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 |
|---|---|---|---|---|---|---|
53,601 | Explanation for Additive Property of Variance? | The first thing to notice is that Var(A+B) equals VarA + Var B only when Cov(A,B)=0.
To gain some intuition behind the relationship between sd(A+B) and sd(A)+sd(B), notice that in order to complete the square in this expression
Cov(A,B) would have to equal sd(A)*sd(B). The next question is whether that ever happens? ... | Explanation for Additive Property of Variance? | The first thing to notice is that Var(A+B) equals VarA + Var B only when Cov(A,B)=0.
To gain some intuition behind the relationship between sd(A+B) and sd(A)+sd(B), notice that in order to complete th | Explanation for Additive Property of Variance?
The first thing to notice is that Var(A+B) equals VarA + Var B only when Cov(A,B)=0.
To gain some intuition behind the relationship between sd(A+B) and sd(A)+sd(B), notice that in order to complete the square in this expression
Cov(A,B) would have to equal sd(A)*sd(B). T... | Explanation for Additive Property of Variance?
The first thing to notice is that Var(A+B) equals VarA + Var B only when Cov(A,B)=0.
To gain some intuition behind the relationship between sd(A+B) and sd(A)+sd(B), notice that in order to complete th |
53,602 | Moment Generating Function for Lognormal Random Variable | Other answers to this question claims that the moment generating function (mgf) of the lognormal distribution do not exist. That is a strange claim. The mgf is
$$\DeclareMathOperator{\E}{\mathbb{E}}
M_X(t) = \E e^{tX}.
$$
And for the lognormal this only exists for $t\le 0$. The claim is then that the "mgf only exists... | Moment Generating Function for Lognormal Random Variable | Other answers to this question claims that the moment generating function (mgf) of the lognormal distribution do not exist. That is a strange claim. The mgf is
$$\DeclareMathOperator{\E}{\mathbb{E}} | Moment Generating Function for Lognormal Random Variable
Other answers to this question claims that the moment generating function (mgf) of the lognormal distribution do not exist. That is a strange claim. The mgf is
$$\DeclareMathOperator{\E}{\mathbb{E}}
M_X(t) = \E e^{tX}.
$$
And for the lognormal this only exists ... | Moment Generating Function for Lognormal Random Variable
Other answers to this question claims that the moment generating function (mgf) of the lognormal distribution do not exist. That is a strange claim. The mgf is
$$\DeclareMathOperator{\E}{\mathbb{E}} |
53,603 | Moment Generating Function for Lognormal Random Variable | The lognormal doesn't have an MGF; the integral needs to converge for $t$ in a neighborhood of 0, but the integral for $E(e^{tX})$ is not defined on the positive side.
(edit: see the correction i kjetil's answer; of course it does have an MGF, just for $t<0$ -- indeed I originally mentioned that above, but my claim th... | Moment Generating Function for Lognormal Random Variable | The lognormal doesn't have an MGF; the integral needs to converge for $t$ in a neighborhood of 0, but the integral for $E(e^{tX})$ is not defined on the positive side.
(edit: see the correction i kje | Moment Generating Function for Lognormal Random Variable
The lognormal doesn't have an MGF; the integral needs to converge for $t$ in a neighborhood of 0, but the integral for $E(e^{tX})$ is not defined on the positive side.
(edit: see the correction i kjetil's answer; of course it does have an MGF, just for $t<0$ -- ... | Moment Generating Function for Lognormal Random Variable
The lognormal doesn't have an MGF; the integral needs to converge for $t$ in a neighborhood of 0, but the integral for $E(e^{tX})$ is not defined on the positive side.
(edit: see the correction i kje |
53,604 | What is the Joint Density Function of a Three-Level Mixed-Effects Model? | Using the general mixed model formulation, the log-likelihood of the 3-level model will have the same form as that of the 2-level model. This is because the formulation of the linear mixed effects model as $\mathbf{y} = \mathbf{X\beta}+\mathbf{Z}\boldsymbol{b}+\mathbf{e}$ does not say anything about the number of group... | What is the Joint Density Function of a Three-Level Mixed-Effects Model? | Using the general mixed model formulation, the log-likelihood of the 3-level model will have the same form as that of the 2-level model. This is because the formulation of the linear mixed effects mod | What is the Joint Density Function of a Three-Level Mixed-Effects Model?
Using the general mixed model formulation, the log-likelihood of the 3-level model will have the same form as that of the 2-level model. This is because the formulation of the linear mixed effects model as $\mathbf{y} = \mathbf{X\beta}+\mathbf{Z}\... | What is the Joint Density Function of a Three-Level Mixed-Effects Model?
Using the general mixed model formulation, the log-likelihood of the 3-level model will have the same form as that of the 2-level model. This is because the formulation of the linear mixed effects mod |
53,605 | What is the Joint Density Function of a Three-Level Mixed-Effects Model? | Maximum likelihood estimation of mixed models typically works with the marginal likelihood of the observed response outcome data $y$. This marginal likelihood is obtained by integrating out the random effects from the joint density, i.e., for the $i$-th sample unit we have
$$\left \{
\begin{array}{l}
y_i = X_i\beta + Z... | What is the Joint Density Function of a Three-Level Mixed-Effects Model? | Maximum likelihood estimation of mixed models typically works with the marginal likelihood of the observed response outcome data $y$. This marginal likelihood is obtained by integrating out the random | What is the Joint Density Function of a Three-Level Mixed-Effects Model?
Maximum likelihood estimation of mixed models typically works with the marginal likelihood of the observed response outcome data $y$. This marginal likelihood is obtained by integrating out the random effects from the joint density, i.e., for the ... | What is the Joint Density Function of a Three-Level Mixed-Effects Model?
Maximum likelihood estimation of mixed models typically works with the marginal likelihood of the observed response outcome data $y$. This marginal likelihood is obtained by integrating out the random |
53,606 | variance of conditional multivariate gaussian | The problem is the sampling, which is to say that you're trying to compare the conditional density with the distribution of slices of data that were sampled from a bivariate density.
The theoretical variance of $x_1|x_2$ doesn't depend on the value of $x_2$ but the observed does because the further out you get from the... | variance of conditional multivariate gaussian | The problem is the sampling, which is to say that you're trying to compare the conditional density with the distribution of slices of data that were sampled from a bivariate density.
The theoretical v | variance of conditional multivariate gaussian
The problem is the sampling, which is to say that you're trying to compare the conditional density with the distribution of slices of data that were sampled from a bivariate density.
The theoretical variance of $x_1|x_2$ doesn't depend on the value of $x_2$ but the observed... | variance of conditional multivariate gaussian
The problem is the sampling, which is to say that you're trying to compare the conditional density with the distribution of slices of data that were sampled from a bivariate density.
The theoretical v |
53,607 | variance of conditional multivariate gaussian | The situation is addressed in the following paragraphs of your wikipedia link. It is also easier to look at Bivariate case there, since it directly gives the formulas you need. The conditional variance is $(1-\rho^2)\sigma_1^2$.
Using the bivariate formula in here and assuming zero-means for simplicity, wlog, we can fa... | variance of conditional multivariate gaussian | The situation is addressed in the following paragraphs of your wikipedia link. It is also easier to look at Bivariate case there, since it directly gives the formulas you need. The conditional varianc | variance of conditional multivariate gaussian
The situation is addressed in the following paragraphs of your wikipedia link. It is also easier to look at Bivariate case there, since it directly gives the formulas you need. The conditional variance is $(1-\rho^2)\sigma_1^2$.
Using the bivariate formula in here and assum... | variance of conditional multivariate gaussian
The situation is addressed in the following paragraphs of your wikipedia link. It is also easier to look at Bivariate case there, since it directly gives the formulas you need. The conditional varianc |
53,608 | Whats the difference between a dense layer and an output layer in a CNN? | Short:
Dense Layer = Fullyconnected Layer = topology, describes how the neurons are connected to the next layer of neurons (every neuron is connected to every neuron in the next layer), an intermediate layer (also called hidden layer see figure)
Output Layer = Last layer of a Multilayer Perceptron
Long:
The convolutio... | Whats the difference between a dense layer and an output layer in a CNN? | Short:
Dense Layer = Fullyconnected Layer = topology, describes how the neurons are connected to the next layer of neurons (every neuron is connected to every neuron in the next layer), an intermedia | Whats the difference between a dense layer and an output layer in a CNN?
Short:
Dense Layer = Fullyconnected Layer = topology, describes how the neurons are connected to the next layer of neurons (every neuron is connected to every neuron in the next layer), an intermediate layer (also called hidden layer see figure)
... | Whats the difference between a dense layer and an output layer in a CNN?
Short:
Dense Layer = Fullyconnected Layer = topology, describes how the neurons are connected to the next layer of neurons (every neuron is connected to every neuron in the next layer), an intermedia |
53,609 | How to calculate the derivative of crossentropy error function? | There is indeed a mistake:\begin{align}
\frac{\partial E_x}{\partial o_j^x} &=\frac{\partial }{\partial o_j^x} \left( - \sum_{k}[t_k^x \log(o_k^x)] + (1-t_k^x) \log(1-o_k^x)]\right) \\
&=-\frac{\partial }{\partial o_j^x} \left( \sum_{k}[t_k^x \log(o_k^x)] + (1-t_k^x) \log(1-o_k^x)]\right) \\
&=-\frac{\partial }{\parti... | How to calculate the derivative of crossentropy error function? | There is indeed a mistake:\begin{align}
\frac{\partial E_x}{\partial o_j^x} &=\frac{\partial }{\partial o_j^x} \left( - \sum_{k}[t_k^x \log(o_k^x)] + (1-t_k^x) \log(1-o_k^x)]\right) \\
&=-\frac{\parti | How to calculate the derivative of crossentropy error function?
There is indeed a mistake:\begin{align}
\frac{\partial E_x}{\partial o_j^x} &=\frac{\partial }{\partial o_j^x} \left( - \sum_{k}[t_k^x \log(o_k^x)] + (1-t_k^x) \log(1-o_k^x)]\right) \\
&=-\frac{\partial }{\partial o_j^x} \left( \sum_{k}[t_k^x \log(o_k^x)]... | How to calculate the derivative of crossentropy error function?
There is indeed a mistake:\begin{align}
\frac{\partial E_x}{\partial o_j^x} &=\frac{\partial }{\partial o_j^x} \left( - \sum_{k}[t_k^x \log(o_k^x)] + (1-t_k^x) \log(1-o_k^x)]\right) \\
&=-\frac{\parti |
53,610 | How to calculate the derivative of crossentropy error function? | An easy way to remember this is to internalize the gradient of the cross-entropy with respect to network parameters, which is famously $t_i - o_i$.
The last slide does this correctly. So, it looks like the second slide has a mistake. If you follow the derivations you'll notice the mistake where for no reason a minus s... | How to calculate the derivative of crossentropy error function? | An easy way to remember this is to internalize the gradient of the cross-entropy with respect to network parameters, which is famously $t_i - o_i$.
The last slide does this correctly. So, it looks li | How to calculate the derivative of crossentropy error function?
An easy way to remember this is to internalize the gradient of the cross-entropy with respect to network parameters, which is famously $t_i - o_i$.
The last slide does this correctly. So, it looks like the second slide has a mistake. If you follow the der... | How to calculate the derivative of crossentropy error function?
An easy way to remember this is to internalize the gradient of the cross-entropy with respect to network parameters, which is famously $t_i - o_i$.
The last slide does this correctly. So, it looks li |
53,611 | What is the conjugate prior distribution? [duplicate] | A conjugate prior is a probability distribution that, when multiplied by the likelihood and divided by the normalizing constant, yields a posterior probability distribution that is in the same family of distributions as the prior.
In other words, in the formula:
$$p(\theta|x) = \frac{p(x|\theta)p(\theta)}{\int{p(x|\th... | What is the conjugate prior distribution? [duplicate] | A conjugate prior is a probability distribution that, when multiplied by the likelihood and divided by the normalizing constant, yields a posterior probability distribution that is in the same family | What is the conjugate prior distribution? [duplicate]
A conjugate prior is a probability distribution that, when multiplied by the likelihood and divided by the normalizing constant, yields a posterior probability distribution that is in the same family of distributions as the prior.
In other words, in the formula:
$$... | What is the conjugate prior distribution? [duplicate]
A conjugate prior is a probability distribution that, when multiplied by the likelihood and divided by the normalizing constant, yields a posterior probability distribution that is in the same family |
53,612 | Is a GMM-HMM equivalent to a no-mixture HMM enriched with more states? | It is not exactly equivalent: the 6-state HMM can model everything the GMM-HMM can, but not the other way around.
Suppose you start with the GMM-HMM, with $s_5$ being the GMM state, and turn it into the 6-state HMM with states $s_6$ and $s_7$ instead of $s_5$.
Let $p_6$ and $p_7$ be the prior probabilities of the two c... | Is a GMM-HMM equivalent to a no-mixture HMM enriched with more states? | It is not exactly equivalent: the 6-state HMM can model everything the GMM-HMM can, but not the other way around.
Suppose you start with the GMM-HMM, with $s_5$ being the GMM state, and turn it into t | Is a GMM-HMM equivalent to a no-mixture HMM enriched with more states?
It is not exactly equivalent: the 6-state HMM can model everything the GMM-HMM can, but not the other way around.
Suppose you start with the GMM-HMM, with $s_5$ being the GMM state, and turn it into the 6-state HMM with states $s_6$ and $s_7$ instea... | Is a GMM-HMM equivalent to a no-mixture HMM enriched with more states?
It is not exactly equivalent: the 6-state HMM can model everything the GMM-HMM can, but not the other way around.
Suppose you start with the GMM-HMM, with $s_5$ being the GMM state, and turn it into t |
53,613 | Is a GMM-HMM equivalent to a no-mixture HMM enriched with more states? | No you are not wrong thinking that.
If $Y \mid X_1 \sim \alpha f_1(y) + (1-\alpha)f_2(y)$, then you can also let $X_2 \sim \text{Bernoulli}(\alpha)$ independently and say
$$
Y \mid X_1, X_2 = 1 \sim f_1(y)
$$
and
$$
Y \mid X_1, X_2 = 0 \sim f_2(y).
$$
This is because
$$
f_{Y|X_1}(y \mid x_1) = \sum_{i=1}^2f_{Y|X_1,... | Is a GMM-HMM equivalent to a no-mixture HMM enriched with more states? | No you are not wrong thinking that.
If $Y \mid X_1 \sim \alpha f_1(y) + (1-\alpha)f_2(y)$, then you can also let $X_2 \sim \text{Bernoulli}(\alpha)$ independently and say
$$
Y \mid X_1, X_2 = 1 \sim | Is a GMM-HMM equivalent to a no-mixture HMM enriched with more states?
No you are not wrong thinking that.
If $Y \mid X_1 \sim \alpha f_1(y) + (1-\alpha)f_2(y)$, then you can also let $X_2 \sim \text{Bernoulli}(\alpha)$ independently and say
$$
Y \mid X_1, X_2 = 1 \sim f_1(y)
$$
and
$$
Y \mid X_1, X_2 = 0 \sim f_2(y)... | Is a GMM-HMM equivalent to a no-mixture HMM enriched with more states?
No you are not wrong thinking that.
If $Y \mid X_1 \sim \alpha f_1(y) + (1-\alpha)f_2(y)$, then you can also let $X_2 \sim \text{Bernoulli}(\alpha)$ independently and say
$$
Y \mid X_1, X_2 = 1 \sim |
53,614 | How does a fitted linear mixed effects model predict longitudinal output for a new subject? | Provided that you have at least one data point for the new patient, you can calculate individualized (dynamic) predictions.
In particular, say that $y_j^o$ denotes the observed outcome data for the new patient $j$, then you can first obtain an estimate, say $b_j^*$ of his/her random effects from the posterior distribu... | How does a fitted linear mixed effects model predict longitudinal output for a new subject? | Provided that you have at least one data point for the new patient, you can calculate individualized (dynamic) predictions.
In particular, say that $y_j^o$ denotes the observed outcome data for the n | How does a fitted linear mixed effects model predict longitudinal output for a new subject?
Provided that you have at least one data point for the new patient, you can calculate individualized (dynamic) predictions.
In particular, say that $y_j^o$ denotes the observed outcome data for the new patient $j$, then you can... | How does a fitted linear mixed effects model predict longitudinal output for a new subject?
Provided that you have at least one data point for the new patient, you can calculate individualized (dynamic) predictions.
In particular, say that $y_j^o$ denotes the observed outcome data for the n |
53,615 | How does a fitted linear mixed effects model predict longitudinal output for a new subject? | The random intercepts for the subjects represent deviations from a mean population-level response. When predicting for a new subject, the fitted random effects are not helpful; this is because there is no way of knowing a priori how that subject's pattern deviates from the population-level response. Instead, the best p... | How does a fitted linear mixed effects model predict longitudinal output for a new subject? | The random intercepts for the subjects represent deviations from a mean population-level response. When predicting for a new subject, the fitted random effects are not helpful; this is because there i | How does a fitted linear mixed effects model predict longitudinal output for a new subject?
The random intercepts for the subjects represent deviations from a mean population-level response. When predicting for a new subject, the fitted random effects are not helpful; this is because there is no way of knowing a priori... | How does a fitted linear mixed effects model predict longitudinal output for a new subject?
The random intercepts for the subjects represent deviations from a mean population-level response. When predicting for a new subject, the fitted random effects are not helpful; this is because there i |
53,616 | How to present results of time series forecasting | Standard forecasting papers unfortunately usually only show the averages of errors, so you would show the averages of your MAPEs.
The authors often then start to discuss differences in the third significant digit. Without a notion of the variation in errors, this makes no sense. Therefore, I very much recommend that yo... | How to present results of time series forecasting | Standard forecasting papers unfortunately usually only show the averages of errors, so you would show the averages of your MAPEs.
The authors often then start to discuss differences in the third signi | How to present results of time series forecasting
Standard forecasting papers unfortunately usually only show the averages of errors, so you would show the averages of your MAPEs.
The authors often then start to discuss differences in the third significant digit. Without a notion of the variation in errors, this makes ... | How to present results of time series forecasting
Standard forecasting papers unfortunately usually only show the averages of errors, so you would show the averages of your MAPEs.
The authors often then start to discuss differences in the third signi |
53,617 | Spearman's rank correlation coefficient | What does each measure?
Pearson's correlation coefficient is measure of the strength of a linear relationship between x and y. It is swayed by outliers much like a mean and standard deviation.
Spearman's correlation coefficient is a measure of the strength of a monotonic relationship between x and y. This includes but ... | Spearman's rank correlation coefficient | What does each measure?
Pearson's correlation coefficient is measure of the strength of a linear relationship between x and y. It is swayed by outliers much like a mean and standard deviation.
Spearma | Spearman's rank correlation coefficient
What does each measure?
Pearson's correlation coefficient is measure of the strength of a linear relationship between x and y. It is swayed by outliers much like a mean and standard deviation.
Spearman's correlation coefficient is a measure of the strength of a monotonic relation... | Spearman's rank correlation coefficient
What does each measure?
Pearson's correlation coefficient is measure of the strength of a linear relationship between x and y. It is swayed by outliers much like a mean and standard deviation.
Spearma |
53,618 | Leave one out cross validation for LSTM | Leave one out cross validation for LSTM, or any other time-series model, doesn't really make much sense because it would introduce missing values in the series and leaking information from the future.
Time series models learn from historical values, to predict future. In leave one out cross-validation, you remove obser... | Leave one out cross validation for LSTM | Leave one out cross validation for LSTM, or any other time-series model, doesn't really make much sense because it would introduce missing values in the series and leaking information from the future. | Leave one out cross validation for LSTM
Leave one out cross validation for LSTM, or any other time-series model, doesn't really make much sense because it would introduce missing values in the series and leaking information from the future.
Time series models learn from historical values, to predict future. In leave on... | Leave one out cross validation for LSTM
Leave one out cross validation for LSTM, or any other time-series model, doesn't really make much sense because it would introduce missing values in the series and leaking information from the future. |
53,619 | Fitting ARIMA to time series with missing values | The results given by stats::arima in the first approach (ar1) are correct: they have taken into account the missing values. In the second one, they have not.
You can fit ARIMA models with missing values easily because all ARIMA models are state space models and the Kalman filter, which is used to fit state space models... | Fitting ARIMA to time series with missing values | The results given by stats::arima in the first approach (ar1) are correct: they have taken into account the missing values. In the second one, they have not.
You can fit ARIMA models with missing valu | Fitting ARIMA to time series with missing values
The results given by stats::arima in the first approach (ar1) are correct: they have taken into account the missing values. In the second one, they have not.
You can fit ARIMA models with missing values easily because all ARIMA models are state space models and the Kalma... | Fitting ARIMA to time series with missing values
The results given by stats::arima in the first approach (ar1) are correct: they have taken into account the missing values. In the second one, they have not.
You can fit ARIMA models with missing valu |
53,620 | Distance metric for source code | You can check the two links below:
A comparison of code similarity analysers
Measuring Code Similarity in Large-scaled Code Corpora
At the third link below a similarity measure is proposed, which takes into account the amount of the shared information between two sequences. This metric is based on Kolmogorov complexit... | Distance metric for source code | You can check the two links below:
A comparison of code similarity analysers
Measuring Code Similarity in Large-scaled Code Corpora
At the third link below a similarity measure is proposed, which tak | Distance metric for source code
You can check the two links below:
A comparison of code similarity analysers
Measuring Code Similarity in Large-scaled Code Corpora
At the third link below a similarity measure is proposed, which takes into account the amount of the shared information between two sequences. This metric ... | Distance metric for source code
You can check the two links below:
A comparison of code similarity analysers
Measuring Code Similarity in Large-scaled Code Corpora
At the third link below a similarity measure is proposed, which tak |
53,621 | Distance metric for source code | An Approach to Source-Code Plagiarism Detection and Investigation Using Latent Semantic Analysis reported success in this type of task with the general procedure:
Building a term frequency representation of the source code corpus
Performing dimensionality reduction using LSA (they found 30 dimensions to be sufficient)... | Distance metric for source code | An Approach to Source-Code Plagiarism Detection and Investigation Using Latent Semantic Analysis reported success in this type of task with the general procedure:
Building a term frequency representa | Distance metric for source code
An Approach to Source-Code Plagiarism Detection and Investigation Using Latent Semantic Analysis reported success in this type of task with the general procedure:
Building a term frequency representation of the source code corpus
Performing dimensionality reduction using LSA (they found... | Distance metric for source code
An Approach to Source-Code Plagiarism Detection and Investigation Using Latent Semantic Analysis reported success in this type of task with the general procedure:
Building a term frequency representa |
53,622 | Do I need stationary time series for Bayesian structural time series (BSTS)? | No, you don't need to make the time series stationary.
BSTS should be able to handle that. Stationarity is a requirement specifically for AR and ARMA models.
BSTS is supposed to handle structural changes in the time series, which means that by definition it should be able to handle non-stationary data - since a struc... | Do I need stationary time series for Bayesian structural time series (BSTS)? | No, you don't need to make the time series stationary.
BSTS should be able to handle that. Stationarity is a requirement specifically for AR and ARMA models.
BSTS is supposed to handle structural ch | Do I need stationary time series for Bayesian structural time series (BSTS)?
No, you don't need to make the time series stationary.
BSTS should be able to handle that. Stationarity is a requirement specifically for AR and ARMA models.
BSTS is supposed to handle structural changes in the time series, which means that ... | Do I need stationary time series for Bayesian structural time series (BSTS)?
No, you don't need to make the time series stationary.
BSTS should be able to handle that. Stationarity is a requirement specifically for AR and ARMA models.
BSTS is supposed to handle structural ch |
53,623 | Why does the rank order of models differ for R squared and RMSE? | In caret, the calculation for results$RMSE and results$Rsquared is not as simple as what you've indicated. They are in fact the average of RMSE and $R^2$ over the ten holdout sets.
To confirm this, run the summary:
> t1
glmnet
1000 samples
20 predictors
No pre-processing
Resampling: Cross-Validated (10 fold)
Summ... | Why does the rank order of models differ for R squared and RMSE? | In caret, the calculation for results$RMSE and results$Rsquared is not as simple as what you've indicated. They are in fact the average of RMSE and $R^2$ over the ten holdout sets.
To confirm this, ru | Why does the rank order of models differ for R squared and RMSE?
In caret, the calculation for results$RMSE and results$Rsquared is not as simple as what you've indicated. They are in fact the average of RMSE and $R^2$ over the ten holdout sets.
To confirm this, run the summary:
> t1
glmnet
1000 samples
20 predicto... | Why does the rank order of models differ for R squared and RMSE?
In caret, the calculation for results$RMSE and results$Rsquared is not as simple as what you've indicated. They are in fact the average of RMSE and $R^2$ over the ten holdout sets.
To confirm this, ru |
53,624 | Why does the rank order of models differ for R squared and RMSE? | It's because caret calculates R-squared differently than you are. See the answer to this question: How caret calculates R Squared.
To see it in your code,
library(caret)
set.seed(0)
d<-SLC14_1(n=1000)
folds<-createMultiFolds(d$y,k=10,times=1)
tc<-trainControl(index=folds,returnResamp="all",
savePredic... | Why does the rank order of models differ for R squared and RMSE? | It's because caret calculates R-squared differently than you are. See the answer to this question: How caret calculates R Squared.
To see it in your code,
library(caret)
set.seed(0)
d<-SLC14_1(n=1 | Why does the rank order of models differ for R squared and RMSE?
It's because caret calculates R-squared differently than you are. See the answer to this question: How caret calculates R Squared.
To see it in your code,
library(caret)
set.seed(0)
d<-SLC14_1(n=1000)
folds<-createMultiFolds(d$y,k=10,times=1)
tc<-tra... | Why does the rank order of models differ for R squared and RMSE?
It's because caret calculates R-squared differently than you are. See the answer to this question: How caret calculates R Squared.
To see it in your code,
library(caret)
set.seed(0)
d<-SLC14_1(n=1 |
53,625 | Why does the rank order of models differ for R squared and RMSE? | @grand_chat has the correct maths, I'm just growing in a comparative example to help illustrate what the issue is in different terms that will hopefully help understanding.
We're working with fractional terms here, similar to say miles per gallon. If we average mpg over set units of time we get very different results c... | Why does the rank order of models differ for R squared and RMSE? | @grand_chat has the correct maths, I'm just growing in a comparative example to help illustrate what the issue is in different terms that will hopefully help understanding.
We're working with fraction | Why does the rank order of models differ for R squared and RMSE?
@grand_chat has the correct maths, I'm just growing in a comparative example to help illustrate what the issue is in different terms that will hopefully help understanding.
We're working with fractional terms here, similar to say miles per gallon. If we a... | Why does the rank order of models differ for R squared and RMSE?
@grand_chat has the correct maths, I'm just growing in a comparative example to help illustrate what the issue is in different terms that will hopefully help understanding.
We're working with fraction |
53,626 | Intuition on Independence of Random Vectors | Yes, $X_i$ is independent of $Y_j$. To see this, note that if $\mathbf{X}$ and $\mathbf{Y}$ are independent, then for functions $f$ and $g$, $f(\mathbf{X})$ and $g(\mathbf{Y})$ are independent. See discussion here for this statement.
So let $f$ be the function that picks out the $i$th element of $\mathbf{X}$, that is, ... | Intuition on Independence of Random Vectors | Yes, $X_i$ is independent of $Y_j$. To see this, note that if $\mathbf{X}$ and $\mathbf{Y}$ are independent, then for functions $f$ and $g$, $f(\mathbf{X})$ and $g(\mathbf{Y})$ are independent. See di | Intuition on Independence of Random Vectors
Yes, $X_i$ is independent of $Y_j$. To see this, note that if $\mathbf{X}$ and $\mathbf{Y}$ are independent, then for functions $f$ and $g$, $f(\mathbf{X})$ and $g(\mathbf{Y})$ are independent. See discussion here for this statement.
So let $f$ be the function that picks out ... | Intuition on Independence of Random Vectors
Yes, $X_i$ is independent of $Y_j$. To see this, note that if $\mathbf{X}$ and $\mathbf{Y}$ are independent, then for functions $f$ and $g$, $f(\mathbf{X})$ and $g(\mathbf{Y})$ are independent. See di |
53,627 | Intuition on Independence of Random Vectors | It is actually even more general than that.
For real valued random vectors $X = (X_1,X_2,...,X_m)$ and $Y = (Y_1,Y_2,...,Y_n)$ independence implies:
$$F_{X_1,X_2,...X_m,Y_1,Y_2,...,Y_n}
(x_1,x_2,...,x_m,y_1,y_2,...,y_n)=F_{X_1,X_2,...X_m}(x_1,x_2,...,x_m) F_{Y_1,Y_2,...,Y_n}(y_1,y_2,...,y_n)$$
where $F$ is cumulative d... | Intuition on Independence of Random Vectors | It is actually even more general than that.
For real valued random vectors $X = (X_1,X_2,...,X_m)$ and $Y = (Y_1,Y_2,...,Y_n)$ independence implies:
$$F_{X_1,X_2,...X_m,Y_1,Y_2,...,Y_n}
(x_1,x_2,...,x | Intuition on Independence of Random Vectors
It is actually even more general than that.
For real valued random vectors $X = (X_1,X_2,...,X_m)$ and $Y = (Y_1,Y_2,...,Y_n)$ independence implies:
$$F_{X_1,X_2,...X_m,Y_1,Y_2,...,Y_n}
(x_1,x_2,...,x_m,y_1,y_2,...,y_n)=F_{X_1,X_2,...X_m}(x_1,x_2,...,x_m) F_{Y_1,Y_2,...,Y_n}(... | Intuition on Independence of Random Vectors
It is actually even more general than that.
For real valued random vectors $X = (X_1,X_2,...,X_m)$ and $Y = (Y_1,Y_2,...,Y_n)$ independence implies:
$$F_{X_1,X_2,...X_m,Y_1,Y_2,...,Y_n}
(x_1,x_2,...,x |
53,628 | Compare central distribution between two data sets | This answer is oblique to your question, because I am not clear that it's the best question to ask. Whether kurtosis is higher or lower doesn't bear directly on the main differences in level, spread and shape between empirical and simulated distributions.
I can't comment on what is of most scientific interest here. I ... | Compare central distribution between two data sets | This answer is oblique to your question, because I am not clear that it's the best question to ask. Whether kurtosis is higher or lower doesn't bear directly on the main differences in level, spread a | Compare central distribution between two data sets
This answer is oblique to your question, because I am not clear that it's the best question to ask. Whether kurtosis is higher or lower doesn't bear directly on the main differences in level, spread and shape between empirical and simulated distributions.
I can't comm... | Compare central distribution between two data sets
This answer is oblique to your question, because I am not clear that it's the best question to ask. Whether kurtosis is higher or lower doesn't bear directly on the main differences in level, spread a |
53,629 | Compare central distribution between two data sets | At issue is what you mean by "clusters ... around 0." In practice you might not know for sure. Therefore, this answer proposes a flexible exploratory determination: namely, the degree of clustering around any point ought to depend on the scale at which you are viewing the clustering, so for insight, study how apparen... | Compare central distribution between two data sets | At issue is what you mean by "clusters ... around 0." In practice you might not know for sure. Therefore, this answer proposes a flexible exploratory determination: namely, the degree of clustering | Compare central distribution between two data sets
At issue is what you mean by "clusters ... around 0." In practice you might not know for sure. Therefore, this answer proposes a flexible exploratory determination: namely, the degree of clustering around any point ought to depend on the scale at which you are viewin... | Compare central distribution between two data sets
At issue is what you mean by "clusters ... around 0." In practice you might not know for sure. Therefore, this answer proposes a flexible exploratory determination: namely, the degree of clustering |
53,630 | Compare central distribution between two data sets | It seems like what you're looking for is a Levene's test of homogeneity of variance. It should test whether the variance in one distribution is significantly different from the variance in another distribution. Which should get at your question about how the data clusters.
This will not inform whether it is centered o... | Compare central distribution between two data sets | It seems like what you're looking for is a Levene's test of homogeneity of variance. It should test whether the variance in one distribution is significantly different from the variance in another dis | Compare central distribution between two data sets
It seems like what you're looking for is a Levene's test of homogeneity of variance. It should test whether the variance in one distribution is significantly different from the variance in another distribution. Which should get at your question about how the data clust... | Compare central distribution between two data sets
It seems like what you're looking for is a Levene's test of homogeneity of variance. It should test whether the variance in one distribution is significantly different from the variance in another dis |
53,631 | Compare central distribution between two data sets | The OP states,
"I am interested in whether my empirical data (yellow) "clusters" around the midpoint of the plot more than the simulated data (blue)."
This is not a question about kurtosis: kurtosis does not measure "clustering" around the midpoint. Rather, it measures tails of the distribution. (Rare, extreme potenti... | Compare central distribution between two data sets | The OP states,
"I am interested in whether my empirical data (yellow) "clusters" around the midpoint of the plot more than the simulated data (blue)."
This is not a question about kurtosis: kurtosis | Compare central distribution between two data sets
The OP states,
"I am interested in whether my empirical data (yellow) "clusters" around the midpoint of the plot more than the simulated data (blue)."
This is not a question about kurtosis: kurtosis does not measure "clustering" around the midpoint. Rather, it measure... | Compare central distribution between two data sets
The OP states,
"I am interested in whether my empirical data (yellow) "clusters" around the midpoint of the plot more than the simulated data (blue)."
This is not a question about kurtosis: kurtosis |
53,632 | Suppose $X,Y,Z$ are random variables such that $Y,X$ are perfectly correlated. Does it hold that $P(Z|X,Y) = P(Z|Y)$? | In short the answer is that yes this is true, but proving it requires some manipulation of the measure theoretic definitions of probability: largely because the definition of conditional independence is heavily steeped in measure theory.
Note that perfect correlation implies that almost surely $X = aY + b$ for some con... | Suppose $X,Y,Z$ are random variables such that $Y,X$ are perfectly correlated. Does it hold that $P( | In short the answer is that yes this is true, but proving it requires some manipulation of the measure theoretic definitions of probability: largely because the definition of conditional independence | Suppose $X,Y,Z$ are random variables such that $Y,X$ are perfectly correlated. Does it hold that $P(Z|X,Y) = P(Z|Y)$?
In short the answer is that yes this is true, but proving it requires some manipulation of the measure theoretic definitions of probability: largely because the definition of conditional independence is... | Suppose $X,Y,Z$ are random variables such that $Y,X$ are perfectly correlated. Does it hold that $P(
In short the answer is that yes this is true, but proving it requires some manipulation of the measure theoretic definitions of probability: largely because the definition of conditional independence |
53,633 | Linear regression for large dataset | For larger dataset, we use stochastic gradient descent or batch-gradient descent.
But using these may give a optimum value that is close enough. I would suggest you to use batch-gradient descent as it gives better optimum values rather than stochastic gradient descent. | Linear regression for large dataset | For larger dataset, we use stochastic gradient descent or batch-gradient descent.
But using these may give a optimum value that is close enough. I would suggest you to use batch-gradient descent as it | Linear regression for large dataset
For larger dataset, we use stochastic gradient descent or batch-gradient descent.
But using these may give a optimum value that is close enough. I would suggest you to use batch-gradient descent as it gives better optimum values rather than stochastic gradient descent. | Linear regression for large dataset
For larger dataset, we use stochastic gradient descent or batch-gradient descent.
But using these may give a optimum value that is close enough. I would suggest you to use batch-gradient descent as it |
53,634 | Linear regression for large dataset | If data is large, iterative method is better than direct method to solve the linear system.
Details can be found in this post
https://stats.stackexchange.com/a/278779/113777
In addition, stochastic gradient decent can be used to learn from the very large data set. I also discussed it on my answer linked above. The idea... | Linear regression for large dataset | If data is large, iterative method is better than direct method to solve the linear system.
Details can be found in this post
https://stats.stackexchange.com/a/278779/113777
In addition, stochastic gr | Linear regression for large dataset
If data is large, iterative method is better than direct method to solve the linear system.
Details can be found in this post
https://stats.stackexchange.com/a/278779/113777
In addition, stochastic gradient decent can be used to learn from the very large data set. I also discussed it... | Linear regression for large dataset
If data is large, iterative method is better than direct method to solve the linear system.
Details can be found in this post
https://stats.stackexchange.com/a/278779/113777
In addition, stochastic gr |
53,635 | Linear regression for large dataset | If your data is too tall, then a standard technique is batching, where you update the loss function for say, 1000 points at a time. This is how stochastic gradient descent works.
If your data is also too wide, then I would think a similar kind of batching procedure would work, where you also select a subset of feature... | Linear regression for large dataset | If your data is too tall, then a standard technique is batching, where you update the loss function for say, 1000 points at a time. This is how stochastic gradient descent works.
If your data is also | Linear regression for large dataset
If your data is too tall, then a standard technique is batching, where you update the loss function for say, 1000 points at a time. This is how stochastic gradient descent works.
If your data is also too wide, then I would think a similar kind of batching procedure would work, where... | Linear regression for large dataset
If your data is too tall, then a standard technique is batching, where you update the loss function for say, 1000 points at a time. This is how stochastic gradient descent works.
If your data is also |
53,636 | Are both ARIMA and Exponential Smoothing special cases of State Space models? | Yes indeed: both exponential smoothing and ARIMA are special cases of state space models. For ARIMA, see this talk by Rob Hyndman, and for Exponential Smoothing, see Forecasting with Exponential Smoothing - the State Space Approach. This underlies the fact that specific Exponential Smoothing methods can be shown to yie... | Are both ARIMA and Exponential Smoothing special cases of State Space models? | Yes indeed: both exponential smoothing and ARIMA are special cases of state space models. For ARIMA, see this talk by Rob Hyndman, and for Exponential Smoothing, see Forecasting with Exponential Smoot | Are both ARIMA and Exponential Smoothing special cases of State Space models?
Yes indeed: both exponential smoothing and ARIMA are special cases of state space models. For ARIMA, see this talk by Rob Hyndman, and for Exponential Smoothing, see Forecasting with Exponential Smoothing - the State Space Approach. This unde... | Are both ARIMA and Exponential Smoothing special cases of State Space models?
Yes indeed: both exponential smoothing and ARIMA are special cases of state space models. For ARIMA, see this talk by Rob Hyndman, and for Exponential Smoothing, see Forecasting with Exponential Smoot |
53,637 | auto.arima returns a non-seasonal model even though I am forcing seasonality | Rule number 1: when your code does not do what you want, start inspecting your objects.
library(forecast)
set.seed(1)
(Data <- as.ts(rnorm(116), frequency=52) )
yields
Time Series:
Start = 1
End = 116
Frequency = 1
...snip...
Note that Frequency is 1, not 52, as we explicitly set above!
The problem is that as.ts() ... | auto.arima returns a non-seasonal model even though I am forcing seasonality | Rule number 1: when your code does not do what you want, start inspecting your objects.
library(forecast)
set.seed(1)
(Data <- as.ts(rnorm(116), frequency=52) )
yields
Time Series:
Start = 1
End = 1 | auto.arima returns a non-seasonal model even though I am forcing seasonality
Rule number 1: when your code does not do what you want, start inspecting your objects.
library(forecast)
set.seed(1)
(Data <- as.ts(rnorm(116), frequency=52) )
yields
Time Series:
Start = 1
End = 116
Frequency = 1
...snip...
Note that Fre... | auto.arima returns a non-seasonal model even though I am forcing seasonality
Rule number 1: when your code does not do what you want, start inspecting your objects.
library(forecast)
set.seed(1)
(Data <- as.ts(rnorm(116), frequency=52) )
yields
Time Series:
Start = 1
End = 1 |
53,638 | auto.arima returns a non-seasonal model even though I am forcing seasonality | Two things come to mind 1) it is silly to try and fit a seasonal ar model of order 52 to 105 obvservations as you only have 2 cycles of data and 2) see I have correlogram ACF and PACF below for a temperature time series. Can I say it is MA(2) from ACF? What about AR? where ignoring the effect of anomalies is discussed... | auto.arima returns a non-seasonal model even though I am forcing seasonality | Two things come to mind 1) it is silly to try and fit a seasonal ar model of order 52 to 105 obvservations as you only have 2 cycles of data and 2) see I have correlogram ACF and PACF below for a tem | auto.arima returns a non-seasonal model even though I am forcing seasonality
Two things come to mind 1) it is silly to try and fit a seasonal ar model of order 52 to 105 obvservations as you only have 2 cycles of data and 2) see I have correlogram ACF and PACF below for a temperature time series. Can I say it is MA(2)... | auto.arima returns a non-seasonal model even though I am forcing seasonality
Two things come to mind 1) it is silly to try and fit a seasonal ar model of order 52 to 105 obvservations as you only have 2 cycles of data and 2) see I have correlogram ACF and PACF below for a tem |
53,639 | Bootstrap p-value | Actually, both are possible. The definition from Wikipedia in the other answer is somewhat imprecise.
Here, it is necessary to point out that "greater magnitude" in the definition
The probability for a given statistical model that, when the null
hypothesis is true, the statistical summary would be the same as or of... | Bootstrap p-value | Actually, both are possible. The definition from Wikipedia in the other answer is somewhat imprecise.
Here, it is necessary to point out that "greater magnitude" in the definition
The probability fo | Bootstrap p-value
Actually, both are possible. The definition from Wikipedia in the other answer is somewhat imprecise.
Here, it is necessary to point out that "greater magnitude" in the definition
The probability for a given statistical model that, when the null
hypothesis is true, the statistical summary would be... | Bootstrap p-value
Actually, both are possible. The definition from Wikipedia in the other answer is somewhat imprecise.
Here, it is necessary to point out that "greater magnitude" in the definition
The probability fo |
53,640 | Bootstrap p-value | Go back to the definition of the P-value (from Wikipedia ):
The probability for a given statistical model that, when the null hypothesis is true, the statistical summary would be the same as or of greater magnitude than the actual observed results.
For this reason, its estimation by bootstrap is the proportion of t... | Bootstrap p-value | Go back to the definition of the P-value (from Wikipedia ):
The probability for a given statistical model that, when the null hypothesis is true, the statistical summary would be the same as or of g | Bootstrap p-value
Go back to the definition of the P-value (from Wikipedia ):
The probability for a given statistical model that, when the null hypothesis is true, the statistical summary would be the same as or of greater magnitude than the actual observed results.
For this reason, its estimation by bootstrap is t... | Bootstrap p-value
Go back to the definition of the P-value (from Wikipedia ):
The probability for a given statistical model that, when the null hypothesis is true, the statistical summary would be the same as or of g |
53,641 | How to compare logistic regression curves? | I'd suggest putting all three datasets into one. Include in this dataset an indicator variable for each of the three datasets. Then, fit a logistic regression using this complete dataset, including an interaction term of age and the indicator variable. Additionally, fit a logistic regression model that does not include... | How to compare logistic regression curves? | I'd suggest putting all three datasets into one. Include in this dataset an indicator variable for each of the three datasets. Then, fit a logistic regression using this complete dataset, including an | How to compare logistic regression curves?
I'd suggest putting all three datasets into one. Include in this dataset an indicator variable for each of the three datasets. Then, fit a logistic regression using this complete dataset, including an interaction term of age and the indicator variable. Additionally, fit a logi... | How to compare logistic regression curves?
I'd suggest putting all three datasets into one. Include in this dataset an indicator variable for each of the three datasets. Then, fit a logistic regression using this complete dataset, including an |
53,642 | sequential/recursive/online calculation of sample covariance matrix | It's easy if you write
$$
\hat\Sigma_n= \frac{1}{n-1}\sum_{i=1}^nX_i X_i^T - \frac{n}{n-1}\hat{\mu}_n\hat{\mu}_n^T.
$$
Split up the sum over $n$ elements into two parts. One will involve the first $n-1$ terms (which you can make look like the previous sample covariance), and the second will involve the most recent $n... | sequential/recursive/online calculation of sample covariance matrix | It's easy if you write
$$
\hat\Sigma_n= \frac{1}{n-1}\sum_{i=1}^nX_i X_i^T - \frac{n}{n-1}\hat{\mu}_n\hat{\mu}_n^T.
$$
Split up the sum over $n$ elements into two parts. One will involve the first $n | sequential/recursive/online calculation of sample covariance matrix
It's easy if you write
$$
\hat\Sigma_n= \frac{1}{n-1}\sum_{i=1}^nX_i X_i^T - \frac{n}{n-1}\hat{\mu}_n\hat{\mu}_n^T.
$$
Split up the sum over $n$ elements into two parts. One will involve the first $n-1$ terms (which you can make look like the previou... | sequential/recursive/online calculation of sample covariance matrix
It's easy if you write
$$
\hat\Sigma_n= \frac{1}{n-1}\sum_{i=1}^nX_i X_i^T - \frac{n}{n-1}\hat{\mu}_n\hat{\mu}_n^T.
$$
Split up the sum over $n$ elements into two parts. One will involve the first $n |
53,643 | (Practical) Applications or RNN | Image captioning
Sentiment analysis (this is an example of LSTMs in Theano)
Question answering
Speech recognition
Anomaly detection in time series
Wikipedia has a section on applications in LSTM article. | (Practical) Applications or RNN | Image captioning
Sentiment analysis (this is an example of LSTMs in Theano)
Question answering
Speech recognition
Anomaly detection in time series
Wikipedia has a section on applications in LSTM artic | (Practical) Applications or RNN
Image captioning
Sentiment analysis (this is an example of LSTMs in Theano)
Question answering
Speech recognition
Anomaly detection in time series
Wikipedia has a section on applications in LSTM article. | (Practical) Applications or RNN
Image captioning
Sentiment analysis (this is an example of LSTMs in Theano)
Question answering
Speech recognition
Anomaly detection in time series
Wikipedia has a section on applications in LSTM artic |
53,644 | (Practical) Applications or RNN | You have to understand that RNNs deal with "series" of data. It can be time series or it can be sentences which can be thought of as series of words.
One thing very powerful about RNNs is that it allows you to deal with series which are of different length. Having said that, any thing that looks like series or time se... | (Practical) Applications or RNN | You have to understand that RNNs deal with "series" of data. It can be time series or it can be sentences which can be thought of as series of words.
One thing very powerful about RNNs is that it all | (Practical) Applications or RNN
You have to understand that RNNs deal with "series" of data. It can be time series or it can be sentences which can be thought of as series of words.
One thing very powerful about RNNs is that it allows you to deal with series which are of different length. Having said that, any thing t... | (Practical) Applications or RNN
You have to understand that RNNs deal with "series" of data. It can be time series or it can be sentences which can be thought of as series of words.
One thing very powerful about RNNs is that it all |
53,645 | Batch normalisation at the end of each layer and not the input? | According to Ioffe and Szegedy (2015), batch normalization is employed to stabilize the inputs to nonlinear activation functions.
"Batch Normalization seeks a stable distribution
of activation values throughout training, and normalizes
the inputs of a nonlinearity since that is where matching
the moments is more likely... | Batch normalisation at the end of each layer and not the input? | According to Ioffe and Szegedy (2015), batch normalization is employed to stabilize the inputs to nonlinear activation functions.
"Batch Normalization seeks a stable distribution
of activation values | Batch normalisation at the end of each layer and not the input?
According to Ioffe and Szegedy (2015), batch normalization is employed to stabilize the inputs to nonlinear activation functions.
"Batch Normalization seeks a stable distribution
of activation values throughout training, and normalizes
the inputs of a nonl... | Batch normalisation at the end of each layer and not the input?
According to Ioffe and Szegedy (2015), batch normalization is employed to stabilize the inputs to nonlinear activation functions.
"Batch Normalization seeks a stable distribution
of activation values |
53,646 | Calculating t-SNE gradient (a mistake in the original t-SNE paper) | I just signed up for this forum due to your question :)
Nice question! It shows someone is indeed trying to follow & derive the nitty gritty. Your question is totally valid, (28) is indeed missing the $d_{ij}$, but then (24) is missing a $d_{ij}^{-1}$, you can see that from (21) via $\frac{\partial d_{ij}}{\partial y_i... | Calculating t-SNE gradient (a mistake in the original t-SNE paper) | I just signed up for this forum due to your question :)
Nice question! It shows someone is indeed trying to follow & derive the nitty gritty. Your question is totally valid, (28) is indeed missing the | Calculating t-SNE gradient (a mistake in the original t-SNE paper)
I just signed up for this forum due to your question :)
Nice question! It shows someone is indeed trying to follow & derive the nitty gritty. Your question is totally valid, (28) is indeed missing the $d_{ij}$, but then (24) is missing a $d_{ij}^{-1}$, ... | Calculating t-SNE gradient (a mistake in the original t-SNE paper)
I just signed up for this forum due to your question :)
Nice question! It shows someone is indeed trying to follow & derive the nitty gritty. Your question is totally valid, (28) is indeed missing the |
53,647 | Calculating t-SNE gradient (a mistake in the original t-SNE paper) | Let our cost function be $C=KL(P||Q)=\sum_k\sum_{l\neq k}p_{kl}\log(p_{kl})-p_{kl}\log(q_{kl})$, so that we are trying to find the gradient $\frac{\partial C}{\partial y_i}$.
We will define some intermediate terms to try and simplify the notation; let $d_{ij}=||y_i-y_j||=d_{ji}$, and let $W=\sum_{k\neq l}(1+d_{kl}^2)^{... | Calculating t-SNE gradient (a mistake in the original t-SNE paper) | Let our cost function be $C=KL(P||Q)=\sum_k\sum_{l\neq k}p_{kl}\log(p_{kl})-p_{kl}\log(q_{kl})$, so that we are trying to find the gradient $\frac{\partial C}{\partial y_i}$.
We will define some inter | Calculating t-SNE gradient (a mistake in the original t-SNE paper)
Let our cost function be $C=KL(P||Q)=\sum_k\sum_{l\neq k}p_{kl}\log(p_{kl})-p_{kl}\log(q_{kl})$, so that we are trying to find the gradient $\frac{\partial C}{\partial y_i}$.
We will define some intermediate terms to try and simplify the notation; let $... | Calculating t-SNE gradient (a mistake in the original t-SNE paper)
Let our cost function be $C=KL(P||Q)=\sum_k\sum_{l\neq k}p_{kl}\log(p_{kl})-p_{kl}\log(q_{kl})$, so that we are trying to find the gradient $\frac{\partial C}{\partial y_i}$.
We will define some inter |
53,648 | What does it mean to have a probability as random variable? | A probability that's randomly generated is a perfectly legitimate thing to have in a model. Such a model is an example of a hierarchical model: a model in which some parameters are themselves treated as random variables. Hierarchical models come up most frequently in Bayesian statistics, but they see a lot of use in fr... | What does it mean to have a probability as random variable? | A probability that's randomly generated is a perfectly legitimate thing to have in a model. Such a model is an example of a hierarchical model: a model in which some parameters are themselves treated | What does it mean to have a probability as random variable?
A probability that's randomly generated is a perfectly legitimate thing to have in a model. Such a model is an example of a hierarchical model: a model in which some parameters are themselves treated as random variables. Hierarchical models come up most freque... | What does it mean to have a probability as random variable?
A probability that's randomly generated is a perfectly legitimate thing to have in a model. Such a model is an example of a hierarchical model: a model in which some parameters are themselves treated |
53,649 | What does it mean to have a probability as random variable? | Probabilities as random variables come up all the time in a wide variety of contexts.
For one example, imagine you you're trying to model probability of making a claim on a third-party property damage policy in car insurance (insuring against stuff like crashing into someone else's possessions house, car, etc). Indivi... | What does it mean to have a probability as random variable? | Probabilities as random variables come up all the time in a wide variety of contexts.
For one example, imagine you you're trying to model probability of making a claim on a third-party property damag | What does it mean to have a probability as random variable?
Probabilities as random variables come up all the time in a wide variety of contexts.
For one example, imagine you you're trying to model probability of making a claim on a third-party property damage policy in car insurance (insuring against stuff like crash... | What does it mean to have a probability as random variable?
Probabilities as random variables come up all the time in a wide variety of contexts.
For one example, imagine you you're trying to model probability of making a claim on a third-party property damag |
53,650 | Conditional probability of correlated gaussians | I'm going to switch your variables in the statement so that the discussion uses them in a more conventional sense of studying $Y$ conditional on the values of $X$. So, the objective is to show that
$$\Pr(Y\in J\mid X\in I) \ge \Pr(Y\in J).\tag{1}$$
Think of this in terms of regression:
We will exploit the fact that t... | Conditional probability of correlated gaussians | I'm going to switch your variables in the statement so that the discussion uses them in a more conventional sense of studying $Y$ conditional on the values of $X$. So, the objective is to show that
$ | Conditional probability of correlated gaussians
I'm going to switch your variables in the statement so that the discussion uses them in a more conventional sense of studying $Y$ conditional on the values of $X$. So, the objective is to show that
$$\Pr(Y\in J\mid X\in I) \ge \Pr(Y\in J).\tag{1}$$
Think of this in terms... | Conditional probability of correlated gaussians
I'm going to switch your variables in the statement so that the discussion uses them in a more conventional sense of studying $Y$ conditional on the values of $X$. So, the objective is to show that
$ |
53,651 | Conditional probability of correlated gaussians | You want to prove that for any $x^\star \geq 0$ and $y^\star \geq 0$
we have $$ \text{Pr}\{ |X| \leq x^\star,\, |Y| \leq y^\star \} \geq
\text{Pr}\{ |X| \leq x^\star\} \text{Pr}\{ |Y| \leq y^\star \} $$
which is a famous result known as Sidak inequality. It holds for an
arbitrary centered elliptically contoured bivaria... | Conditional probability of correlated gaussians | You want to prove that for any $x^\star \geq 0$ and $y^\star \geq 0$
we have $$ \text{Pr}\{ |X| \leq x^\star,\, |Y| \leq y^\star \} \geq
\text{Pr}\{ |X| \leq x^\star\} \text{Pr}\{ |Y| \leq y^\star \} | Conditional probability of correlated gaussians
You want to prove that for any $x^\star \geq 0$ and $y^\star \geq 0$
we have $$ \text{Pr}\{ |X| \leq x^\star,\, |Y| \leq y^\star \} \geq
\text{Pr}\{ |X| \leq x^\star\} \text{Pr}\{ |Y| \leq y^\star \} $$
which is a famous result known as Sidak inequality. It holds for an
a... | Conditional probability of correlated gaussians
You want to prove that for any $x^\star \geq 0$ and $y^\star \geq 0$
we have $$ \text{Pr}\{ |X| \leq x^\star,\, |Y| \leq y^\star \} \geq
\text{Pr}\{ |X| \leq x^\star\} \text{Pr}\{ |Y| \leq y^\star \} |
53,652 | Conditional probability of correlated gaussians | Your desired result is a special case of the recently-proven Gaussian correlation inequality.
This may seem like overkill (and as the other answers demonstrate, it is), but the proof of the more general result is relatively short and available on the arXiv. | Conditional probability of correlated gaussians | Your desired result is a special case of the recently-proven Gaussian correlation inequality.
This may seem like overkill (and as the other answers demonstrate, it is), but the proof of the more gener | Conditional probability of correlated gaussians
Your desired result is a special case of the recently-proven Gaussian correlation inequality.
This may seem like overkill (and as the other answers demonstrate, it is), but the proof of the more general result is relatively short and available on the arXiv. | Conditional probability of correlated gaussians
Your desired result is a special case of the recently-proven Gaussian correlation inequality.
This may seem like overkill (and as the other answers demonstrate, it is), but the proof of the more gener |
53,653 | Calculating Confidence Intervals for Cross Validated Binary Classifiers | Summary: Whatever you do in order to calculate confidence intervals based on repeated CV, you need to take into account that there are several different sources of uncertainty.
Long version: Let me add my 2 ct with regard to repeated cross validation:
Repeated cross validation allows you to separate 2 sources of vari... | Calculating Confidence Intervals for Cross Validated Binary Classifiers | Summary: Whatever you do in order to calculate confidence intervals based on repeated CV, you need to take into account that there are several different sources of uncertainty.
Long version: Let me a | Calculating Confidence Intervals for Cross Validated Binary Classifiers
Summary: Whatever you do in order to calculate confidence intervals based on repeated CV, you need to take into account that there are several different sources of uncertainty.
Long version: Let me add my 2 ct with regard to repeated cross validat... | Calculating Confidence Intervals for Cross Validated Binary Classifiers
Summary: Whatever you do in order to calculate confidence intervals based on repeated CV, you need to take into account that there are several different sources of uncertainty.
Long version: Let me a |
53,654 | Calculating Confidence Intervals for Cross Validated Binary Classifiers | Since you are computing areas, note that the AUROC is just the concordance probability $c$ between predicted risks and observed binary outcomes. And so you are not needing to engage in classification. Instead your outcomes can be just predicted risks. There are methods for getting confidence intervals for $c$-indexe... | Calculating Confidence Intervals for Cross Validated Binary Classifiers | Since you are computing areas, note that the AUROC is just the concordance probability $c$ between predicted risks and observed binary outcomes. And so you are not needing to engage in classification | Calculating Confidence Intervals for Cross Validated Binary Classifiers
Since you are computing areas, note that the AUROC is just the concordance probability $c$ between predicted risks and observed binary outcomes. And so you are not needing to engage in classification. Instead your outcomes can be just predicted r... | Calculating Confidence Intervals for Cross Validated Binary Classifiers
Since you are computing areas, note that the AUROC is just the concordance probability $c$ between predicted risks and observed binary outcomes. And so you are not needing to engage in classification |
53,655 | What is the rationale behind LARS-OLS hybrid, i.e. using OLS estimate on the variables chosen by LARS? | The coefficient estimates from LARS will be shrunk (biased) towards zero, and the intensity of shrinkage might be suboptimal (too harsh) for forecasting.
However, some shrinkage should be good, as there is a trade-off between bias and variance. For example, if lasso happens to have selected the relevant regressors and... | What is the rationale behind LARS-OLS hybrid, i.e. using OLS estimate on the variables chosen by LAR | The coefficient estimates from LARS will be shrunk (biased) towards zero, and the intensity of shrinkage might be suboptimal (too harsh) for forecasting.
However, some shrinkage should be good, as th | What is the rationale behind LARS-OLS hybrid, i.e. using OLS estimate on the variables chosen by LARS?
The coefficient estimates from LARS will be shrunk (biased) towards zero, and the intensity of shrinkage might be suboptimal (too harsh) for forecasting.
However, some shrinkage should be good, as there is a trade-of... | What is the rationale behind LARS-OLS hybrid, i.e. using OLS estimate on the variables chosen by LAR
The coefficient estimates from LARS will be shrunk (biased) towards zero, and the intensity of shrinkage might be suboptimal (too harsh) for forecasting.
However, some shrinkage should be good, as th |
53,656 | Concentration inequalities for gaussian variables | You've got a random variable $\bar X_n \sim \mathcal N(\mu, \sigma^2/n)$ and you're looking to quantify the probability that $\bar X_n$ is a certain distance from its mean. This means you'll want to make use of a concentration inequality.
I'm going to prove a result that is very similar to your question but with some m... | Concentration inequalities for gaussian variables | You've got a random variable $\bar X_n \sim \mathcal N(\mu, \sigma^2/n)$ and you're looking to quantify the probability that $\bar X_n$ is a certain distance from its mean. This means you'll want to m | Concentration inequalities for gaussian variables
You've got a random variable $\bar X_n \sim \mathcal N(\mu, \sigma^2/n)$ and you're looking to quantify the probability that $\bar X_n$ is a certain distance from its mean. This means you'll want to make use of a concentration inequality.
I'm going to prove a result tha... | Concentration inequalities for gaussian variables
You've got a random variable $\bar X_n \sim \mathcal N(\mu, \sigma^2/n)$ and you're looking to quantify the probability that $\bar X_n$ is a certain distance from its mean. This means you'll want to m |
53,657 | Concentration inequalities for gaussian variables | Let $X$ denote a standard normal random variable. As the comments and Chaconne's answer have noted, the question here is to bound $P\{|X| > x\} = 2Q(x)$ where $Q(x) = 1 - \Phi(x)$ is the complementary normal distribution function. Now, a well-known bound is
$$ Q(x) < \frac 12e^{-x^2/2} ~~ \text{for } x > 0 \tag{1}$$
w... | Concentration inequalities for gaussian variables | Let $X$ denote a standard normal random variable. As the comments and Chaconne's answer have noted, the question here is to bound $P\{|X| > x\} = 2Q(x)$ where $Q(x) = 1 - \Phi(x)$ is the complementary | Concentration inequalities for gaussian variables
Let $X$ denote a standard normal random variable. As the comments and Chaconne's answer have noted, the question here is to bound $P\{|X| > x\} = 2Q(x)$ where $Q(x) = 1 - \Phi(x)$ is the complementary normal distribution function. Now, a well-known bound is
$$ Q(x) < \... | Concentration inequalities for gaussian variables
Let $X$ denote a standard normal random variable. As the comments and Chaconne's answer have noted, the question here is to bound $P\{|X| > x\} = 2Q(x)$ where $Q(x) = 1 - \Phi(x)$ is the complementary |
53,658 | Time to event with no censoring - use survival or normal regression? | Survival methods are about modeling some time to event data. There is no need for there to be censoring! the methods will work and be more effective without censoring. Time to event data will probably not be well fitted by normal distribution models, so usual linear regression is not indicated. I say you should go w... | Time to event with no censoring - use survival or normal regression? | Survival methods are about modeling some time to event data. There is no need for there to be censoring! the methods will work and be more effective without censoring. Time to event data will probab | Time to event with no censoring - use survival or normal regression?
Survival methods are about modeling some time to event data. There is no need for there to be censoring! the methods will work and be more effective without censoring. Time to event data will probably not be well fitted by normal distribution models... | Time to event with no censoring - use survival or normal regression?
Survival methods are about modeling some time to event data. There is no need for there to be censoring! the methods will work and be more effective without censoring. Time to event data will probab |
53,659 | Reference request for robust statistics | I would not start with Huber's book, even with its 2009 revision, unless you possess strong mathematical background, i.e. measure theory and topology. The book by Maronna and Yohai entitled Robust Statistics: Theory and Methods is much more accessible for beginners and covers both univariate and multivariate theory, al... | Reference request for robust statistics | I would not start with Huber's book, even with its 2009 revision, unless you possess strong mathematical background, i.e. measure theory and topology. The book by Maronna and Yohai entitled Robust Sta | Reference request for robust statistics
I would not start with Huber's book, even with its 2009 revision, unless you possess strong mathematical background, i.e. measure theory and topology. The book by Maronna and Yohai entitled Robust Statistics: Theory and Methods is much more accessible for beginners and covers bot... | Reference request for robust statistics
I would not start with Huber's book, even with its 2009 revision, unless you possess strong mathematical background, i.e. measure theory and topology. The book by Maronna and Yohai entitled Robust Sta |
53,660 | Reference request for robust statistics | Maronna's book from 2006, titled "Robust Statistics: Theory and Methods" is a very good introduction to the topic that covers roughly the same as Huber's. Depending on what aspect you want to touch on, I would focus on articles written by both Huber and Maronna to better help you understand how the field was developed. | Reference request for robust statistics | Maronna's book from 2006, titled "Robust Statistics: Theory and Methods" is a very good introduction to the topic that covers roughly the same as Huber's. Depending on what aspect you want to touch on | Reference request for robust statistics
Maronna's book from 2006, titled "Robust Statistics: Theory and Methods" is a very good introduction to the topic that covers roughly the same as Huber's. Depending on what aspect you want to touch on, I would focus on articles written by both Huber and Maronna to better help you... | Reference request for robust statistics
Maronna's book from 2006, titled "Robust Statistics: Theory and Methods" is a very good introduction to the topic that covers roughly the same as Huber's. Depending on what aspect you want to touch on |
53,661 | How exactly does curse of dimensionality curse? | The idea of nearest neighbours is that, due to continuity, other points close to your point of interest have values close to the value of your point of interest. If you have to spread very far out to find the 100 (for example) closest points, well then these points are not very close or neighbours anymore, and thus the... | How exactly does curse of dimensionality curse? | The idea of nearest neighbours is that, due to continuity, other points close to your point of interest have values close to the value of your point of interest. If you have to spread very far out to | How exactly does curse of dimensionality curse?
The idea of nearest neighbours is that, due to continuity, other points close to your point of interest have values close to the value of your point of interest. If you have to spread very far out to find the 100 (for example) closest points, well then these points are no... | How exactly does curse of dimensionality curse?
The idea of nearest neighbours is that, due to continuity, other points close to your point of interest have values close to the value of your point of interest. If you have to spread very far out to |
53,662 | How exactly does curse of dimensionality curse? | The curse is that a lot of of things that work in lower dimension don't scale well (i.e. grow/shrink too fast compare to linear) with dimension. E.g. a measure of data quality is more than 2 times worse when you double the number of dimension. The curse comes in many form: the range of the data, the density of the data... | How exactly does curse of dimensionality curse? | The curse is that a lot of of things that work in lower dimension don't scale well (i.e. grow/shrink too fast compare to linear) with dimension. E.g. a measure of data quality is more than 2 times wor | How exactly does curse of dimensionality curse?
The curse is that a lot of of things that work in lower dimension don't scale well (i.e. grow/shrink too fast compare to linear) with dimension. E.g. a measure of data quality is more than 2 times worse when you double the number of dimension. The curse comes in many form... | How exactly does curse of dimensionality curse?
The curse is that a lot of of things that work in lower dimension don't scale well (i.e. grow/shrink too fast compare to linear) with dimension. E.g. a measure of data quality is more than 2 times wor |
53,663 | How exactly does curse of dimensionality curse? | It curses mainly in computational sense. However, if you expand the dimensionality from small to large to infinite, asymptotically any point that's not this point becomes infinitely far away.
If you're at point O, and are looking at points A and B, then both $OA=\infty$ and $OB=\infty$, and you can't distinguish which... | How exactly does curse of dimensionality curse? | It curses mainly in computational sense. However, if you expand the dimensionality from small to large to infinite, asymptotically any point that's not this point becomes infinitely far away.
If you' | How exactly does curse of dimensionality curse?
It curses mainly in computational sense. However, if you expand the dimensionality from small to large to infinite, asymptotically any point that's not this point becomes infinitely far away.
If you're at point O, and are looking at points A and B, then both $OA=\infty$ ... | How exactly does curse of dimensionality curse?
It curses mainly in computational sense. However, if you expand the dimensionality from small to large to infinite, asymptotically any point that's not this point becomes infinitely far away.
If you' |
53,664 | What is the connection between binomial and poisson distribution? [duplicate] | They are strongly related to each other. For $n \rightarrow \infty,\ p \rightarrow 0$ such that $np \rightarrow \lambda\ $we have
$$P_{Bin(n,p)}(k) = \binom{n}{k}p^k(1-p)^{n-k} \eqsim \frac{\lambda^k}{k!}\exp^{-\lambda} = P_{Poiss(\lambda)}(k)$$
So Poisson distribution is a limiting binomial distribution with $\lambda... | What is the connection between binomial and poisson distribution? [duplicate] | They are strongly related to each other. For $n \rightarrow \infty,\ p \rightarrow 0$ such that $np \rightarrow \lambda\ $we have
$$P_{Bin(n,p)}(k) = \binom{n}{k}p^k(1-p)^{n-k} \eqsim \frac{\lambda^k | What is the connection between binomial and poisson distribution? [duplicate]
They are strongly related to each other. For $n \rightarrow \infty,\ p \rightarrow 0$ such that $np \rightarrow \lambda\ $we have
$$P_{Bin(n,p)}(k) = \binom{n}{k}p^k(1-p)^{n-k} \eqsim \frac{\lambda^k}{k!}\exp^{-\lambda} = P_{Poiss(\lambda)}(... | What is the connection between binomial and poisson distribution? [duplicate]
They are strongly related to each other. For $n \rightarrow \infty,\ p \rightarrow 0$ such that $np \rightarrow \lambda\ $we have
$$P_{Bin(n,p)}(k) = \binom{n}{k}p^k(1-p)^{n-k} \eqsim \frac{\lambda^k |
53,665 | What is the connection between binomial and poisson distribution? [duplicate] | One can get the Poisson from Binomial by taking limit, and the Binomial from Poisson by conditioning. More precisely, we have the following.
If $X\sim\text{Pois}(\lambda_1)$, $Y\sim\text{Pois}(\lambda_2)$ are independent random variables, then the distribution of $X$ given $X+Y=n$ is $X_{\text{cond}}\sim\text{Bin}(n,\... | What is the connection between binomial and poisson distribution? [duplicate] | One can get the Poisson from Binomial by taking limit, and the Binomial from Poisson by conditioning. More precisely, we have the following.
If $X\sim\text{Pois}(\lambda_1)$, $Y\sim\text{Pois}(\lambd | What is the connection between binomial and poisson distribution? [duplicate]
One can get the Poisson from Binomial by taking limit, and the Binomial from Poisson by conditioning. More precisely, we have the following.
If $X\sim\text{Pois}(\lambda_1)$, $Y\sim\text{Pois}(\lambda_2)$ are independent random variables, th... | What is the connection between binomial and poisson distribution? [duplicate]
One can get the Poisson from Binomial by taking limit, and the Binomial from Poisson by conditioning. More precisely, we have the following.
If $X\sim\text{Pois}(\lambda_1)$, $Y\sim\text{Pois}(\lambd |
53,666 | What is the name of this type of vector product? | Your direction question:
In the two-dimensional case, you're looking for the outer product. The Euclidean inner product is $x^T y$ while the outer product is $xy^T$. The outer product generates a matrix.
In the general case, you're asking for a tensor
product.
What you're asking for is also the Kronecker product of th... | What is the name of this type of vector product? | Your direction question:
In the two-dimensional case, you're looking for the outer product. The Euclidean inner product is $x^T y$ while the outer product is $xy^T$. The outer product generates a mat | What is the name of this type of vector product?
Your direction question:
In the two-dimensional case, you're looking for the outer product. The Euclidean inner product is $x^T y$ while the outer product is $xy^T$. The outer product generates a matrix.
In the general case, you're asking for a tensor
product.
What you'... | What is the name of this type of vector product?
Your direction question:
In the two-dimensional case, you're looking for the outer product. The Euclidean inner product is $x^T y$ while the outer product is $xy^T$. The outer product generates a mat |
53,667 | What is the name of this type of vector product? | Let $\mathrm x, \mathrm y \in \mathbb R^d$. The Kronecker product of these two $d$-dimensional column vectors is the following $d^2$-dimensional column vector
$$\mathrm x \otimes \mathrm y = \begin{bmatrix} x_1 \mathrm y\\ x_2 \mathrm y\\ \vdots\\ x_d \mathrm y\\\end{bmatrix} = \begin{bmatrix} x_1 y_1\\ x_1 y_2\\ \vdot... | What is the name of this type of vector product? | Let $\mathrm x, \mathrm y \in \mathbb R^d$. The Kronecker product of these two $d$-dimensional column vectors is the following $d^2$-dimensional column vector
$$\mathrm x \otimes \mathrm y = \begin{bm | What is the name of this type of vector product?
Let $\mathrm x, \mathrm y \in \mathbb R^d$. The Kronecker product of these two $d$-dimensional column vectors is the following $d^2$-dimensional column vector
$$\mathrm x \otimes \mathrm y = \begin{bmatrix} x_1 \mathrm y\\ x_2 \mathrm y\\ \vdots\\ x_d \mathrm y\\\end{bma... | What is the name of this type of vector product?
Let $\mathrm x, \mathrm y \in \mathbb R^d$. The Kronecker product of these two $d$-dimensional column vectors is the following $d^2$-dimensional column vector
$$\mathrm x \otimes \mathrm y = \begin{bm |
53,668 | Inferring alleles distribution from the blood types distribution | The probability of the blood types can be defined in terms of the alleles:
$$O = o^2$$
$$A=a^2+2oa$$
$$B=b^2+2ob$$
$$AB=2ab$$
These are 4 equations with 3 variables, and thus a solution is not guaranteed.
Solving for the first 3 equations we get:
$$o=\sqrt{O}$$
$$a=\sqrt{A+O}-\sqrt{O}$$
$$b=\sqrt{B+O}-\sqrt{O}$$
We get... | Inferring alleles distribution from the blood types distribution | The probability of the blood types can be defined in terms of the alleles:
$$O = o^2$$
$$A=a^2+2oa$$
$$B=b^2+2ob$$
$$AB=2ab$$
These are 4 equations with 3 variables, and thus a solution is not guarant | Inferring alleles distribution from the blood types distribution
The probability of the blood types can be defined in terms of the alleles:
$$O = o^2$$
$$A=a^2+2oa$$
$$B=b^2+2ob$$
$$AB=2ab$$
These are 4 equations with 3 variables, and thus a solution is not guaranteed.
Solving for the first 3 equations we get:
$$o=\sqr... | Inferring alleles distribution from the blood types distribution
The probability of the blood types can be defined in terms of the alleles:
$$O = o^2$$
$$A=a^2+2oa$$
$$B=b^2+2ob$$
$$AB=2ab$$
These are 4 equations with 3 variables, and thus a solution is not guarant |
53,669 | Inferring alleles distribution from the blood types distribution | EDIT: Wrong logic here, disregard this answer and focus on the accepted one.
Keeping the original one for reference of what no to do.
How about simply reversing the probability ? It sounds simple but it might be what you are looking for ?
if aa, oa and ao makes A and there are 40% of A, then the simplest assumption is... | Inferring alleles distribution from the blood types distribution | EDIT: Wrong logic here, disregard this answer and focus on the accepted one.
Keeping the original one for reference of what no to do.
How about simply reversing the probability ? It sounds simple but | Inferring alleles distribution from the blood types distribution
EDIT: Wrong logic here, disregard this answer and focus on the accepted one.
Keeping the original one for reference of what no to do.
How about simply reversing the probability ? It sounds simple but it might be what you are looking for ?
if aa, oa and a... | Inferring alleles distribution from the blood types distribution
EDIT: Wrong logic here, disregard this answer and focus on the accepted one.
Keeping the original one for reference of what no to do.
How about simply reversing the probability ? It sounds simple but |
53,670 | How to assign new data to an existing clustering | Assigning new points to a clustering algorithm is always a bit perplexing because the results of a clustering algorithm are imperfect; they represent a snapshot of a (hopefully good) segmentation of the current data.
How good they generalise to new data and what is the actual definition of good are open questions. May... | How to assign new data to an existing clustering | Assigning new points to a clustering algorithm is always a bit perplexing because the results of a clustering algorithm are imperfect; they represent a snapshot of a (hopefully good) segmentation of t | How to assign new data to an existing clustering
Assigning new points to a clustering algorithm is always a bit perplexing because the results of a clustering algorithm are imperfect; they represent a snapshot of a (hopefully good) segmentation of the current data.
How good they generalise to new data and what is the ... | How to assign new data to an existing clustering
Assigning new points to a clustering algorithm is always a bit perplexing because the results of a clustering algorithm are imperfect; they represent a snapshot of a (hopefully good) segmentation of t |
53,671 | How to assign new data to an existing clustering | I guess just 2 points is not gonna mess it so badly, but for more than 10% (to say a number) it might be better to recalculate the centroids (just an opinion)
def Labs( dataset,centroids ):
l = []
for i in range(len(dataset)):
m = []
for j in range(n):
p = np.linalg.norm(dataset[(i),:]-centr... | How to assign new data to an existing clustering | I guess just 2 points is not gonna mess it so badly, but for more than 10% (to say a number) it might be better to recalculate the centroids (just an opinion)
def Labs( dataset,centroids ):
l = [] | How to assign new data to an existing clustering
I guess just 2 points is not gonna mess it so badly, but for more than 10% (to say a number) it might be better to recalculate the centroids (just an opinion)
def Labs( dataset,centroids ):
l = []
for i in range(len(dataset)):
m = []
for j in range(n): ... | How to assign new data to an existing clustering
I guess just 2 points is not gonna mess it so badly, but for more than 10% (to say a number) it might be better to recalculate the centroids (just an opinion)
def Labs( dataset,centroids ):
l = [] |
53,672 | Basic confusion about Restricted Boltzmann Machines (RBM) | Have a look at section $\textbf{13.2}$ of Hinton's guide to train an RBM, at equation $\textbf{17}$ or a similar and better description in Salakhutdinov's Learning Deep Generative Models, section $\textbf{2.2}$.
http://www.cs.toronto.edu/~hinton/absps/guideTR.pdf
http://www.cs.cmu.edu/~rsalakhu/papers/annrev.pdf
The Ga... | Basic confusion about Restricted Boltzmann Machines (RBM) | Have a look at section $\textbf{13.2}$ of Hinton's guide to train an RBM, at equation $\textbf{17}$ or a similar and better description in Salakhutdinov's Learning Deep Generative Models, section $\te | Basic confusion about Restricted Boltzmann Machines (RBM)
Have a look at section $\textbf{13.2}$ of Hinton's guide to train an RBM, at equation $\textbf{17}$ or a similar and better description in Salakhutdinov's Learning Deep Generative Models, section $\textbf{2.2}$.
http://www.cs.toronto.edu/~hinton/absps/guideTR.pd... | Basic confusion about Restricted Boltzmann Machines (RBM)
Have a look at section $\textbf{13.2}$ of Hinton's guide to train an RBM, at equation $\textbf{17}$ or a similar and better description in Salakhutdinov's Learning Deep Generative Models, section $\te |
53,673 | Basic confusion about Restricted Boltzmann Machines (RBM) | Yeah there are simple extensions to real numbers, but it's kind of an easy trick to scale your data between 0 and 1 (like a probability). Then you can learn using binary stochastic units.
Scaling your data between 0 and 1 is one of many pre-data-filtering tricks to make learning faster - the ultimate goal. Whitening pi... | Basic confusion about Restricted Boltzmann Machines (RBM) | Yeah there are simple extensions to real numbers, but it's kind of an easy trick to scale your data between 0 and 1 (like a probability). Then you can learn using binary stochastic units.
Scaling your | Basic confusion about Restricted Boltzmann Machines (RBM)
Yeah there are simple extensions to real numbers, but it's kind of an easy trick to scale your data between 0 and 1 (like a probability). Then you can learn using binary stochastic units.
Scaling your data between 0 and 1 is one of many pre-data-filtering tricks... | Basic confusion about Restricted Boltzmann Machines (RBM)
Yeah there are simple extensions to real numbers, but it's kind of an easy trick to scale your data between 0 and 1 (like a probability). Then you can learn using binary stochastic units.
Scaling your |
53,674 | Basic confusion about Restricted Boltzmann Machines (RBM) | By definition, an RBM with binary visible units can only model binary observations. So in the case of MNIST with integer pixel values in [0, 255], some sort of thresholding can be done to binarize the input. Or, like you suggested, rescale the pixel values to real numbers and use Gaussian visible units to model them. A... | Basic confusion about Restricted Boltzmann Machines (RBM) | By definition, an RBM with binary visible units can only model binary observations. So in the case of MNIST with integer pixel values in [0, 255], some sort of thresholding can be done to binarize the | Basic confusion about Restricted Boltzmann Machines (RBM)
By definition, an RBM with binary visible units can only model binary observations. So in the case of MNIST with integer pixel values in [0, 255], some sort of thresholding can be done to binarize the input. Or, like you suggested, rescale the pixel values to re... | Basic confusion about Restricted Boltzmann Machines (RBM)
By definition, an RBM with binary visible units can only model binary observations. So in the case of MNIST with integer pixel values in [0, 255], some sort of thresholding can be done to binarize the |
53,675 | How does procedure failure rate affect sample size in a randomized clinical trial? | From the point of intention to treat it is not necessary to take this into account because everybody should be included in the analysis in the arm to which they are randomised. The failure rate is an inherent part of the treatment. If you want to compare the effect of actually receiving the treatment in the two arms th... | How does procedure failure rate affect sample size in a randomized clinical trial? | From the point of intention to treat it is not necessary to take this into account because everybody should be included in the analysis in the arm to which they are randomised. The failure rate is an | How does procedure failure rate affect sample size in a randomized clinical trial?
From the point of intention to treat it is not necessary to take this into account because everybody should be included in the analysis in the arm to which they are randomised. The failure rate is an inherent part of the treatment. If yo... | How does procedure failure rate affect sample size in a randomized clinical trial?
From the point of intention to treat it is not necessary to take this into account because everybody should be included in the analysis in the arm to which they are randomised. The failure rate is an |
53,676 | How does procedure failure rate affect sample size in a randomized clinical trial? | The power of your study depends on the magnitude of the difference you hope to detect between the two treatments, the variability among participants in terms of their responses to the treatments, and the number of participants. Insofar as the possibility of placement failure increases the variability of responses among... | How does procedure failure rate affect sample size in a randomized clinical trial? | The power of your study depends on the magnitude of the difference you hope to detect between the two treatments, the variability among participants in terms of their responses to the treatments, and | How does procedure failure rate affect sample size in a randomized clinical trial?
The power of your study depends on the magnitude of the difference you hope to detect between the two treatments, the variability among participants in terms of their responses to the treatments, and the number of participants. Insofar a... | How does procedure failure rate affect sample size in a randomized clinical trial?
The power of your study depends on the magnitude of the difference you hope to detect between the two treatments, the variability among participants in terms of their responses to the treatments, and |
53,677 | How does procedure failure rate affect sample size in a randomized clinical trial? | Random uncertainty decreases the precision of an experiment.
Systematic uncertainty decreases the accuracy of an experiment.
The Standard deviation , $s$ equals the square root of the sum of squares of differences $/ N$ (population).
The standard deviation of the mean value of a set of measurements $σ_m$
, (“sigma-em”... | How does procedure failure rate affect sample size in a randomized clinical trial? | Random uncertainty decreases the precision of an experiment.
Systematic uncertainty decreases the accuracy of an experiment.
The Standard deviation , $s$ equals the square root of the sum of squares | How does procedure failure rate affect sample size in a randomized clinical trial?
Random uncertainty decreases the precision of an experiment.
Systematic uncertainty decreases the accuracy of an experiment.
The Standard deviation , $s$ equals the square root of the sum of squares of differences $/ N$ (population).
Th... | How does procedure failure rate affect sample size in a randomized clinical trial?
Random uncertainty decreases the precision of an experiment.
Systematic uncertainty decreases the accuracy of an experiment.
The Standard deviation , $s$ equals the square root of the sum of squares |
53,678 | What is the difference between the probabilistic and non-probabilistic learning methods? [duplicate] | The task of classification enables a simple comparison:
A probabilistic approach (such as Random Forest) would yield a probability distribution over a set of classes for each input sample.
A deterministic approach (such as SVM) does not model the distribution of classes but rather separates the feature space and return... | What is the difference between the probabilistic and non-probabilistic learning methods? [duplicate] | The task of classification enables a simple comparison:
A probabilistic approach (such as Random Forest) would yield a probability distribution over a set of classes for each input sample.
A determini | What is the difference between the probabilistic and non-probabilistic learning methods? [duplicate]
The task of classification enables a simple comparison:
A probabilistic approach (such as Random Forest) would yield a probability distribution over a set of classes for each input sample.
A deterministic approach (such... | What is the difference between the probabilistic and non-probabilistic learning methods? [duplicate]
The task of classification enables a simple comparison:
A probabilistic approach (such as Random Forest) would yield a probability distribution over a set of classes for each input sample.
A determini |
53,679 | Why Discriminator converges to 1/2 in Generative Adversarial Networks? | I'll try to skip math, and use intuition instead.
You show Discriminator a lot of examples. Some are real, some are fake (coming from the Generator).
Intuitively, you want Generator to be able to fool Discriminator every time into thinking that a fake example is a real one. It shouldn't be able to differentiate between... | Why Discriminator converges to 1/2 in Generative Adversarial Networks? | I'll try to skip math, and use intuition instead.
You show Discriminator a lot of examples. Some are real, some are fake (coming from the Generator).
Intuitively, you want Generator to be able to fool | Why Discriminator converges to 1/2 in Generative Adversarial Networks?
I'll try to skip math, and use intuition instead.
You show Discriminator a lot of examples. Some are real, some are fake (coming from the Generator).
Intuitively, you want Generator to be able to fool Discriminator every time into thinking that a fa... | Why Discriminator converges to 1/2 in Generative Adversarial Networks?
I'll try to skip math, and use intuition instead.
You show Discriminator a lot of examples. Some are real, some are fake (coming from the Generator).
Intuitively, you want Generator to be able to fool |
53,680 | Why Discriminator converges to 1/2 in Generative Adversarial Networks? | {1} explains why the output of discriminator network $D$ converges to $\frac{1}{2}$:
For $G$ fixed, the optimal discriminator $D$ is $D^*_G(\mathbb{x}) = \frac{p_\text{data}(\mathbb{x})}{p_\text{data}(\mathbb{x}) + p_g(\mathbb{x})}$.
Therefore, if you have $p_g=p_\text{data}$, meaning that the neural network $G$ has... | Why Discriminator converges to 1/2 in Generative Adversarial Networks? | {1} explains why the output of discriminator network $D$ converges to $\frac{1}{2}$:
For $G$ fixed, the optimal discriminator $D$ is $D^*_G(\mathbb{x}) = \frac{p_\text{data}(\mathbb{x})}{p_\text{dat | Why Discriminator converges to 1/2 in Generative Adversarial Networks?
{1} explains why the output of discriminator network $D$ converges to $\frac{1}{2}$:
For $G$ fixed, the optimal discriminator $D$ is $D^*_G(\mathbb{x}) = \frac{p_\text{data}(\mathbb{x})}{p_\text{data}(\mathbb{x}) + p_g(\mathbb{x})}$.
Therefore, i... | Why Discriminator converges to 1/2 in Generative Adversarial Networks?
{1} explains why the output of discriminator network $D$ converges to $\frac{1}{2}$:
For $G$ fixed, the optimal discriminator $D$ is $D^*_G(\mathbb{x}) = \frac{p_\text{data}(\mathbb{x})}{p_\text{dat |
53,681 | Why Discriminator converges to 1/2 in Generative Adversarial Networks? | If $p_g=p_d$ the input data $x_1,...,x_n\sim p_d$ and the generated data $G(z_1),...,G(z_n)\sim p_g$ come from the same distribution. It is thus impossible to distinguish between samples of real and generated data because they are samples of the same distribution. The best the discriminator can do is thus guessing if $... | Why Discriminator converges to 1/2 in Generative Adversarial Networks? | If $p_g=p_d$ the input data $x_1,...,x_n\sim p_d$ and the generated data $G(z_1),...,G(z_n)\sim p_g$ come from the same distribution. It is thus impossible to distinguish between samples of real and g | Why Discriminator converges to 1/2 in Generative Adversarial Networks?
If $p_g=p_d$ the input data $x_1,...,x_n\sim p_d$ and the generated data $G(z_1),...,G(z_n)\sim p_g$ come from the same distribution. It is thus impossible to distinguish between samples of real and generated data because they are samples of the sam... | Why Discriminator converges to 1/2 in Generative Adversarial Networks?
If $p_g=p_d$ the input data $x_1,...,x_n\sim p_d$ and the generated data $G(z_1),...,G(z_n)\sim p_g$ come from the same distribution. It is thus impossible to distinguish between samples of real and g |
53,682 | Which model is better: One that overfits or one that underfits? | Compare the two models on the plot below. First (red curve) heavily overfitts the data, while the second one (blue line) underfitts it. Can you tell which one is better? I'd say that both are bad.
If your model overfitts, then it perfectly fits your data, but can possibly be poor for making out-of-sample predictions. ... | Which model is better: One that overfits or one that underfits? | Compare the two models on the plot below. First (red curve) heavily overfitts the data, while the second one (blue line) underfitts it. Can you tell which one is better? I'd say that both are bad.
If | Which model is better: One that overfits or one that underfits?
Compare the two models on the plot below. First (red curve) heavily overfitts the data, while the second one (blue line) underfitts it. Can you tell which one is better? I'd say that both are bad.
If your model overfitts, then it perfectly fits your data,... | Which model is better: One that overfits or one that underfits?
Compare the two models on the plot below. First (red curve) heavily overfitts the data, while the second one (blue line) underfitts it. Can you tell which one is better? I'd say that both are bad.
If |
53,683 | Which model is better: One that overfits or one that underfits? | It's hard to say in general whether overfitting or underfitting is less desireable — this probably depends on your application.
In practice though, it's probably better to start with a model that has enough capacity to overfit your training data since there are lots of techniques for dealing with overfitting (e.g., reg... | Which model is better: One that overfits or one that underfits? | It's hard to say in general whether overfitting or underfitting is less desireable — this probably depends on your application.
In practice though, it's probably better to start with a model that has | Which model is better: One that overfits or one that underfits?
It's hard to say in general whether overfitting or underfitting is less desireable — this probably depends on your application.
In practice though, it's probably better to start with a model that has enough capacity to overfit your training data since ther... | Which model is better: One that overfits or one that underfits?
It's hard to say in general whether overfitting or underfitting is less desireable — this probably depends on your application.
In practice though, it's probably better to start with a model that has |
53,684 | Which model is better: One that overfits or one that underfits? | In ARIMA model over-fitting is often performed due to model mis-specifcation incorporating an unwarranted differencing operator and a self-cancelling ma operator leads to poor forecasts. Incorporating self-cancelling ARMA structure also has the same effect. In terms of incorporating statistically non-significant (unnec... | Which model is better: One that overfits or one that underfits? | In ARIMA model over-fitting is often performed due to model mis-specifcation incorporating an unwarranted differencing operator and a self-cancelling ma operator leads to poor forecasts. Incorporating | Which model is better: One that overfits or one that underfits?
In ARIMA model over-fitting is often performed due to model mis-specifcation incorporating an unwarranted differencing operator and a self-cancelling ma operator leads to poor forecasts. Incorporating self-cancelling ARMA structure also has the same effect... | Which model is better: One that overfits or one that underfits?
In ARIMA model over-fitting is often performed due to model mis-specifcation incorporating an unwarranted differencing operator and a self-cancelling ma operator leads to poor forecasts. Incorporating |
53,685 | $\int_a^b \mathbb{P}(\mathrm{d}x) = \int_a^b \mathbb{P}(x)\mathrm{d}x$? | In general, the $\mathbb{P}$-integral of a measurable function $X$ on $\left(\Omega, \mathcal{A}, \mathbb{P} \right)$ is given by
$$\int_{\Omega} X(\omega) \ d \mathbb{P}(\omega)$$
which is also written as
$$\int_{\Omega} X(\omega) \ \mathbb{P}(d\omega) $$
In probability theory this is just the expectation of $X$ und... | $\int_a^b \mathbb{P}(\mathrm{d}x) = \int_a^b \mathbb{P}(x)\mathrm{d}x$? | In general, the $\mathbb{P}$-integral of a measurable function $X$ on $\left(\Omega, \mathcal{A}, \mathbb{P} \right)$ is given by
$$\int_{\Omega} X(\omega) \ d \mathbb{P}(\omega)$$
which is also writ | $\int_a^b \mathbb{P}(\mathrm{d}x) = \int_a^b \mathbb{P}(x)\mathrm{d}x$?
In general, the $\mathbb{P}$-integral of a measurable function $X$ on $\left(\Omega, \mathcal{A}, \mathbb{P} \right)$ is given by
$$\int_{\Omega} X(\omega) \ d \mathbb{P}(\omega)$$
which is also written as
$$\int_{\Omega} X(\omega) \ \mathbb{P}(d... | $\int_a^b \mathbb{P}(\mathrm{d}x) = \int_a^b \mathbb{P}(x)\mathrm{d}x$?
In general, the $\mathbb{P}$-integral of a measurable function $X$ on $\left(\Omega, \mathcal{A}, \mathbb{P} \right)$ is given by
$$\int_{\Omega} X(\omega) \ d \mathbb{P}(\omega)$$
which is also writ |
53,686 | $\int_a^b \mathbb{P}(\mathrm{d}x) = \int_a^b \mathbb{P}(x)\mathrm{d}x$? | Just started to write a similar question before already finding it asked before on SO. Your suspicion is probably correct, at least as the notation $Pr(dx,dy)$ instead of $\mathbb P$ is concerned. See this SO answer to a question regarding an equation in the book The elements of statistical learning.
@Jerry wrote:
For... | $\int_a^b \mathbb{P}(\mathrm{d}x) = \int_a^b \mathbb{P}(x)\mathrm{d}x$? | Just started to write a similar question before already finding it asked before on SO. Your suspicion is probably correct, at least as the notation $Pr(dx,dy)$ instead of $\mathbb P$ is concerned. See | $\int_a^b \mathbb{P}(\mathrm{d}x) = \int_a^b \mathbb{P}(x)\mathrm{d}x$?
Just started to write a similar question before already finding it asked before on SO. Your suspicion is probably correct, at least as the notation $Pr(dx,dy)$ instead of $\mathbb P$ is concerned. See this SO answer to a question regarding an equat... | $\int_a^b \mathbb{P}(\mathrm{d}x) = \int_a^b \mathbb{P}(x)\mathrm{d}x$?
Just started to write a similar question before already finding it asked before on SO. Your suspicion is probably correct, at least as the notation $Pr(dx,dy)$ instead of $\mathbb P$ is concerned. See |
53,687 | Does the square of the minimum of two correlated Normal variables have a chi-squared distribution? | The result is not true.
As a counterexample, let $(X,Y)$ have standard Normal margins with a Clayton copula, as illustrated at https://stats.stackexchange.com/a/30205. Generating 10,000 independent realizations of this bivariate distribution, as shown in the lower left of the figure, produces 10,000 realizations of $Z... | Does the square of the minimum of two correlated Normal variables have a chi-squared distribution? | The result is not true.
As a counterexample, let $(X,Y)$ have standard Normal margins with a Clayton copula, as illustrated at https://stats.stackexchange.com/a/30205. Generating 10,000 independent r | Does the square of the minimum of two correlated Normal variables have a chi-squared distribution?
The result is not true.
As a counterexample, let $(X,Y)$ have standard Normal margins with a Clayton copula, as illustrated at https://stats.stackexchange.com/a/30205. Generating 10,000 independent realizations of this b... | Does the square of the minimum of two correlated Normal variables have a chi-squared distribution?
The result is not true.
As a counterexample, let $(X,Y)$ have standard Normal margins with a Clayton copula, as illustrated at https://stats.stackexchange.com/a/30205. Generating 10,000 independent r |
53,688 | Does the square of the minimum of two correlated Normal variables have a chi-squared distribution? | Let $M=min(X,Y)^2$,
$$
P(M<m) = P(M<m,X<Y) + P(M<m,X>Y) ~~~~~~~~~~~\\
= P(M<m|X<Y)P(X<Y) + P(M<m|X>Y)P(X>Y) \\
= P(X^2<m)P(X<Y) + P(Y^2<m)P(X>Y) ~~~~~~~~~~~~~~~~~~~~~~\\
= \frac{1}{2}P(X^2<m) + \frac{1}{2}P(Y^2<m) \quad \quad \quad\quad\quad\quad\quad\quad\quad\quad~ \\
=P(X^2<m) \qquad \qquad \qquad \qquad \qquad ... | Does the square of the minimum of two correlated Normal variables have a chi-squared distribution? | Let $M=min(X,Y)^2$,
$$
P(M<m) = P(M<m,X<Y) + P(M<m,X>Y) ~~~~~~~~~~~\\
= P(M<m|X<Y)P(X<Y) + P(M<m|X>Y)P(X>Y) \\
= P(X^2<m)P(X<Y) + P(Y^2<m)P(X>Y) ~~~~~~~~~~~~~~~~~~~~~~\\
= \frac{1}{2}P(X^2<m) + \frac{ | Does the square of the minimum of two correlated Normal variables have a chi-squared distribution?
Let $M=min(X,Y)^2$,
$$
P(M<m) = P(M<m,X<Y) + P(M<m,X>Y) ~~~~~~~~~~~\\
= P(M<m|X<Y)P(X<Y) + P(M<m|X>Y)P(X>Y) \\
= P(X^2<m)P(X<Y) + P(Y^2<m)P(X>Y) ~~~~~~~~~~~~~~~~~~~~~~\\
= \frac{1}{2}P(X^2<m) + \frac{1}{2}P(Y^2<m) \quad \... | Does the square of the minimum of two correlated Normal variables have a chi-squared distribution?
Let $M=min(X,Y)^2$,
$$
P(M<m) = P(M<m,X<Y) + P(M<m,X>Y) ~~~~~~~~~~~\\
= P(M<m|X<Y)P(X<Y) + P(M<m|X>Y)P(X>Y) \\
= P(X^2<m)P(X<Y) + P(Y^2<m)P(X>Y) ~~~~~~~~~~~~~~~~~~~~~~\\
= \frac{1}{2}P(X^2<m) + \frac{ |
53,689 | Normality test before testing the difference between two groups. Is it necessary? | While it is possible to test for normality, it is often not very useful to do so. Very few datasets come from an exactly normal distribution and many parametric statistical procedures work well even when the distribution is only "kind of normalish".
(I will note that the unequal sample size may mean that procedures mi... | Normality test before testing the difference between two groups. Is it necessary? | While it is possible to test for normality, it is often not very useful to do so. Very few datasets come from an exactly normal distribution and many parametric statistical procedures work well even w | Normality test before testing the difference between two groups. Is it necessary?
While it is possible to test for normality, it is often not very useful to do so. Very few datasets come from an exactly normal distribution and many parametric statistical procedures work well even when the distribution is only "kind of ... | Normality test before testing the difference between two groups. Is it necessary?
While it is possible to test for normality, it is often not very useful to do so. Very few datasets come from an exactly normal distribution and many parametric statistical procedures work well even w |
53,690 | Normalizing Features for use with KNN | RESCALING attribute data to values to scale the range in [0, 1] or [−1, 1] is useful for the optimization algorithms, such as gradient descent, that are used within machine learning algorithms that weight inputs (e.g. regression and neural networks). Rescaling is also used for algorithms that use distance measurements ... | Normalizing Features for use with KNN | RESCALING attribute data to values to scale the range in [0, 1] or [−1, 1] is useful for the optimization algorithms, such as gradient descent, that are used within machine learning algorithms that we | Normalizing Features for use with KNN
RESCALING attribute data to values to scale the range in [0, 1] or [−1, 1] is useful for the optimization algorithms, such as gradient descent, that are used within machine learning algorithms that weight inputs (e.g. regression and neural networks). Rescaling is also used for algo... | Normalizing Features for use with KNN
RESCALING attribute data to values to scale the range in [0, 1] or [−1, 1] is useful for the optimization algorithms, such as gradient descent, that are used within machine learning algorithms that we |
53,691 | Practical meaning of expected value (mean value), variance and standard deviation? | I'll go with the cliche example - coin flipping. Note that I'm abandoning rigor and some important assumptions in this example, but that's just fine.
Let's say I have a regular coin - that is, once I flip it, it has a 50% chance of landing heads and a 50% chance of landing tails.
So if I flip it 10 times, I'd expect 5 ... | Practical meaning of expected value (mean value), variance and standard deviation? | I'll go with the cliche example - coin flipping. Note that I'm abandoning rigor and some important assumptions in this example, but that's just fine.
Let's say I have a regular coin - that is, once I | Practical meaning of expected value (mean value), variance and standard deviation?
I'll go with the cliche example - coin flipping. Note that I'm abandoning rigor and some important assumptions in this example, but that's just fine.
Let's say I have a regular coin - that is, once I flip it, it has a 50% chance of landi... | Practical meaning of expected value (mean value), variance and standard deviation?
I'll go with the cliche example - coin flipping. Note that I'm abandoning rigor and some important assumptions in this example, but that's just fine.
Let's say I have a regular coin - that is, once I |
53,692 | Practical meaning of expected value (mean value), variance and standard deviation? | A random variable is a quantity whose value appears to be random when measured. As @ilan man describes, the observation of Heads or Tails in a coin flip experiment is one simple example. You could also define a random variable to be the average value of the last ten tosses of the coin (mapping H to 1 and T to 0, for ex... | Practical meaning of expected value (mean value), variance and standard deviation? | A random variable is a quantity whose value appears to be random when measured. As @ilan man describes, the observation of Heads or Tails in a coin flip experiment is one simple example. You could als | Practical meaning of expected value (mean value), variance and standard deviation?
A random variable is a quantity whose value appears to be random when measured. As @ilan man describes, the observation of Heads or Tails in a coin flip experiment is one simple example. You could also define a random variable to be the ... | Practical meaning of expected value (mean value), variance and standard deviation?
A random variable is a quantity whose value appears to be random when measured. As @ilan man describes, the observation of Heads or Tails in a coin flip experiment is one simple example. You could als |
53,693 | Practical meaning of expected value (mean value), variance and standard deviation? | May be for someone it will be helpful to see how expected value $\largeμ$, variance $\largeσ^2$ and standard deviation $\largeσ$ are related in normal distribution for random variables.
In formula:
$ f(x) = \Large\frac{1}{\sqrt{2 \pi \sigma^2}} e^{-\frac{(x-\mu)^2}{2 \sigma^2}}
$
On the graph:
For the normal distribut... | Practical meaning of expected value (mean value), variance and standard deviation? | May be for someone it will be helpful to see how expected value $\largeμ$, variance $\largeσ^2$ and standard deviation $\largeσ$ are related in normal distribution for random variables.
In formula:
$ | Practical meaning of expected value (mean value), variance and standard deviation?
May be for someone it will be helpful to see how expected value $\largeμ$, variance $\largeσ^2$ and standard deviation $\largeσ$ are related in normal distribution for random variables.
In formula:
$ f(x) = \Large\frac{1}{\sqrt{2 \pi \si... | Practical meaning of expected value (mean value), variance and standard deviation?
May be for someone it will be helpful to see how expected value $\largeμ$, variance $\largeσ^2$ and standard deviation $\largeσ$ are related in normal distribution for random variables.
In formula:
$ |
53,694 | Practical meaning of expected value (mean value), variance and standard deviation? | I suspect that probability density function is called after the density in physics. Hence, the mean corresponds to a center of mass of a body. | Practical meaning of expected value (mean value), variance and standard deviation? | I suspect that probability density function is called after the density in physics. Hence, the mean corresponds to a center of mass of a body. | Practical meaning of expected value (mean value), variance and standard deviation?
I suspect that probability density function is called after the density in physics. Hence, the mean corresponds to a center of mass of a body. | Practical meaning of expected value (mean value), variance and standard deviation?
I suspect that probability density function is called after the density in physics. Hence, the mean corresponds to a center of mass of a body. |
53,695 | Make prediction equation from logistic regression coefficients | Unfortunately, what you seem to have run was not a logistic regression model. Note that linear regression (i.e., with normally-distributed residuals) is a special case of the generalized linear model. By default, R assumes a call to glm() is requesting that. You can see that you got that at the bottom of your output... | Make prediction equation from logistic regression coefficients | Unfortunately, what you seem to have run was not a logistic regression model. Note that linear regression (i.e., with normally-distributed residuals) is a special case of the generalized linear model | Make prediction equation from logistic regression coefficients
Unfortunately, what you seem to have run was not a logistic regression model. Note that linear regression (i.e., with normally-distributed residuals) is a special case of the generalized linear model. By default, R assumes a call to glm() is requesting th... | Make prediction equation from logistic regression coefficients
Unfortunately, what you seem to have run was not a logistic regression model. Note that linear regression (i.e., with normally-distributed residuals) is a special case of the generalized linear model |
53,696 | Practical applications of the Laplace and Cauchy distributions | One example is using them as robust priors for regression parameters, where Laplace prior corresponds to LASSO (Tibshirani, 1996) , but $t$-distribution, or Cauchy are other alternatives (Gelman et al, 2008).
Moreover, you can have L1 regularized regression with Laplace errors (i.e. minimizing absolute error).
Another ... | Practical applications of the Laplace and Cauchy distributions | One example is using them as robust priors for regression parameters, where Laplace prior corresponds to LASSO (Tibshirani, 1996) , but $t$-distribution, or Cauchy are other alternatives (Gelman et al | Practical applications of the Laplace and Cauchy distributions
One example is using them as robust priors for regression parameters, where Laplace prior corresponds to LASSO (Tibshirani, 1996) , but $t$-distribution, or Cauchy are other alternatives (Gelman et al, 2008).
Moreover, you can have L1 regularized regression... | Practical applications of the Laplace and Cauchy distributions
One example is using them as robust priors for regression parameters, where Laplace prior corresponds to LASSO (Tibshirani, 1996) , but $t$-distribution, or Cauchy are other alternatives (Gelman et al |
53,697 | Practical applications of the Laplace and Cauchy distributions | I would like to add an interesting case where the Cauchy distribution can arise in Biology.
Imagine you are a shark roaming around a space $A \subset \mathbb R^3$ in search of food, which is represented mathematically by the neighborhoods $N_\epsilon(x_i)$ of several food sources $x_i$.
Brownian motion refers to the ... | Practical applications of the Laplace and Cauchy distributions | I would like to add an interesting case where the Cauchy distribution can arise in Biology.
Imagine you are a shark roaming around a space $A \subset \mathbb R^3$ in search of food, which is represen | Practical applications of the Laplace and Cauchy distributions
I would like to add an interesting case where the Cauchy distribution can arise in Biology.
Imagine you are a shark roaming around a space $A \subset \mathbb R^3$ in search of food, which is represented mathematically by the neighborhoods $N_\epsilon(x_i)$... | Practical applications of the Laplace and Cauchy distributions
I would like to add an interesting case where the Cauchy distribution can arise in Biology.
Imagine you are a shark roaming around a space $A \subset \mathbb R^3$ in search of food, which is represen |
53,698 | Practical applications of the Laplace and Cauchy distributions | The Laplace distribution is also related to median linear regression models. For a model:
$$y_i=x_i^T\beta + \epsilon_i,$$
where $\epsilon_i$ are iid Laplace with location $0$ and scale $\sigma$, the maximum likelihood estimators of $\beta$ coincide with the median regression estimators
$$\hat{\beta} =\text{argmin} \su... | Practical applications of the Laplace and Cauchy distributions | The Laplace distribution is also related to median linear regression models. For a model:
$$y_i=x_i^T\beta + \epsilon_i,$$
where $\epsilon_i$ are iid Laplace with location $0$ and scale $\sigma$, the | Practical applications of the Laplace and Cauchy distributions
The Laplace distribution is also related to median linear regression models. For a model:
$$y_i=x_i^T\beta + \epsilon_i,$$
where $\epsilon_i$ are iid Laplace with location $0$ and scale $\sigma$, the maximum likelihood estimators of $\beta$ coincide with th... | Practical applications of the Laplace and Cauchy distributions
The Laplace distribution is also related to median linear regression models. For a model:
$$y_i=x_i^T\beta + \epsilon_i,$$
where $\epsilon_i$ are iid Laplace with location $0$ and scale $\sigma$, the |
53,699 | In linear regression, is there any meaning for the term $X^Ty$? | I'll try to explain it from the linear algebra point of view, but I'm not sure if it's what you need.
First of all, when solving the equation in the case of inconsistent system, we know that $\hat y$ is the orthogonal projection of $y$ onto the column space of $X$. In other words, $\hat y$ can be estimated by $X \hat \... | In linear regression, is there any meaning for the term $X^Ty$? | I'll try to explain it from the linear algebra point of view, but I'm not sure if it's what you need.
First of all, when solving the equation in the case of inconsistent system, we know that $\hat y$ | In linear regression, is there any meaning for the term $X^Ty$?
I'll try to explain it from the linear algebra point of view, but I'm not sure if it's what you need.
First of all, when solving the equation in the case of inconsistent system, we know that $\hat y$ is the orthogonal projection of $y$ onto the column spac... | In linear regression, is there any meaning for the term $X^Ty$?
I'll try to explain it from the linear algebra point of view, but I'm not sure if it's what you need.
First of all, when solving the equation in the case of inconsistent system, we know that $\hat y$ |
53,700 | In linear regression, is there any meaning for the term $X^Ty$? | People sometimes break that quantity up a little differently and call $\bf{P=X(X^T X)^{-1}}X^{T}$ the Projection matrix, influence matrix, or hat matrix. You can think of the projection matrix as mapping between the actual $y$ values and the predicted ones.
The projection matrix has a number of handy properties. In ... | In linear regression, is there any meaning for the term $X^Ty$? | People sometimes break that quantity up a little differently and call $\bf{P=X(X^T X)^{-1}}X^{T}$ the Projection matrix, influence matrix, or hat matrix. You can think of the projection matrix as mapp | In linear regression, is there any meaning for the term $X^Ty$?
People sometimes break that quantity up a little differently and call $\bf{P=X(X^T X)^{-1}}X^{T}$ the Projection matrix, influence matrix, or hat matrix. You can think of the projection matrix as mapping between the actual $y$ values and the predicted ones... | In linear regression, is there any meaning for the term $X^Ty$?
People sometimes break that quantity up a little differently and call $\bf{P=X(X^T X)^{-1}}X^{T}$ the Projection matrix, influence matrix, or hat matrix. You can think of the projection matrix as mapp |
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