idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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40,601 | Is this a valid way to construct a confidence interval? | Given $k=0$ successes of $n$ trials, the exact (Clopper–Pearson) confidence interval is $[p_1,p_2]$ such that $$P(K \ge k=0 \vert p=p_1)=\frac{\alpha}{2}$$
and $$P(K \le k=0 \vert p=p_2)=\frac{\alpha}{2},$$
where $K \sim Binomial(n,p)$. You can calculate $[p_1,p_2]$ using the inverse binomial function. However, it is a... | Is this a valid way to construct a confidence interval? | Given $k=0$ successes of $n$ trials, the exact (Clopper–Pearson) confidence interval is $[p_1,p_2]$ such that $$P(K \ge k=0 \vert p=p_1)=\frac{\alpha}{2}$$
and $$P(K \le k=0 \vert p=p_2)=\frac{\alpha} | Is this a valid way to construct a confidence interval?
Given $k=0$ successes of $n$ trials, the exact (Clopper–Pearson) confidence interval is $[p_1,p_2]$ such that $$P(K \ge k=0 \vert p=p_1)=\frac{\alpha}{2}$$
and $$P(K \le k=0 \vert p=p_2)=\frac{\alpha}{2},$$
where $K \sim Binomial(n,p)$. You can calculate $[p_1,p_2... | Is this a valid way to construct a confidence interval?
Given $k=0$ successes of $n$ trials, the exact (Clopper–Pearson) confidence interval is $[p_1,p_2]$ such that $$P(K \ge k=0 \vert p=p_1)=\frac{\alpha}{2}$$
and $$P(K \le k=0 \vert p=p_2)=\frac{\alpha} |
40,602 | t-SNE dimensions as additional predictor variables | When you computed the tSNE representation of the data, presumably you used all of the data and so the data in your CV hold-out set was actually considered in your training data. It is built into the tSNE components. I do not believe that there is any way to predict the tSNE coordinates of new data points, so this meth... | t-SNE dimensions as additional predictor variables | When you computed the tSNE representation of the data, presumably you used all of the data and so the data in your CV hold-out set was actually considered in your training data. It is built into the t | t-SNE dimensions as additional predictor variables
When you computed the tSNE representation of the data, presumably you used all of the data and so the data in your CV hold-out set was actually considered in your training data. It is built into the tSNE components. I do not believe that there is any way to predict th... | t-SNE dimensions as additional predictor variables
When you computed the tSNE representation of the data, presumably you used all of the data and so the data in your CV hold-out set was actually considered in your training data. It is built into the t |
40,603 | t-SNE dimensions as additional predictor variables | Not worthy of an answer, but too long for a comment. I am also interested in this question. The theory seems quite difficult as you are layering a non-linear algorithm over top of another one. TL;DR I'm surprised it works very well, I would look into the hyperparameters of your random forest. But since the theory is qu... | t-SNE dimensions as additional predictor variables | Not worthy of an answer, but too long for a comment. I am also interested in this question. The theory seems quite difficult as you are layering a non-linear algorithm over top of another one. TL;DR I | t-SNE dimensions as additional predictor variables
Not worthy of an answer, but too long for a comment. I am also interested in this question. The theory seems quite difficult as you are layering a non-linear algorithm over top of another one. TL;DR I'm surprised it works very well, I would look into the hyperparameter... | t-SNE dimensions as additional predictor variables
Not worthy of an answer, but too long for a comment. I am also interested in this question. The theory seems quite difficult as you are layering a non-linear algorithm over top of another one. TL;DR I |
40,604 | t-SNE dimensions as additional predictor variables | Do not use $t$-SNE as predictor variables (in general).
As it has been pointed out in a previous answer in a best-case scenario using all the data to compute the $t$-SNE representation is a bad practice even if one holds out the response variable. In addition using $t$-SNE directly also renders the original modelling ... | t-SNE dimensions as additional predictor variables | Do not use $t$-SNE as predictor variables (in general).
As it has been pointed out in a previous answer in a best-case scenario using all the data to compute the $t$-SNE representation is a bad pract | t-SNE dimensions as additional predictor variables
Do not use $t$-SNE as predictor variables (in general).
As it has been pointed out in a previous answer in a best-case scenario using all the data to compute the $t$-SNE representation is a bad practice even if one holds out the response variable. In addition using $t... | t-SNE dimensions as additional predictor variables
Do not use $t$-SNE as predictor variables (in general).
As it has been pointed out in a previous answer in a best-case scenario using all the data to compute the $t$-SNE representation is a bad pract |
40,605 | t-SNE dimensions as additional predictor variables | I'll also assume, as did G5W, that you used all your data in generating your coordinates. Given this, I'm aware of perhaps two mechanisms to use t-SNE as a predictor on a go-forward basis:
For all new "live" data, rebuild the model after running t-SNE on your entire dataset. The order would be something like: 1) Get... | t-SNE dimensions as additional predictor variables | I'll also assume, as did G5W, that you used all your data in generating your coordinates. Given this, I'm aware of perhaps two mechanisms to use t-SNE as a predictor on a go-forward basis:
For all n | t-SNE dimensions as additional predictor variables
I'll also assume, as did G5W, that you used all your data in generating your coordinates. Given this, I'm aware of perhaps two mechanisms to use t-SNE as a predictor on a go-forward basis:
For all new "live" data, rebuild the model after running t-SNE on your entire ... | t-SNE dimensions as additional predictor variables
I'll also assume, as did G5W, that you used all your data in generating your coordinates. Given this, I'm aware of perhaps two mechanisms to use t-SNE as a predictor on a go-forward basis:
For all n |
40,606 | How to use "IDs" as an input variable to a ML model? | ID variables like phone number should not be included as predictors, because you are trying to train a model to understand general patterns. Phone number doesn't offer the model any real insight into what drives fraud vs non-fraud. You'd be better off using a lookup table after the fact to flag transactions linked to t... | How to use "IDs" as an input variable to a ML model? | ID variables like phone number should not be included as predictors, because you are trying to train a model to understand general patterns. Phone number doesn't offer the model any real insight into | How to use "IDs" as an input variable to a ML model?
ID variables like phone number should not be included as predictors, because you are trying to train a model to understand general patterns. Phone number doesn't offer the model any real insight into what drives fraud vs non-fraud. You'd be better off using a lookup ... | How to use "IDs" as an input variable to a ML model?
ID variables like phone number should not be included as predictors, because you are trying to train a model to understand general patterns. Phone number doesn't offer the model any real insight into |
40,607 | How to use "IDs" as an input variable to a ML model? | With new functionalities implemented in tensorflow such as hashing and embedding, I was able to take advantage of ID variables in my data and use them as predictive variables. You can find the explanation in this post:
https://developers.googleblog.com/2017/11/introducing-tensorflow-feature-columns.html | How to use "IDs" as an input variable to a ML model? | With new functionalities implemented in tensorflow such as hashing and embedding, I was able to take advantage of ID variables in my data and use them as predictive variables. You can find the explana | How to use "IDs" as an input variable to a ML model?
With new functionalities implemented in tensorflow such as hashing and embedding, I was able to take advantage of ID variables in my data and use them as predictive variables. You can find the explanation in this post:
https://developers.googleblog.com/2017/11/introd... | How to use "IDs" as an input variable to a ML model?
With new functionalities implemented in tensorflow such as hashing and embedding, I was able to take advantage of ID variables in my data and use them as predictive variables. You can find the explana |
40,608 | How does the ReLU function work for z < 0? | Both back and forward propagation are faster to evaluate for the same reason: relu doesn't need any calculation. The gradient is either 0 on the negative value or 1 for the positive.
I wouldn't say that the gradient descent moves faster due to gradient being 1 on the positive values. It's only the calculations are fast... | How does the ReLU function work for z < 0? | Both back and forward propagation are faster to evaluate for the same reason: relu doesn't need any calculation. The gradient is either 0 on the negative value or 1 for the positive.
I wouldn't say th | How does the ReLU function work for z < 0?
Both back and forward propagation are faster to evaluate for the same reason: relu doesn't need any calculation. The gradient is either 0 on the negative value or 1 for the positive.
I wouldn't say that the gradient descent moves faster due to gradient being 1 on the positive ... | How does the ReLU function work for z < 0?
Both back and forward propagation are faster to evaluate for the same reason: relu doesn't need any calculation. The gradient is either 0 on the negative value or 1 for the positive.
I wouldn't say th |
40,609 | How does the ReLU function work for z < 0? | The gradient is zero, which means nothing gets backpropagated through them; the precise value fed to this neuron doesn't matter when $z<0$. If a RELU unit is always in the left part of the graph, you get the dying/dead RELU problem; this is one of the reasons that people have looked for alternatives to RELUs.
Sigmoid... | How does the ReLU function work for z < 0? | The gradient is zero, which means nothing gets backpropagated through them; the precise value fed to this neuron doesn't matter when $z<0$. If a RELU unit is always in the left part of the graph, yo | How does the ReLU function work for z < 0?
The gradient is zero, which means nothing gets backpropagated through them; the precise value fed to this neuron doesn't matter when $z<0$. If a RELU unit is always in the left part of the graph, you get the dying/dead RELU problem; this is one of the reasons that people hav... | How does the ReLU function work for z < 0?
The gradient is zero, which means nothing gets backpropagated through them; the precise value fed to this neuron doesn't matter when $z<0$. If a RELU unit is always in the left part of the graph, yo |
40,610 | Difference between (factor|group) and (1|factor:group) specifications in lme4 | At first sight, there are two main differences:
mod1 is a random intercept and random slope model while mod2 is a random intercept model (without random slope): (year|cluster) implicitly includes the intercept and thus expands to (1 + year|cluster). In this case you assume a different baseline for each cluster and all... | Difference between (factor|group) and (1|factor:group) specifications in lme4 | At first sight, there are two main differences:
mod1 is a random intercept and random slope model while mod2 is a random intercept model (without random slope): (year|cluster) implicitly includes the | Difference between (factor|group) and (1|factor:group) specifications in lme4
At first sight, there are two main differences:
mod1 is a random intercept and random slope model while mod2 is a random intercept model (without random slope): (year|cluster) implicitly includes the intercept and thus expands to (1 + year|c... | Difference between (factor|group) and (1|factor:group) specifications in lme4
At first sight, there are two main differences:
mod1 is a random intercept and random slope model while mod2 is a random intercept model (without random slope): (year|cluster) implicitly includes the |
40,611 | Entropy of distribution with uniform sub-distribution | Simply apply the entropy formula: the result drops right out. The idea is that $A$ alone contributes at least $$-|A| \left(\frac{1}{|A|}\right)\log\left(\frac{1}{|A|}\right)=\log|A|$$ to the entropy and any other terms in the entropy formula can only increase it further. Details follow.
First, let's be clear about t... | Entropy of distribution with uniform sub-distribution | Simply apply the entropy formula: the result drops right out. The idea is that $A$ alone contributes at least $$-|A| \left(\frac{1}{|A|}\right)\log\left(\frac{1}{|A|}\right)=\log|A|$$ to the entropy | Entropy of distribution with uniform sub-distribution
Simply apply the entropy formula: the result drops right out. The idea is that $A$ alone contributes at least $$-|A| \left(\frac{1}{|A|}\right)\log\left(\frac{1}{|A|}\right)=\log|A|$$ to the entropy and any other terms in the entropy formula can only increase it fu... | Entropy of distribution with uniform sub-distribution
Simply apply the entropy formula: the result drops right out. The idea is that $A$ alone contributes at least $$-|A| \left(\frac{1}{|A|}\right)\log\left(\frac{1}{|A|}\right)=\log|A|$$ to the entropy |
40,612 | How can I show whether or not two time series are “different” from one another? | Because the variance in a count or proportion tends to be proportional to the count or proportion itself, theory (and much experience) suggest analyzing the square roots of the data.
See for yourself by plotting the proportions and overall counts on square-root axes.
So that each column has a visual impact directly pr... | How can I show whether or not two time series are “different” from one another? | Because the variance in a count or proportion tends to be proportional to the count or proportion itself, theory (and much experience) suggest analyzing the square roots of the data.
See for yourself | How can I show whether or not two time series are “different” from one another?
Because the variance in a count or proportion tends to be proportional to the count or proportion itself, theory (and much experience) suggest analyzing the square roots of the data.
See for yourself by plotting the proportions and overall ... | How can I show whether or not two time series are “different” from one another?
Because the variance in a count or proportion tends to be proportional to the count or proportion itself, theory (and much experience) suggest analyzing the square roots of the data.
See for yourself |
40,613 | Are deep neural networks robust to outliers? | Relative to a standard multiple regression model, I believe an MLP is much more robust to outliers. This is the case for several reasons:
1) the multiple regression has only one single shot at fitting the data. Meanwhile the MLP has so many more opportunities to fit the data by varying the number of nodes and hidden ... | Are deep neural networks robust to outliers? | Relative to a standard multiple regression model, I believe an MLP is much more robust to outliers. This is the case for several reasons:
1) the multiple regression has only one single shot at fittin | Are deep neural networks robust to outliers?
Relative to a standard multiple regression model, I believe an MLP is much more robust to outliers. This is the case for several reasons:
1) the multiple regression has only one single shot at fitting the data. Meanwhile the MLP has so many more opportunities to fit the da... | Are deep neural networks robust to outliers?
Relative to a standard multiple regression model, I believe an MLP is much more robust to outliers. This is the case for several reasons:
1) the multiple regression has only one single shot at fittin |
40,614 | Are deep neural networks robust to outliers? | Based on this article by Lin and Tegmark (below), I think the answer is "it depends." In other words and as they state, most deep learning algorithms assume a lognormal distribution. As long as your data fits that assumption, then there is no problem. The problem is when the tails of the distribution are more extreme t... | Are deep neural networks robust to outliers? | Based on this article by Lin and Tegmark (below), I think the answer is "it depends." In other words and as they state, most deep learning algorithms assume a lognormal distribution. As long as your d | Are deep neural networks robust to outliers?
Based on this article by Lin and Tegmark (below), I think the answer is "it depends." In other words and as they state, most deep learning algorithms assume a lognormal distribution. As long as your data fits that assumption, then there is no problem. The problem is when the... | Are deep neural networks robust to outliers?
Based on this article by Lin and Tegmark (below), I think the answer is "it depends." In other words and as they state, most deep learning algorithms assume a lognormal distribution. As long as your d |
40,615 | Are deep neural networks robust to outliers? | Multilayer Perceptron (MLP) are sensitive to outliers.
MLP are universal approximators i.e. they can be used to approximate any target function. With such an expressive hypothesis space, MLP may risk overfitting by learning from noise (outliers).
Outliers can also cause slow/no learning to take place because of the van... | Are deep neural networks robust to outliers? | Multilayer Perceptron (MLP) are sensitive to outliers.
MLP are universal approximators i.e. they can be used to approximate any target function. With such an expressive hypothesis space, MLP may risk | Are deep neural networks robust to outliers?
Multilayer Perceptron (MLP) are sensitive to outliers.
MLP are universal approximators i.e. they can be used to approximate any target function. With such an expressive hypothesis space, MLP may risk overfitting by learning from noise (outliers).
Outliers can also cause slow... | Are deep neural networks robust to outliers?
Multilayer Perceptron (MLP) are sensitive to outliers.
MLP are universal approximators i.e. they can be used to approximate any target function. With such an expressive hypothesis space, MLP may risk |
40,616 | Computing Bayesian Credible Intervals for Bayesian Regression | Unfortunately, the interval that you are looking for is not uniquely determined. Essentially, what you need is the Posterior Predictive Density (PPD, see https://en.wikipedia.org/wiki/Posterior_predictive_distribution), which is the density function of new/unseen data given the observed data. This PPD depends on the po... | Computing Bayesian Credible Intervals for Bayesian Regression | Unfortunately, the interval that you are looking for is not uniquely determined. Essentially, what you need is the Posterior Predictive Density (PPD, see https://en.wikipedia.org/wiki/Posterior_predic | Computing Bayesian Credible Intervals for Bayesian Regression
Unfortunately, the interval that you are looking for is not uniquely determined. Essentially, what you need is the Posterior Predictive Density (PPD, see https://en.wikipedia.org/wiki/Posterior_predictive_distribution), which is the density function of new/u... | Computing Bayesian Credible Intervals for Bayesian Regression
Unfortunately, the interval that you are looking for is not uniquely determined. Essentially, what you need is the Posterior Predictive Density (PPD, see https://en.wikipedia.org/wiki/Posterior_predic |
40,617 | How are robust standard errors calculated in the case of logistic regression? | The definition is completely analogous if you use the so-called working residuals and if regressors and residuals are weighted appropriately. The working weights are part of the usual iteratively weighted least squares (IWLS) algorithm employed for generalized linear models (including logistic regression).
The main ide... | How are robust standard errors calculated in the case of logistic regression? | The definition is completely analogous if you use the so-called working residuals and if regressors and residuals are weighted appropriately. The working weights are part of the usual iteratively weig | How are robust standard errors calculated in the case of logistic regression?
The definition is completely analogous if you use the so-called working residuals and if regressors and residuals are weighted appropriately. The working weights are part of the usual iteratively weighted least squares (IWLS) algorithm employ... | How are robust standard errors calculated in the case of logistic regression?
The definition is completely analogous if you use the so-called working residuals and if regressors and residuals are weighted appropriately. The working weights are part of the usual iteratively weig |
40,618 | Multiple polynomial regression versus GAM | The two models you fitted are exactly equivalent (up to implementational details). The advantage of the GAM framework is that you are not limited to global basis expansions of your covariates. Instead you can use a range of penalized spline bases that may better adapt to the data rather than imposing a particular funct... | Multiple polynomial regression versus GAM | The two models you fitted are exactly equivalent (up to implementational details). The advantage of the GAM framework is that you are not limited to global basis expansions of your covariates. Instead | Multiple polynomial regression versus GAM
The two models you fitted are exactly equivalent (up to implementational details). The advantage of the GAM framework is that you are not limited to global basis expansions of your covariates. Instead you can use a range of penalized spline bases that may better adapt to the da... | Multiple polynomial regression versus GAM
The two models you fitted are exactly equivalent (up to implementational details). The advantage of the GAM framework is that you are not limited to global basis expansions of your covariates. Instead |
40,619 | Multiple polynomial regression versus GAM | If we use lo and s basis expansion in gam, we will see the difference. Here is the demo:
Using no basis expansion and polynomial, gam and lm are the same.
> library(gam)
> anova(lm(mpg~wt,data=mtcars),gam(mpg~wt,data=mtcars))
Analysis of Variance Table
Model 1: mpg ~ wt
Model 2: mpg ~ wt
Res.Df RSS Df Sum of Sq ... | Multiple polynomial regression versus GAM | If we use lo and s basis expansion in gam, we will see the difference. Here is the demo:
Using no basis expansion and polynomial, gam and lm are the same.
> library(gam)
> anova(lm(mpg~wt,data=mtcars) | Multiple polynomial regression versus GAM
If we use lo and s basis expansion in gam, we will see the difference. Here is the demo:
Using no basis expansion and polynomial, gam and lm are the same.
> library(gam)
> anova(lm(mpg~wt,data=mtcars),gam(mpg~wt,data=mtcars))
Analysis of Variance Table
Model 1: mpg ~ wt
Model ... | Multiple polynomial regression versus GAM
If we use lo and s basis expansion in gam, we will see the difference. Here is the demo:
Using no basis expansion and polynomial, gam and lm are the same.
> library(gam)
> anova(lm(mpg~wt,data=mtcars) |
40,620 | How does a Generator (GAN) create samples similar to the data space from a vector of random numbers? | I am not sure I understand probability distribution and random sampling enough to understand this part. Could someone explain what is going on?
In non-math words: the generator $G$ is a network and as such needs some kind of input to produce an image, we call this input $z$ and so the generated images can be seen as $... | How does a Generator (GAN) create samples similar to the data space from a vector of random numbers? | I am not sure I understand probability distribution and random sampling enough to understand this part. Could someone explain what is going on?
In non-math words: the generator $G$ is a network and a | How does a Generator (GAN) create samples similar to the data space from a vector of random numbers?
I am not sure I understand probability distribution and random sampling enough to understand this part. Could someone explain what is going on?
In non-math words: the generator $G$ is a network and as such needs some k... | How does a Generator (GAN) create samples similar to the data space from a vector of random numbers?
I am not sure I understand probability distribution and random sampling enough to understand this part. Could someone explain what is going on?
In non-math words: the generator $G$ is a network and a |
40,621 | How does a Generator (GAN) create samples similar to the data space from a vector of random numbers? | The following idea from this awesome Stanford lecture about generative models was very helpful to me in understanding the sample generations in GANs:
Deep Neural Networks (DNNs) are great in learning mappings from an input X to an output Y but are deterministic, hence cannot generate new samples. To overcome this, we ... | How does a Generator (GAN) create samples similar to the data space from a vector of random numbers? | The following idea from this awesome Stanford lecture about generative models was very helpful to me in understanding the sample generations in GANs:
Deep Neural Networks (DNNs) are great in learning | How does a Generator (GAN) create samples similar to the data space from a vector of random numbers?
The following idea from this awesome Stanford lecture about generative models was very helpful to me in understanding the sample generations in GANs:
Deep Neural Networks (DNNs) are great in learning mappings from an i... | How does a Generator (GAN) create samples similar to the data space from a vector of random numbers?
The following idea from this awesome Stanford lecture about generative models was very helpful to me in understanding the sample generations in GANs:
Deep Neural Networks (DNNs) are great in learning |
40,622 | How to calculate the mean and CI for a percentage | Let me see if I understood your question correctly.
You have a sample of n = 20;
For each observation in this sample you have computed a percentage reduction as a consequence of some treatment: i.e.
\begin{equation}p_i =\frac{x_i,t - x_{i,t-1}}{x_{i,t-1}}\end{equation}
where $x_{i,t}$ is the i-th observation in your ... | How to calculate the mean and CI for a percentage | Let me see if I understood your question correctly.
You have a sample of n = 20;
For each observation in this sample you have computed a percentage reduction as a consequence of some treatment: i.e.
| How to calculate the mean and CI for a percentage
Let me see if I understood your question correctly.
You have a sample of n = 20;
For each observation in this sample you have computed a percentage reduction as a consequence of some treatment: i.e.
\begin{equation}p_i =\frac{x_i,t - x_{i,t-1}}{x_{i,t-1}}\end{equation... | How to calculate the mean and CI for a percentage
Let me see if I understood your question correctly.
You have a sample of n = 20;
For each observation in this sample you have computed a percentage reduction as a consequence of some treatment: i.e.
|
40,623 | How to calculate the mean and CI for a percentage | The data size is small, so I recommend bootstrap confidence intervals.
Resample 20 observations with replacement from your dataset, compute your percent reduction on that resample, and repeat 1000 times. Your x% confidence interval is simply the $\frac{1 - x}{2}$ quantile of your collection to the $\frac{100 - x}{2}$ ... | How to calculate the mean and CI for a percentage | The data size is small, so I recommend bootstrap confidence intervals.
Resample 20 observations with replacement from your dataset, compute your percent reduction on that resample, and repeat 1000 tim | How to calculate the mean and CI for a percentage
The data size is small, so I recommend bootstrap confidence intervals.
Resample 20 observations with replacement from your dataset, compute your percent reduction on that resample, and repeat 1000 times. Your x% confidence interval is simply the $\frac{1 - x}{2}$ quant... | How to calculate the mean and CI for a percentage
The data size is small, so I recommend bootstrap confidence intervals.
Resample 20 observations with replacement from your dataset, compute your percent reduction on that resample, and repeat 1000 tim |
40,624 | How to calculate the mean and CI for a percentage | One very reasonable approach is to log-transform the data (final values and pre-values), perform a linear regression/ANCOVA on the log-transformed data. Then you backtransform (simply exp(x)) to the original scale.
The result can be interpreted as the ratio of geometric means compared to the pre-values. I would then t... | How to calculate the mean and CI for a percentage | One very reasonable approach is to log-transform the data (final values and pre-values), perform a linear regression/ANCOVA on the log-transformed data. Then you backtransform (simply exp(x)) to the o | How to calculate the mean and CI for a percentage
One very reasonable approach is to log-transform the data (final values and pre-values), perform a linear regression/ANCOVA on the log-transformed data. Then you backtransform (simply exp(x)) to the original scale.
The result can be interpreted as the ratio of geometri... | How to calculate the mean and CI for a percentage
One very reasonable approach is to log-transform the data (final values and pre-values), perform a linear regression/ANCOVA on the log-transformed data. Then you backtransform (simply exp(x)) to the o |
40,625 | How to calculate the mean and CI for a percentage | A common approach to this would to use a risk ratio and create the confidence interval around logged risk ratio. The risk ratio is the ratio of the two proportions and can be computed as
$$ RR = \frac{p_1}{p_2} $$
where $p_1$ is the proportion for group 1, and $p_2$ is the proportion for group 2. Working from a 2 by 2 ... | How to calculate the mean and CI for a percentage | A common approach to this would to use a risk ratio and create the confidence interval around logged risk ratio. The risk ratio is the ratio of the two proportions and can be computed as
$$ RR = \frac | How to calculate the mean and CI for a percentage
A common approach to this would to use a risk ratio and create the confidence interval around logged risk ratio. The risk ratio is the ratio of the two proportions and can be computed as
$$ RR = \frac{p_1}{p_2} $$
where $p_1$ is the proportion for group 1, and $p_2$ is ... | How to calculate the mean and CI for a percentage
A common approach to this would to use a risk ratio and create the confidence interval around logged risk ratio. The risk ratio is the ratio of the two proportions and can be computed as
$$ RR = \frac |
40,626 | SVM: Why does the number of support vectors decrease when C is increased? | In short, C is the penalty on the slack variables, which measure the degree to which the margin constraints are violated. A training pattern violates the margin constraint if the kernel expansion (i.e. the output of the SVM) has a value between -1 and +1, and all patterns violating this constraint will be support vect... | SVM: Why does the number of support vectors decrease when C is increased? | In short, C is the penalty on the slack variables, which measure the degree to which the margin constraints are violated. A training pattern violates the margin constraint if the kernel expansion (i. | SVM: Why does the number of support vectors decrease when C is increased?
In short, C is the penalty on the slack variables, which measure the degree to which the margin constraints are violated. A training pattern violates the margin constraint if the kernel expansion (i.e. the output of the SVM) has a value between ... | SVM: Why does the number of support vectors decrease when C is increased?
In short, C is the penalty on the slack variables, which measure the degree to which the margin constraints are violated. A training pattern violates the margin constraint if the kernel expansion (i. |
40,627 | need intuition: why is there no winning strategy to this game? | It's because the numbers R2 and B2 are fixed. If I have unlimited tokens of either color, then the result might be different. But... imagine you only have blue cards left, by some fluke of chance. By this time, I have a certain number of blue tokens and red tokens left. No matter which order I play them the result will... | need intuition: why is there no winning strategy to this game? | It's because the numbers R2 and B2 are fixed. If I have unlimited tokens of either color, then the result might be different. But... imagine you only have blue cards left, by some fluke of chance. By | need intuition: why is there no winning strategy to this game?
It's because the numbers R2 and B2 are fixed. If I have unlimited tokens of either color, then the result might be different. But... imagine you only have blue cards left, by some fluke of chance. By this time, I have a certain number of blue tokens and red... | need intuition: why is there no winning strategy to this game?
It's because the numbers R2 and B2 are fixed. If I have unlimited tokens of either color, then the result might be different. But... imagine you only have blue cards left, by some fluke of chance. By |
40,628 | What's the difference between regression and analysis of variance? | ANOVA isn't a model --- it is a method within a model
The analysis of variance (ANOVA) is a method that occurs within regression models. The technique is based on the law of iterated variance. Suppose you have some regression model:
$$Y_i = f(\mathbf{x}_i, \theta) + \varepsilon_i
\quad \quad \quad
\varepsilon_1,...,\... | What's the difference between regression and analysis of variance? | ANOVA isn't a model --- it is a method within a model
The analysis of variance (ANOVA) is a method that occurs within regression models. The technique is based on the law of iterated variance. Suppo | What's the difference between regression and analysis of variance?
ANOVA isn't a model --- it is a method within a model
The analysis of variance (ANOVA) is a method that occurs within regression models. The technique is based on the law of iterated variance. Suppose you have some regression model:
$$Y_i = f(\mathbf{... | What's the difference between regression and analysis of variance?
ANOVA isn't a model --- it is a method within a model
The analysis of variance (ANOVA) is a method that occurs within regression models. The technique is based on the law of iterated variance. Suppo |
40,629 | What's the difference between regression and analysis of variance? | Yes, they are both OLS linear regression, but:
$X_i$ in the first regression is a continuous predictor. You can subtitle whatever your values you have in your data set into the equation.
$X_i$ in the second regression is a dummy variable. It's $0$ if the response belongs to group 1 otherwise it's $1$.
The look simila... | What's the difference between regression and analysis of variance? | Yes, they are both OLS linear regression, but:
$X_i$ in the first regression is a continuous predictor. You can subtitle whatever your values you have in your data set into the equation.
$X_i$ in the | What's the difference between regression and analysis of variance?
Yes, they are both OLS linear regression, but:
$X_i$ in the first regression is a continuous predictor. You can subtitle whatever your values you have in your data set into the equation.
$X_i$ in the second regression is a dummy variable. It's $0$ if t... | What's the difference between regression and analysis of variance?
Yes, they are both OLS linear regression, but:
$X_i$ in the first regression is a continuous predictor. You can subtitle whatever your values you have in your data set into the equation.
$X_i$ in the |
40,630 | Finding location and scale parameters from PDF | Let's talk about what a location parameter is. (The discussion of scale parameters will exactly parallel it and offers little new.)
The setting concerns a set $\mathcal{F}$ of probability distributions $F_\theta$ indexed by a parameter $\theta \in \Theta \subset \mathbb{R}^p$. "Indexed by" not only means each $\theta... | Finding location and scale parameters from PDF | Let's talk about what a location parameter is. (The discussion of scale parameters will exactly parallel it and offers little new.)
The setting concerns a set $\mathcal{F}$ of probability distributio | Finding location and scale parameters from PDF
Let's talk about what a location parameter is. (The discussion of scale parameters will exactly parallel it and offers little new.)
The setting concerns a set $\mathcal{F}$ of probability distributions $F_\theta$ indexed by a parameter $\theta \in \Theta \subset \mathbb{R... | Finding location and scale parameters from PDF
Let's talk about what a location parameter is. (The discussion of scale parameters will exactly parallel it and offers little new.)
The setting concerns a set $\mathcal{F}$ of probability distributio |
40,631 | Finding location and scale parameters from PDF | Consider a random variable $Z$ with any density function $f_Z(z)$. You can define a location–scale family with the transform $X=\phi Z +\theta$, & the new density function is given by
$$f_X(x;\theta,\phi) = \frac{1}{\phi}\cdot f_Z\left(\frac{x-\theta}{\phi}\right)$$
So any family of distributions whose density function... | Finding location and scale parameters from PDF | Consider a random variable $Z$ with any density function $f_Z(z)$. You can define a location–scale family with the transform $X=\phi Z +\theta$, & the new density function is given by
$$f_X(x;\theta,\ | Finding location and scale parameters from PDF
Consider a random variable $Z$ with any density function $f_Z(z)$. You can define a location–scale family with the transform $X=\phi Z +\theta$, & the new density function is given by
$$f_X(x;\theta,\phi) = \frac{1}{\phi}\cdot f_Z\left(\frac{x-\theta}{\phi}\right)$$
So any... | Finding location and scale parameters from PDF
Consider a random variable $Z$ with any density function $f_Z(z)$. You can define a location–scale family with the transform $X=\phi Z +\theta$, & the new density function is given by
$$f_X(x;\theta,\ |
40,632 | Which binomial prediction interval works well for tail probabilities, i.e. $\hat{p}=1/n$ for large $n$ | There is a simple nonparametric prediction limit. Recall that a prediction limit is a procedure consisting of two independent samples $\mathcal{X}=x_1,\ldots, x_n$ and $\mathcal{Y}=y_1, \ldots, y_m$, two statistics $t$ and $s$, and a size $1-\alpha$. When the chance that $s(\mathcal{Y})$ is less than $t(\mathcal{X})$... | Which binomial prediction interval works well for tail probabilities, i.e. $\hat{p}=1/n$ for large $ | There is a simple nonparametric prediction limit. Recall that a prediction limit is a procedure consisting of two independent samples $\mathcal{X}=x_1,\ldots, x_n$ and $\mathcal{Y}=y_1, \ldots, y_m$, | Which binomial prediction interval works well for tail probabilities, i.e. $\hat{p}=1/n$ for large $n$
There is a simple nonparametric prediction limit. Recall that a prediction limit is a procedure consisting of two independent samples $\mathcal{X}=x_1,\ldots, x_n$ and $\mathcal{Y}=y_1, \ldots, y_m$, two statistics $... | Which binomial prediction interval works well for tail probabilities, i.e. $\hat{p}=1/n$ for large $
There is a simple nonparametric prediction limit. Recall that a prediction limit is a procedure consisting of two independent samples $\mathcal{X}=x_1,\ldots, x_n$ and $\mathcal{Y}=y_1, \ldots, y_m$, |
40,633 | How do I get the Box-Cox log likelihood using the Jacobian? | To ensure that the likelihoods for different values of $\lambda$ are compareable, we need the log likelihood based on the untransformed non-Gaussian data $y_1,\dots,y_n$, that is,
$$
l(\lambda,\boldsymbol{\beta},\sigma^2)=\ln f(y_1,\dots,y_n).\tag{1}
$$
According to the model, the pdf of the transformed data, say $f_{(... | How do I get the Box-Cox log likelihood using the Jacobian? | To ensure that the likelihoods for different values of $\lambda$ are compareable, we need the log likelihood based on the untransformed non-Gaussian data $y_1,\dots,y_n$, that is,
$$
l(\lambda,\boldsy | How do I get the Box-Cox log likelihood using the Jacobian?
To ensure that the likelihoods for different values of $\lambda$ are compareable, we need the log likelihood based on the untransformed non-Gaussian data $y_1,\dots,y_n$, that is,
$$
l(\lambda,\boldsymbol{\beta},\sigma^2)=\ln f(y_1,\dots,y_n).\tag{1}
$$
Accord... | How do I get the Box-Cox log likelihood using the Jacobian?
To ensure that the likelihoods for different values of $\lambda$ are compareable, we need the log likelihood based on the untransformed non-Gaussian data $y_1,\dots,y_n$, that is,
$$
l(\lambda,\boldsy |
40,634 | Variance of a stationary AR(2) model | Stationarity
Considering your AR(2) process with mean zero i.i.d. noise $\epsilon_t$ of variance $\sigma_\epsilon^2$,
$$
y_t = \beta_1 y_{t-1} + \beta_2 y_{t-2} + \epsilon_t \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(*)
$$
we can rewrite it in terms of the lag operator $L$
$$
(1 - \beta_1 L - \beta_2 L^2)y_t = \epsilon_t
$$
s... | Variance of a stationary AR(2) model | Stationarity
Considering your AR(2) process with mean zero i.i.d. noise $\epsilon_t$ of variance $\sigma_\epsilon^2$,
$$
y_t = \beta_1 y_{t-1} + \beta_2 y_{t-2} + \epsilon_t \,\,\,\,\,\,\,\,\,\,\,\,\ | Variance of a stationary AR(2) model
Stationarity
Considering your AR(2) process with mean zero i.i.d. noise $\epsilon_t$ of variance $\sigma_\epsilon^2$,
$$
y_t = \beta_1 y_{t-1} + \beta_2 y_{t-2} + \epsilon_t \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(*)
$$
we can rewrite it in terms of the lag operator $L$
$$
(1 - \beta_1 ... | Variance of a stationary AR(2) model
Stationarity
Considering your AR(2) process with mean zero i.i.d. noise $\epsilon_t$ of variance $\sigma_\epsilon^2$,
$$
y_t = \beta_1 y_{t-1} + \beta_2 y_{t-2} + \epsilon_t \,\,\,\,\,\,\,\,\,\,\,\,\ |
40,635 | Variance of a stationary AR(2) model | I do not have enough reputation to comment, so I’ll post it as an answer instead:
The accepted answer can be simplified to:
$$
\sigma = \frac{\sigma_Z^2}{1-\beta_1^2 (\frac{1+\beta_2}{1-\beta_2})-\beta_2^2}
$$
See also:
Prove the Variance of an AR(2) Model
EDIT:
So I re-did the math and it seems the answer of the poste... | Variance of a stationary AR(2) model | I do not have enough reputation to comment, so I’ll post it as an answer instead:
The accepted answer can be simplified to:
$$
\sigma = \frac{\sigma_Z^2}{1-\beta_1^2 (\frac{1+\beta_2}{1-\beta_2})-\bet | Variance of a stationary AR(2) model
I do not have enough reputation to comment, so I’ll post it as an answer instead:
The accepted answer can be simplified to:
$$
\sigma = \frac{\sigma_Z^2}{1-\beta_1^2 (\frac{1+\beta_2}{1-\beta_2})-\beta_2^2}
$$
See also:
Prove the Variance of an AR(2) Model
EDIT:
So I re-did the math... | Variance of a stationary AR(2) model
I do not have enough reputation to comment, so I’ll post it as an answer instead:
The accepted answer can be simplified to:
$$
\sigma = \frac{\sigma_Z^2}{1-\beta_1^2 (\frac{1+\beta_2}{1-\beta_2})-\bet |
40,636 | Variance of a stationary AR(2) model | Stack it, i.e. write as VAR(1) for the vector x(t) = [y(t),y(t-1)]', x(t) = [beta1,beta2;1,0] x(t-1) + [epsilon(t),0]'. Vectorize the resulting matrix equation and exploit vec(ABC)=(C' kron A) vec(B) | Variance of a stationary AR(2) model | Stack it, i.e. write as VAR(1) for the vector x(t) = [y(t),y(t-1)]', x(t) = [beta1,beta2;1,0] x(t-1) + [epsilon(t),0]'. Vectorize the resulting matrix equation and exploit vec(ABC)=(C' kron A) vec(B) | Variance of a stationary AR(2) model
Stack it, i.e. write as VAR(1) for the vector x(t) = [y(t),y(t-1)]', x(t) = [beta1,beta2;1,0] x(t-1) + [epsilon(t),0]'. Vectorize the resulting matrix equation and exploit vec(ABC)=(C' kron A) vec(B) | Variance of a stationary AR(2) model
Stack it, i.e. write as VAR(1) for the vector x(t) = [y(t),y(t-1)]', x(t) = [beta1,beta2;1,0] x(t-1) + [epsilon(t),0]'. Vectorize the resulting matrix equation and exploit vec(ABC)=(C' kron A) vec(B) |
40,637 | Variance of a stationary AR(2) model | From $X_t = \phi_1 X_{t-1} + \phi_2 X_{t-2} $,
\begin{eqnarray*}
E[ X_t X_{t-k}] &=& \phi_1 E[X_{t-1} X_{t-k}] + \phi_2 E[X_{t-2} X_{t-k}] + E[X_t X_{t-1}] \\
\gamma_k &=& \phi_1 \gamma_{k-1} + \phi_2 \gamma_{k-2} + E[Z_t X_{t-k}] \quad (*)
\end{eqnarray*}
Now,
\begin{eqnarray}
E[Z_t X_{t-k}] = \left \... | Variance of a stationary AR(2) model | From $X_t = \phi_1 X_{t-1} + \phi_2 X_{t-2} $,
\begin{eqnarray*}
E[ X_t X_{t-k}] &=& \phi_1 E[X_{t-1} X_{t-k}] + \phi_2 E[X_{t-2} X_{t-k}] + E[X_t X_{t-1}] \\
\gamma_k &=& \phi_1 \gamma_{k-1} + | Variance of a stationary AR(2) model
From $X_t = \phi_1 X_{t-1} + \phi_2 X_{t-2} $,
\begin{eqnarray*}
E[ X_t X_{t-k}] &=& \phi_1 E[X_{t-1} X_{t-k}] + \phi_2 E[X_{t-2} X_{t-k}] + E[X_t X_{t-1}] \\
\gamma_k &=& \phi_1 \gamma_{k-1} + \phi_2 \gamma_{k-2} + E[Z_t X_{t-k}] \quad (*)
\end{eqnarray*}
Now,
\begin{e... | Variance of a stationary AR(2) model
From $X_t = \phi_1 X_{t-1} + \phi_2 X_{t-2} $,
\begin{eqnarray*}
E[ X_t X_{t-k}] &=& \phi_1 E[X_{t-1} X_{t-k}] + \phi_2 E[X_{t-2} X_{t-k}] + E[X_t X_{t-1}] \\
\gamma_k &=& \phi_1 \gamma_{k-1} + |
40,638 | Forecasting time series using ARMA-GARCH in R | Obtaining accurate point forecasts for financial time series is notoriously hard. That has to do with the nature of the financial markets; actors look for opportunities to exploit any predictability, and they remove it while they are doing it (change in expected profitability of an asset $\rightarrow$ change in supply/... | Forecasting time series using ARMA-GARCH in R | Obtaining accurate point forecasts for financial time series is notoriously hard. That has to do with the nature of the financial markets; actors look for opportunities to exploit any predictability, | Forecasting time series using ARMA-GARCH in R
Obtaining accurate point forecasts for financial time series is notoriously hard. That has to do with the nature of the financial markets; actors look for opportunities to exploit any predictability, and they remove it while they are doing it (change in expected profitabili... | Forecasting time series using ARMA-GARCH in R
Obtaining accurate point forecasts for financial time series is notoriously hard. That has to do with the nature of the financial markets; actors look for opportunities to exploit any predictability, |
40,639 | Time series data with seasonality using VAR? | VAR models are routinely used with seasonal data, e.g. in macroeconomics where most of the time series (such as GDP or unemployment) are seasonal. Seasonality is handled either (1) outside of the model (by seasonally adjusting the series before fitting a VAR model) or (2) within the model (by including seasonal dummy v... | Time series data with seasonality using VAR? | VAR models are routinely used with seasonal data, e.g. in macroeconomics where most of the time series (such as GDP or unemployment) are seasonal. Seasonality is handled either (1) outside of the mode | Time series data with seasonality using VAR?
VAR models are routinely used with seasonal data, e.g. in macroeconomics where most of the time series (such as GDP or unemployment) are seasonal. Seasonality is handled either (1) outside of the model (by seasonally adjusting the series before fitting a VAR model) or (2) wi... | Time series data with seasonality using VAR?
VAR models are routinely used with seasonal data, e.g. in macroeconomics where most of the time series (such as GDP or unemployment) are seasonal. Seasonality is handled either (1) outside of the mode |
40,640 | Time series data with seasonality using VAR? | Let me explain you in steps on removing seasonality:
Detect the trend: first find if the time series is additive or multiplicative
Detrend the time series: this will expose seasonality.
Average seasonality: from the detrend time series, it’s easy to compute the average seasonality. We add the seasonality together and ... | Time series data with seasonality using VAR? | Let me explain you in steps on removing seasonality:
Detect the trend: first find if the time series is additive or multiplicative
Detrend the time series: this will expose seasonality.
Average seaso | Time series data with seasonality using VAR?
Let me explain you in steps on removing seasonality:
Detect the trend: first find if the time series is additive or multiplicative
Detrend the time series: this will expose seasonality.
Average seasonality: from the detrend time series, it’s easy to compute the average seas... | Time series data with seasonality using VAR?
Let me explain you in steps on removing seasonality:
Detect the trend: first find if the time series is additive or multiplicative
Detrend the time series: this will expose seasonality.
Average seaso |
40,641 | Multiple Regression - Testing for multicollinearity | I don't think it matters much. Checking it later will save you unnecessary work and agitation at needless transformations that might prove pointless if the variables won't be in the final model. That being said, checking vif(model) is not time consuming, and you can always wait with the application of solutions to pote... | Multiple Regression - Testing for multicollinearity | I don't think it matters much. Checking it later will save you unnecessary work and agitation at needless transformations that might prove pointless if the variables won't be in the final model. That | Multiple Regression - Testing for multicollinearity
I don't think it matters much. Checking it later will save you unnecessary work and agitation at needless transformations that might prove pointless if the variables won't be in the final model. That being said, checking vif(model) is not time consuming, and you can a... | Multiple Regression - Testing for multicollinearity
I don't think it matters much. Checking it later will save you unnecessary work and agitation at needless transformations that might prove pointless if the variables won't be in the final model. That |
40,642 | Multiple Regression - Testing for multicollinearity | I'm perhaps the last person to answer this question, but what would be the disadvantage of running a correlation analysis before the regression just to get an insight to the data and then think if the multicollinearity affect the model prediction? | Multiple Regression - Testing for multicollinearity | I'm perhaps the last person to answer this question, but what would be the disadvantage of running a correlation analysis before the regression just to get an insight to the data and then think if the | Multiple Regression - Testing for multicollinearity
I'm perhaps the last person to answer this question, but what would be the disadvantage of running a correlation analysis before the regression just to get an insight to the data and then think if the multicollinearity affect the model prediction? | Multiple Regression - Testing for multicollinearity
I'm perhaps the last person to answer this question, but what would be the disadvantage of running a correlation analysis before the regression just to get an insight to the data and then think if the |
40,643 | Multiple Regression - Testing for multicollinearity | The question is about "testing" for multicollinearity. I'd argue it's not possible because multicollinearity is a characteristic of the sample not the population.
Reference: http://davegiles.blogspot.com.au/2013/06/can-you-actually-test-for.html
The answers given by @Yuval and @user3640761 give useful diagnostics, bu... | Multiple Regression - Testing for multicollinearity | The question is about "testing" for multicollinearity. I'd argue it's not possible because multicollinearity is a characteristic of the sample not the population.
Reference: http://davegiles.blogspot | Multiple Regression - Testing for multicollinearity
The question is about "testing" for multicollinearity. I'd argue it's not possible because multicollinearity is a characteristic of the sample not the population.
Reference: http://davegiles.blogspot.com.au/2013/06/can-you-actually-test-for.html
The answers given by... | Multiple Regression - Testing for multicollinearity
The question is about "testing" for multicollinearity. I'd argue it's not possible because multicollinearity is a characteristic of the sample not the population.
Reference: http://davegiles.blogspot |
40,644 | Bayesian recurrent neural network with keras and pymc3/edward | From a pure implementation perspective, it should be straightforward: take your model code, replace every trainable Variable creation with ed.Normal(...) or sth similar, establish variational posteriors as well, zip them in a dict, feed it to some inference object from edward et voila.
The problem is that variational t... | Bayesian recurrent neural network with keras and pymc3/edward | From a pure implementation perspective, it should be straightforward: take your model code, replace every trainable Variable creation with ed.Normal(...) or sth similar, establish variational posterio | Bayesian recurrent neural network with keras and pymc3/edward
From a pure implementation perspective, it should be straightforward: take your model code, replace every trainable Variable creation with ed.Normal(...) or sth similar, establish variational posteriors as well, zip them in a dict, feed it to some inference ... | Bayesian recurrent neural network with keras and pymc3/edward
From a pure implementation perspective, it should be straightforward: take your model code, replace every trainable Variable creation with ed.Normal(...) or sth similar, establish variational posterio |
40,645 | Bayesian recurrent neural network with keras and pymc3/edward | Meanwhile, other papers related to Bayesian RNNs have been published. For example, Bayesian Recurrent Neural Networks and Bayesian Recurrent Neural Network Models for Forecasting and Quantifying Uncertainty in Spatial-Temporal Data. | Bayesian recurrent neural network with keras and pymc3/edward | Meanwhile, other papers related to Bayesian RNNs have been published. For example, Bayesian Recurrent Neural Networks and Bayesian Recurrent Neural Network Models for Forecasting and Quantifying Uncer | Bayesian recurrent neural network with keras and pymc3/edward
Meanwhile, other papers related to Bayesian RNNs have been published. For example, Bayesian Recurrent Neural Networks and Bayesian Recurrent Neural Network Models for Forecasting and Quantifying Uncertainty in Spatial-Temporal Data. | Bayesian recurrent neural network with keras and pymc3/edward
Meanwhile, other papers related to Bayesian RNNs have been published. For example, Bayesian Recurrent Neural Networks and Bayesian Recurrent Neural Network Models for Forecasting and Quantifying Uncer |
40,646 | Use BIC or AIC as approximation for Bayesian Model Averaging [duplicate] | I don't understand the first sentence very well, but if your asking whether you should use BIC or AIC to approximate BMA than the answer is fairly straightforward.
You would use BIC rather than AIC to approximate posterior model probabilities which can then be used as weights in BMA.
Given a set of models $M_1,M_2,…,... | Use BIC or AIC as approximation for Bayesian Model Averaging [duplicate] | I don't understand the first sentence very well, but if your asking whether you should use BIC or AIC to approximate BMA than the answer is fairly straightforward.
You would use BIC rather than AIC to | Use BIC or AIC as approximation for Bayesian Model Averaging [duplicate]
I don't understand the first sentence very well, but if your asking whether you should use BIC or AIC to approximate BMA than the answer is fairly straightforward.
You would use BIC rather than AIC to approximate posterior model probabilities whic... | Use BIC or AIC as approximation for Bayesian Model Averaging [duplicate]
I don't understand the first sentence very well, but if your asking whether you should use BIC or AIC to approximate BMA than the answer is fairly straightforward.
You would use BIC rather than AIC to |
40,647 | How can endogeneity arise in OLS estimation? | from my point of view this problem stems from the fact that OLS models a linear projection $L(Y|X)=X\beta$ that is defined such that we always have $(Y-L(Y|X))⊥X$ but it does not hold in general that $L(Y|X)=X\beta=E[Y|X]$.
As a example assume that $Y=X+X^2+e$ and $E[Y|X]=X+X^2$, if we now do not account for the square... | How can endogeneity arise in OLS estimation? | from my point of view this problem stems from the fact that OLS models a linear projection $L(Y|X)=X\beta$ that is defined such that we always have $(Y-L(Y|X))⊥X$ but it does not hold in general that | How can endogeneity arise in OLS estimation?
from my point of view this problem stems from the fact that OLS models a linear projection $L(Y|X)=X\beta$ that is defined such that we always have $(Y-L(Y|X))⊥X$ but it does not hold in general that $L(Y|X)=X\beta=E[Y|X]$.
As a example assume that $Y=X+X^2+e$ and $E[Y|X]=X+... | How can endogeneity arise in OLS estimation?
from my point of view this problem stems from the fact that OLS models a linear projection $L(Y|X)=X\beta$ that is defined such that we always have $(Y-L(Y|X))⊥X$ but it does not hold in general that |
40,648 | Practical description of LOESS and smoothing splines? | [In the later discussion of LOESS here I attempt to describe LOWESS and its implementation in the R function lowess as well as outline some of the modifications made for the function loess (though some details that don't seem to be directly relevant to your questions are omitted).]
In particular: with smoothing spline... | Practical description of LOESS and smoothing splines? | [In the later discussion of LOESS here I attempt to describe LOWESS and its implementation in the R function lowess as well as outline some of the modifications made for the function loess (though som | Practical description of LOESS and smoothing splines?
[In the later discussion of LOESS here I attempt to describe LOWESS and its implementation in the R function lowess as well as outline some of the modifications made for the function loess (though some details that don't seem to be directly relevant to your question... | Practical description of LOESS and smoothing splines?
[In the later discussion of LOESS here I attempt to describe LOWESS and its implementation in the R function lowess as well as outline some of the modifications made for the function loess (though som |
40,649 | How to threshold multiclass probability prediction to get confusion matrix? | According to @cangrejo's answer: https://stats.stackexchange.com/a/310956/194535, suppose the original output probability of your model is the vector $v$, and then you can define the prior distribution:
$\pi=(\frac{1}{\theta_1}, \frac{1}{\theta_2},..., \frac{1}{\theta_N})$, for $\theta_i \in (0,1)$ and $\sum_i\theta_i... | How to threshold multiclass probability prediction to get confusion matrix? | According to @cangrejo's answer: https://stats.stackexchange.com/a/310956/194535, suppose the original output probability of your model is the vector $v$, and then you can define the prior distributio | How to threshold multiclass probability prediction to get confusion matrix?
According to @cangrejo's answer: https://stats.stackexchange.com/a/310956/194535, suppose the original output probability of your model is the vector $v$, and then you can define the prior distribution:
$\pi=(\frac{1}{\theta_1}, \frac{1}{\thet... | How to threshold multiclass probability prediction to get confusion matrix?
According to @cangrejo's answer: https://stats.stackexchange.com/a/310956/194535, suppose the original output probability of your model is the vector $v$, and then you can define the prior distributio |
40,650 | How to threshold multiclass probability prediction to get confusion matrix? | This was helpful, thanks! But it is not applicable during model training. When it comes to using this method after training the model (after finding the hyperparameters relevant to the model), it's valid; only that there has to be some way of standardizing this to avoid loss of generality and for it to be applicable on... | How to threshold multiclass probability prediction to get confusion matrix? | This was helpful, thanks! But it is not applicable during model training. When it comes to using this method after training the model (after finding the hyperparameters relevant to the model), it's va | How to threshold multiclass probability prediction to get confusion matrix?
This was helpful, thanks! But it is not applicable during model training. When it comes to using this method after training the model (after finding the hyperparameters relevant to the model), it's valid; only that there has to be some way of s... | How to threshold multiclass probability prediction to get confusion matrix?
This was helpful, thanks! But it is not applicable during model training. When it comes to using this method after training the model (after finding the hyperparameters relevant to the model), it's va |
40,651 | Is the Shapiro-Wilk test only applicable to smaller sample sizes? | The Shapiro Wilk test applies at any sample size above $n=2$ (it can't work at $n=1$ or $n=2$).
However, implementations of the test will generally not cover the very largest sample sizes (such as $n>5000$ -- though if you're using tables rather than a computer to do the test the tables might only go up to say $n=50$ ... | Is the Shapiro-Wilk test only applicable to smaller sample sizes? | The Shapiro Wilk test applies at any sample size above $n=2$ (it can't work at $n=1$ or $n=2$).
However, implementations of the test will generally not cover the very largest sample sizes (such as $n | Is the Shapiro-Wilk test only applicable to smaller sample sizes?
The Shapiro Wilk test applies at any sample size above $n=2$ (it can't work at $n=1$ or $n=2$).
However, implementations of the test will generally not cover the very largest sample sizes (such as $n>5000$ -- though if you're using tables rather than a ... | Is the Shapiro-Wilk test only applicable to smaller sample sizes?
The Shapiro Wilk test applies at any sample size above $n=2$ (it can't work at $n=1$ or $n=2$).
However, implementations of the test will generally not cover the very largest sample sizes (such as $n |
40,652 | Choose probability distribution to maximize evaluation function (for CDC flu forecasting contest) | Cool problem! As Xi'an's derivation shows, it is related to minimizing the KL-divergence from Q to P. Cliff provides some important context as well.
The problem can be solved trivially using optimization software, but I don't see a way to write a closed-form formula for the general solution. If $q_i \geq 0 $ never bind... | Choose probability distribution to maximize evaluation function (for CDC flu forecasting contest) | Cool problem! As Xi'an's derivation shows, it is related to minimizing the KL-divergence from Q to P. Cliff provides some important context as well.
The problem can be solved trivially using optimizat | Choose probability distribution to maximize evaluation function (for CDC flu forecasting contest)
Cool problem! As Xi'an's derivation shows, it is related to minimizing the KL-divergence from Q to P. Cliff provides some important context as well.
The problem can be solved trivially using optimization software, but I do... | Choose probability distribution to maximize evaluation function (for CDC flu forecasting contest)
Cool problem! As Xi'an's derivation shows, it is related to minimizing the KL-divergence from Q to P. Cliff provides some important context as well.
The problem can be solved trivially using optimizat |
40,653 | Choose probability distribution to maximize evaluation function (for CDC flu forecasting contest) | Since $\mathbf{q}=\mathbf{p}$ solves$$\arg\min_\mathbf{q} \sum p_i\log\{ p_i\big/q_i\}$$ what about just solving
$$q_{i-1}+q_i+q_{i+1}=3p_i\qquad i=1,\ldots,n-1$$ to find the solution to
$$\arg\max_\mathbf{q} \sum p_i\log\{ p_i\big/(q_{i-1}+q_i+q_{i+1})\}$$
If the solution to this system of equations does not belong t... | Choose probability distribution to maximize evaluation function (for CDC flu forecasting contest) | Since $\mathbf{q}=\mathbf{p}$ solves$$\arg\min_\mathbf{q} \sum p_i\log\{ p_i\big/q_i\}$$ what about just solving
$$q_{i-1}+q_i+q_{i+1}=3p_i\qquad i=1,\ldots,n-1$$ to find the solution to
$$\arg\max_\m | Choose probability distribution to maximize evaluation function (for CDC flu forecasting contest)
Since $\mathbf{q}=\mathbf{p}$ solves$$\arg\min_\mathbf{q} \sum p_i\log\{ p_i\big/q_i\}$$ what about just solving
$$q_{i-1}+q_i+q_{i+1}=3p_i\qquad i=1,\ldots,n-1$$ to find the solution to
$$\arg\max_\mathbf{q} \sum p_i\log\... | Choose probability distribution to maximize evaluation function (for CDC flu forecasting contest)
Since $\mathbf{q}=\mathbf{p}$ solves$$\arg\min_\mathbf{q} \sum p_i\log\{ p_i\big/q_i\}$$ what about just solving
$$q_{i-1}+q_i+q_{i+1}=3p_i\qquad i=1,\ldots,n-1$$ to find the solution to
$$\arg\max_\m |
40,654 | Choose probability distribution to maximize evaluation function (for CDC flu forecasting contest) | If I understand this correctly, I do not think this will have a closed form solution. Or moreover, it's at least a specialization of a problem that is not in closed form.
The reason I say this is that it is exactly the likelihood that appears in the NPMLE for interval censored data, the specialization being that all t... | Choose probability distribution to maximize evaluation function (for CDC flu forecasting contest) | If I understand this correctly, I do not think this will have a closed form solution. Or moreover, it's at least a specialization of a problem that is not in closed form.
The reason I say this is tha | Choose probability distribution to maximize evaluation function (for CDC flu forecasting contest)
If I understand this correctly, I do not think this will have a closed form solution. Or moreover, it's at least a specialization of a problem that is not in closed form.
The reason I say this is that it is exactly the li... | Choose probability distribution to maximize evaluation function (for CDC flu forecasting contest)
If I understand this correctly, I do not think this will have a closed form solution. Or moreover, it's at least a specialization of a problem that is not in closed form.
The reason I say this is tha |
40,655 | What is low rank intuitively for an adjacency matrix? | I'm not sure if your question is easy to answer, but I will try to provide an intuition. I am not an expert in non-negative matrix factorisation so I can't explain the connections there.
Let's restrict out attention to simple, undirected graphs $G$ with $n$ vertices. I will assume by low-rank you mean, low-rank of the... | What is low rank intuitively for an adjacency matrix? | I'm not sure if your question is easy to answer, but I will try to provide an intuition. I am not an expert in non-negative matrix factorisation so I can't explain the connections there.
Let's restri | What is low rank intuitively for an adjacency matrix?
I'm not sure if your question is easy to answer, but I will try to provide an intuition. I am not an expert in non-negative matrix factorisation so I can't explain the connections there.
Let's restrict out attention to simple, undirected graphs $G$ with $n$ vertice... | What is low rank intuitively for an adjacency matrix?
I'm not sure if your question is easy to answer, but I will try to provide an intuition. I am not an expert in non-negative matrix factorisation so I can't explain the connections there.
Let's restri |
40,656 | Positive Poisson regression: what is the effect on the model of shifting vs truncating? | Although you are modeling counts, your data cannot be Poisson. The easy way to see this is because it cannot be $0$, which is a possible value for the Poisson distribution. But this isn't really a shifted or truncated Poisson, either. Nor could the number of resits be Poisson. What you are calling "the number of re... | Positive Poisson regression: what is the effect on the model of shifting vs truncating? | Although you are modeling counts, your data cannot be Poisson. The easy way to see this is because it cannot be $0$, which is a possible value for the Poisson distribution. But this isn't really a s | Positive Poisson regression: what is the effect on the model of shifting vs truncating?
Although you are modeling counts, your data cannot be Poisson. The easy way to see this is because it cannot be $0$, which is a possible value for the Poisson distribution. But this isn't really a shifted or truncated Poisson, eit... | Positive Poisson regression: what is the effect on the model of shifting vs truncating?
Although you are modeling counts, your data cannot be Poisson. The easy way to see this is because it cannot be $0$, which is a possible value for the Poisson distribution. But this isn't really a s |
40,657 | Positive Poisson regression: what is the effect on the model of shifting vs truncating? | You have to use the distribution that explains the phenomenon. Sometime a simple rewording can do the trick of thinking outside the box. For instance, instead of framing the question as "how many attempts to pass?" you frame it as "How many re-takes?".
You see, in your case it's impossible to have an observations of a ... | Positive Poisson regression: what is the effect on the model of shifting vs truncating? | You have to use the distribution that explains the phenomenon. Sometime a simple rewording can do the trick of thinking outside the box. For instance, instead of framing the question as "how many atte | Positive Poisson regression: what is the effect on the model of shifting vs truncating?
You have to use the distribution that explains the phenomenon. Sometime a simple rewording can do the trick of thinking outside the box. For instance, instead of framing the question as "how many attempts to pass?" you frame it as "... | Positive Poisson regression: what is the effect on the model of shifting vs truncating?
You have to use the distribution that explains the phenomenon. Sometime a simple rewording can do the trick of thinking outside the box. For instance, instead of framing the question as "how many atte |
40,658 | Were professors Samuel S. Wilks and Daniel S. Wilks related? | I am Daniel Wilks. No relation to Samuel S, but I get this question a lot. | Were professors Samuel S. Wilks and Daniel S. Wilks related? | I am Daniel Wilks. No relation to Samuel S, but I get this question a lot. | Were professors Samuel S. Wilks and Daniel S. Wilks related?
I am Daniel Wilks. No relation to Samuel S, but I get this question a lot. | Were professors Samuel S. Wilks and Daniel S. Wilks related?
I am Daniel Wilks. No relation to Samuel S, but I get this question a lot. |
40,659 | Were professors Samuel S. Wilks and Daniel S. Wilks related? | I cannot currently say that they were not related, but we can at least say that Daniel is not Samuel's son. This biography of Samuel S Wilks says [1]:
On 1 September 1931 Wilks married Hattie Eugenia Orr (1906-2000), known as Gena. They had one child, a son named Stanley Neal Wilks born in 1932.
However, the elder W... | Were professors Samuel S. Wilks and Daniel S. Wilks related? | I cannot currently say that they were not related, but we can at least say that Daniel is not Samuel's son. This biography of Samuel S Wilks says [1]:
On 1 September 1931 Wilks married Hattie Eugenia | Were professors Samuel S. Wilks and Daniel S. Wilks related?
I cannot currently say that they were not related, but we can at least say that Daniel is not Samuel's son. This biography of Samuel S Wilks says [1]:
On 1 September 1931 Wilks married Hattie Eugenia Orr (1906-2000), known as Gena. They had one child, a son ... | Were professors Samuel S. Wilks and Daniel S. Wilks related?
I cannot currently say that they were not related, but we can at least say that Daniel is not Samuel's son. This biography of Samuel S Wilks says [1]:
On 1 September 1931 Wilks married Hattie Eugenia |
40,660 | Monte Carlo method cannot be used | Edit: I strongly recommend getting a new book to study from because this book is garbage by the looks of it. First off, there is a gross typo: the integral to estimate should be $\int_{-\infty}^\infty xf(x)dx$ as can plainly be seen in the explanation presented. Second, the expectation is NOT infinite, it simply doesn'... | Monte Carlo method cannot be used | Edit: I strongly recommend getting a new book to study from because this book is garbage by the looks of it. First off, there is a gross typo: the integral to estimate should be $\int_{-\infty}^\infty | Monte Carlo method cannot be used
Edit: I strongly recommend getting a new book to study from because this book is garbage by the looks of it. First off, there is a gross typo: the integral to estimate should be $\int_{-\infty}^\infty xf(x)dx$ as can plainly be seen in the explanation presented. Second, the expectation... | Monte Carlo method cannot be used
Edit: I strongly recommend getting a new book to study from because this book is garbage by the looks of it. First off, there is a gross typo: the integral to estimate should be $\int_{-\infty}^\infty |
40,661 | Monte Carlo method cannot be used | There might be the need for a caveat for the question, in term of what is it that you call Monte Carlo integration.
You want to use Monte Carlo to estimate $\int_{-\infty}^{\infty} f(x) dx$, a quantity we know to be 1. One way to to do this is to find a pdf $g(x)$ such that you can sample from $g$, and then
$$\int_{-\i... | Monte Carlo method cannot be used | There might be the need for a caveat for the question, in term of what is it that you call Monte Carlo integration.
You want to use Monte Carlo to estimate $\int_{-\infty}^{\infty} f(x) dx$, a quantit | Monte Carlo method cannot be used
There might be the need for a caveat for the question, in term of what is it that you call Monte Carlo integration.
You want to use Monte Carlo to estimate $\int_{-\infty}^{\infty} f(x) dx$, a quantity we know to be 1. One way to to do this is to find a pdf $g(x)$ such that you can sam... | Monte Carlo method cannot be used
There might be the need for a caveat for the question, in term of what is it that you call Monte Carlo integration.
You want to use Monte Carlo to estimate $\int_{-\infty}^{\infty} f(x) dx$, a quantit |
40,662 | Why do we need to model RNA-seq data using Poisson, negative binomial, | The data is count data because it's the number of counts aligned to a gene. It's not continuous and therefore can't be modelled as say a normal distribution.
Poisson distribution is designed for modelling count data.
However, the Poisson distribution assumes the first and second moments (mean and variance) are equal. T... | Why do we need to model RNA-seq data using Poisson, negative binomial, | The data is count data because it's the number of counts aligned to a gene. It's not continuous and therefore can't be modelled as say a normal distribution.
Poisson distribution is designed for model | Why do we need to model RNA-seq data using Poisson, negative binomial,
The data is count data because it's the number of counts aligned to a gene. It's not continuous and therefore can't be modelled as say a normal distribution.
Poisson distribution is designed for modelling count data.
However, the Poisson distributio... | Why do we need to model RNA-seq data using Poisson, negative binomial,
The data is count data because it's the number of counts aligned to a gene. It's not continuous and therefore can't be modelled as say a normal distribution.
Poisson distribution is designed for model |
40,663 | Why do we need to model RNA-seq data using Poisson, negative binomial, | It is usual to model counts taking into account that:
1 - they only take on integer values
2 - they are always non-negative
3 - (most importantly) their variability increases with their mean
The negative binomial is used when the dispersion of the counts is greater than would be expected from the Poisson. In both cases... | Why do we need to model RNA-seq data using Poisson, negative binomial, | It is usual to model counts taking into account that:
1 - they only take on integer values
2 - they are always non-negative
3 - (most importantly) their variability increases with their mean
The negat | Why do we need to model RNA-seq data using Poisson, negative binomial,
It is usual to model counts taking into account that:
1 - they only take on integer values
2 - they are always non-negative
3 - (most importantly) their variability increases with their mean
The negative binomial is used when the dispersion of the c... | Why do we need to model RNA-seq data using Poisson, negative binomial,
It is usual to model counts taking into account that:
1 - they only take on integer values
2 - they are always non-negative
3 - (most importantly) their variability increases with their mean
The negat |
40,664 | SUTVA vs. independence | I think SUTVA violations come in two flavors, which are not always distinct:
"spillovers/interferences" that arise from contact across individuals in social, commodity, or physical space (independence flavor)
dilution/concentration of treatment effects that stem from changes in the prevalence of treatment (what econom... | SUTVA vs. independence | I think SUTVA violations come in two flavors, which are not always distinct:
"spillovers/interferences" that arise from contact across individuals in social, commodity, or physical space (independenc | SUTVA vs. independence
I think SUTVA violations come in two flavors, which are not always distinct:
"spillovers/interferences" that arise from contact across individuals in social, commodity, or physical space (independence flavor)
dilution/concentration of treatment effects that stem from changes in the prevalence of... | SUTVA vs. independence
I think SUTVA violations come in two flavors, which are not always distinct:
"spillovers/interferences" that arise from contact across individuals in social, commodity, or physical space (independenc |
40,665 | Why would one ever use z-score over a t-score? | The image you used is wrong. If you know the population standard deviation then your statistic follows a normal distribution. When you do not know it, and you estimate from the sample than your statistic follows a t distribution and that is all. In your image and the text that follows the image you reverted yes with no... | Why would one ever use z-score over a t-score? | The image you used is wrong. If you know the population standard deviation then your statistic follows a normal distribution. When you do not know it, and you estimate from the sample than your statis | Why would one ever use z-score over a t-score?
The image you used is wrong. If you know the population standard deviation then your statistic follows a normal distribution. When you do not know it, and you estimate from the sample than your statistic follows a t distribution and that is all. In your image and the text ... | Why would one ever use z-score over a t-score?
The image you used is wrong. If you know the population standard deviation then your statistic follows a normal distribution. When you do not know it, and you estimate from the sample than your statis |
40,666 | Why is the mean of a Chi Square distribution equal to the degree of freedom? | You don't define the mean to be the degrees of freedom (d.f.) -- it follows from the definition of the pdf and the definition of expectation of a random variable.
The pdf of a chi-squared random variable with $k$ d.f. is:
${\frac {1}{2^{\frac {k}{2}}\Gamma \left({\frac {k}{2}}\right)}}\;x^{{\frac {k}{2}}-1}e^{-{\frac ... | Why is the mean of a Chi Square distribution equal to the degree of freedom? | You don't define the mean to be the degrees of freedom (d.f.) -- it follows from the definition of the pdf and the definition of expectation of a random variable.
The pdf of a chi-squared random vari | Why is the mean of a Chi Square distribution equal to the degree of freedom?
You don't define the mean to be the degrees of freedom (d.f.) -- it follows from the definition of the pdf and the definition of expectation of a random variable.
The pdf of a chi-squared random variable with $k$ d.f. is:
${\frac {1}{2^{\frac... | Why is the mean of a Chi Square distribution equal to the degree of freedom?
You don't define the mean to be the degrees of freedom (d.f.) -- it follows from the definition of the pdf and the definition of expectation of a random variable.
The pdf of a chi-squared random vari |
40,667 | Why is the mean of a Chi Square distribution equal to the degree of freedom? | Chi squared distribution is Gamma distribution with parameters $(\lambda, \alpha) = (\frac12, \frac{n}2)$.
And we know that expected value of Gamma is $\frac{\alpha}{\lambda}$ .
Hence the expected value of a chi squared r.v. is $ \frac{n/2}{1/2} = n$. | Why is the mean of a Chi Square distribution equal to the degree of freedom? | Chi squared distribution is Gamma distribution with parameters $(\lambda, \alpha) = (\frac12, \frac{n}2)$.
And we know that expected value of Gamma is $\frac{\alpha}{\lambda}$ .
Hence the expected val | Why is the mean of a Chi Square distribution equal to the degree of freedom?
Chi squared distribution is Gamma distribution with parameters $(\lambda, \alpha) = (\frac12, \frac{n}2)$.
And we know that expected value of Gamma is $\frac{\alpha}{\lambda}$ .
Hence the expected value of a chi squared r.v. is $ \frac{n/2}{1/... | Why is the mean of a Chi Square distribution equal to the degree of freedom?
Chi squared distribution is Gamma distribution with parameters $(\lambda, \alpha) = (\frac12, \frac{n}2)$.
And we know that expected value of Gamma is $\frac{\alpha}{\lambda}$ .
Hence the expected val |
40,668 | Match Quality Graph | It seems to me it is worth noting that these are, in essence, agreement data. We should use a plot designed for displaying and assessing such data. The plot I'm most familiar with for this purpose is Bangdawala's agreement chart. You can find it discussed here:
Bangdiwala, SI, & Shankar, V (2013). The agreement ... | Match Quality Graph | It seems to me it is worth noting that these are, in essence, agreement data. We should use a plot designed for displaying and assessing such data. The plot I'm most familiar with for this purpose i | Match Quality Graph
It seems to me it is worth noting that these are, in essence, agreement data. We should use a plot designed for displaying and assessing such data. The plot I'm most familiar with for this purpose is Bangdawala's agreement chart. You can find it discussed here:
Bangdiwala, SI, & Shankar, V (20... | Match Quality Graph
It seems to me it is worth noting that these are, in essence, agreement data. We should use a plot designed for displaying and assessing such data. The plot I'm most familiar with for this purpose i |
40,669 | Match Quality Graph | I think the biggest weakness of the original is that the color intensity dominates our perception even though it is practically meaningless in that it duplicates information already represented by the positions. I imagine that leading to your dissatisfaction and search for alternatives.
Here is a version using color in... | Match Quality Graph | I think the biggest weakness of the original is that the color intensity dominates our perception even though it is practically meaningless in that it duplicates information already represented by the | Match Quality Graph
I think the biggest weakness of the original is that the color intensity dominates our perception even though it is practically meaningless in that it duplicates information already represented by the positions. I imagine that leading to your dissatisfaction and search for alternatives.
Here is a ve... | Match Quality Graph
I think the biggest weakness of the original is that the color intensity dominates our perception even though it is practically meaningless in that it duplicates information already represented by the |
40,670 | Match Quality Graph | I think the current charts show the data pretty well. The stacked bar chart has such nice progressions it is easier to follow along than most stacked bar charts. The original bubble chart shows that there is a reasonable correlation between the two (I calculated it at 0.36).
One alternative is a dot plot/line chart.
... | Match Quality Graph | I think the current charts show the data pretty well. The stacked bar chart has such nice progressions it is easier to follow along than most stacked bar charts. The original bubble chart shows that t | Match Quality Graph
I think the current charts show the data pretty well. The stacked bar chart has such nice progressions it is easier to follow along than most stacked bar charts. The original bubble chart shows that there is a reasonable correlation between the two (I calculated it at 0.36).
One alternative is a do... | Match Quality Graph
I think the current charts show the data pretty well. The stacked bar chart has such nice progressions it is easier to follow along than most stacked bar charts. The original bubble chart shows that t |
40,671 | Equivalent of a flipped lognormal distribution | A reversed Lognormal ...
I will use the notation here that is common in defining the Johnson family, since the latter commonly provides a 3 or 4 parameter version of the Lognormal that captures that which you seek.
If $Z \sim N(0,1)$, and $Y=\exp\big({\frac{Z-\gamma}{\delta }}\big)$, then $Y$ has a Lognormal distribu... | Equivalent of a flipped lognormal distribution | A reversed Lognormal ...
I will use the notation here that is common in defining the Johnson family, since the latter commonly provides a 3 or 4 parameter version of the Lognormal that captures that | Equivalent of a flipped lognormal distribution
A reversed Lognormal ...
I will use the notation here that is common in defining the Johnson family, since the latter commonly provides a 3 or 4 parameter version of the Lognormal that captures that which you seek.
If $Z \sim N(0,1)$, and $Y=\exp\big({\frac{Z-\gamma}{\de... | Equivalent of a flipped lognormal distribution
A reversed Lognormal ...
I will use the notation here that is common in defining the Johnson family, since the latter commonly provides a 3 or 4 parameter version of the Lognormal that captures that |
40,672 | Equivalent of a flipped lognormal distribution | Independent of scale (min,max of x-values), a beta distribution can have a left tail, and so can a power function distribution. However, if your data did result in a left tail on a histogram, you could probably fit it very well using the stable distribution, which has four parameters. The stable is used in QF (quanti... | Equivalent of a flipped lognormal distribution | Independent of scale (min,max of x-values), a beta distribution can have a left tail, and so can a power function distribution. However, if your data did result in a left tail on a histogram, you cou | Equivalent of a flipped lognormal distribution
Independent of scale (min,max of x-values), a beta distribution can have a left tail, and so can a power function distribution. However, if your data did result in a left tail on a histogram, you could probably fit it very well using the stable distribution, which has fou... | Equivalent of a flipped lognormal distribution
Independent of scale (min,max of x-values), a beta distribution can have a left tail, and so can a power function distribution. However, if your data did result in a left tail on a histogram, you cou |
40,673 | How to find a maximum likelihood estimator for a discrete parameter? | This problem is simpler than it might look: although it might get confusing when one tries to apply routine Calculus methods, it is easy when worked from general principles.
By definition, the likelihood $\mathcal L$ is the probability of the data. Since the data are (implicitly) assumed independent, this is the prod... | How to find a maximum likelihood estimator for a discrete parameter? | This problem is simpler than it might look: although it might get confusing when one tries to apply routine Calculus methods, it is easy when worked from general principles.
By definition, the likeli | How to find a maximum likelihood estimator for a discrete parameter?
This problem is simpler than it might look: although it might get confusing when one tries to apply routine Calculus methods, it is easy when worked from general principles.
By definition, the likelihood $\mathcal L$ is the probability of the data. ... | How to find a maximum likelihood estimator for a discrete parameter?
This problem is simpler than it might look: although it might get confusing when one tries to apply routine Calculus methods, it is easy when worked from general principles.
By definition, the likeli |
40,674 | How to find a maximum likelihood estimator for a discrete parameter? | This has a few tricky points, so let's work it out.
First, we note that $2n$ is an even number, so the function that wants to be a density will be non-negative from that respect, as it should, even though the variable $X$ may take negative values.
Second we need to determine the value of $c$ so that we have a prope... | How to find a maximum likelihood estimator for a discrete parameter? | This has a few tricky points, so let's work it out.
First, we note that $2n$ is an even number, so the function that wants to be a density will be non-negative from that respect, as it should, even | How to find a maximum likelihood estimator for a discrete parameter?
This has a few tricky points, so let's work it out.
First, we note that $2n$ is an even number, so the function that wants to be a density will be non-negative from that respect, as it should, even though the variable $X$ may take negative values. ... | How to find a maximum likelihood estimator for a discrete parameter?
This has a few tricky points, so let's work it out.
First, we note that $2n$ is an even number, so the function that wants to be a density will be non-negative from that respect, as it should, even |
40,675 | distance measure of two discrete probability histograms (distance between two vectors) | Jensen-Shannon distance is the 1st thing I'd consider. If you don't insist on having a "distance function", you can directly use Jensen–Shannon divergence, from which this distance is derived.
JS divergence is widely used to measure the difference between two probability distributions. It fits your case, as the inputs ... | distance measure of two discrete probability histograms (distance between two vectors) | Jensen-Shannon distance is the 1st thing I'd consider. If you don't insist on having a "distance function", you can directly use Jensen–Shannon divergence, from which this distance is derived.
JS dive | distance measure of two discrete probability histograms (distance between two vectors)
Jensen-Shannon distance is the 1st thing I'd consider. If you don't insist on having a "distance function", you can directly use Jensen–Shannon divergence, from which this distance is derived.
JS divergence is widely used to measure ... | distance measure of two discrete probability histograms (distance between two vectors)
Jensen-Shannon distance is the 1st thing I'd consider. If you don't insist on having a "distance function", you can directly use Jensen–Shannon divergence, from which this distance is derived.
JS dive |
40,676 | distance measure of two discrete probability histograms (distance between two vectors) | There is also the Wasserstein metric, which has become more popular in the Bayesian inference literature. In your case, the 'wasserstein1d' function from package 'transport' should do the trick:
x <- rnorm(200)
y <- rnorm(150,2)
wasserstein1d(x,y) | distance measure of two discrete probability histograms (distance between two vectors) | There is also the Wasserstein metric, which has become more popular in the Bayesian inference literature. In your case, the 'wasserstein1d' function from package 'transport' should do the trick:
x < | distance measure of two discrete probability histograms (distance between two vectors)
There is also the Wasserstein metric, which has become more popular in the Bayesian inference literature. In your case, the 'wasserstein1d' function from package 'transport' should do the trick:
x <- rnorm(200)
y <- rnorm(150,2)
... | distance measure of two discrete probability histograms (distance between two vectors)
There is also the Wasserstein metric, which has become more popular in the Bayesian inference literature. In your case, the 'wasserstein1d' function from package 'transport' should do the trick:
x < |
40,677 | To select variables or not in logistic regression | Approaches that naively select model terms based on some p-values or some AIC cut-offs (either in a multivariate model via some kind of stepwise or other selection or by looking at lots of univariate models) lead to extremely problematic fits that may fit the particular dataset well, but will otherwise not be useful. M... | To select variables or not in logistic regression | Approaches that naively select model terms based on some p-values or some AIC cut-offs (either in a multivariate model via some kind of stepwise or other selection or by looking at lots of univariate | To select variables or not in logistic regression
Approaches that naively select model terms based on some p-values or some AIC cut-offs (either in a multivariate model via some kind of stepwise or other selection or by looking at lots of univariate models) lead to extremely problematic fits that may fit the particular... | To select variables or not in logistic regression
Approaches that naively select model terms based on some p-values or some AIC cut-offs (either in a multivariate model via some kind of stepwise or other selection or by looking at lots of univariate |
40,678 | What's wrong with data-guided modeling in regression? | First, there is no way to "guarantee" any model other than perhaps in physics. As discussed in detail in my book and Course Notes there is a safe strategy for assigning d.f. to predictors based on a properly masked analysis of "predictive potential" when subject matter knowledge is lacking. For categorical variables,... | What's wrong with data-guided modeling in regression? | First, there is no way to "guarantee" any model other than perhaps in physics. As discussed in detail in my book and Course Notes there is a safe strategy for assigning d.f. to predictors based on a | What's wrong with data-guided modeling in regression?
First, there is no way to "guarantee" any model other than perhaps in physics. As discussed in detail in my book and Course Notes there is a safe strategy for assigning d.f. to predictors based on a properly masked analysis of "predictive potential" when subject ma... | What's wrong with data-guided modeling in regression?
First, there is no way to "guarantee" any model other than perhaps in physics. As discussed in detail in my book and Course Notes there is a safe strategy for assigning d.f. to predictors based on a |
40,679 | What's wrong with data-guided modeling in regression? | a) hopefully it is clear that standard statistical measures are dealing with the chance of getting a result at random and do not include the possibilities of you eyeballing the data and using your own particular experience and perception.
b) Prof Harrell doesn't say you couldnt use bootstrap, just that its too much wo... | What's wrong with data-guided modeling in regression? | a) hopefully it is clear that standard statistical measures are dealing with the chance of getting a result at random and do not include the possibilities of you eyeballing the data and using your ow | What's wrong with data-guided modeling in regression?
a) hopefully it is clear that standard statistical measures are dealing with the chance of getting a result at random and do not include the possibilities of you eyeballing the data and using your own particular experience and perception.
b) Prof Harrell doesn't sa... | What's wrong with data-guided modeling in regression?
a) hopefully it is clear that standard statistical measures are dealing with the chance of getting a result at random and do not include the possibilities of you eyeballing the data and using your ow |
40,680 | Different results using Brier score and Logarithmic scoring rule | Without getting into the Bayesian vs. frequentist part of your question, the two proper accuracy scores are rewarding different things and it's not surprising they behave differently. The logarithmic score rewards more extreme predictions that are in the right direction. This score can be ruined by a single predictio... | Different results using Brier score and Logarithmic scoring rule | Without getting into the Bayesian vs. frequentist part of your question, the two proper accuracy scores are rewarding different things and it's not surprising they behave differently. The logarithmic | Different results using Brier score and Logarithmic scoring rule
Without getting into the Bayesian vs. frequentist part of your question, the two proper accuracy scores are rewarding different things and it's not surprising they behave differently. The logarithmic score rewards more extreme predictions that are in the... | Different results using Brier score and Logarithmic scoring rule
Without getting into the Bayesian vs. frequentist part of your question, the two proper accuracy scores are rewarding different things and it's not surprising they behave differently. The logarithmic |
40,681 | Combining Binomial Random Variables | [I've put some material on how to sum geometric progressions and expectation of geometric random variables at the end; this answer relies on such results but they're fairly well known so I figured I wouldn't start with them. If any readers are not, then skip to the end to see one way to get them out. It's worth doing s... | Combining Binomial Random Variables | [I've put some material on how to sum geometric progressions and expectation of geometric random variables at the end; this answer relies on such results but they're fairly well known so I figured I w | Combining Binomial Random Variables
[I've put some material on how to sum geometric progressions and expectation of geometric random variables at the end; this answer relies on such results but they're fairly well known so I figured I wouldn't start with them. If any readers are not, then skip to the end to see one way... | Combining Binomial Random Variables
[I've put some material on how to sum geometric progressions and expectation of geometric random variables at the end; this answer relies on such results but they're fairly well known so I figured I w |
40,682 | Combining Binomial Random Variables | Let us define a round of tosses as two tosses; the first toss
by A who tosses a coin with $P(\text{Heads}) = p_1$ and the
second toss by B who tosses a coin with $P(\text{Heads}) = p_2$.
The outcomes of a round and the corresponding probabilities are
$$\begin{matrix} HH & &p_1p_2\\
HT & &p_1(1-p_2)\\ TH & &(1-p_1)p_2... | Combining Binomial Random Variables | Let us define a round of tosses as two tosses; the first toss
by A who tosses a coin with $P(\text{Heads}) = p_1$ and the
second toss by B who tosses a coin with $P(\text{Heads}) = p_2$.
The outcomes | Combining Binomial Random Variables
Let us define a round of tosses as two tosses; the first toss
by A who tosses a coin with $P(\text{Heads}) = p_1$ and the
second toss by B who tosses a coin with $P(\text{Heads}) = p_2$.
The outcomes of a round and the corresponding probabilities are
$$\begin{matrix} HH & &p_1p_2\\... | Combining Binomial Random Variables
Let us define a round of tosses as two tosses; the first toss
by A who tosses a coin with $P(\text{Heads}) = p_1$ and the
second toss by B who tosses a coin with $P(\text{Heads}) = p_2$.
The outcomes |
40,683 | What is the two alternative forced choice paradigm | Two-alternative forced choice is a psychophysical method ("paradigm") used to solicit behavioral or perceptual responses from subjects.
The name comes from two aspects of the method. It is called two-alternative because the subjects are shown two alternative stimuli (A or B), and forced choice because they are "forced"... | What is the two alternative forced choice paradigm | Two-alternative forced choice is a psychophysical method ("paradigm") used to solicit behavioral or perceptual responses from subjects.
The name comes from two aspects of the method. It is called two- | What is the two alternative forced choice paradigm
Two-alternative forced choice is a psychophysical method ("paradigm") used to solicit behavioral or perceptual responses from subjects.
The name comes from two aspects of the method. It is called two-alternative because the subjects are shown two alternative stimuli (A... | What is the two alternative forced choice paradigm
Two-alternative forced choice is a psychophysical method ("paradigm") used to solicit behavioral or perceptual responses from subjects.
The name comes from two aspects of the method. It is called two- |
40,684 | What is the two alternative forced choice paradigm | Two-alternative forced choice (2AFC) refers to the methodology used to solicit responses from participants. It is used in many different paradigms across different domains. As the name implies, participants are presented only two choices, and they must make a response (indifference is not allowed).
For example, the lex... | What is the two alternative forced choice paradigm | Two-alternative forced choice (2AFC) refers to the methodology used to solicit responses from participants. It is used in many different paradigms across different domains. As the name implies, partic | What is the two alternative forced choice paradigm
Two-alternative forced choice (2AFC) refers to the methodology used to solicit responses from participants. It is used in many different paradigms across different domains. As the name implies, participants are presented only two choices, and they must make a response ... | What is the two alternative forced choice paradigm
Two-alternative forced choice (2AFC) refers to the methodology used to solicit responses from participants. It is used in many different paradigms across different domains. As the name implies, partic |
40,685 | What is the two alternative forced choice paradigm | Having read the other two answers, I think we are still missing an important point. As @Jeff notes, many tasks involve two alternatives, e.g., a detection task. In a detection task, or indeed, in any task with a single stimulus and a decision that must be made about that stimulus, the subject must set a criterion leve... | What is the two alternative forced choice paradigm | Having read the other two answers, I think we are still missing an important point. As @Jeff notes, many tasks involve two alternatives, e.g., a detection task. In a detection task, or indeed, in any | What is the two alternative forced choice paradigm
Having read the other two answers, I think we are still missing an important point. As @Jeff notes, many tasks involve two alternatives, e.g., a detection task. In a detection task, or indeed, in any task with a single stimulus and a decision that must be made about t... | What is the two alternative forced choice paradigm
Having read the other two answers, I think we are still missing an important point. As @Jeff notes, many tasks involve two alternatives, e.g., a detection task. In a detection task, or indeed, in any |
40,686 | Why is ROC curve always increasing (or non-decreasing)? | (WLOG) Because no case which is classified as a positive will ever be classified as a negative for any lower threshold. | Why is ROC curve always increasing (or non-decreasing)? | (WLOG) Because no case which is classified as a positive will ever be classified as a negative for any lower threshold. | Why is ROC curve always increasing (or non-decreasing)?
(WLOG) Because no case which is classified as a positive will ever be classified as a negative for any lower threshold. | Why is ROC curve always increasing (or non-decreasing)?
(WLOG) Because no case which is classified as a positive will ever be classified as a negative for any lower threshold. |
40,687 | Appropriate way to calculate cross-validated R square | That is incorrect because it allows for recalibration of predictions with a new overall slope and intercept. Use this formula after freezing all coefficients: 1 - (sum of squared errors) / (sum of squares total). The denominator is $(n-1)\times$ the observed variance of $Y$ in the holdout sample. When you do it corr... | Appropriate way to calculate cross-validated R square | That is incorrect because it allows for recalibration of predictions with a new overall slope and intercept. Use this formula after freezing all coefficients: 1 - (sum of squared errors) / (sum of sq | Appropriate way to calculate cross-validated R square
That is incorrect because it allows for recalibration of predictions with a new overall slope and intercept. Use this formula after freezing all coefficients: 1 - (sum of squared errors) / (sum of squares total). The denominator is $(n-1)\times$ the observed varia... | Appropriate way to calculate cross-validated R square
That is incorrect because it allows for recalibration of predictions with a new overall slope and intercept. Use this formula after freezing all coefficients: 1 - (sum of squared errors) / (sum of sq |
40,688 | Relationship between logistic regression and hyperplane | The picture below will probably answer your question.
A logistic regression model with 2 features creates a wave based on the logit link function.
Applying the decision rule (for example above 50%) transforms the wave to a separating hyperplane like that, but not similar to, one found in SVM. This is illustrated in ... | Relationship between logistic regression and hyperplane | The picture below will probably answer your question.
A logistic regression model with 2 features creates a wave based on the logit link function.
Applying the decision rule (for example above 50%) | Relationship between logistic regression and hyperplane
The picture below will probably answer your question.
A logistic regression model with 2 features creates a wave based on the logit link function.
Applying the decision rule (for example above 50%) transforms the wave to a separating hyperplane like that, but n... | Relationship between logistic regression and hyperplane
The picture below will probably answer your question.
A logistic regression model with 2 features creates a wave based on the logit link function.
Applying the decision rule (for example above 50%) |
40,689 | Feature scaling (normalization) in multiple regression analysis with normal equation method? | Well, in the second article there is a sentence:
Note that before conducting linear regression, you should normalize
the data. One way is $\frac{x_i−mean(x)}{Range(x)}$, and some use
$sd(x)$ as the denominator. Both work.
But is not said that it applies specifically to normal equations. And in gradient descent s... | Feature scaling (normalization) in multiple regression analysis with normal equation method? | Well, in the second article there is a sentence:
Note that before conducting linear regression, you should normalize
the data. One way is $\frac{x_i−mean(x)}{Range(x)}$, and some use
$sd(x)$ as | Feature scaling (normalization) in multiple regression analysis with normal equation method?
Well, in the second article there is a sentence:
Note that before conducting linear regression, you should normalize
the data. One way is $\frac{x_i−mean(x)}{Range(x)}$, and some use
$sd(x)$ as the denominator. Both work.... | Feature scaling (normalization) in multiple regression analysis with normal equation method?
Well, in the second article there is a sentence:
Note that before conducting linear regression, you should normalize
the data. One way is $\frac{x_i−mean(x)}{Range(x)}$, and some use
$sd(x)$ as |
40,690 | What math background do I need to read ESL effectively? | In terms of Mathematics one does not need a heavy background for a first comprehensive read of ESL. What a first year CS/Engineering undergraduate would know is adequate. For example, in terms of Linear Algebra the levels of G. Strang's Introduction to Linear Algebra and in terms of Multivariate Calculus J. Stewart's C... | What math background do I need to read ESL effectively? | In terms of Mathematics one does not need a heavy background for a first comprehensive read of ESL. What a first year CS/Engineering undergraduate would know is adequate. For example, in terms of Line | What math background do I need to read ESL effectively?
In terms of Mathematics one does not need a heavy background for a first comprehensive read of ESL. What a first year CS/Engineering undergraduate would know is adequate. For example, in terms of Linear Algebra the levels of G. Strang's Introduction to Linear Alge... | What math background do I need to read ESL effectively?
In terms of Mathematics one does not need a heavy background for a first comprehensive read of ESL. What a first year CS/Engineering undergraduate would know is adequate. For example, in terms of Line |
40,691 | What's wrong if I fit the auto-regression with OLS? | To answer the title question, fitting an AR($p$) model using OLS will yield biased estimates. The reason is that for unbiasedness, the model errors should be uncorrelated with past, current and future values of regressors, which is not the case in autoregressive models. For example, in case of AR(1)
$$ y_t=\varphi y_{... | What's wrong if I fit the auto-regression with OLS? | To answer the title question, fitting an AR($p$) model using OLS will yield biased estimates. The reason is that for unbiasedness, the model errors should be uncorrelated with past, current and future | What's wrong if I fit the auto-regression with OLS?
To answer the title question, fitting an AR($p$) model using OLS will yield biased estimates. The reason is that for unbiasedness, the model errors should be uncorrelated with past, current and future values of regressors, which is not the case in autoregressive model... | What's wrong if I fit the auto-regression with OLS?
To answer the title question, fitting an AR($p$) model using OLS will yield biased estimates. The reason is that for unbiasedness, the model errors should be uncorrelated with past, current and future |
40,692 | What's wrong if I fit the auto-regression with OLS? | If you fit by regressing $\mathbf{y}_{p+1:n}=(y_{p+1},...,y_n)^\top$ on its lags $X=[\mathbf{y}_{p:n-1},\mathbf{y}_{p-1:n-2},...,\mathbf{y}_{1:n-p}]$ the lags of that on you're going to be conditioning on the first $p$ values (for an AR(p)). If you fit by say maximum likelihood you're able to incorporate the likelihood... | What's wrong if I fit the auto-regression with OLS? | If you fit by regressing $\mathbf{y}_{p+1:n}=(y_{p+1},...,y_n)^\top$ on its lags $X=[\mathbf{y}_{p:n-1},\mathbf{y}_{p-1:n-2},...,\mathbf{y}_{1:n-p}]$ the lags of that on you're going to be conditionin | What's wrong if I fit the auto-regression with OLS?
If you fit by regressing $\mathbf{y}_{p+1:n}=(y_{p+1},...,y_n)^\top$ on its lags $X=[\mathbf{y}_{p:n-1},\mathbf{y}_{p-1:n-2},...,\mathbf{y}_{1:n-p}]$ the lags of that on you're going to be conditioning on the first $p$ values (for an AR(p)). If you fit by say maximum ... | What's wrong if I fit the auto-regression with OLS?
If you fit by regressing $\mathbf{y}_{p+1:n}=(y_{p+1},...,y_n)^\top$ on its lags $X=[\mathbf{y}_{p:n-1},\mathbf{y}_{p-1:n-2},...,\mathbf{y}_{1:n-p}]$ the lags of that on you're going to be conditionin |
40,693 | why does R rlm {MASS} return different coefficients almost each time it is called? | Because of the algorithm you choose to compute the initial values (init) (from which the second stage of the algorithm, i.e. the MM steps, start).
Setting init=lts uses the coefficients fitted by the FastLTS algorithm as starting points of the MM iterations. The FastLTS algorithm in turn uses many random starting poi... | why does R rlm {MASS} return different coefficients almost each time it is called? | Because of the algorithm you choose to compute the initial values (init) (from which the second stage of the algorithm, i.e. the MM steps, start).
Setting init=lts uses the coefficients fitted by the | why does R rlm {MASS} return different coefficients almost each time it is called?
Because of the algorithm you choose to compute the initial values (init) (from which the second stage of the algorithm, i.e. the MM steps, start).
Setting init=lts uses the coefficients fitted by the FastLTS algorithm as starting points... | why does R rlm {MASS} return different coefficients almost each time it is called?
Because of the algorithm you choose to compute the initial values (init) (from which the second stage of the algorithm, i.e. the MM steps, start).
Setting init=lts uses the coefficients fitted by the |
40,694 | Proof of the Derivation of the marginal and conditional Gaussian | Let's write the RV $X$, $Y$ as
$$
X = \mu + \varepsilon _x \\
Y = AX + b + \varepsilon _y
$$
with $ \varepsilon _x \sim \mathcal N (0, \Lambda ^{-1})$, $ \varepsilon _y \sim \mathcal N (0, L ^{-1})$. Now pluging in X in the second equation above gives
$$
Y = A\mu + b + A\varepsilon _x + \varepsilon _y.
$$
This is a lin... | Proof of the Derivation of the marginal and conditional Gaussian | Let's write the RV $X$, $Y$ as
$$
X = \mu + \varepsilon _x \\
Y = AX + b + \varepsilon _y
$$
with $ \varepsilon _x \sim \mathcal N (0, \Lambda ^{-1})$, $ \varepsilon _y \sim \mathcal N (0, L ^{-1})$. | Proof of the Derivation of the marginal and conditional Gaussian
Let's write the RV $X$, $Y$ as
$$
X = \mu + \varepsilon _x \\
Y = AX + b + \varepsilon _y
$$
with $ \varepsilon _x \sim \mathcal N (0, \Lambda ^{-1})$, $ \varepsilon _y \sim \mathcal N (0, L ^{-1})$. Now pluging in X in the second equation above gives
$$
... | Proof of the Derivation of the marginal and conditional Gaussian
Let's write the RV $X$, $Y$ as
$$
X = \mu + \varepsilon _x \\
Y = AX + b + \varepsilon _y
$$
with $ \varepsilon _x \sim \mathcal N (0, \Lambda ^{-1})$, $ \varepsilon _y \sim \mathcal N (0, L ^{-1})$. |
40,695 | Proof of the Derivation of the marginal and conditional Gaussian | I would like to also give a algebraic response to this question showing that by multiplying the Gaussians together and integrating you can get this result. I did this using the covariance matrix defined as $L, \Lambda$ instead of $L^{-1}$ and $\Lambda^{-1}$ because that is my preference.
\begin{align}
y|x \sim & N(A... | Proof of the Derivation of the marginal and conditional Gaussian | I would like to also give a algebraic response to this question showing that by multiplying the Gaussians together and integrating you can get this result. I did this using the covariance matrix defin | Proof of the Derivation of the marginal and conditional Gaussian
I would like to also give a algebraic response to this question showing that by multiplying the Gaussians together and integrating you can get this result. I did this using the covariance matrix defined as $L, \Lambda$ instead of $L^{-1}$ and $\Lambda^{-1... | Proof of the Derivation of the marginal and conditional Gaussian
I would like to also give a algebraic response to this question showing that by multiplying the Gaussians together and integrating you can get this result. I did this using the covariance matrix defin |
40,696 | Why do autoencoders come under unsupervised learning? | An autoencoder is unsupervised since it's not using labeled data.
The goal is to minimize reconstruction error based on a loss function, such as the mean squared error:
$\mathcal{L}(\mathbf{x},\mathbf{x'})=\|\mathbf{x}-\mathbf{x'}\|^2=\|\mathbf{x}-f(\mathbf{W'}(f(\mathbf{Wx}+\mathbf{b}))+\mathbf{b'})\|^2$
All algorithm... | Why do autoencoders come under unsupervised learning? | An autoencoder is unsupervised since it's not using labeled data.
The goal is to minimize reconstruction error based on a loss function, such as the mean squared error:
$\mathcal{L}(\mathbf{x},\mathbf | Why do autoencoders come under unsupervised learning?
An autoencoder is unsupervised since it's not using labeled data.
The goal is to minimize reconstruction error based on a loss function, such as the mean squared error:
$\mathcal{L}(\mathbf{x},\mathbf{x'})=\|\mathbf{x}-\mathbf{x'}\|^2=\|\mathbf{x}-f(\mathbf{W'}(f(\m... | Why do autoencoders come under unsupervised learning?
An autoencoder is unsupervised since it's not using labeled data.
The goal is to minimize reconstruction error based on a loss function, such as the mean squared error:
$\mathcal{L}(\mathbf{x},\mathbf |
40,697 | Why do autoencoders come under unsupervised learning? | Before answering the question, I quote from (Artificial Intelligence: A Modern Approach):
In unsupervised learning the agent learns pattern in the input even
though no explicit feedback is supplied. The most common unsupervised
learning task is clustering.
...
In supervised learning the agent observe some example inpu... | Why do autoencoders come under unsupervised learning? | Before answering the question, I quote from (Artificial Intelligence: A Modern Approach):
In unsupervised learning the agent learns pattern in the input even
though no explicit feedback is supplied. | Why do autoencoders come under unsupervised learning?
Before answering the question, I quote from (Artificial Intelligence: A Modern Approach):
In unsupervised learning the agent learns pattern in the input even
though no explicit feedback is supplied. The most common unsupervised
learning task is clustering.
...
In s... | Why do autoencoders come under unsupervised learning?
Before answering the question, I quote from (Artificial Intelligence: A Modern Approach):
In unsupervised learning the agent learns pattern in the input even
though no explicit feedback is supplied. |
40,698 | Why do autoencoders come under unsupervised learning? | This is pretty heuristic explanation :(
Autoencoders with sparsity enforcement seek to arrive at a more efficient representation of the data. Because we effectively restricting the number of how many neurons we allow to "fire" at a given layer, we are actually imposing sort-of bound on dimensionality of data which make... | Why do autoencoders come under unsupervised learning? | This is pretty heuristic explanation :(
Autoencoders with sparsity enforcement seek to arrive at a more efficient representation of the data. Because we effectively restricting the number of how many | Why do autoencoders come under unsupervised learning?
This is pretty heuristic explanation :(
Autoencoders with sparsity enforcement seek to arrive at a more efficient representation of the data. Because we effectively restricting the number of how many neurons we allow to "fire" at a given layer, we are actually impos... | Why do autoencoders come under unsupervised learning?
This is pretty heuristic explanation :(
Autoencoders with sparsity enforcement seek to arrive at a more efficient representation of the data. Because we effectively restricting the number of how many |
40,699 | Why do autoencoders come under unsupervised learning? | Since terminology is so confusing someone invented the term "self-supervised" to describe autoencoders learning mode:
I now call it “self-supervised learning”, because “unsupervised” is
both a loaded and confusing term. …
Self-supervised learning uses way more supervisory signals than
supervised learning, and enormous... | Why do autoencoders come under unsupervised learning? | Since terminology is so confusing someone invented the term "self-supervised" to describe autoencoders learning mode:
I now call it “self-supervised learning”, because “unsupervised” is
both a loaded | Why do autoencoders come under unsupervised learning?
Since terminology is so confusing someone invented the term "self-supervised" to describe autoencoders learning mode:
I now call it “self-supervised learning”, because “unsupervised” is
both a loaded and confusing term. …
Self-supervised learning uses way more supe... | Why do autoencoders come under unsupervised learning?
Since terminology is so confusing someone invented the term "self-supervised" to describe autoencoders learning mode:
I now call it “self-supervised learning”, because “unsupervised” is
both a loaded |
40,700 | Relationship between least-squares regression and information theory | The entropy of the random variable $Y$, $H(Y$) is sometimes called a measure of your "uncertainty" about $Y$. What if you know about this other variable, $X$? Your uncertainty about $Y$ given $X$ will go down. This reduction is called mutual information and is written $I(Y;X) = H(Y) - H(Y|X)$. From an information point... | Relationship between least-squares regression and information theory | The entropy of the random variable $Y$, $H(Y$) is sometimes called a measure of your "uncertainty" about $Y$. What if you know about this other variable, $X$? Your uncertainty about $Y$ given $X$ will | Relationship between least-squares regression and information theory
The entropy of the random variable $Y$, $H(Y$) is sometimes called a measure of your "uncertainty" about $Y$. What if you know about this other variable, $X$? Your uncertainty about $Y$ given $X$ will go down. This reduction is called mutual informati... | Relationship between least-squares regression and information theory
The entropy of the random variable $Y$, $H(Y$) is sometimes called a measure of your "uncertainty" about $Y$. What if you know about this other variable, $X$? Your uncertainty about $Y$ given $X$ will |
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