learning linear regression?
Assuming that by deep learning you meant more precisely neural networks: a vanilla fully connected feedforward neural network with only linear activation functions will perform linear regression, regardless of how many laye... | What is the difference between 'regular' linear regression and deep learning linear regression?
Assuming that by deep learning you meant more precisely neural networks: a vanilla fully connected feedforward neural network with only linear activation functions will perform linear regression, reg |
14,925 | What is the difference between 'regular' linear regression and deep learning linear regression? | For regression, which for deep learning is nonlinear in most cases, final layer has 1 neuron with identity function and loss function we optimize is MSE, MAE instead of binary or categorical cross-entropy used for classification. | What is the difference between 'regular' linear regression and deep learning linear regression? | For regression, which for deep learning is nonlinear in most cases, final layer has 1 neuron with identity function and loss function we optimize is MSE, MAE instead of binary or categorical cross-ent | What is the difference between 'regular' linear regression and deep learning linear regression?
For regression, which for deep learning is nonlinear in most cases, final layer has 1 neuron with identity function and loss function we optimize is MSE, MAE instead of binary or categorical cross-entropy used for classifica... | What is the difference between 'regular' linear regression and deep learning linear regression?
For regression, which for deep learning is nonlinear in most cases, final layer has 1 neuron with identity function and loss function we optimize is MSE, MAE instead of binary or categorical cross-ent |
14,926 | Why P>0.5 cutoff is not "optimal" for logistic regression? | You don't have to get predicted categories from a logistic regression model. It can be fine stay with predicted probabilities. If you do get predicted categories, you should not use that information to do anything other than say 'this observation is best classified into this category'. For example, you should not us... | Why P>0.5 cutoff is not "optimal" for logistic regression? | You don't have to get predicted categories from a logistic regression model. It can be fine stay with predicted probabilities. If you do get predicted categories, you should not use that information | Why P>0.5 cutoff is not "optimal" for logistic regression?
You don't have to get predicted categories from a logistic regression model. It can be fine stay with predicted probabilities. If you do get predicted categories, you should not use that information to do anything other than say 'this observation is best clas... | Why P>0.5 cutoff is not "optimal" for logistic regression?
You don't have to get predicted categories from a logistic regression model. It can be fine stay with predicted probabilities. If you do get predicted categories, you should not use that information |
14,927 | Why P>0.5 cutoff is not "optimal" for logistic regression? | I think, it could be because of multiple reasons:
There might be non-linearity in your data, so linearly adding the weights, might not always result in correct probabilities
Variables are a mix of good predictors and weak predictors, so scored population that is around .5 is because of weak predictors or less effect o... | Why P>0.5 cutoff is not "optimal" for logistic regression? | I think, it could be because of multiple reasons:
There might be non-linearity in your data, so linearly adding the weights, might not always result in correct probabilities
Variables are a mix of go | Why P>0.5 cutoff is not "optimal" for logistic regression?
I think, it could be because of multiple reasons:
There might be non-linearity in your data, so linearly adding the weights, might not always result in correct probabilities
Variables are a mix of good predictors and weak predictors, so scored population that ... | Why P>0.5 cutoff is not "optimal" for logistic regression?
I think, it could be because of multiple reasons:
There might be non-linearity in your data, so linearly adding the weights, might not always result in correct probabilities
Variables are a mix of go |
14,928 | Difference between multilevel modelling and mixed effects models? | Section 2.2.2.1 from lme4 book
Because each level of sample occurs with one and only one level of batch we
say that sample is nested within batch. Some presentations of mixed-effects
models, especially those related to multilevel modeling˜[Rasbash et˜al., 2000]
or hierarchical linear models˜[Raudenbush and Bryk,... | Difference between multilevel modelling and mixed effects models? | Section 2.2.2.1 from lme4 book
Because each level of sample occurs with one and only one level of batch we
say that sample is nested within batch. Some presentations of mixed-effects
models, espe | Difference between multilevel modelling and mixed effects models?
Section 2.2.2.1 from lme4 book
Because each level of sample occurs with one and only one level of batch we
say that sample is nested within batch. Some presentations of mixed-effects
models, especially those related to multilevel modeling˜[Rasbash e... | Difference between multilevel modelling and mixed effects models?
Section 2.2.2.1 from lme4 book
Because each level of sample occurs with one and only one level of batch we
say that sample is nested within batch. Some presentations of mixed-effects
models, espe |
14,929 | do logs modify the correlation between two variables? | There are multiple different types of correlation. The most common one is Pearson's correlation coefficient, which measures the amount of linear dependence between two vectors. That is, it essentially lays a straight line through the scatterplot and calculates its slope. This will of course change if you take logs!
If ... | do logs modify the correlation between two variables? | There are multiple different types of correlation. The most common one is Pearson's correlation coefficient, which measures the amount of linear dependence between two vectors. That is, it essentially | do logs modify the correlation between two variables?
There are multiple different types of correlation. The most common one is Pearson's correlation coefficient, which measures the amount of linear dependence between two vectors. That is, it essentially lays a straight line through the scatterplot and calculates its s... | do logs modify the correlation between two variables?
There are multiple different types of correlation. The most common one is Pearson's correlation coefficient, which measures the amount of linear dependence between two vectors. That is, it essentially |
14,930 | What does the convolution step in a Convolutional Neural Network do? | I'll first try to share some intuition behind CNN and then comment the particular topics you listed.
The convolution and sub-sampling layers in a CNN are not different from the hidden layers in a common MLP, i. e. their function is to extract features from their input. These features are then given to the next hidden l... | What does the convolution step in a Convolutional Neural Network do? | I'll first try to share some intuition behind CNN and then comment the particular topics you listed.
The convolution and sub-sampling layers in a CNN are not different from the hidden layers in a comm | What does the convolution step in a Convolutional Neural Network do?
I'll first try to share some intuition behind CNN and then comment the particular topics you listed.
The convolution and sub-sampling layers in a CNN are not different from the hidden layers in a common MLP, i. e. their function is to extract features... | What does the convolution step in a Convolutional Neural Network do?
I'll first try to share some intuition behind CNN and then comment the particular topics you listed.
The convolution and sub-sampling layers in a CNN are not different from the hidden layers in a comm |
14,931 | What does the convolution step in a Convolutional Neural Network do? | I have no idea what you mean by "why the first convolution step works." In order for a CNN to be successful it needs to have many layers. One of the fundamental ideas behind CNN and many other deep learning approaches is that larger signals can be identified by the spatial correlation of their smaller parts which can... | What does the convolution step in a Convolutional Neural Network do? | I have no idea what you mean by "why the first convolution step works." In order for a CNN to be successful it needs to have many layers. One of the fundamental ideas behind CNN and many other deep | What does the convolution step in a Convolutional Neural Network do?
I have no idea what you mean by "why the first convolution step works." In order for a CNN to be successful it needs to have many layers. One of the fundamental ideas behind CNN and many other deep learning approaches is that larger signals can be i... | What does the convolution step in a Convolutional Neural Network do?
I have no idea what you mean by "why the first convolution step works." In order for a CNN to be successful it needs to have many layers. One of the fundamental ideas behind CNN and many other deep |
14,932 | Why is controlling FDR less stringent than controlling FWER? | Indeed, @cardinal is quite right that the paper is as clear as it gets. So, for what it's worth, in case you do not have access to the paper, here's a slightly elaborated version of how Benjamini–Hochberg argue:
The FDR $Q_e$ is the expected value of the proportion of false rejections $v$ to all rejections $r$. Now, $r... | Why is controlling FDR less stringent than controlling FWER? | Indeed, @cardinal is quite right that the paper is as clear as it gets. So, for what it's worth, in case you do not have access to the paper, here's a slightly elaborated version of how Benjamini–Hoch | Why is controlling FDR less stringent than controlling FWER?
Indeed, @cardinal is quite right that the paper is as clear as it gets. So, for what it's worth, in case you do not have access to the paper, here's a slightly elaborated version of how Benjamini–Hochberg argue:
The FDR $Q_e$ is the expected value of the prop... | Why is controlling FDR less stringent than controlling FWER?
Indeed, @cardinal is quite right that the paper is as clear as it gets. So, for what it's worth, in case you do not have access to the paper, here's a slightly elaborated version of how Benjamini–Hoch |
14,933 | Why use Platt's scaling? | I suggest to check out the wikipedia page of logistic regression. It states that in case of a binary dependent variable logistic regression maps the predictors to the probability of occurrence of the dependent variable. Without any transformation, the probability used for training the model is either 1 (if y is positiv... | Why use Platt's scaling? | I suggest to check out the wikipedia page of logistic regression. It states that in case of a binary dependent variable logistic regression maps the predictors to the probability of occurrence of the | Why use Platt's scaling?
I suggest to check out the wikipedia page of logistic regression. It states that in case of a binary dependent variable logistic regression maps the predictors to the probability of occurrence of the dependent variable. Without any transformation, the probability used for training the model is ... | Why use Platt's scaling?
I suggest to check out the wikipedia page of logistic regression. It states that in case of a binary dependent variable logistic regression maps the predictors to the probability of occurrence of the |
14,934 | Why use Platt's scaling? | Another method of avoiding over-fitting that I have found useful is to fit the univariate logistic regression model to the leave-out-out cross-validation output of the SVM, which can be approximated efficiently using the Span bound.
However, if you want a classifier that produces estimates of the probability of class m... | Why use Platt's scaling? | Another method of avoiding over-fitting that I have found useful is to fit the univariate logistic regression model to the leave-out-out cross-validation output of the SVM, which can be approximated e | Why use Platt's scaling?
Another method of avoiding over-fitting that I have found useful is to fit the univariate logistic regression model to the leave-out-out cross-validation output of the SVM, which can be approximated efficiently using the Span bound.
However, if you want a classifier that produces estimates of t... | Why use Platt's scaling?
Another method of avoiding over-fitting that I have found useful is to fit the univariate logistic regression model to the leave-out-out cross-validation output of the SVM, which can be approximated e |
14,935 | How is causation defined mathematically? | What is the mathematical definition of a causal relationship between
two random variables?
Mathematically, a causal model consists of functional relationships between variables. For instance, consider the system of structural equations below:
$$
x = f_x(\epsilon_{x})\\
y = f_y(x, \epsilon_{y})
$$
This means that $x$... | How is causation defined mathematically? | What is the mathematical definition of a causal relationship between
two random variables?
Mathematically, a causal model consists of functional relationships between variables. For instance, consi | How is causation defined mathematically?
What is the mathematical definition of a causal relationship between
two random variables?
Mathematically, a causal model consists of functional relationships between variables. For instance, consider the system of structural equations below:
$$
x = f_x(\epsilon_{x})\\
y = f_... | How is causation defined mathematically?
What is the mathematical definition of a causal relationship between
two random variables?
Mathematically, a causal model consists of functional relationships between variables. For instance, consi |
14,936 | How is causation defined mathematically? | There are a variety of approaches to formalizing causality (which is in keeping with substantial philosophical disagreement about causality that has been around for centuries). A popular one is in terms of potential outcomes. The potential-outcomes approach, called the Rubin causal model, supposes that for each causal ... | How is causation defined mathematically? | There are a variety of approaches to formalizing causality (which is in keeping with substantial philosophical disagreement about causality that has been around for centuries). A popular one is in ter | How is causation defined mathematically?
There are a variety of approaches to formalizing causality (which is in keeping with substantial philosophical disagreement about causality that has been around for centuries). A popular one is in terms of potential outcomes. The potential-outcomes approach, called the Rubin cau... | How is causation defined mathematically?
There are a variety of approaches to formalizing causality (which is in keeping with substantial philosophical disagreement about causality that has been around for centuries). A popular one is in ter |
14,937 | How is causation defined mathematically? | There are two ways to determine whether $X$ is the cause of $Y$. The first is standard while the second is my own claim.
There exists an intervention on $X$ such that the value of $Y$ is changed
An intervention is a surgical change to a variable that does not affect variables it depends on. Interventions have been ... | How is causation defined mathematically? | There are two ways to determine whether $X$ is the cause of $Y$. The first is standard while the second is my own claim.
There exists an intervention on $X$ such that the value of $Y$ is changed
An | How is causation defined mathematically?
There are two ways to determine whether $X$ is the cause of $Y$. The first is standard while the second is my own claim.
There exists an intervention on $X$ such that the value of $Y$ is changed
An intervention is a surgical change to a variable that does not affect variables... | How is causation defined mathematically?
There are two ways to determine whether $X$ is the cause of $Y$. The first is standard while the second is my own claim.
There exists an intervention on $X$ such that the value of $Y$ is changed
An |
14,938 | logloss vs gini/auc | Whereas the AUC is computed with regards to binary classification with a varying decision threshold, logloss actually takes "certainty" of classification into account.
Therefore to my understanding, logloss conceptually goes beyond AUC and is especially relevant in cases with imbalanced data or in case of unequally di... | logloss vs gini/auc | Whereas the AUC is computed with regards to binary classification with a varying decision threshold, logloss actually takes "certainty" of classification into account.
Therefore to my understanding, | logloss vs gini/auc
Whereas the AUC is computed with regards to binary classification with a varying decision threshold, logloss actually takes "certainty" of classification into account.
Therefore to my understanding, logloss conceptually goes beyond AUC and is especially relevant in cases with imbalanced data or in ... | logloss vs gini/auc
Whereas the AUC is computed with regards to binary classification with a varying decision threshold, logloss actually takes "certainty" of classification into account.
Therefore to my understanding, |
14,939 | Is the sample correlation coefficient an unbiased estimator of the population correlation coefficient? | This is not an easy question but some expressions are available. If you are talking about the Normal distribution in particular, then the answer is NO! We have
$$\mathbb{E} \widehat{\rho} = \rho \left[1 - \frac{\left(1-\rho^2 \right)}{2n} + O\left( \frac{1}{n^2} \right) \right]$$
as seen in Chapter 2 of Lehmann's Theo... | Is the sample correlation coefficient an unbiased estimator of the population correlation coefficien | This is not an easy question but some expressions are available. If you are talking about the Normal distribution in particular, then the answer is NO! We have
$$\mathbb{E} \widehat{\rho} = \rho \left | Is the sample correlation coefficient an unbiased estimator of the population correlation coefficient?
This is not an easy question but some expressions are available. If you are talking about the Normal distribution in particular, then the answer is NO! We have
$$\mathbb{E} \widehat{\rho} = \rho \left[1 - \frac{\left(... | Is the sample correlation coefficient an unbiased estimator of the population correlation coefficien
This is not an easy question but some expressions are available. If you are talking about the Normal distribution in particular, then the answer is NO! We have
$$\mathbb{E} \widehat{\rho} = \rho \left |
14,940 | Bootstrap methodology. Why resample "with replacement" instead of random subsampling? | One way to understand this choice is to think of the sample at hand as being the best representation you have of the underlying population. You may not have the whole population to sample from any more, but you do have this particular representation of the population. A truly random re-sample from this representation o... | Bootstrap methodology. Why resample "with replacement" instead of random subsampling? | One way to understand this choice is to think of the sample at hand as being the best representation you have of the underlying population. You may not have the whole population to sample from any mor | Bootstrap methodology. Why resample "with replacement" instead of random subsampling?
One way to understand this choice is to think of the sample at hand as being the best representation you have of the underlying population. You may not have the whole population to sample from any more, but you do have this particular... | Bootstrap methodology. Why resample "with replacement" instead of random subsampling?
One way to understand this choice is to think of the sample at hand as being the best representation you have of the underlying population. You may not have the whole population to sample from any mor |
14,941 | Pearson VS Deviance Residuals in logistic regression | Logistic regression seeks to maximize the log likelihood function
$LL = \sum^k \ln(P_i) + \sum^r \ln(1-P_i)$
where $P_i$ is the predicted probability that case i is $\hat Y=1$; $k$ is the number of cases observed as $Y=1$ and $r$ is the number of (the rest) cases observed as $Y=0$.
That expression is equal to
$LL = ({\... | Pearson VS Deviance Residuals in logistic regression | Logistic regression seeks to maximize the log likelihood function
$LL = \sum^k \ln(P_i) + \sum^r \ln(1-P_i)$
where $P_i$ is the predicted probability that case i is $\hat Y=1$; $k$ is the number of ca | Pearson VS Deviance Residuals in logistic regression
Logistic regression seeks to maximize the log likelihood function
$LL = \sum^k \ln(P_i) + \sum^r \ln(1-P_i)$
where $P_i$ is the predicted probability that case i is $\hat Y=1$; $k$ is the number of cases observed as $Y=1$ and $r$ is the number of (the rest) cases obs... | Pearson VS Deviance Residuals in logistic regression
Logistic regression seeks to maximize the log likelihood function
$LL = \sum^k \ln(P_i) + \sum^r \ln(1-P_i)$
where $P_i$ is the predicted probability that case i is $\hat Y=1$; $k$ is the number of ca |
14,942 | Pearson VS Deviance Residuals in logistic regression | In response to this question I have added som R code to show how to manually apply the formula for calculation of deviance residuals
The model in the code is a logit model where
$$p_i := Pr(Y_i = 1) = \frac{\exp(b_0 + b_1x_i)}{1+\exp(b_0 + b_1x_i)}.$$
I define $v_i := b_0 + b_1x_i$ such that the model can be written a... | Pearson VS Deviance Residuals in logistic regression | In response to this question I have added som R code to show how to manually apply the formula for calculation of deviance residuals
The model in the code is a logit model where
$$p_i := Pr(Y_i = 1) | Pearson VS Deviance Residuals in logistic regression
In response to this question I have added som R code to show how to manually apply the formula for calculation of deviance residuals
The model in the code is a logit model where
$$p_i := Pr(Y_i = 1) = \frac{\exp(b_0 + b_1x_i)}{1+\exp(b_0 + b_1x_i)}.$$
I define $v_i ... | Pearson VS Deviance Residuals in logistic regression
In response to this question I have added som R code to show how to manually apply the formula for calculation of deviance residuals
The model in the code is a logit model where
$$p_i := Pr(Y_i = 1) |
14,943 | Combining multiple metrics to provide comparisons/ranking of k objects [Question and Reference Request] | Awesome question.
Question 1:
I approach this problem using standard deviations ($n\sigma$) to create a standardized scale where $n$ is the number of standard deviations from the mean ($\mu$) and $\sigma$ is the standard deviation.
I will use an example of a call center agent making calls. Here is a possible way to... | Combining multiple metrics to provide comparisons/ranking of k objects [Question and Reference Reque | Awesome question.
Question 1:
I approach this problem using standard deviations ($n\sigma$) to create a standardized scale where $n$ is the number of standard deviations from the mean ($\mu$) and $\ | Combining multiple metrics to provide comparisons/ranking of k objects [Question and Reference Request]
Awesome question.
Question 1:
I approach this problem using standard deviations ($n\sigma$) to create a standardized scale where $n$ is the number of standard deviations from the mean ($\mu$) and $\sigma$ is the st... | Combining multiple metrics to provide comparisons/ranking of k objects [Question and Reference Reque
Awesome question.
Question 1:
I approach this problem using standard deviations ($n\sigma$) to create a standardized scale where $n$ is the number of standard deviations from the mean ($\mu$) and $\ |
14,944 | Understanding the Chi-squared test and the Chi-squared distribution | We could as well use a binomial distribution but it is not the point of the question…
Nevertheless, it is our starting point even for your actual question. I'll cover it somewhat informally.
Let's consider with the binomial case more generally:
$Y\sim \text{Bin}(n,p)$
Assume $n$ and $p$ are such that $Y$ is well appro... | Understanding the Chi-squared test and the Chi-squared distribution | We could as well use a binomial distribution but it is not the point of the question…
Nevertheless, it is our starting point even for your actual question. I'll cover it somewhat informally.
Let's co | Understanding the Chi-squared test and the Chi-squared distribution
We could as well use a binomial distribution but it is not the point of the question…
Nevertheless, it is our starting point even for your actual question. I'll cover it somewhat informally.
Let's consider with the binomial case more generally:
$Y\sim... | Understanding the Chi-squared test and the Chi-squared distribution
We could as well use a binomial distribution but it is not the point of the question…
Nevertheless, it is our starting point even for your actual question. I'll cover it somewhat informally.
Let's co |
14,945 | How to interpret PCA loadings? | Loadings (which should not be confused with eigenvectors) have the following properties:
Their sums of squares within each component are the eigenvalues
(components' variances).
Loadings are coefficients in linear
combination predicting a variable by the (standardized) components.
You extracted 2 first PCs out of 4. ... | How to interpret PCA loadings? | Loadings (which should not be confused with eigenvectors) have the following properties:
Their sums of squares within each component are the eigenvalues
(components' variances).
Loadings are coeffici | How to interpret PCA loadings?
Loadings (which should not be confused with eigenvectors) have the following properties:
Their sums of squares within each component are the eigenvalues
(components' variances).
Loadings are coefficients in linear
combination predicting a variable by the (standardized) components.
You e... | How to interpret PCA loadings?
Loadings (which should not be confused with eigenvectors) have the following properties:
Their sums of squares within each component are the eigenvalues
(components' variances).
Loadings are coeffici |
14,946 | How to interpret PCA loadings? | Although years are passed since last comments, I think the answer to the original question should be toward a more qualitative interpretation on how to read a "loadings matrix" (regardless of the assumptions we used to build it). If the vertical 'weights' are all the same (as in the original case for PC1 with all 0.5) ... | How to interpret PCA loadings? | Although years are passed since last comments, I think the answer to the original question should be toward a more qualitative interpretation on how to read a "loadings matrix" (regardless of the assu | How to interpret PCA loadings?
Although years are passed since last comments, I think the answer to the original question should be toward a more qualitative interpretation on how to read a "loadings matrix" (regardless of the assumptions we used to build it). If the vertical 'weights' are all the same (as in the origi... | How to interpret PCA loadings?
Although years are passed since last comments, I think the answer to the original question should be toward a more qualitative interpretation on how to read a "loadings matrix" (regardless of the assu |
14,947 | Proper bootstrapping technique for clustered data? | The second approach you suggest seems reasonable, but it turns out that it is better to only sample with replacement at the highest level, and without replacement at the remaining sublevels when bootstrapping hierarchical data. This is shown from simulations by Ren et al (2010) :
http://www.tandfonline.com/doi/abs/10.1... | Proper bootstrapping technique for clustered data? | The second approach you suggest seems reasonable, but it turns out that it is better to only sample with replacement at the highest level, and without replacement at the remaining sublevels when boots | Proper bootstrapping technique for clustered data?
The second approach you suggest seems reasonable, but it turns out that it is better to only sample with replacement at the highest level, and without replacement at the remaining sublevels when bootstrapping hierarchical data. This is shown from simulations by Ren et ... | Proper bootstrapping technique for clustered data?
The second approach you suggest seems reasonable, but it turns out that it is better to only sample with replacement at the highest level, and without replacement at the remaining sublevels when boots |
14,948 | Time dependent coefficients in R - how to do it? | @mpiktas came close in offering a feasible model, however the term that needs to be used for the quadratic in time=t would be I(t^2)) . This is so because in R the formula interpretation of "^" creates interactions and does not perform exponentiation, so the interaction of "t" with "t" is just "t". (Shouldn't this be m... | Time dependent coefficients in R - how to do it? | @mpiktas came close in offering a feasible model, however the term that needs to be used for the quadratic in time=t would be I(t^2)) . This is so because in R the formula interpretation of "^" create | Time dependent coefficients in R - how to do it?
@mpiktas came close in offering a feasible model, however the term that needs to be used for the quadratic in time=t would be I(t^2)) . This is so because in R the formula interpretation of "^" creates interactions and does not perform exponentiation, so the interaction ... | Time dependent coefficients in R - how to do it?
@mpiktas came close in offering a feasible model, however the term that needs to be used for the quadratic in time=t would be I(t^2)) . This is so because in R the formula interpretation of "^" create |
14,949 | Time dependent coefficients in R - how to do it? | I've changed the answer to this as neither @DWin's or @Zach's answers fully answers how to model time-varying coefficients. I've recently wrote a post about this. Here's the gist of it.
The core concept in the Cox regression model is the hazard function, $h(t)$. It is defined as:
$$h(t) = \frac{f(t)}{S(t)}$$
Where the... | Time dependent coefficients in R - how to do it? | I've changed the answer to this as neither @DWin's or @Zach's answers fully answers how to model time-varying coefficients. I've recently wrote a post about this. Here's the gist of it.
The core conce | Time dependent coefficients in R - how to do it?
I've changed the answer to this as neither @DWin's or @Zach's answers fully answers how to model time-varying coefficients. I've recently wrote a post about this. Here's the gist of it.
The core concept in the Cox regression model is the hazard function, $h(t)$. It is de... | Time dependent coefficients in R - how to do it?
I've changed the answer to this as neither @DWin's or @Zach's answers fully answers how to model time-varying coefficients. I've recently wrote a post about this. Here's the gist of it.
The core conce |
14,950 | Time dependent coefficients in R - how to do it? | You can use the apply.rolling function in PerformanceAnalytics to run a linear regression through a rolling window, which will allow your coefficients to vary over time.
For example:
library(PerformanceAnalytics)
library(quantmod)
getSymbols(c('AAPL','SPY'), from='01-01-1900')
chart.RollingRegression(Cl(AAPL),Cl(SPY), ... | Time dependent coefficients in R - how to do it? | You can use the apply.rolling function in PerformanceAnalytics to run a linear regression through a rolling window, which will allow your coefficients to vary over time.
For example:
library(Performan | Time dependent coefficients in R - how to do it?
You can use the apply.rolling function in PerformanceAnalytics to run a linear regression through a rolling window, which will allow your coefficients to vary over time.
For example:
library(PerformanceAnalytics)
library(quantmod)
getSymbols(c('AAPL','SPY'), from='01-01-... | Time dependent coefficients in R - how to do it?
You can use the apply.rolling function in PerformanceAnalytics to run a linear regression through a rolling window, which will allow your coefficients to vary over time.
For example:
library(Performan |
14,951 | Average precision vs precision | Precision refers to precision at a particular decision threshold. For example, if you count any model output less than 0.5 as negative, and greater than 0.5 as positive. But sometimes (especially if your classes are not balanced, or if you want to favor precision over recall or vice versa), you may want to vary this th... | Average precision vs precision | Precision refers to precision at a particular decision threshold. For example, if you count any model output less than 0.5 as negative, and greater than 0.5 as positive. But sometimes (especially if y | Average precision vs precision
Precision refers to precision at a particular decision threshold. For example, if you count any model output less than 0.5 as negative, and greater than 0.5 as positive. But sometimes (especially if your classes are not balanced, or if you want to favor precision over recall or vice versa... | Average precision vs precision
Precision refers to precision at a particular decision threshold. For example, if you count any model output less than 0.5 as negative, and greater than 0.5 as positive. But sometimes (especially if y |
14,952 | Average precision vs precision | Precision is Pr = TP/(TP+FP) where is TP and FP are True positives and False positives. so, we use this metric to evaluate systems like classifiers to know how precisely we found positives. if your classifier marked an entry True even if it is False in real, it increases FP, which in turn decreases Pr. So your system i... | Average precision vs precision | Precision is Pr = TP/(TP+FP) where is TP and FP are True positives and False positives. so, we use this metric to evaluate systems like classifiers to know how precisely we found positives. if your cl | Average precision vs precision
Precision is Pr = TP/(TP+FP) where is TP and FP are True positives and False positives. so, we use this metric to evaluate systems like classifiers to know how precisely we found positives. if your classifier marked an entry True even if it is False in real, it increases FP, which in turn... | Average precision vs precision
Precision is Pr = TP/(TP+FP) where is TP and FP are True positives and False positives. so, we use this metric to evaluate systems like classifiers to know how precisely we found positives. if your cl |
14,953 | Tensors in neural network literature: what's the simplest definition out there? | For the purposes of data analysis, you can effectively consider them as arrays, possibly multidimensional. Thus they include scalars, vectors, matrices, and all higher order arrays.
The precise mathematical definition is more complicated. Basically the idea is that tensors transform multilinear functions to linear fun... | Tensors in neural network literature: what's the simplest definition out there? | For the purposes of data analysis, you can effectively consider them as arrays, possibly multidimensional. Thus they include scalars, vectors, matrices, and all higher order arrays.
The precise mathe | Tensors in neural network literature: what's the simplest definition out there?
For the purposes of data analysis, you can effectively consider them as arrays, possibly multidimensional. Thus they include scalars, vectors, matrices, and all higher order arrays.
The precise mathematical definition is more complicated. ... | Tensors in neural network literature: what's the simplest definition out there?
For the purposes of data analysis, you can effectively consider them as arrays, possibly multidimensional. Thus they include scalars, vectors, matrices, and all higher order arrays.
The precise mathe |
14,954 | Tensors in neural network literature: what's the simplest definition out there? | Tensor = multi-dimensional array
In the machine learning literature, a tensor is simply a synonym for multi-dimensional array:
Tensors, also known as multidimensional arrays, are generalizations of matrices to higher orders and are useful data representation architectures.
Tensors in Statistics Annual Review of Stat... | Tensors in neural network literature: what's the simplest definition out there? | Tensor = multi-dimensional array
In the machine learning literature, a tensor is simply a synonym for multi-dimensional array:
Tensors, also known as multidimensional arrays, are generalizations of m | Tensors in neural network literature: what's the simplest definition out there?
Tensor = multi-dimensional array
In the machine learning literature, a tensor is simply a synonym for multi-dimensional array:
Tensors, also known as multidimensional arrays, are generalizations of matrices to higher orders and are useful ... | Tensors in neural network literature: what's the simplest definition out there?
Tensor = multi-dimensional array
In the machine learning literature, a tensor is simply a synonym for multi-dimensional array:
Tensors, also known as multidimensional arrays, are generalizations of m |
14,955 | What are the differences between autoencoders and t-SNE? | Both of them try to find a lower dimensionality embedding of your data. However, there are different minimization problems. More specifically, an autoencoder tries to minimize the reconstruction error, while t-SNE tries to find a lower dimensional space and at the same time it tries to preserve the neighborhood distanc... | What are the differences between autoencoders and t-SNE? | Both of them try to find a lower dimensionality embedding of your data. However, there are different minimization problems. More specifically, an autoencoder tries to minimize the reconstruction error | What are the differences between autoencoders and t-SNE?
Both of them try to find a lower dimensionality embedding of your data. However, there are different minimization problems. More specifically, an autoencoder tries to minimize the reconstruction error, while t-SNE tries to find a lower dimensional space and at th... | What are the differences between autoencoders and t-SNE?
Both of them try to find a lower dimensionality embedding of your data. However, there are different minimization problems. More specifically, an autoencoder tries to minimize the reconstruction error |
14,956 | What are the differences between autoencoders and t-SNE? | [Autoencoders] primarily
focus on maximizing the variance of the data in the latent space, as a
result of which autoencoders are less successful in retaining the
local structure of the data in the latent space than manifold
learners...
From "Learning a Parametric Embedding by Preserving Local Structure", Laure... | What are the differences between autoencoders and t-SNE? | [Autoencoders] primarily
focus on maximizing the variance of the data in the latent space, as a
result of which autoencoders are less successful in retaining the
local structure of the data in t | What are the differences between autoencoders and t-SNE?
[Autoencoders] primarily
focus on maximizing the variance of the data in the latent space, as a
result of which autoencoders are less successful in retaining the
local structure of the data in the latent space than manifold
learners...
From "Learning a P... | What are the differences between autoencoders and t-SNE?
[Autoencoders] primarily
focus on maximizing the variance of the data in the latent space, as a
result of which autoencoders are less successful in retaining the
local structure of the data in t |
14,957 | What are the differences between autoencoders and t-SNE? | Autoencoder and t-SNE can be used together for better visualization in high dimensional data, as described in [1]:
For 2D visualization specifically, t-SNE is probably the best
algorithm around, but it typically requires relatively low-dimensional
data. So a good strategy for visualizing similarity relationships ... | What are the differences between autoencoders and t-SNE? | Autoencoder and t-SNE can be used together for better visualization in high dimensional data, as described in [1]:
For 2D visualization specifically, t-SNE is probably the best
algorithm around, b | What are the differences between autoencoders and t-SNE?
Autoencoder and t-SNE can be used together for better visualization in high dimensional data, as described in [1]:
For 2D visualization specifically, t-SNE is probably the best
algorithm around, but it typically requires relatively low-dimensional
data. So ... | What are the differences between autoencoders and t-SNE?
Autoencoder and t-SNE can be used together for better visualization in high dimensional data, as described in [1]:
For 2D visualization specifically, t-SNE is probably the best
algorithm around, b |
14,958 | What are the differences between autoencoders and t-SNE? | Autoencoder is designed to preserve previous data in a 2-norm sense, which can be thought as preserve the kinetic energy of the data, if data is velocity.
While t-SNE, use KL divergence which is not symmetrical, it will lead to t-SNE focus more on local structure, while autoencoder tends to keep overall L2 error small... | What are the differences between autoencoders and t-SNE? | Autoencoder is designed to preserve previous data in a 2-norm sense, which can be thought as preserve the kinetic energy of the data, if data is velocity.
While t-SNE, use KL divergence which is not | What are the differences between autoencoders and t-SNE?
Autoencoder is designed to preserve previous data in a 2-norm sense, which can be thought as preserve the kinetic energy of the data, if data is velocity.
While t-SNE, use KL divergence which is not symmetrical, it will lead to t-SNE focus more on local structur... | What are the differences between autoencoders and t-SNE?
Autoencoder is designed to preserve previous data in a 2-norm sense, which can be thought as preserve the kinetic energy of the data, if data is velocity.
While t-SNE, use KL divergence which is not |
14,959 | Creating a single index from several principal components or factors retained from PCA/FA | This answer is deliberately non-mathematical and is oriented towards non-statistician psychologist (say) who inquires whether he may sum/average factor scores of different factors to obtain a "composite index" score for each respondent.
Summing or averaging some variables' scores assumes that the variables belong to th... | Creating a single index from several principal components or factors retained from PCA/FA | This answer is deliberately non-mathematical and is oriented towards non-statistician psychologist (say) who inquires whether he may sum/average factor scores of different factors to obtain a "composi | Creating a single index from several principal components or factors retained from PCA/FA
This answer is deliberately non-mathematical and is oriented towards non-statistician psychologist (say) who inquires whether he may sum/average factor scores of different factors to obtain a "composite index" score for each respo... | Creating a single index from several principal components or factors retained from PCA/FA
This answer is deliberately non-mathematical and is oriented towards non-statistician psychologist (say) who inquires whether he may sum/average factor scores of different factors to obtain a "composi |
14,960 | Creating a single index from several principal components or factors retained from PCA/FA | Creating composite index using PCA from time series links to http://www.cup.ualberta.ca/wp-content/uploads/2013/04/SEICUPWebsite_10April13.pdf.
In that article on page 19, the authors mention a way to create a Non-Standardised Index (NSI) by using the proportion of variation explained by each factor to the total varia... | Creating a single index from several principal components or factors retained from PCA/FA | Creating composite index using PCA from time series links to http://www.cup.ualberta.ca/wp-content/uploads/2013/04/SEICUPWebsite_10April13.pdf.
In that article on page 19, the authors mention a way t | Creating a single index from several principal components or factors retained from PCA/FA
Creating composite index using PCA from time series links to http://www.cup.ualberta.ca/wp-content/uploads/2013/04/SEICUPWebsite_10April13.pdf.
In that article on page 19, the authors mention a way to create a Non-Standardised In... | Creating a single index from several principal components or factors retained from PCA/FA
Creating composite index using PCA from time series links to http://www.cup.ualberta.ca/wp-content/uploads/2013/04/SEICUPWebsite_10April13.pdf.
In that article on page 19, the authors mention a way t |
14,961 | Under exactly what conditions is ridge regression able to provide an improvement over ordinary least squares regression? | The answer to both 1 and 2 is no, but care is needed in interpreting the existence theorem.
Variance of Ridge Estimator
Let $\hat{\beta^*}$ be the ridge estimate under penalty $k$, and let $\beta$ be the true parameter for the model $Y = X \beta + \epsilon$. Let $\lambda_1, \dotsc, \lambda_p$ be the eigenvalues of $X^... | Under exactly what conditions is ridge regression able to provide an improvement over ordinary least | The answer to both 1 and 2 is no, but care is needed in interpreting the existence theorem.
Variance of Ridge Estimator
Let $\hat{\beta^*}$ be the ridge estimate under penalty $k$, and let $\beta$ be | Under exactly what conditions is ridge regression able to provide an improvement over ordinary least squares regression?
The answer to both 1 and 2 is no, but care is needed in interpreting the existence theorem.
Variance of Ridge Estimator
Let $\hat{\beta^*}$ be the ridge estimate under penalty $k$, and let $\beta$ be... | Under exactly what conditions is ridge regression able to provide an improvement over ordinary least
The answer to both 1 and 2 is no, but care is needed in interpreting the existence theorem.
Variance of Ridge Estimator
Let $\hat{\beta^*}$ be the ridge estimate under penalty $k$, and let $\beta$ be |
14,962 | Methods in R or Python to perform feature selection in unsupervised learning [closed] | It's a year old but I still feel it is relevant, so I just wanted to share my python implementation of Principal Feature Analysis (PFA) as proposed in the paper that Charles linked to in his answer.
from sklearn.decomposition import PCA
from sklearn.cluster import KMeans
from collections import defaultdict
from sklearn... | Methods in R or Python to perform feature selection in unsupervised learning [closed] | It's a year old but I still feel it is relevant, so I just wanted to share my python implementation of Principal Feature Analysis (PFA) as proposed in the paper that Charles linked to in his answer.
f | Methods in R or Python to perform feature selection in unsupervised learning [closed]
It's a year old but I still feel it is relevant, so I just wanted to share my python implementation of Principal Feature Analysis (PFA) as proposed in the paper that Charles linked to in his answer.
from sklearn.decomposition import P... | Methods in R or Python to perform feature selection in unsupervised learning [closed]
It's a year old but I still feel it is relevant, so I just wanted to share my python implementation of Principal Feature Analysis (PFA) as proposed in the paper that Charles linked to in his answer.
f |
14,963 | Methods in R or Python to perform feature selection in unsupervised learning [closed] | The sparcl package in R performs sparse hierarchical and sparse K-means clustering. This may be useful. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2930825/ | Methods in R or Python to perform feature selection in unsupervised learning [closed] | The sparcl package in R performs sparse hierarchical and sparse K-means clustering. This may be useful. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2930825/ | Methods in R or Python to perform feature selection in unsupervised learning [closed]
The sparcl package in R performs sparse hierarchical and sparse K-means clustering. This may be useful. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2930825/ | Methods in R or Python to perform feature selection in unsupervised learning [closed]
The sparcl package in R performs sparse hierarchical and sparse K-means clustering. This may be useful. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2930825/ |
14,964 | Methods in R or Python to perform feature selection in unsupervised learning [closed] | Principal Feature Analysis looks to be a solution to unsupervised feature selection. It's described in this paper. | Methods in R or Python to perform feature selection in unsupervised learning [closed] | Principal Feature Analysis looks to be a solution to unsupervised feature selection. It's described in this paper. | Methods in R or Python to perform feature selection in unsupervised learning [closed]
Principal Feature Analysis looks to be a solution to unsupervised feature selection. It's described in this paper. | Methods in R or Python to perform feature selection in unsupervised learning [closed]
Principal Feature Analysis looks to be a solution to unsupervised feature selection. It's described in this paper. |
14,965 | Methods in R or Python to perform feature selection in unsupervised learning [closed] | I've found a link wich could be useful, those are matlab implementations, they may work out for you
http://www.cad.zju.edu.cn/home/dengcai/Data/MCFS.html
it's a multicluster feature selection method, you can find strong foundation about it in recent papers
Let me know if it works for you | Methods in R or Python to perform feature selection in unsupervised learning [closed] | I've found a link wich could be useful, those are matlab implementations, they may work out for you
http://www.cad.zju.edu.cn/home/dengcai/Data/MCFS.html
it's a multicluster feature selection method, | Methods in R or Python to perform feature selection in unsupervised learning [closed]
I've found a link wich could be useful, those are matlab implementations, they may work out for you
http://www.cad.zju.edu.cn/home/dengcai/Data/MCFS.html
it's a multicluster feature selection method, you can find strong foundation abo... | Methods in R or Python to perform feature selection in unsupervised learning [closed]
I've found a link wich could be useful, those are matlab implementations, they may work out for you
http://www.cad.zju.edu.cn/home/dengcai/Data/MCFS.html
it's a multicluster feature selection method, |
14,966 | Methods in R or Python to perform feature selection in unsupervised learning [closed] | There are many options available in R. A nice place to look is the caret package which provides a nice interface to many other packages and options. You can take a look at the website here. There are many options out there, but I will illustrate one.
Here is an example of using a simple filter using the built into R... | Methods in R or Python to perform feature selection in unsupervised learning [closed] | There are many options available in R. A nice place to look is the caret package which provides a nice interface to many other packages and options. You can take a look at the website here. There a | Methods in R or Python to perform feature selection in unsupervised learning [closed]
There are many options available in R. A nice place to look is the caret package which provides a nice interface to many other packages and options. You can take a look at the website here. There are many options out there, but I w... | Methods in R or Python to perform feature selection in unsupervised learning [closed]
There are many options available in R. A nice place to look is the caret package which provides a nice interface to many other packages and options. You can take a look at the website here. There a |
14,967 | Methods in R or Python to perform feature selection in unsupervised learning [closed] | The nsprcomp R package provides methods for sparse Principal Component Analysis, which could suit your needs.
For example, if you believe your features are generally correlated linearly, and want to select the top five, you could run sparse PCA with a max of five features, and limit to the first principal component:
m... | Methods in R or Python to perform feature selection in unsupervised learning [closed] | The nsprcomp R package provides methods for sparse Principal Component Analysis, which could suit your needs.
For example, if you believe your features are generally correlated linearly, and want to | Methods in R or Python to perform feature selection in unsupervised learning [closed]
The nsprcomp R package provides methods for sparse Principal Component Analysis, which could suit your needs.
For example, if you believe your features are generally correlated linearly, and want to select the top five, you could run... | Methods in R or Python to perform feature selection in unsupervised learning [closed]
The nsprcomp R package provides methods for sparse Principal Component Analysis, which could suit your needs.
For example, if you believe your features are generally correlated linearly, and want to |
14,968 | Kernel Bandwidth: Scott's vs. Silverman's rules | The comments in the code seem to end up defining the two essentially identically (aside a relatively small difference in the constant).
Both are of the form $cAn^{-1/5}$, both with what looks like the same $A$ (estimate of scale), and $c$'s very close to 1 (close relative to the typical uncertainty in the estimate of t... | Kernel Bandwidth: Scott's vs. Silverman's rules | The comments in the code seem to end up defining the two essentially identically (aside a relatively small difference in the constant).
Both are of the form $cAn^{-1/5}$, both with what looks like the | Kernel Bandwidth: Scott's vs. Silverman's rules
The comments in the code seem to end up defining the two essentially identically (aside a relatively small difference in the constant).
Both are of the form $cAn^{-1/5}$, both with what looks like the same $A$ (estimate of scale), and $c$'s very close to 1 (close relative... | Kernel Bandwidth: Scott's vs. Silverman's rules
The comments in the code seem to end up defining the two essentially identically (aside a relatively small difference in the constant).
Both are of the form $cAn^{-1/5}$, both with what looks like the |
14,969 | Set seed before each code block or once per project? | It depends how you will run the code or if there is any code that is somewhat stochastic in that it draws random numbers in a random way. (An example of this is the permutation tests in our vegan package where we only continue permuting until we have amassed enough data to know whether a result is different from the st... | Set seed before each code block or once per project? | It depends how you will run the code or if there is any code that is somewhat stochastic in that it draws random numbers in a random way. (An example of this is the permutation tests in our vegan pack | Set seed before each code block or once per project?
It depends how you will run the code or if there is any code that is somewhat stochastic in that it draws random numbers in a random way. (An example of this is the permutation tests in our vegan package where we only continue permuting until we have amassed enough d... | Set seed before each code block or once per project?
It depends how you will run the code or if there is any code that is somewhat stochastic in that it draws random numbers in a random way. (An example of this is the permutation tests in our vegan pack |
14,970 | Under which conditions do Bayesian and frequentist point estimators coincide? | The question is interesting but somewhat hopeless unless the notion of frequentist estimator is made precise. It is definitely not the one set in the question
$$\hat x(\,. ) = \text{argmin} \; \mathbb{E} \left( L(x,\hat x(Y)) \; | \; x \right)$$
since the answer to the minimisation is $\hat{x}(y)=x$ for all $y$'s as po... | Under which conditions do Bayesian and frequentist point estimators coincide? | The question is interesting but somewhat hopeless unless the notion of frequentist estimator is made precise. It is definitely not the one set in the question
$$\hat x(\,. ) = \text{argmin} \; \mathbb | Under which conditions do Bayesian and frequentist point estimators coincide?
The question is interesting but somewhat hopeless unless the notion of frequentist estimator is made precise. It is definitely not the one set in the question
$$\hat x(\,. ) = \text{argmin} \; \mathbb{E} \left( L(x,\hat x(Y)) \; | \; x \right... | Under which conditions do Bayesian and frequentist point estimators coincide?
The question is interesting but somewhat hopeless unless the notion of frequentist estimator is made precise. It is definitely not the one set in the question
$$\hat x(\,. ) = \text{argmin} \; \mathbb |
14,971 | Under which conditions do Bayesian and frequentist point estimators coincide? | In general, frequentist and Bayesian estimators do not coincide, unless you use a degenerate flat prior. The main reason is this: Frequentist estimators often strive to be unbiased. For example, frequentists often try to find the minimum variance unbiased estimator (http://en.wikipedia.org/wiki/Minimum-variance_unbiase... | Under which conditions do Bayesian and frequentist point estimators coincide? | In general, frequentist and Bayesian estimators do not coincide, unless you use a degenerate flat prior. The main reason is this: Frequentist estimators often strive to be unbiased. For example, frequ | Under which conditions do Bayesian and frequentist point estimators coincide?
In general, frequentist and Bayesian estimators do not coincide, unless you use a degenerate flat prior. The main reason is this: Frequentist estimators often strive to be unbiased. For example, frequentists often try to find the minimum vari... | Under which conditions do Bayesian and frequentist point estimators coincide?
In general, frequentist and Bayesian estimators do not coincide, unless you use a degenerate flat prior. The main reason is this: Frequentist estimators often strive to be unbiased. For example, frequ |
14,972 | Under which conditions do Bayesian and frequentist point estimators coincide? | This is not a full answer, but while these two $\text{argmin}$'s look very similar, they are fundamentally different in a way: the Bayesian one minimizes the expression with respect to a single value (that is, the value of $\hat x(y)$, depending on $y$).
But the Frequentist one has to minimize the loss function with r... | Under which conditions do Bayesian and frequentist point estimators coincide? | This is not a full answer, but while these two $\text{argmin}$'s look very similar, they are fundamentally different in a way: the Bayesian one minimizes the expression with respect to a single value | Under which conditions do Bayesian and frequentist point estimators coincide?
This is not a full answer, but while these two $\text{argmin}$'s look very similar, they are fundamentally different in a way: the Bayesian one minimizes the expression with respect to a single value (that is, the value of $\hat x(y)$, depend... | Under which conditions do Bayesian and frequentist point estimators coincide?
This is not a full answer, but while these two $\text{argmin}$'s look very similar, they are fundamentally different in a way: the Bayesian one minimizes the expression with respect to a single value |
14,973 | Under which conditions do Bayesian and frequentist point estimators coincide? | There may exist no answer to this question.
An alternative could be to ask for methods to determine the two estimates efficiently for any problem at hand. The Bayesian methods are pretty close to this ideal. However, even though minimax methods could be used to determine the frequentist point estimate, in general, the... | Under which conditions do Bayesian and frequentist point estimators coincide? | There may exist no answer to this question.
An alternative could be to ask for methods to determine the two estimates efficiently for any problem at hand. The Bayesian methods are pretty close to thi | Under which conditions do Bayesian and frequentist point estimators coincide?
There may exist no answer to this question.
An alternative could be to ask for methods to determine the two estimates efficiently for any problem at hand. The Bayesian methods are pretty close to this ideal. However, even though minimax meth... | Under which conditions do Bayesian and frequentist point estimators coincide?
There may exist no answer to this question.
An alternative could be to ask for methods to determine the two estimates efficiently for any problem at hand. The Bayesian methods are pretty close to thi |
14,974 | Pearson's residuals | The standard statistical model underlying analysis of contingency tables is to assume that (unconditional on the total count) the cell counts are independent Poisson random variables. So if you have an $n \times m$ contingency table, the statistical model used as a basis for analysis takes each cell count to have unco... | Pearson's residuals | The standard statistical model underlying analysis of contingency tables is to assume that (unconditional on the total count) the cell counts are independent Poisson random variables. So if you have | Pearson's residuals
The standard statistical model underlying analysis of contingency tables is to assume that (unconditional on the total count) the cell counts are independent Poisson random variables. So if you have an $n \times m$ contingency table, the statistical model used as a basis for analysis takes each cel... | Pearson's residuals
The standard statistical model underlying analysis of contingency tables is to assume that (unconditional on the total count) the cell counts are independent Poisson random variables. So if you have |
14,975 | Pearson's residuals | In the context of goodness of fit, you may refer to this http://www.stat.yale.edu/Courses/1997-98/101/chigf.htm.
If you want to know how the denominator got there, you will have to view the chi-squared here as a normal approximation to the binomial, for starters, which then can be extended to multinomials. | Pearson's residuals | In the context of goodness of fit, you may refer to this http://www.stat.yale.edu/Courses/1997-98/101/chigf.htm.
If you want to know how the denominator got there, you will have to view the chi-square | Pearson's residuals
In the context of goodness of fit, you may refer to this http://www.stat.yale.edu/Courses/1997-98/101/chigf.htm.
If you want to know how the denominator got there, you will have to view the chi-squared here as a normal approximation to the binomial, for starters, which then can be extended to multin... | Pearson's residuals
In the context of goodness of fit, you may refer to this http://www.stat.yale.edu/Courses/1997-98/101/chigf.htm.
If you want to know how the denominator got there, you will have to view the chi-square |
14,976 | Finding the MLE for a univariate exponential Hawkes process | The Nelder-Mead simplex algorithm seems to work well.. It is implemented in Java by the Apache Commons Math library at https://commons.apache.org/math/ . I've also written a paper about the Hawkes processes at Point Process Models for Multivariate High-Frequency Irregularly Spaced Data .
felix, using exp/log transforms... | Finding the MLE for a univariate exponential Hawkes process | The Nelder-Mead simplex algorithm seems to work well.. It is implemented in Java by the Apache Commons Math library at https://commons.apache.org/math/ . I've also written a paper about the Hawkes pro | Finding the MLE for a univariate exponential Hawkes process
The Nelder-Mead simplex algorithm seems to work well.. It is implemented in Java by the Apache Commons Math library at https://commons.apache.org/math/ . I've also written a paper about the Hawkes processes at Point Process Models for Multivariate High-Frequen... | Finding the MLE for a univariate exponential Hawkes process
The Nelder-Mead simplex algorithm seems to work well.. It is implemented in Java by the Apache Commons Math library at https://commons.apache.org/math/ . I've also written a paper about the Hawkes pro |
14,977 | Finding the MLE for a univariate exponential Hawkes process | I solved this problem using the nlopt library. I found a number of the methods converged quite quickly. | Finding the MLE for a univariate exponential Hawkes process | I solved this problem using the nlopt library. I found a number of the methods converged quite quickly. | Finding the MLE for a univariate exponential Hawkes process
I solved this problem using the nlopt library. I found a number of the methods converged quite quickly. | Finding the MLE for a univariate exponential Hawkes process
I solved this problem using the nlopt library. I found a number of the methods converged quite quickly. |
14,978 | Finding the MLE for a univariate exponential Hawkes process | You could also do a simple maximization. In R:
neg.loglik <- function(params, data, opt=TRUE) {
mu <- params[1]
alpha <- params[2]
beta <- params[3]
t <- sort(data)
r <- rep(0,length(t))
for(i in 2:length(t)) {
r[i] <- exp(-beta*(t[i]-t[i-1]))*(1+r[i-1])
}
loglik <- -tail(t,1)*mu
loglik <- loglik+... | Finding the MLE for a univariate exponential Hawkes process | You could also do a simple maximization. In R:
neg.loglik <- function(params, data, opt=TRUE) {
mu <- params[1]
alpha <- params[2]
beta <- params[3]
t <- sort(data)
r <- rep(0,length(t))
f | Finding the MLE for a univariate exponential Hawkes process
You could also do a simple maximization. In R:
neg.loglik <- function(params, data, opt=TRUE) {
mu <- params[1]
alpha <- params[2]
beta <- params[3]
t <- sort(data)
r <- rep(0,length(t))
for(i in 2:length(t)) {
r[i] <- exp(-beta*(t[i]-t[i-1]))*... | Finding the MLE for a univariate exponential Hawkes process
You could also do a simple maximization. In R:
neg.loglik <- function(params, data, opt=TRUE) {
mu <- params[1]
alpha <- params[2]
beta <- params[3]
t <- sort(data)
r <- rep(0,length(t))
f |
14,979 | Finding the MLE for a univariate exponential Hawkes process | Here is my solution to "What is the simplest practical method to implement?" using python, specifically numpy, scipy and tick.
One modification is that I set the exponential kernel such that alpha x beta x exp (-beta (t - ti)), to coincide with how tick defines exponential kernels:
https://x-datainitiative.github.io/t... | Finding the MLE for a univariate exponential Hawkes process | Here is my solution to "What is the simplest practical method to implement?" using python, specifically numpy, scipy and tick.
One modification is that I set the exponential kernel such that alpha x b | Finding the MLE for a univariate exponential Hawkes process
Here is my solution to "What is the simplest practical method to implement?" using python, specifically numpy, scipy and tick.
One modification is that I set the exponential kernel such that alpha x beta x exp (-beta (t - ti)), to coincide with how tick defin... | Finding the MLE for a univariate exponential Hawkes process
Here is my solution to "What is the simplest practical method to implement?" using python, specifically numpy, scipy and tick.
One modification is that I set the exponential kernel such that alpha x b |
14,980 | What does it mean to make the sample size a random variable? | I'm not meaning to use models close to the data collecting process but rather doing continuous Bayesian monitoring of posterior probabilities, which require no penalty for multiplicity. Instead of computing an arbitrary target sample size I'd prefer to compute a maximum possible sample size (for budget approval) and o... | What does it mean to make the sample size a random variable? | I'm not meaning to use models close to the data collecting process but rather doing continuous Bayesian monitoring of posterior probabilities, which require no penalty for multiplicity. Instead of co | What does it mean to make the sample size a random variable?
I'm not meaning to use models close to the data collecting process but rather doing continuous Bayesian monitoring of posterior probabilities, which require no penalty for multiplicity. Instead of computing an arbitrary target sample size I'd prefer to compu... | What does it mean to make the sample size a random variable?
I'm not meaning to use models close to the data collecting process but rather doing continuous Bayesian monitoring of posterior probabilities, which require no penalty for multiplicity. Instead of co |
14,981 | How to calculate prediction intervals for LOESS? | I don't know how to do prediction bands with the original loess function but there is a function loess.sd in the msir package that does just that! Almost verbatim from the msir documentation:
library(msir)
data(cars)
# Calculates and plots a 1.96 * SD prediction band, that is,
# a 95% prediction band
l <- loess.sd(cars... | How to calculate prediction intervals for LOESS? | I don't know how to do prediction bands with the original loess function but there is a function loess.sd in the msir package that does just that! Almost verbatim from the msir documentation:
library( | How to calculate prediction intervals for LOESS?
I don't know how to do prediction bands with the original loess function but there is a function loess.sd in the msir package that does just that! Almost verbatim from the msir documentation:
library(msir)
data(cars)
# Calculates and plots a 1.96 * SD prediction band, th... | How to calculate prediction intervals for LOESS?
I don't know how to do prediction bands with the original loess function but there is a function loess.sd in the msir package that does just that! Almost verbatim from the msir documentation:
library( |
14,982 | Why is "relaxed lasso" different from standard lasso? | From definition 1 of Meinshausen(2007), there are two parameters controlling the solution of the relaxed Lasso.
The first one, $\lambda$, controls the variable selection, whereas the second, $\phi$, controls the shrinkage level. When $\phi= 1$ both Lasso and relaxed-Lasso are the same (as you said!), but for $\phi<1$ y... | Why is "relaxed lasso" different from standard lasso? | From definition 1 of Meinshausen(2007), there are two parameters controlling the solution of the relaxed Lasso.
The first one, $\lambda$, controls the variable selection, whereas the second, $\phi$, c | Why is "relaxed lasso" different from standard lasso?
From definition 1 of Meinshausen(2007), there are two parameters controlling the solution of the relaxed Lasso.
The first one, $\lambda$, controls the variable selection, whereas the second, $\phi$, controls the shrinkage level. When $\phi= 1$ both Lasso and relaxed... | Why is "relaxed lasso" different from standard lasso?
From definition 1 of Meinshausen(2007), there are two parameters controlling the solution of the relaxed Lasso.
The first one, $\lambda$, controls the variable selection, whereas the second, $\phi$, c |
14,983 | Good data example needed with covariate affected by treatments | You may want to check out the mediation R package. It does include experimental data like jobs and framing where the treatment variable affects both a response variable and covariates (i.e., mediators of the treatment effect), along with covariates not affected by the treatment.
I looked into the mediation literature b... | Good data example needed with covariate affected by treatments | You may want to check out the mediation R package. It does include experimental data like jobs and framing where the treatment variable affects both a response variable and covariates (i.e., mediators | Good data example needed with covariate affected by treatments
You may want to check out the mediation R package. It does include experimental data like jobs and framing where the treatment variable affects both a response variable and covariates (i.e., mediators of the treatment effect), along with covariates not affe... | Good data example needed with covariate affected by treatments
You may want to check out the mediation R package. It does include experimental data like jobs and framing where the treatment variable affects both a response variable and covariates (i.e., mediators |
14,984 | Good data example needed with covariate affected by treatments | I thought I'd show how an analysis comes out with one of the datasets in the mediation package. In framing, an experiment is done where subjects have the opportunity to send a message to Congress regarding immigration. However, some subjects (treat=1) were first shown a news story that portrays Latinos in a negative wa... | Good data example needed with covariate affected by treatments | I thought I'd show how an analysis comes out with one of the datasets in the mediation package. In framing, an experiment is done where subjects have the opportunity to send a message to Congress rega | Good data example needed with covariate affected by treatments
I thought I'd show how an analysis comes out with one of the datasets in the mediation package. In framing, an experiment is done where subjects have the opportunity to send a message to Congress regarding immigration. However, some subjects (treat=1) were ... | Good data example needed with covariate affected by treatments
I thought I'd show how an analysis comes out with one of the datasets in the mediation package. In framing, an experiment is done where subjects have the opportunity to send a message to Congress rega |
14,985 | Good data example needed with covariate affected by treatments | Look up gene-environment interaction GWAS studies. The statistical analysis they perform in essence is what you have described. The question is does your environment matter to a phenotype (observable feature)? One school of thought generally ignores all environmental information and says your genetic makeup describes y... | Good data example needed with covariate affected by treatments | Look up gene-environment interaction GWAS studies. The statistical analysis they perform in essence is what you have described. The question is does your environment matter to a phenotype (observable | Good data example needed with covariate affected by treatments
Look up gene-environment interaction GWAS studies. The statistical analysis they perform in essence is what you have described. The question is does your environment matter to a phenotype (observable feature)? One school of thought generally ignores all env... | Good data example needed with covariate affected by treatments
Look up gene-environment interaction GWAS studies. The statistical analysis they perform in essence is what you have described. The question is does your environment matter to a phenotype (observable |
14,986 | Good data example needed with covariate affected by treatments | I'd recommend reading Freakonomics, and finding the papers their work is based on, and seeing if you can grab that data. They have some really interesting work on really interesting datasets, and in some cases they figure out very clever ways to test hypotheses despite limitations in the data. | Good data example needed with covariate affected by treatments | I'd recommend reading Freakonomics, and finding the papers their work is based on, and seeing if you can grab that data. They have some really interesting work on really interesting datasets, and in s | Good data example needed with covariate affected by treatments
I'd recommend reading Freakonomics, and finding the papers their work is based on, and seeing if you can grab that data. They have some really interesting work on really interesting datasets, and in some cases they figure out very clever ways to test hypoth... | Good data example needed with covariate affected by treatments
I'd recommend reading Freakonomics, and finding the papers their work is based on, and seeing if you can grab that data. They have some really interesting work on really interesting datasets, and in s |
14,987 | max_delta_step in xgboost | eta introduces a 'relative' regularization (multiplying the weight by a constant factor) but in extreme cases where hessian is nearly zero (like when we have very unbalanced classes) this isn't enough because the weights (in which computation the hessian is in denominator) becomes to nearly infinite.
So what max_delta_... | max_delta_step in xgboost | eta introduces a 'relative' regularization (multiplying the weight by a constant factor) but in extreme cases where hessian is nearly zero (like when we have very unbalanced classes) this isn't enough | max_delta_step in xgboost
eta introduces a 'relative' regularization (multiplying the weight by a constant factor) but in extreme cases where hessian is nearly zero (like when we have very unbalanced classes) this isn't enough because the weights (in which computation the hessian is in denominator) becomes to nearly in... | max_delta_step in xgboost
eta introduces a 'relative' regularization (multiplying the weight by a constant factor) but in extreme cases where hessian is nearly zero (like when we have very unbalanced classes) this isn't enough |
14,988 | Is gradient boosting appropriate for data with low event rates like 1%? | (To give short answer to this:)
It is fine to use a gradient boosting machine algorithm when dealing with an imbalanced dataset. When dealing with a strongly imbalanced dataset it much more relevant to question the suitability of the metric used. We should potentially avoid metrics, like Accuracy or Recall, that are ba... | Is gradient boosting appropriate for data with low event rates like 1%? | (To give short answer to this:)
It is fine to use a gradient boosting machine algorithm when dealing with an imbalanced dataset. When dealing with a strongly imbalanced dataset it much more relevant t | Is gradient boosting appropriate for data with low event rates like 1%?
(To give short answer to this:)
It is fine to use a gradient boosting machine algorithm when dealing with an imbalanced dataset. When dealing with a strongly imbalanced dataset it much more relevant to question the suitability of the metric used. W... | Is gradient boosting appropriate for data with low event rates like 1%?
(To give short answer to this:)
It is fine to use a gradient boosting machine algorithm when dealing with an imbalanced dataset. When dealing with a strongly imbalanced dataset it much more relevant t |
14,989 | ARIMA estimation by hand | There is the concept of exact likelihood. It requires the knowledge of initial parameters such as the fist value of the MA error (one of your questions). Implementations usually differ regarding how they treat the initial values. What I usually do is (which is not mentioned in many books) is to also maximize ML w.r.t. ... | ARIMA estimation by hand | There is the concept of exact likelihood. It requires the knowledge of initial parameters such as the fist value of the MA error (one of your questions). Implementations usually differ regarding how t | ARIMA estimation by hand
There is the concept of exact likelihood. It requires the knowledge of initial parameters such as the fist value of the MA error (one of your questions). Implementations usually differ regarding how they treat the initial values. What I usually do is (which is not mentioned in many books) is to... | ARIMA estimation by hand
There is the concept of exact likelihood. It requires the knowledge of initial parameters such as the fist value of the MA error (one of your questions). Implementations usually differ regarding how t |
14,990 | ARIMA estimation by hand | Did you read the the help page of arima function? Here is the relevant excerpt:
The exact likelihood is computed via a state-space representation of
the ARIMA process, and the innovations and their variance found by a
Kalman filter. The initialization of the differenced ARMA process uses
stationarity and is base... | ARIMA estimation by hand | Did you read the the help page of arima function? Here is the relevant excerpt:
The exact likelihood is computed via a state-space representation of
the ARIMA process, and the innovations and their | ARIMA estimation by hand
Did you read the the help page of arima function? Here is the relevant excerpt:
The exact likelihood is computed via a state-space representation of
the ARIMA process, and the innovations and their variance found by a
Kalman filter. The initialization of the differenced ARMA process uses
... | ARIMA estimation by hand
Did you read the the help page of arima function? Here is the relevant excerpt:
The exact likelihood is computed via a state-space representation of
the ARIMA process, and the innovations and their |
14,991 | Computation of new standard deviation using old standard deviation after change in dataset | A section in the Wikipedia article on "Algorithms for calculating variance" shows how to compute the variance if elements are added to your observations. (Recall that the standard deviation is the square root of the variance.) Assume that you append $x_{n+1}$ to your array, then
$$\sigma_{new}^2 = \sigma_{old}^2 + (x_{... | Computation of new standard deviation using old standard deviation after change in dataset | A section in the Wikipedia article on "Algorithms for calculating variance" shows how to compute the variance if elements are added to your observations. (Recall that the standard deviation is the squ | Computation of new standard deviation using old standard deviation after change in dataset
A section in the Wikipedia article on "Algorithms for calculating variance" shows how to compute the variance if elements are added to your observations. (Recall that the standard deviation is the square root of the variance.) As... | Computation of new standard deviation using old standard deviation after change in dataset
A section in the Wikipedia article on "Algorithms for calculating variance" shows how to compute the variance if elements are added to your observations. (Recall that the standard deviation is the squ |
14,992 | Computation of new standard deviation using old standard deviation after change in dataset | Based on what i think i'm reading on the linked Wikipedia article you can maintain a "running" standard deviation:
real sum = 0;
int count = 0;
real S = 0;
real variance = 0;
real GetRunningStandardDeviation(ref sum, ref count, ref S, x)
{
real oldMean;
if (count >= 1)
{
real oldMean = sum / count;
... | Computation of new standard deviation using old standard deviation after change in dataset | Based on what i think i'm reading on the linked Wikipedia article you can maintain a "running" standard deviation:
real sum = 0;
int count = 0;
real S = 0;
real variance = 0;
real GetRunningStandardD | Computation of new standard deviation using old standard deviation after change in dataset
Based on what i think i'm reading on the linked Wikipedia article you can maintain a "running" standard deviation:
real sum = 0;
int count = 0;
real S = 0;
real variance = 0;
real GetRunningStandardDeviation(ref sum, ref count, ... | Computation of new standard deviation using old standard deviation after change in dataset
Based on what i think i'm reading on the linked Wikipedia article you can maintain a "running" standard deviation:
real sum = 0;
int count = 0;
real S = 0;
real variance = 0;
real GetRunningStandardD |
14,993 | Computation of new standard deviation using old standard deviation after change in dataset | Given original $\bar x$, $s$, and $n$, as well as the change of a given element $x_n$ to $x_n'$, I believe your new standard deviation $s'$ will be the square root of
$$s^2 + \frac{1}{n-1}\left(2n\Delta \bar x(x_n-\bar x) +n(n-1)(\Delta \bar x)^2\right),$$
where $\Delta \bar x = \bar x' - \bar x$, with $\bar x'$ denoti... | Computation of new standard deviation using old standard deviation after change in dataset | Given original $\bar x$, $s$, and $n$, as well as the change of a given element $x_n$ to $x_n'$, I believe your new standard deviation $s'$ will be the square root of
$$s^2 + \frac{1}{n-1}\left(2n\Del | Computation of new standard deviation using old standard deviation after change in dataset
Given original $\bar x$, $s$, and $n$, as well as the change of a given element $x_n$ to $x_n'$, I believe your new standard deviation $s'$ will be the square root of
$$s^2 + \frac{1}{n-1}\left(2n\Delta \bar x(x_n-\bar x) +n(n-1)... | Computation of new standard deviation using old standard deviation after change in dataset
Given original $\bar x$, $s$, and $n$, as well as the change of a given element $x_n$ to $x_n'$, I believe your new standard deviation $s'$ will be the square root of
$$s^2 + \frac{1}{n-1}\left(2n\Del |
14,994 | Computation of new standard deviation using old standard deviation after change in dataset | If you make the assumption that the preliminary data that you have represents all of the values within the population with the relative frequencies, then increasing the sample size as a multiple of $n$ will be like copying the data set and pasting it below and then recalculating the mean and standard deviation.
The m... | Computation of new standard deviation using old standard deviation after change in dataset | If you make the assumption that the preliminary data that you have represents all of the values within the population with the relative frequencies, then increasing the sample size as a multiple of $n | Computation of new standard deviation using old standard deviation after change in dataset
If you make the assumption that the preliminary data that you have represents all of the values within the population with the relative frequencies, then increasing the sample size as a multiple of $n$ will be like copying the da... | Computation of new standard deviation using old standard deviation after change in dataset
If you make the assumption that the preliminary data that you have represents all of the values within the population with the relative frequencies, then increasing the sample size as a multiple of $n |
14,995 | RMSProp and Adam vs SGD | After researching a few articles online and Keras documentation it is suggested that the RMSProp optimizer is recommended for recurrent neural networks.https://github.com/keras-team/keras/blob/master/keras/optimizers.py#L209
Stochastic Gradient Descent seems to take advantage of its learning rate and momentum between e... | RMSProp and Adam vs SGD | After researching a few articles online and Keras documentation it is suggested that the RMSProp optimizer is recommended for recurrent neural networks.https://github.com/keras-team/keras/blob/master/ | RMSProp and Adam vs SGD
After researching a few articles online and Keras documentation it is suggested that the RMSProp optimizer is recommended for recurrent neural networks.https://github.com/keras-team/keras/blob/master/keras/optimizers.py#L209
Stochastic Gradient Descent seems to take advantage of its learning rat... | RMSProp and Adam vs SGD
After researching a few articles online and Keras documentation it is suggested that the RMSProp optimizer is recommended for recurrent neural networks.https://github.com/keras-team/keras/blob/master/ |
14,996 | How to calculate average length of adherence to vegetarianism when we only have survey data about current vegetarians? | Let $f_X(x)$ denote the pdf of adherence length $X$ of vegetarianism in the population. Our objective is to estimate $EX=\int_0^\infty x f_X(x)\;dx$.
Assuming that the probability of being included in the survey (the event $S$) is proportional to $X$, the pdf of adherence length $X$ among those included in the survey ... | How to calculate average length of adherence to vegetarianism when we only have survey data about cu | Let $f_X(x)$ denote the pdf of adherence length $X$ of vegetarianism in the population. Our objective is to estimate $EX=\int_0^\infty x f_X(x)\;dx$.
Assuming that the probability of being included i | How to calculate average length of adherence to vegetarianism when we only have survey data about current vegetarians?
Let $f_X(x)$ denote the pdf of adherence length $X$ of vegetarianism in the population. Our objective is to estimate $EX=\int_0^\infty x f_X(x)\;dx$.
Assuming that the probability of being included in... | How to calculate average length of adherence to vegetarianism when we only have survey data about cu
Let $f_X(x)$ denote the pdf of adherence length $X$ of vegetarianism in the population. Our objective is to estimate $EX=\int_0^\infty x f_X(x)\;dx$.
Assuming that the probability of being included i |
14,997 | How to calculate average length of adherence to vegetarianism when we only have survey data about current vegetarians? | (I've dithered over adding this, as it appears @JarleTufto has already given a nice mathematical approach; However I'm not clever enough to understand his answer, and now I'm curious if it is exactly the same approach, or if the approach I describe below ever has its uses.)
What I would do is guess an average length, a... | How to calculate average length of adherence to vegetarianism when we only have survey data about cu | (I've dithered over adding this, as it appears @JarleTufto has already given a nice mathematical approach; However I'm not clever enough to understand his answer, and now I'm curious if it is exactly | How to calculate average length of adherence to vegetarianism when we only have survey data about current vegetarians?
(I've dithered over adding this, as it appears @JarleTufto has already given a nice mathematical approach; However I'm not clever enough to understand his answer, and now I'm curious if it is exactly t... | How to calculate average length of adherence to vegetarianism when we only have survey data about cu
(I've dithered over adding this, as it appears @JarleTufto has already given a nice mathematical approach; However I'm not clever enough to understand his answer, and now I'm curious if it is exactly |
14,998 | How will random effects with only 1 observation affect a generalized linear mixed model? | In general, you have an issue with identifiability. Linear models with a random effect assigned to a parameter with only one measurement can't distinguish between the random effect and the residual error.
A typical linear mixed effect equation will look like:
$E = \beta + \eta_i + \epsilon_j$
Where $\beta$ is the fixe... | How will random effects with only 1 observation affect a generalized linear mixed model? | In general, you have an issue with identifiability. Linear models with a random effect assigned to a parameter with only one measurement can't distinguish between the random effect and the residual e | How will random effects with only 1 observation affect a generalized linear mixed model?
In general, you have an issue with identifiability. Linear models with a random effect assigned to a parameter with only one measurement can't distinguish between the random effect and the residual error.
A typical linear mixed ef... | How will random effects with only 1 observation affect a generalized linear mixed model?
In general, you have an issue with identifiability. Linear models with a random effect assigned to a parameter with only one measurement can't distinguish between the random effect and the residual e |
14,999 | How will random effects with only 1 observation affect a generalized linear mixed model? | This example used poisson distribution, which defaults to link log, right?
I'd expect the random effect, even if ALL groups had one observation, to
estimate the variance in the log, whereas the residual error would then
measure the error in the prediction including the random effect.
Example, 10 observations, first wit... | How will random effects with only 1 observation affect a generalized linear mixed model? | This example used poisson distribution, which defaults to link log, right?
I'd expect the random effect, even if ALL groups had one observation, to
estimate the variance in the log, whereas the residu | How will random effects with only 1 observation affect a generalized linear mixed model?
This example used poisson distribution, which defaults to link log, right?
I'd expect the random effect, even if ALL groups had one observation, to
estimate the variance in the log, whereas the residual error would then
measure the... | How will random effects with only 1 observation affect a generalized linear mixed model?
This example used poisson distribution, which defaults to link log, right?
I'd expect the random effect, even if ALL groups had one observation, to
estimate the variance in the log, whereas the residu |
15,000 | Modern Use Cases of Restricted Boltzmann Machines (RBM's)? | This is kind of an old question, but since it asks essentially asks for 'best practices', rather than what is actually technically possible (ie, doesnt need too much research focus), current best practices is something like:
RBMs are not normally used currently
linear models (linear regression, logistic regression) ar... | Modern Use Cases of Restricted Boltzmann Machines (RBM's)? | This is kind of an old question, but since it asks essentially asks for 'best practices', rather than what is actually technically possible (ie, doesnt need too much research focus), current best prac | Modern Use Cases of Restricted Boltzmann Machines (RBM's)?
This is kind of an old question, but since it asks essentially asks for 'best practices', rather than what is actually technically possible (ie, doesnt need too much research focus), current best practices is something like:
RBMs are not normally used currentl... | Modern Use Cases of Restricted Boltzmann Machines (RBM's)?
This is kind of an old question, but since it asks essentially asks for 'best practices', rather than what is actually technically possible (ie, doesnt need too much research focus), current best prac |
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