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 |
|---|---|---|---|---|---|---|
8,501 | Why will ridge regression not shrink some coefficients to zero like lasso? | Ridge Regression
$L_{2}=(y-x\beta)^2+\lambda\sum_{i=1}^{p}\beta_{i}^2$
Will solve this equation only for one β for now and latter you can generalize this:
So, $(y-xβ)^2+λβ^2$ this is our equation for one β.
Our goal is to minimize the above equation, to be able to do this, will equate this to zero and take the derivati... | Why will ridge regression not shrink some coefficients to zero like lasso? | Ridge Regression
$L_{2}=(y-x\beta)^2+\lambda\sum_{i=1}^{p}\beta_{i}^2$
Will solve this equation only for one β for now and latter you can generalize this:
So, $(y-xβ)^2+λβ^2$ this is our equation for | Why will ridge regression not shrink some coefficients to zero like lasso?
Ridge Regression
$L_{2}=(y-x\beta)^2+\lambda\sum_{i=1}^{p}\beta_{i}^2$
Will solve this equation only for one β for now and latter you can generalize this:
So, $(y-xβ)^2+λβ^2$ this is our equation for one β.
Our goal is to minimize the above equa... | Why will ridge regression not shrink some coefficients to zero like lasso?
Ridge Regression
$L_{2}=(y-x\beta)^2+\lambda\sum_{i=1}^{p}\beta_{i}^2$
Will solve this equation only for one β for now and latter you can generalize this:
So, $(y-xβ)^2+λβ^2$ this is our equation for |
8,502 | Does it make sense to combine PCA and LDA? | Summary: PCA can be performed before LDA to regularize the problem and avoid over-fitting.
Recall that LDA projections are computed via eigendecomposition of $\boldsymbol \Sigma_W^{-1} \boldsymbol \Sigma_B$, where $\boldsymbol \Sigma_W$ and $\boldsymbol \Sigma_B$ are within- and between-class covariance matrices. If th... | Does it make sense to combine PCA and LDA? | Summary: PCA can be performed before LDA to regularize the problem and avoid over-fitting.
Recall that LDA projections are computed via eigendecomposition of $\boldsymbol \Sigma_W^{-1} \boldsymbol \Si | Does it make sense to combine PCA and LDA?
Summary: PCA can be performed before LDA to regularize the problem and avoid over-fitting.
Recall that LDA projections are computed via eigendecomposition of $\boldsymbol \Sigma_W^{-1} \boldsymbol \Sigma_B$, where $\boldsymbol \Sigma_W$ and $\boldsymbol \Sigma_B$ are within- a... | Does it make sense to combine PCA and LDA?
Summary: PCA can be performed before LDA to regularize the problem and avoid over-fitting.
Recall that LDA projections are computed via eigendecomposition of $\boldsymbol \Sigma_W^{-1} \boldsymbol \Si |
8,503 | Does it make sense to combine PCA and LDA? | If you have a two class problem then LDA will take you down to 1 dimension. There is no reason to do PCA first. | Does it make sense to combine PCA and LDA? | If you have a two class problem then LDA will take you down to 1 dimension. There is no reason to do PCA first. | Does it make sense to combine PCA and LDA?
If you have a two class problem then LDA will take you down to 1 dimension. There is no reason to do PCA first. | Does it make sense to combine PCA and LDA?
If you have a two class problem then LDA will take you down to 1 dimension. There is no reason to do PCA first. |
8,504 | Comparing smoothing splines vs loess for smoothing? | Here is some R code/example that will let you compare the fits for a loess fit and a spline fit:
library(TeachingDemos)
library(splines)
tmpfun <- function(x,y,span=.75,df=3) {
plot(x,y)
fit1 <- lm(y ~ ns(x,df))
xx <- seq( min(x), max(x), length.out=250 )
yy <- predict(fit1, data.frame(x=xx))
lines... | Comparing smoothing splines vs loess for smoothing? | Here is some R code/example that will let you compare the fits for a loess fit and a spline fit:
library(TeachingDemos)
library(splines)
tmpfun <- function(x,y,span=.75,df=3) {
plot(x,y)
fit1 | Comparing smoothing splines vs loess for smoothing?
Here is some R code/example that will let you compare the fits for a loess fit and a spline fit:
library(TeachingDemos)
library(splines)
tmpfun <- function(x,y,span=.75,df=3) {
plot(x,y)
fit1 <- lm(y ~ ns(x,df))
xx <- seq( min(x), max(x), length.out=250 )... | Comparing smoothing splines vs loess for smoothing?
Here is some R code/example that will let you compare the fits for a loess fit and a spline fit:
library(TeachingDemos)
library(splines)
tmpfun <- function(x,y,span=.75,df=3) {
plot(x,y)
fit1 |
8,505 | Comparing smoothing splines vs loess for smoothing? | The actual results from a smoothing spline or loess are going to be pretty similar. They might look a little different at the edges of the support, but as long as you make sure it's a "natural" smoothing spline they will look really similar.
If you are just using one to add a "smoother" to a scatterplot, there's no re... | Comparing smoothing splines vs loess for smoothing? | The actual results from a smoothing spline or loess are going to be pretty similar. They might look a little different at the edges of the support, but as long as you make sure it's a "natural" smoot | Comparing smoothing splines vs loess for smoothing?
The actual results from a smoothing spline or loess are going to be pretty similar. They might look a little different at the edges of the support, but as long as you make sure it's a "natural" smoothing spline they will look really similar.
If you are just using one... | Comparing smoothing splines vs loess for smoothing?
The actual results from a smoothing spline or loess are going to be pretty similar. They might look a little different at the edges of the support, but as long as you make sure it's a "natural" smoot |
8,506 | Difference between Cohen's d and Hedges' g for effect size metrics | Both Cohen's d and Hedges' g pool variances on the assumption of equal population variances, but g pools using n - 1 for each sample instead of n, which provides a better estimate, especially the smaller the sample sizes. Both d and g are somewhat positively biased, but only negligibly for moderate or larger sample si... | Difference between Cohen's d and Hedges' g for effect size metrics | Both Cohen's d and Hedges' g pool variances on the assumption of equal population variances, but g pools using n - 1 for each sample instead of n, which provides a better estimate, especially the smal | Difference between Cohen's d and Hedges' g for effect size metrics
Both Cohen's d and Hedges' g pool variances on the assumption of equal population variances, but g pools using n - 1 for each sample instead of n, which provides a better estimate, especially the smaller the sample sizes. Both d and g are somewhat posi... | Difference between Cohen's d and Hedges' g for effect size metrics
Both Cohen's d and Hedges' g pool variances on the assumption of equal population variances, but g pools using n - 1 for each sample instead of n, which provides a better estimate, especially the smal |
8,507 | Difference between Cohen's d and Hedges' g for effect size metrics | It seems when people say Cohen's d they mostly mean:
$$d = \frac{\bar{x}_1 - \bar{x}_2}{s}$$
Where $s$ is the pooled standard deviation,
$$s = \sqrt{\frac{\sum(x_1 - \bar{x}_1)^2 + (x_2 - \bar{x}_2)^2}{n_1 + n_2 - 2}}$$
There are other estimators for the pooled standard deviation, probably the most common apart fro... | Difference between Cohen's d and Hedges' g for effect size metrics | It seems when people say Cohen's d they mostly mean:
$$d = \frac{\bar{x}_1 - \bar{x}_2}{s}$$
Where $s$ is the pooled standard deviation,
$$s = \sqrt{\frac{\sum(x_1 - \bar{x}_1)^2 + (x_2 - \bar{x}_2 | Difference between Cohen's d and Hedges' g for effect size metrics
It seems when people say Cohen's d they mostly mean:
$$d = \frac{\bar{x}_1 - \bar{x}_2}{s}$$
Where $s$ is the pooled standard deviation,
$$s = \sqrt{\frac{\sum(x_1 - \bar{x}_1)^2 + (x_2 - \bar{x}_2)^2}{n_1 + n_2 - 2}}$$
There are other estimators fo... | Difference between Cohen's d and Hedges' g for effect size metrics
It seems when people say Cohen's d they mostly mean:
$$d = \frac{\bar{x}_1 - \bar{x}_2}{s}$$
Where $s$ is the pooled standard deviation,
$$s = \sqrt{\frac{\sum(x_1 - \bar{x}_1)^2 + (x_2 - \bar{x}_2 |
8,508 | Difference between Cohen's d and Hedges' g for effect size metrics | To my understanding, Hedges's g is a somewhat more accurate version of Cohen's d (with pooled SD) in that we add a correction factor for small sample. Both measures generally agree when the homoscedasticity assumption is not violated, but we may found situations where this is not the case, see e.g. McGrath & Meyer, Psy... | Difference between Cohen's d and Hedges' g for effect size metrics | To my understanding, Hedges's g is a somewhat more accurate version of Cohen's d (with pooled SD) in that we add a correction factor for small sample. Both measures generally agree when the homoscedas | Difference between Cohen's d and Hedges' g for effect size metrics
To my understanding, Hedges's g is a somewhat more accurate version of Cohen's d (with pooled SD) in that we add a correction factor for small sample. Both measures generally agree when the homoscedasticity assumption is not violated, but we may found s... | Difference between Cohen's d and Hedges' g for effect size metrics
To my understanding, Hedges's g is a somewhat more accurate version of Cohen's d (with pooled SD) in that we add a correction factor for small sample. Both measures generally agree when the homoscedas |
8,509 | Difference between Cohen's d and Hedges' g for effect size metrics | If you're just trying to understand the basic meaning of Hedges' g, as I am, you might also find this helpful:
The magnitude of Hedges’ g may be interpreted using Cohen's (1988 [2])
convention as small (0.2), medium (0.5), and large (0.8). [1]
Their definition is short and clear:
Hedges’ g is a variation of Cohe... | Difference between Cohen's d and Hedges' g for effect size metrics | If you're just trying to understand the basic meaning of Hedges' g, as I am, you might also find this helpful:
The magnitude of Hedges’ g may be interpreted using Cohen's (1988 [2])
convention as s | Difference between Cohen's d and Hedges' g for effect size metrics
If you're just trying to understand the basic meaning of Hedges' g, as I am, you might also find this helpful:
The magnitude of Hedges’ g may be interpreted using Cohen's (1988 [2])
convention as small (0.2), medium (0.5), and large (0.8). [1]
Thei... | Difference between Cohen's d and Hedges' g for effect size metrics
If you're just trying to understand the basic meaning of Hedges' g, as I am, you might also find this helpful:
The magnitude of Hedges’ g may be interpreted using Cohen's (1988 [2])
convention as s |
8,510 | Difference between Cohen's d and Hedges' g for effect size metrics | The other posters have covered the issue of similarities and differences between g and d. Just to add to this, some scholars do feel that the effect size values offered by Cohen are far too generous leading to overinterpretation of weak effects. They are also not tied to r leading to the possibility scholars may conv... | Difference between Cohen's d and Hedges' g for effect size metrics | The other posters have covered the issue of similarities and differences between g and d. Just to add to this, some scholars do feel that the effect size values offered by Cohen are far too generous | Difference between Cohen's d and Hedges' g for effect size metrics
The other posters have covered the issue of similarities and differences between g and d. Just to add to this, some scholars do feel that the effect size values offered by Cohen are far too generous leading to overinterpretation of weak effects. They ... | Difference between Cohen's d and Hedges' g for effect size metrics
The other posters have covered the issue of similarities and differences between g and d. Just to add to this, some scholars do feel that the effect size values offered by Cohen are far too generous |
8,511 | Difference between Cohen's d and Hedges' g for effect size metrics | Bruce Thompson did warn about using Cohen's (0.2) as small (0.5) as medium and (0.8) as large. Cohen never meant for these to be used as rigid interpretations. All effect sizes must be interpreted based on the context of the related literature. If you are analyzing the related effect sizes reported on your topic and th... | Difference between Cohen's d and Hedges' g for effect size metrics | Bruce Thompson did warn about using Cohen's (0.2) as small (0.5) as medium and (0.8) as large. Cohen never meant for these to be used as rigid interpretations. All effect sizes must be interpreted bas | Difference between Cohen's d and Hedges' g for effect size metrics
Bruce Thompson did warn about using Cohen's (0.2) as small (0.5) as medium and (0.8) as large. Cohen never meant for these to be used as rigid interpretations. All effect sizes must be interpreted based on the context of the related literature. If you a... | Difference between Cohen's d and Hedges' g for effect size metrics
Bruce Thompson did warn about using Cohen's (0.2) as small (0.5) as medium and (0.8) as large. Cohen never meant for these to be used as rigid interpretations. All effect sizes must be interpreted bas |
8,512 | Difference between Cohen's d and Hedges' g for effect size metrics | Effect size is measure of association, we should always describe the results in terms of measures of magnitude- our study result must be able to tell not just if treatment is effective or not but how much it is effective.
Hedges’ g and Cohen's d are incredibly comparable. Both have an upwards predisposition (a swelling... | Difference between Cohen's d and Hedges' g for effect size metrics | Effect size is measure of association, we should always describe the results in terms of measures of magnitude- our study result must be able to tell not just if treatment is effective or not but how | Difference between Cohen's d and Hedges' g for effect size metrics
Effect size is measure of association, we should always describe the results in terms of measures of magnitude- our study result must be able to tell not just if treatment is effective or not but how much it is effective.
Hedges’ g and Cohen's d are inc... | Difference between Cohen's d and Hedges' g for effect size metrics
Effect size is measure of association, we should always describe the results in terms of measures of magnitude- our study result must be able to tell not just if treatment is effective or not but how |
8,513 | In statistics, should I assume $\log$ to mean $\log_{10}$ or the natural logarithm $\ln$? | It's safe to assume that without explicit base $\log=\ln$ in statistics, because base 10 log is not used very often in statistics. However, other posters bring up a point that $\log_{10}$ or other bases can be common in some other fields, where statistics is applied, e.g. information theory. So, when you read papers in... | In statistics, should I assume $\log$ to mean $\log_{10}$ or the natural logarithm $\ln$? | It's safe to assume that without explicit base $\log=\ln$ in statistics, because base 10 log is not used very often in statistics. However, other posters bring up a point that $\log_{10}$ or other bas | In statistics, should I assume $\log$ to mean $\log_{10}$ or the natural logarithm $\ln$?
It's safe to assume that without explicit base $\log=\ln$ in statistics, because base 10 log is not used very often in statistics. However, other posters bring up a point that $\log_{10}$ or other bases can be common in some other... | In statistics, should I assume $\log$ to mean $\log_{10}$ or the natural logarithm $\ln$?
It's safe to assume that without explicit base $\log=\ln$ in statistics, because base 10 log is not used very often in statistics. However, other posters bring up a point that $\log_{10}$ or other bas |
8,514 | In statistics, should I assume $\log$ to mean $\log_{10}$ or the natural logarithm $\ln$? | It depends.
Base 10 logarithms are pretty rare in equations. However, log-scale plots are often in base-10, though this should be pretty easy to verify from the labels on the axes. In a mathematical context, an unadorned $\log$ is likely to be the natural log (i.e., $\log_{e}$ or $\ln$). On the other hand, computer sci... | In statistics, should I assume $\log$ to mean $\log_{10}$ or the natural logarithm $\ln$? | It depends.
Base 10 logarithms are pretty rare in equations. However, log-scale plots are often in base-10, though this should be pretty easy to verify from the labels on the axes. In a mathematical c | In statistics, should I assume $\log$ to mean $\log_{10}$ or the natural logarithm $\ln$?
It depends.
Base 10 logarithms are pretty rare in equations. However, log-scale plots are often in base-10, though this should be pretty easy to verify from the labels on the axes. In a mathematical context, an unadorned $\log$ is... | In statistics, should I assume $\log$ to mean $\log_{10}$ or the natural logarithm $\ln$?
It depends.
Base 10 logarithms are pretty rare in equations. However, log-scale plots are often in base-10, though this should be pretty easy to verify from the labels on the axes. In a mathematical c |
8,515 | In statistics, should I assume $\log$ to mean $\log_{10}$ or the natural logarithm $\ln$? | To answer your question: no, you cannot assume a general fixed notation for the logarithm.
A similar question was recently discussed in SE.Math: What is the difference between the three types of logarithms? from a mathematical point of view. Generally, there are different notations that depend on habits ($\log_{10}$ se... | In statistics, should I assume $\log$ to mean $\log_{10}$ or the natural logarithm $\ln$? | To answer your question: no, you cannot assume a general fixed notation for the logarithm.
A similar question was recently discussed in SE.Math: What is the difference between the three types of logar | In statistics, should I assume $\log$ to mean $\log_{10}$ or the natural logarithm $\ln$?
To answer your question: no, you cannot assume a general fixed notation for the logarithm.
A similar question was recently discussed in SE.Math: What is the difference between the three types of logarithms? from a mathematical poi... | In statistics, should I assume $\log$ to mean $\log_{10}$ or the natural logarithm $\ln$?
To answer your question: no, you cannot assume a general fixed notation for the logarithm.
A similar question was recently discussed in SE.Math: What is the difference between the three types of logar |
8,516 | In statistics, should I assume $\log$ to mean $\log_{10}$ or the natural logarithm $\ln$? | In the Akaike Information Criterion the base is $e$, and $\ln(\hat L)$ of the maximum likelihood $\hat L$ is being compared additively to the number of parameters $k$:
$$
\mathrm{AIC} = 2(k-\ln(L)).$$
Thus it seems that if you use any other base for the logarithm in the AIC, you may end up drawing the wrong conclusion ... | In statistics, should I assume $\log$ to mean $\log_{10}$ or the natural logarithm $\ln$? | In the Akaike Information Criterion the base is $e$, and $\ln(\hat L)$ of the maximum likelihood $\hat L$ is being compared additively to the number of parameters $k$:
$$
\mathrm{AIC} = 2(k-\ln(L)).$$ | In statistics, should I assume $\log$ to mean $\log_{10}$ or the natural logarithm $\ln$?
In the Akaike Information Criterion the base is $e$, and $\ln(\hat L)$ of the maximum likelihood $\hat L$ is being compared additively to the number of parameters $k$:
$$
\mathrm{AIC} = 2(k-\ln(L)).$$
Thus it seems that if you use... | In statistics, should I assume $\log$ to mean $\log_{10}$ or the natural logarithm $\ln$?
In the Akaike Information Criterion the base is $e$, and $\ln(\hat L)$ of the maximum likelihood $\hat L$ is being compared additively to the number of parameters $k$:
$$
\mathrm{AIC} = 2(k-\ln(L)).$$ |
8,517 | In statistics, should I assume $\log$ to mean $\log_{10}$ or the natural logarithm $\ln$? | For many applications, the natural logarithm of the likelihood function, called the log-likelihood, is more convenient to work with in our case."
In statistics we often work with likelihood function, it is usually the ln that is considered. However, the two are related: log(x) = ln(x) / ln(10) = ln(x) / 2.303, and the ... | In statistics, should I assume $\log$ to mean $\log_{10}$ or the natural logarithm $\ln$? | For many applications, the natural logarithm of the likelihood function, called the log-likelihood, is more convenient to work with in our case."
In statistics we often work with likelihood function, | In statistics, should I assume $\log$ to mean $\log_{10}$ or the natural logarithm $\ln$?
For many applications, the natural logarithm of the likelihood function, called the log-likelihood, is more convenient to work with in our case."
In statistics we often work with likelihood function, it is usually the ln that is c... | In statistics, should I assume $\log$ to mean $\log_{10}$ or the natural logarithm $\ln$?
For many applications, the natural logarithm of the likelihood function, called the log-likelihood, is more convenient to work with in our case."
In statistics we often work with likelihood function, |
8,518 | In statistics, should I assume $\log$ to mean $\log_{10}$ or the natural logarithm $\ln$? | it completely depends.
and it is sometimes confusing!
for example in the process of derivation of logistic regression cost function...
Remember, when talking about log odds with logistic regression, we always mean the natural logarithm of the odds (Ln[Odds]). Natural log is often abbreviated as “log” or “ln,” which can... | In statistics, should I assume $\log$ to mean $\log_{10}$ or the natural logarithm $\ln$? | it completely depends.
and it is sometimes confusing!
for example in the process of derivation of logistic regression cost function...
Remember, when talking about log odds with logistic regression, w | In statistics, should I assume $\log$ to mean $\log_{10}$ or the natural logarithm $\ln$?
it completely depends.
and it is sometimes confusing!
for example in the process of derivation of logistic regression cost function...
Remember, when talking about log odds with logistic regression, we always mean the natural loga... | In statistics, should I assume $\log$ to mean $\log_{10}$ or the natural logarithm $\ln$?
it completely depends.
and it is sometimes confusing!
for example in the process of derivation of logistic regression cost function...
Remember, when talking about log odds with logistic regression, w |
8,519 | Imputation of missing values for PCA | There is in fact a well documented way to deal with gappy matrices - you can decompose a covariance matrix $\textbf{C}$ contructed from of your data $\textbf{X}$, which is scaled by the number of shared values $n$:
$$
\textbf{C}=\frac{1}{n} \textbf{X} ^ {\text{T}} \textbf{X},~~~~~~~~~~~~~~~~ C_{jl} = \overline{X_{.j}Y_... | Imputation of missing values for PCA | There is in fact a well documented way to deal with gappy matrices - you can decompose a covariance matrix $\textbf{C}$ contructed from of your data $\textbf{X}$, which is scaled by the number of shar | Imputation of missing values for PCA
There is in fact a well documented way to deal with gappy matrices - you can decompose a covariance matrix $\textbf{C}$ contructed from of your data $\textbf{X}$, which is scaled by the number of shared values $n$:
$$
\textbf{C}=\frac{1}{n} \textbf{X} ^ {\text{T}} \textbf{X},~~~~~~~... | Imputation of missing values for PCA
There is in fact a well documented way to deal with gappy matrices - you can decompose a covariance matrix $\textbf{C}$ contructed from of your data $\textbf{X}$, which is scaled by the number of shar |
8,520 | Imputation of missing values for PCA | A recent paper which reviews approaches for dealing with missing values in PCA analyses is "Principal component analysis with missing values: a comparative survey of methods" by Dray & Josse (2015). Two of the best known methods of PCA methods that allow for missing values are the NIPALS algorithm, implemented in the ... | Imputation of missing values for PCA | A recent paper which reviews approaches for dealing with missing values in PCA analyses is "Principal component analysis with missing values: a comparative survey of methods" by Dray & Josse (2015). | Imputation of missing values for PCA
A recent paper which reviews approaches for dealing with missing values in PCA analyses is "Principal component analysis with missing values: a comparative survey of methods" by Dray & Josse (2015). Two of the best known methods of PCA methods that allow for missing values are the ... | Imputation of missing values for PCA
A recent paper which reviews approaches for dealing with missing values in PCA analyses is "Principal component analysis with missing values: a comparative survey of methods" by Dray & Josse (2015). |
8,521 | Imputation of missing values for PCA | My suggestion depends on how much data is missing and why it is missing. But this has nothing to do with PCA, really. If there is very little data missing, then it won't much matter what you do. Replacing with the median isn't ideal, but if there is not much missing, it won't be much different from a better solution. Y... | Imputation of missing values for PCA | My suggestion depends on how much data is missing and why it is missing. But this has nothing to do with PCA, really. If there is very little data missing, then it won't much matter what you do. Repla | Imputation of missing values for PCA
My suggestion depends on how much data is missing and why it is missing. But this has nothing to do with PCA, really. If there is very little data missing, then it won't much matter what you do. Replacing with the median isn't ideal, but if there is not much missing, it won't be muc... | Imputation of missing values for PCA
My suggestion depends on how much data is missing and why it is missing. But this has nothing to do with PCA, really. If there is very little data missing, then it won't much matter what you do. Repla |
8,522 | Imputation of missing values for PCA | You could solve the problem of the missing value in different way.
Below I'm going to illustrate them.
You should use the mean of the variable that includes NA values or impute the missing values with a linear regression.
You should use missMDA and then FactoMineR or the pcaMethods.
Below an example.
library(missMDA... | Imputation of missing values for PCA | You could solve the problem of the missing value in different way.
Below I'm going to illustrate them.
You should use the mean of the variable that includes NA values or impute the missing values wi | Imputation of missing values for PCA
You could solve the problem of the missing value in different way.
Below I'm going to illustrate them.
You should use the mean of the variable that includes NA values or impute the missing values with a linear regression.
You should use missMDA and then FactoMineR or the pcaMetho... | Imputation of missing values for PCA
You could solve the problem of the missing value in different way.
Below I'm going to illustrate them.
You should use the mean of the variable that includes NA values or impute the missing values wi |
8,523 | Imputation of missing values for PCA | There is no correct solution to the problem. Every coordinate in the vector has to be specified to get the correct set of principal components. If a coordinate is missing and replaced by some imputed value you will get a result but it will be dependent on the imputed value. so if there are two reasonable choices for... | Imputation of missing values for PCA | There is no correct solution to the problem. Every coordinate in the vector has to be specified to get the correct set of principal components. If a coordinate is missing and replaced by some impute | Imputation of missing values for PCA
There is no correct solution to the problem. Every coordinate in the vector has to be specified to get the correct set of principal components. If a coordinate is missing and replaced by some imputed value you will get a result but it will be dependent on the imputed value. so if... | Imputation of missing values for PCA
There is no correct solution to the problem. Every coordinate in the vector has to be specified to get the correct set of principal components. If a coordinate is missing and replaced by some impute |
8,524 | Why does Bayesian Optimization perform poorly in more than 20 Dimensions? | To be completely honest, it's because everything performs poorly in more than 20 dimensions. Bayesian optimization isn't special here.
Trying to optimize any function in a lot of dimensions is hard, because the volume of a high-dimensional space goes up exponentially with the number of dimensions. Consider a line segme... | Why does Bayesian Optimization perform poorly in more than 20 Dimensions? | To be completely honest, it's because everything performs poorly in more than 20 dimensions. Bayesian optimization isn't special here.
Trying to optimize any function in a lot of dimensions is hard, b | Why does Bayesian Optimization perform poorly in more than 20 Dimensions?
To be completely honest, it's because everything performs poorly in more than 20 dimensions. Bayesian optimization isn't special here.
Trying to optimize any function in a lot of dimensions is hard, because the volume of a high-dimensional space ... | Why does Bayesian Optimization perform poorly in more than 20 Dimensions?
To be completely honest, it's because everything performs poorly in more than 20 dimensions. Bayesian optimization isn't special here.
Trying to optimize any function in a lot of dimensions is hard, b |
8,525 | Why does Bayesian Optimization perform poorly in more than 20 Dimensions? | You will not find a theoretical/scientific justification for this statement as there is none!
The difficulty of optimisation is related to a lot of things, dimension being just one of them and most likely not even a very important one. For example, if you just assume continuity and not differentiability of your objecti... | Why does Bayesian Optimization perform poorly in more than 20 Dimensions? | You will not find a theoretical/scientific justification for this statement as there is none!
The difficulty of optimisation is related to a lot of things, dimension being just one of them and most li | Why does Bayesian Optimization perform poorly in more than 20 Dimensions?
You will not find a theoretical/scientific justification for this statement as there is none!
The difficulty of optimisation is related to a lot of things, dimension being just one of them and most likely not even a very important one. For exampl... | Why does Bayesian Optimization perform poorly in more than 20 Dimensions?
You will not find a theoretical/scientific justification for this statement as there is none!
The difficulty of optimisation is related to a lot of things, dimension being just one of them and most li |
8,526 | Why does Bayesian Optimization perform poorly in more than 20 Dimensions? | Yes, high dimensional space is tough in general, but there a couple things that make Bayesian optimization with Gaussian processes particularly perplexing on those prickly problems.
In my view, there isn't a single reason high dimension makes BO difficult, but the difficulty is rather due to a confluence of multiple fa... | Why does Bayesian Optimization perform poorly in more than 20 Dimensions? | Yes, high dimensional space is tough in general, but there a couple things that make Bayesian optimization with Gaussian processes particularly perplexing on those prickly problems.
In my view, there | Why does Bayesian Optimization perform poorly in more than 20 Dimensions?
Yes, high dimensional space is tough in general, but there a couple things that make Bayesian optimization with Gaussian processes particularly perplexing on those prickly problems.
In my view, there isn't a single reason high dimension makes BO ... | Why does Bayesian Optimization perform poorly in more than 20 Dimensions?
Yes, high dimensional space is tough in general, but there a couple things that make Bayesian optimization with Gaussian processes particularly perplexing on those prickly problems.
In my view, there |
8,527 | Can I trust ANOVA results for a non-normally distributed DV? | Like other parametric tests, the analysis of variance assumes that the data fit the normal distribution. If your measurement variable is not normally distributed, you may be increasing your chance of a false positive result if you analyze the data with an anova or other test that assumes normality. Fortunately, an anov... | Can I trust ANOVA results for a non-normally distributed DV? | Like other parametric tests, the analysis of variance assumes that the data fit the normal distribution. If your measurement variable is not normally distributed, you may be increasing your chance of | Can I trust ANOVA results for a non-normally distributed DV?
Like other parametric tests, the analysis of variance assumes that the data fit the normal distribution. If your measurement variable is not normally distributed, you may be increasing your chance of a false positive result if you analyze the data with an ano... | Can I trust ANOVA results for a non-normally distributed DV?
Like other parametric tests, the analysis of variance assumes that the data fit the normal distribution. If your measurement variable is not normally distributed, you may be increasing your chance of |
8,528 | Can I trust ANOVA results for a non-normally distributed DV? | Specifically regarding error rates as a DV, Dixon (2008) very cogently demonstrates that null hypothesis testing via ANOVA can cause both increased false alarm rates (calling effects "significant" when they're not) and increased miss rates (missing real effects). He also shows that mixed effects modelling, specifying b... | Can I trust ANOVA results for a non-normally distributed DV? | Specifically regarding error rates as a DV, Dixon (2008) very cogently demonstrates that null hypothesis testing via ANOVA can cause both increased false alarm rates (calling effects "significant" whe | Can I trust ANOVA results for a non-normally distributed DV?
Specifically regarding error rates as a DV, Dixon (2008) very cogently demonstrates that null hypothesis testing via ANOVA can cause both increased false alarm rates (calling effects "significant" when they're not) and increased miss rates (missing real effec... | Can I trust ANOVA results for a non-normally distributed DV?
Specifically regarding error rates as a DV, Dixon (2008) very cogently demonstrates that null hypothesis testing via ANOVA can cause both increased false alarm rates (calling effects "significant" whe |
8,529 | Can I trust ANOVA results for a non-normally distributed DV? | You cannot trust your ANOVA with that much skew and a large number of 0s. A more appropriate method would be to use number of errors as your DV (thus turning your DV into count data) and doing a Poisson analysis. This approach would require using a mixed effects analysis and specifying the error distribution family a... | Can I trust ANOVA results for a non-normally distributed DV? | You cannot trust your ANOVA with that much skew and a large number of 0s. A more appropriate method would be to use number of errors as your DV (thus turning your DV into count data) and doing a Pois | Can I trust ANOVA results for a non-normally distributed DV?
You cannot trust your ANOVA with that much skew and a large number of 0s. A more appropriate method would be to use number of errors as your DV (thus turning your DV into count data) and doing a Poisson analysis. This approach would require using a mixed ef... | Can I trust ANOVA results for a non-normally distributed DV?
You cannot trust your ANOVA with that much skew and a large number of 0s. A more appropriate method would be to use number of errors as your DV (thus turning your DV into count data) and doing a Pois |
8,530 | Can I trust ANOVA results for a non-normally distributed DV? | Juan has offered a lot, although I'll echo others and repeat that for best accuracy the variables themselves can be nonnormal as long as their residuals aren't. Also, a simplified and slightly more structured answer (via an annotated flow chart) is available at yellowbrickstats.com. | Can I trust ANOVA results for a non-normally distributed DV? | Juan has offered a lot, although I'll echo others and repeat that for best accuracy the variables themselves can be nonnormal as long as their residuals aren't. Also, a simplified and slightly more s | Can I trust ANOVA results for a non-normally distributed DV?
Juan has offered a lot, although I'll echo others and repeat that for best accuracy the variables themselves can be nonnormal as long as their residuals aren't. Also, a simplified and slightly more structured answer (via an annotated flow chart) is available... | Can I trust ANOVA results for a non-normally distributed DV?
Juan has offered a lot, although I'll echo others and repeat that for best accuracy the variables themselves can be nonnormal as long as their residuals aren't. Also, a simplified and slightly more s |
8,531 | Can I trust ANOVA results for a non-normally distributed DV? | Ceiling effects are the problem here. A non parametric test is your safest bet, although ANOVAs are robust to this violation of normality if n is large. Typically people just use a histogram to test this, but if the issue is with residuals it might be more advanced than that. Also bear in mind HOW this effects your res... | Can I trust ANOVA results for a non-normally distributed DV? | Ceiling effects are the problem here. A non parametric test is your safest bet, although ANOVAs are robust to this violation of normality if n is large. Typically people just use a histogram to test t | Can I trust ANOVA results for a non-normally distributed DV?
Ceiling effects are the problem here. A non parametric test is your safest bet, although ANOVAs are robust to this violation of normality if n is large. Typically people just use a histogram to test this, but if the issue is with residuals it might be more ad... | Can I trust ANOVA results for a non-normally distributed DV?
Ceiling effects are the problem here. A non parametric test is your safest bet, although ANOVAs are robust to this violation of normality if n is large. Typically people just use a histogram to test t |
8,532 | When should we discretize/bin continuous independent variables/features and when should not? | Aggregation is substantively meaningful (whether or not the researcher is aware of that).
One should bin data, including independent variables, based on the data itself when one wants:
To hemorrhage statistical power.
To bias measures of association.
A literature starting, I believe, with Ghelke and Biehl (1934—def... | When should we discretize/bin continuous independent variables/features and when should not? | Aggregation is substantively meaningful (whether or not the researcher is aware of that).
One should bin data, including independent variables, based on the data itself when one wants:
To hemorrhage | When should we discretize/bin continuous independent variables/features and when should not?
Aggregation is substantively meaningful (whether or not the researcher is aware of that).
One should bin data, including independent variables, based on the data itself when one wants:
To hemorrhage statistical power.
To bias... | When should we discretize/bin continuous independent variables/features and when should not?
Aggregation is substantively meaningful (whether or not the researcher is aware of that).
One should bin data, including independent variables, based on the data itself when one wants:
To hemorrhage |
8,533 | When should we discretize/bin continuous independent variables/features and when should not? | Looks like you're also looking for an answer from a predictive standpoint, so I put together a short demonstration of two approaches in R
Binning a variable into equal sized factors.
Natural cubic splines.
Below, I've given the code for a function that will compare the two methods automatically for any given true sig... | When should we discretize/bin continuous independent variables/features and when should not? | Looks like you're also looking for an answer from a predictive standpoint, so I put together a short demonstration of two approaches in R
Binning a variable into equal sized factors.
Natural cubic sp | When should we discretize/bin continuous independent variables/features and when should not?
Looks like you're also looking for an answer from a predictive standpoint, so I put together a short demonstration of two approaches in R
Binning a variable into equal sized factors.
Natural cubic splines.
Below, I've given t... | When should we discretize/bin continuous independent variables/features and when should not?
Looks like you're also looking for an answer from a predictive standpoint, so I put together a short demonstration of two approaches in R
Binning a variable into equal sized factors.
Natural cubic sp |
8,534 | Is Kernel PCA with linear kernel equivalent to standard PCA? | Summary: kernel PCA with linear kernel is exactly equivalent to the standard PCA.
Let $\mathbf{X}$ be the centered data matrix of $N \times D$ size with $D$ variables in columns and $N$ data points in rows. Then the $D \times D$ covariance matrix is given by $\mathbf{X}^\top\mathbf{X}/(n-1)$, its eigenvectors are princ... | Is Kernel PCA with linear kernel equivalent to standard PCA? | Summary: kernel PCA with linear kernel is exactly equivalent to the standard PCA.
Let $\mathbf{X}$ be the centered data matrix of $N \times D$ size with $D$ variables in columns and $N$ data points in | Is Kernel PCA with linear kernel equivalent to standard PCA?
Summary: kernel PCA with linear kernel is exactly equivalent to the standard PCA.
Let $\mathbf{X}$ be the centered data matrix of $N \times D$ size with $D$ variables in columns and $N$ data points in rows. Then the $D \times D$ covariance matrix is given by ... | Is Kernel PCA with linear kernel equivalent to standard PCA?
Summary: kernel PCA with linear kernel is exactly equivalent to the standard PCA.
Let $\mathbf{X}$ be the centered data matrix of $N \times D$ size with $D$ variables in columns and $N$ data points in |
8,535 | Is Kernel PCA with linear kernel equivalent to standard PCA? | In addition to amoeba's nice answer, there is an even simpler way to see the equivalence. Again let $X$ be the data matrix of $N \times D$ size with $D$ variables in columns and $N$ data points in rows. Standard PCA corresponds to taking a singular value decomposition of the matrix $X = U \Sigma V^\top$ with $U$ the p... | Is Kernel PCA with linear kernel equivalent to standard PCA? | In addition to amoeba's nice answer, there is an even simpler way to see the equivalence. Again let $X$ be the data matrix of $N \times D$ size with $D$ variables in columns and $N$ data points in row | Is Kernel PCA with linear kernel equivalent to standard PCA?
In addition to amoeba's nice answer, there is an even simpler way to see the equivalence. Again let $X$ be the data matrix of $N \times D$ size with $D$ variables in columns and $N$ data points in rows. Standard PCA corresponds to taking a singular value dec... | Is Kernel PCA with linear kernel equivalent to standard PCA?
In addition to amoeba's nice answer, there is an even simpler way to see the equivalence. Again let $X$ be the data matrix of $N \times D$ size with $D$ variables in columns and $N$ data points in row |
8,536 | Is Kernel PCA with linear kernel equivalent to standard PCA? | It seems to me that that a KPCA with linear kernel should be the same as the simple PCA.
The covariance matrix that you are going to get the eigenvalues from is the same:
$$ linearKPCA_{matrix} = \frac{1}{l} \sum_{j=1}^{l}K(x_{j},x_{j}) = \frac{1}{l} \sum_{j=1}^{l}x_{j}x_{j}^T = PCA_{matrix} $$
You can check with mor... | Is Kernel PCA with linear kernel equivalent to standard PCA? | It seems to me that that a KPCA with linear kernel should be the same as the simple PCA.
The covariance matrix that you are going to get the eigenvalues from is the same:
$$ linearKPCA_{matrix} = \f | Is Kernel PCA with linear kernel equivalent to standard PCA?
It seems to me that that a KPCA with linear kernel should be the same as the simple PCA.
The covariance matrix that you are going to get the eigenvalues from is the same:
$$ linearKPCA_{matrix} = \frac{1}{l} \sum_{j=1}^{l}K(x_{j},x_{j}) = \frac{1}{l} \sum_{... | Is Kernel PCA with linear kernel equivalent to standard PCA?
It seems to me that that a KPCA with linear kernel should be the same as the simple PCA.
The covariance matrix that you are going to get the eigenvalues from is the same:
$$ linearKPCA_{matrix} = \f |
8,537 | Implementation of CRF in python | CRF++ is a popular choice in general, and has Python bindings. CRFSuite also has bindings documented here, but doesn't seem to have seen as much widespread use as CRF++. As of this writing, higher level machine learning frameworks such as scikit-learn lack CRF support (see this pull request). | Implementation of CRF in python | CRF++ is a popular choice in general, and has Python bindings. CRFSuite also has bindings documented here, but doesn't seem to have seen as much widespread use as CRF++. As of this writing, higher lev | Implementation of CRF in python
CRF++ is a popular choice in general, and has Python bindings. CRFSuite also has bindings documented here, but doesn't seem to have seen as much widespread use as CRF++. As of this writing, higher level machine learning frameworks such as scikit-learn lack CRF support (see this pull requ... | Implementation of CRF in python
CRF++ is a popular choice in general, and has Python bindings. CRFSuite also has bindings documented here, but doesn't seem to have seen as much widespread use as CRF++. As of this writing, higher lev |
8,538 | Implementation of CRF in python | CRF++ has more incoming links because it is an older library.
CRFSuite is superior in my opinion.
CRFSuite's author's claim that it is 20x faster than CRF++ at
training a model.
Less rigid requirements for the input data.
If you are looking for Python bindings CRFSuite is also better because you can train a mode... | Implementation of CRF in python | CRF++ has more incoming links because it is an older library.
CRFSuite is superior in my opinion.
CRFSuite's author's claim that it is 20x faster than CRF++ at
training a model.
Less rigid requi | Implementation of CRF in python
CRF++ has more incoming links because it is an older library.
CRFSuite is superior in my opinion.
CRFSuite's author's claim that it is 20x faster than CRF++ at
training a model.
Less rigid requirements for the input data.
If you are looking for Python bindings CRFSuite is also bet... | Implementation of CRF in python
CRF++ has more incoming links because it is an older library.
CRFSuite is superior in my opinion.
CRFSuite's author's claim that it is 20x faster than CRF++ at
training a model.
Less rigid requi |
8,539 | Implementation of CRF in python | Here are some other wrappers/implementations:
https://github.com/adsva/python-wapiti - Python wrapper for http://wapiti.limsi.fr/. Wapiti is fast; crfsuite benchmarks are not fair to wapiti because wapiti can parallelize L-BFGS training to multiple CPU cores, and this feature was not used in benchmarks. The problem wi... | Implementation of CRF in python | Here are some other wrappers/implementations:
https://github.com/adsva/python-wapiti - Python wrapper for http://wapiti.limsi.fr/. Wapiti is fast; crfsuite benchmarks are not fair to wapiti because w | Implementation of CRF in python
Here are some other wrappers/implementations:
https://github.com/adsva/python-wapiti - Python wrapper for http://wapiti.limsi.fr/. Wapiti is fast; crfsuite benchmarks are not fair to wapiti because wapiti can parallelize L-BFGS training to multiple CPU cores, and this feature was not us... | Implementation of CRF in python
Here are some other wrappers/implementations:
https://github.com/adsva/python-wapiti - Python wrapper for http://wapiti.limsi.fr/. Wapiti is fast; crfsuite benchmarks are not fair to wapiti because w |
8,540 | Implementation of CRF in python | I think what you are looking for is PyStruct.
PyStruct aims at being an easy-to-use structured learning and prediction library. Currently it implements only max-margin methods and a perceptron, but other algorithms might follow.
The goal of PyStruct is to provide a well-documented tool for researchers as well as non-e... | Implementation of CRF in python | I think what you are looking for is PyStruct.
PyStruct aims at being an easy-to-use structured learning and prediction library. Currently it implements only max-margin methods and a perceptron, but o | Implementation of CRF in python
I think what you are looking for is PyStruct.
PyStruct aims at being an easy-to-use structured learning and prediction library. Currently it implements only max-margin methods and a perceptron, but other algorithms might follow.
The goal of PyStruct is to provide a well-documented tool ... | Implementation of CRF in python
I think what you are looking for is PyStruct.
PyStruct aims at being an easy-to-use structured learning and prediction library. Currently it implements only max-margin methods and a perceptron, but o |
8,541 | How could stochastic gradient descent save time compared to standard gradient descent? | Short answer:
In many big data setting (say several million data points), calculating cost or gradient takes very long time, because we need to sum over all data points.
We do NOT need to have exact gradient to reduce the cost in a given iteration. Some approximation of gradient would work OK.
Stochastic gradient dece... | How could stochastic gradient descent save time compared to standard gradient descent? | Short answer:
In many big data setting (say several million data points), calculating cost or gradient takes very long time, because we need to sum over all data points.
We do NOT need to have exact | How could stochastic gradient descent save time compared to standard gradient descent?
Short answer:
In many big data setting (say several million data points), calculating cost or gradient takes very long time, because we need to sum over all data points.
We do NOT need to have exact gradient to reduce the cost in a ... | How could stochastic gradient descent save time compared to standard gradient descent?
Short answer:
In many big data setting (say several million data points), calculating cost or gradient takes very long time, because we need to sum over all data points.
We do NOT need to have exact |
8,542 | How could stochastic gradient descent save time compared to standard gradient descent? | First of all, if you do the same number of epochs, SGD won't be faster than GD, because the per-epoch computation complexity is same for SGD and GD, as you pointed out.
However, GD only does one iteration of gradient descent per epoch while SGD does n/m iterations. Those n/m iterations brings greater improvement than t... | How could stochastic gradient descent save time compared to standard gradient descent? | First of all, if you do the same number of epochs, SGD won't be faster than GD, because the per-epoch computation complexity is same for SGD and GD, as you pointed out.
However, GD only does one itera | How could stochastic gradient descent save time compared to standard gradient descent?
First of all, if you do the same number of epochs, SGD won't be faster than GD, because the per-epoch computation complexity is same for SGD and GD, as you pointed out.
However, GD only does one iteration of gradient descent per epoc... | How could stochastic gradient descent save time compared to standard gradient descent?
First of all, if you do the same number of epochs, SGD won't be faster than GD, because the per-epoch computation complexity is same for SGD and GD, as you pointed out.
However, GD only does one itera |
8,543 | How could stochastic gradient descent save time compared to standard gradient descent? | Not only does SGD iterate gradients much faster, the stochasticity (noise from randomly picking samples) itself can be an asset for generalization: see ex. On the Generalization Benefit of Noise in Stochastic Gradient Descent (Smith, Elsen, De, ICML 2020) | How could stochastic gradient descent save time compared to standard gradient descent? | Not only does SGD iterate gradients much faster, the stochasticity (noise from randomly picking samples) itself can be an asset for generalization: see ex. On the Generalization Benefit of Noise in St | How could stochastic gradient descent save time compared to standard gradient descent?
Not only does SGD iterate gradients much faster, the stochasticity (noise from randomly picking samples) itself can be an asset for generalization: see ex. On the Generalization Benefit of Noise in Stochastic Gradient Descent (Smith,... | How could stochastic gradient descent save time compared to standard gradient descent?
Not only does SGD iterate gradients much faster, the stochasticity (noise from randomly picking samples) itself can be an asset for generalization: see ex. On the Generalization Benefit of Noise in St |
8,544 | Why use Lasso estimates over OLS estimates on the Lasso-identified subset of variables? | I don't believe there is anything wrong with using LASSO for variable selection and then using OLS. From "Elements of Statistical Learning" (pg. 91)
...the lasso shrinkage causes the estimates of the non-zero coefficients to be biased towards zero and in general they are not consistent [Added Note: This means that, as... | Why use Lasso estimates over OLS estimates on the Lasso-identified subset of variables? | I don't believe there is anything wrong with using LASSO for variable selection and then using OLS. From "Elements of Statistical Learning" (pg. 91)
...the lasso shrinkage causes the estimates of the | Why use Lasso estimates over OLS estimates on the Lasso-identified subset of variables?
I don't believe there is anything wrong with using LASSO for variable selection and then using OLS. From "Elements of Statistical Learning" (pg. 91)
...the lasso shrinkage causes the estimates of the non-zero coefficients to be bia... | Why use Lasso estimates over OLS estimates on the Lasso-identified subset of variables?
I don't believe there is anything wrong with using LASSO for variable selection and then using OLS. From "Elements of Statistical Learning" (pg. 91)
...the lasso shrinkage causes the estimates of the |
8,545 | Why use Lasso estimates over OLS estimates on the Lasso-identified subset of variables? | If your aim is optimal in-sample performance (wrt highest R-squared), then just use OLS on every available variable. Dropping variables will decrease R-squared.
If your aim is good out-of-sample performance (which is usually what is much more important), then your proposed strategy will suffer from two sources of overf... | Why use Lasso estimates over OLS estimates on the Lasso-identified subset of variables? | If your aim is optimal in-sample performance (wrt highest R-squared), then just use OLS on every available variable. Dropping variables will decrease R-squared.
If your aim is good out-of-sample perfo | Why use Lasso estimates over OLS estimates on the Lasso-identified subset of variables?
If your aim is optimal in-sample performance (wrt highest R-squared), then just use OLS on every available variable. Dropping variables will decrease R-squared.
If your aim is good out-of-sample performance (which is usually what is... | Why use Lasso estimates over OLS estimates on the Lasso-identified subset of variables?
If your aim is optimal in-sample performance (wrt highest R-squared), then just use OLS on every available variable. Dropping variables will decrease R-squared.
If your aim is good out-of-sample perfo |
8,546 | Why use Lasso estimates over OLS estimates on the Lasso-identified subset of variables? | Regarding the OPs question of why Lasso can select at most n features:
Consider why an OLS might be biased: this is when there are more predictors (p) than observations (n). Thus $X^{T}X$ is of size [p,p] in $\beta = (X^{T} X)^{-1}X^{T}Y$. Taking an inverse of such a matrix is not possible (it may be singular).
Lasso i... | Why use Lasso estimates over OLS estimates on the Lasso-identified subset of variables? | Regarding the OPs question of why Lasso can select at most n features:
Consider why an OLS might be biased: this is when there are more predictors (p) than observations (n). Thus $X^{T}X$ is of size [ | Why use Lasso estimates over OLS estimates on the Lasso-identified subset of variables?
Regarding the OPs question of why Lasso can select at most n features:
Consider why an OLS might be biased: this is when there are more predictors (p) than observations (n). Thus $X^{T}X$ is of size [p,p] in $\beta = (X^{T} X)^{-1}X... | Why use Lasso estimates over OLS estimates on the Lasso-identified subset of variables?
Regarding the OPs question of why Lasso can select at most n features:
Consider why an OLS might be biased: this is when there are more predictors (p) than observations (n). Thus $X^{T}X$ is of size [ |
8,547 | How to know if a data follows a Poisson Distribution in R? | There are an infinite number of ways for a distribution to be slightly different from a Poisson distribution; you can't identify that a set of data is drawn from a Poisson distribution. What you can do is look for inconsistency with what you should see with a Poisson, but a lack of obvious inconsistency doesn't make it... | How to know if a data follows a Poisson Distribution in R? | There are an infinite number of ways for a distribution to be slightly different from a Poisson distribution; you can't identify that a set of data is drawn from a Poisson distribution. What you can d | How to know if a data follows a Poisson Distribution in R?
There are an infinite number of ways for a distribution to be slightly different from a Poisson distribution; you can't identify that a set of data is drawn from a Poisson distribution. What you can do is look for inconsistency with what you should see with a P... | How to know if a data follows a Poisson Distribution in R?
There are an infinite number of ways for a distribution to be slightly different from a Poisson distribution; you can't identify that a set of data is drawn from a Poisson distribution. What you can d |
8,548 | How to know if a data follows a Poisson Distribution in R? | Perform the chi-squared goodness of fit test. In case of count data, we can use goodfit() included in the vcd package. Note that if the p value is larger than 0.05, we can not reject h0: the process is a Poisson process. Or else, it is not a Poisson process.
# load the vcd package
library(vcd) ## loading vcd package
#... | How to know if a data follows a Poisson Distribution in R? | Perform the chi-squared goodness of fit test. In case of count data, we can use goodfit() included in the vcd package. Note that if the p value is larger than 0.05, we can not reject h0: the process i | How to know if a data follows a Poisson Distribution in R?
Perform the chi-squared goodness of fit test. In case of count data, we can use goodfit() included in the vcd package. Note that if the p value is larger than 0.05, we can not reject h0: the process is a Poisson process. Or else, it is not a Poisson process.
# ... | How to know if a data follows a Poisson Distribution in R?
Perform the chi-squared goodness of fit test. In case of count data, we can use goodfit() included in the vcd package. Note that if the p value is larger than 0.05, we can not reject h0: the process i |
8,549 | What is an acceptable value of the Calinski & Harabasz (CH) criterion? | There are a few things one should be aware of.
Like most internal clustering criteria, Calinski-Harabasz is a
heuristic device. The proper way to use it is to compare clustering
solutions obtained on the same data, - solutions which differ either
by the number of clusters or by the clustering method used.
There is no ... | What is an acceptable value of the Calinski & Harabasz (CH) criterion? | There are a few things one should be aware of.
Like most internal clustering criteria, Calinski-Harabasz is a
heuristic device. The proper way to use it is to compare clustering
solutions obtained on | What is an acceptable value of the Calinski & Harabasz (CH) criterion?
There are a few things one should be aware of.
Like most internal clustering criteria, Calinski-Harabasz is a
heuristic device. The proper way to use it is to compare clustering
solutions obtained on the same data, - solutions which differ either
b... | What is an acceptable value of the Calinski & Harabasz (CH) criterion?
There are a few things one should be aware of.
Like most internal clustering criteria, Calinski-Harabasz is a
heuristic device. The proper way to use it is to compare clustering
solutions obtained on |
8,550 | How to obtain a confidence interval for a percentile? | This question, which covers a common situation, deserves a simple, non-approximate answer. Fortunately, there is one.
Suppose $X_1, \ldots, X_n$ are independent values from an unknown distribution $F$ whose $q^\text{th}$ quantile I will write $F^{-1}(q)$. This means each $X_i$ has a chance of (at least) $q$ of being ... | How to obtain a confidence interval for a percentile? | This question, which covers a common situation, deserves a simple, non-approximate answer. Fortunately, there is one.
Suppose $X_1, \ldots, X_n$ are independent values from an unknown distribution $F | How to obtain a confidence interval for a percentile?
This question, which covers a common situation, deserves a simple, non-approximate answer. Fortunately, there is one.
Suppose $X_1, \ldots, X_n$ are independent values from an unknown distribution $F$ whose $q^\text{th}$ quantile I will write $F^{-1}(q)$. This mea... | How to obtain a confidence interval for a percentile?
This question, which covers a common situation, deserves a simple, non-approximate answer. Fortunately, there is one.
Suppose $X_1, \ldots, X_n$ are independent values from an unknown distribution $F |
8,551 | How to obtain a confidence interval for a percentile? | Derivation
The $\tau$-quantile $q_\tau$ (this is the more general concept than percentile) of a random variable $X$ is given by $F_X^{-1}(\tau)$. The sample counterpart can be written as $\hat{q}_\tau = \hat{F}^{-1}(\tau)$ -- this is just the sample quantile. We are interested in the distribution of:
$\sqrt{n}(\hat{q... | How to obtain a confidence interval for a percentile? | Derivation
The $\tau$-quantile $q_\tau$ (this is the more general concept than percentile) of a random variable $X$ is given by $F_X^{-1}(\tau)$. The sample counterpart can be written as $\hat{q}_\ta | How to obtain a confidence interval for a percentile?
Derivation
The $\tau$-quantile $q_\tau$ (this is the more general concept than percentile) of a random variable $X$ is given by $F_X^{-1}(\tau)$. The sample counterpart can be written as $\hat{q}_\tau = \hat{F}^{-1}(\tau)$ -- this is just the sample quantile. We a... | How to obtain a confidence interval for a percentile?
Derivation
The $\tau$-quantile $q_\tau$ (this is the more general concept than percentile) of a random variable $X$ is given by $F_X^{-1}(\tau)$. The sample counterpart can be written as $\hat{q}_\ta |
8,552 | How to obtain a confidence interval for a percentile? | A brute-force computing intensive solution is to use the bootstrap resampling method. The following function returns the bootstrap confidence intervals of a quantile.
quantile.CI.via.bootstrap <- function(x, p, alpha = 0.1) {
## Purpose:
## Calculate a two-sided confidence interval with confidence level of (1... | How to obtain a confidence interval for a percentile? | A brute-force computing intensive solution is to use the bootstrap resampling method. The following function returns the bootstrap confidence intervals of a quantile.
quantile.CI.via.bootstrap <- func | How to obtain a confidence interval for a percentile?
A brute-force computing intensive solution is to use the bootstrap resampling method. The following function returns the bootstrap confidence intervals of a quantile.
quantile.CI.via.bootstrap <- function(x, p, alpha = 0.1) {
## Purpose:
## Calculate a two... | How to obtain a confidence interval for a percentile?
A brute-force computing intensive solution is to use the bootstrap resampling method. The following function returns the bootstrap confidence intervals of a quantile.
quantile.CI.via.bootstrap <- func |
8,553 | How do I decide what span to use in LOESS regression in R? | A cross-validation is often used, for example k-fold, if the aim is to find a fit with lowest RMSEP. Split your data into k groups and, leaving each group out in turn, fit a loess model using the k-1 groups of data and a chosen value of the smoothing parameter, and use that model to predict for the left out group. Stor... | How do I decide what span to use in LOESS regression in R? | A cross-validation is often used, for example k-fold, if the aim is to find a fit with lowest RMSEP. Split your data into k groups and, leaving each group out in turn, fit a loess model using the k-1 | How do I decide what span to use in LOESS regression in R?
A cross-validation is often used, for example k-fold, if the aim is to find a fit with lowest RMSEP. Split your data into k groups and, leaving each group out in turn, fit a loess model using the k-1 groups of data and a chosen value of the smoothing parameter,... | How do I decide what span to use in LOESS regression in R?
A cross-validation is often used, for example k-fold, if the aim is to find a fit with lowest RMSEP. Split your data into k groups and, leaving each group out in turn, fit a loess model using the k-1 |
8,554 | How do I decide what span to use in LOESS regression in R? | I suggest checking out generalized additive models (GAM, see the mgcv package in R). I'm just learning about them myself, but they seem to automatically figure out how much "wiggly-ness" is justified by the data. I also see that you're dealing with binomial data (strike vs not a strike), so be sure to analyze the raw d... | How do I decide what span to use in LOESS regression in R? | I suggest checking out generalized additive models (GAM, see the mgcv package in R). I'm just learning about them myself, but they seem to automatically figure out how much "wiggly-ness" is justified | How do I decide what span to use in LOESS regression in R?
I suggest checking out generalized additive models (GAM, see the mgcv package in R). I'm just learning about them myself, but they seem to automatically figure out how much "wiggly-ness" is justified by the data. I also see that you're dealing with binomial dat... | How do I decide what span to use in LOESS regression in R?
I suggest checking out generalized additive models (GAM, see the mgcv package in R). I'm just learning about them myself, but they seem to automatically figure out how much "wiggly-ness" is justified |
8,555 | How do I decide what span to use in LOESS regression in R? | For a loess regression, my understanding as a non-statistician, is that you can choose your span based on visual interpretation (plot with numerous span values can choose the one with the least amount of smoothing that seems appropriate) or you can use cross validation (CV) or generalized cross validation (GCV). Below ... | How do I decide what span to use in LOESS regression in R? | For a loess regression, my understanding as a non-statistician, is that you can choose your span based on visual interpretation (plot with numerous span values can choose the one with the least amount | How do I decide what span to use in LOESS regression in R?
For a loess regression, my understanding as a non-statistician, is that you can choose your span based on visual interpretation (plot with numerous span values can choose the one with the least amount of smoothing that seems appropriate) or you can use cross va... | How do I decide what span to use in LOESS regression in R?
For a loess regression, my understanding as a non-statistician, is that you can choose your span based on visual interpretation (plot with numerous span values can choose the one with the least amount |
8,556 | How do I decide what span to use in LOESS regression in R? | If you switch to a generlized additive model, you could use the gam() function from the mgcv package, in which the author assures us:
So, exact choice of k is not generally critical: it should be chosen to be large enough that you are reasonably sure of having enough degrees of freedom to represent the underlying ‘tru... | How do I decide what span to use in LOESS regression in R? | If you switch to a generlized additive model, you could use the gam() function from the mgcv package, in which the author assures us:
So, exact choice of k is not generally critical: it should be cho | How do I decide what span to use in LOESS regression in R?
If you switch to a generlized additive model, you could use the gam() function from the mgcv package, in which the author assures us:
So, exact choice of k is not generally critical: it should be chosen to be large enough that you are reasonably sure of having... | How do I decide what span to use in LOESS regression in R?
If you switch to a generlized additive model, you could use the gam() function from the mgcv package, in which the author assures us:
So, exact choice of k is not generally critical: it should be cho |
8,557 | How do I decide what span to use in LOESS regression in R? | You could write your own cross validation loop from scratch that uses the loess() function from the stats package.
Set up a toy data frame.
set.seed(4)
x <- rnorm(n = 500)
y <- (x)^3 + (x - 3)^2 + (x - 8) - 1 + rnorm(n = 500, sd = 0.5)
plot(x, y)
df <- data.frame(x, y)
Set up useful variables to handle cross-validati... | How do I decide what span to use in LOESS regression in R? | You could write your own cross validation loop from scratch that uses the loess() function from the stats package.
Set up a toy data frame.
set.seed(4)
x <- rnorm(n = 500)
y <- (x)^3 + (x - 3)^2 + (x | How do I decide what span to use in LOESS regression in R?
You could write your own cross validation loop from scratch that uses the loess() function from the stats package.
Set up a toy data frame.
set.seed(4)
x <- rnorm(n = 500)
y <- (x)^3 + (x - 3)^2 + (x - 8) - 1 + rnorm(n = 500, sd = 0.5)
plot(x, y)
df <- data.fr... | How do I decide what span to use in LOESS regression in R?
You could write your own cross validation loop from scratch that uses the loess() function from the stats package.
Set up a toy data frame.
set.seed(4)
x <- rnorm(n = 500)
y <- (x)^3 + (x - 3)^2 + (x |
8,558 | How do I decide what span to use in LOESS regression in R? | Use locfit package. Its a slightly modified version of the loess but way faster. It also has an inbuilt function to calculate gcv.
Reference. | How do I decide what span to use in LOESS regression in R? | Use locfit package. Its a slightly modified version of the loess but way faster. It also has an inbuilt function to calculate gcv.
Reference. | How do I decide what span to use in LOESS regression in R?
Use locfit package. Its a slightly modified version of the loess but way faster. It also has an inbuilt function to calculate gcv.
Reference. | How do I decide what span to use in LOESS regression in R?
Use locfit package. Its a slightly modified version of the loess but way faster. It also has an inbuilt function to calculate gcv.
Reference. |
8,559 | How do I decide what span to use in LOESS regression in R? | The fANCOVA package provides an automated way to compute the ideal span using gcv or aic:
FTSE.lo3 <- loess.as(Index, FTSE_close, degree = 1, criterion = c("aicc", "gcv")[2], user.span = NULL, plot = F)
FTSE.lo.predict3 <- predict(FTSE.lo3, data.frame(Index=Index)) | How do I decide what span to use in LOESS regression in R? | The fANCOVA package provides an automated way to compute the ideal span using gcv or aic:
FTSE.lo3 <- loess.as(Index, FTSE_close, degree = 1, criterion = c("aicc", "gcv")[2], user.span = NULL, plot = | How do I decide what span to use in LOESS regression in R?
The fANCOVA package provides an automated way to compute the ideal span using gcv or aic:
FTSE.lo3 <- loess.as(Index, FTSE_close, degree = 1, criterion = c("aicc", "gcv")[2], user.span = NULL, plot = F)
FTSE.lo.predict3 <- predict(FTSE.lo3, data.frame(Index=Ind... | How do I decide what span to use in LOESS regression in R?
The fANCOVA package provides an automated way to compute the ideal span using gcv or aic:
FTSE.lo3 <- loess.as(Index, FTSE_close, degree = 1, criterion = c("aicc", "gcv")[2], user.span = NULL, plot = |
8,560 | How can a statistician who has the data for a non-normal distribution guess better than one who only has the mean? | For a uniform distribution between $0$ and $2 \mu$, the player who guesses the sample mean would do worse than one which guesses $\frac{3}{5} \max(x_i)$ (the sample maximum is a sufficient statistic for the mean of a uniform distribution lower bounded by 0).
In this particular case, it can be verified numerically. With... | How can a statistician who has the data for a non-normal distribution guess better than one who only | For a uniform distribution between $0$ and $2 \mu$, the player who guesses the sample mean would do worse than one which guesses $\frac{3}{5} \max(x_i)$ (the sample maximum is a sufficient statistic f | How can a statistician who has the data for a non-normal distribution guess better than one who only has the mean?
For a uniform distribution between $0$ and $2 \mu$, the player who guesses the sample mean would do worse than one which guesses $\frac{3}{5} \max(x_i)$ (the sample maximum is a sufficient statistic for th... | How can a statistician who has the data for a non-normal distribution guess better than one who only
For a uniform distribution between $0$ and $2 \mu$, the player who guesses the sample mean would do worse than one which guesses $\frac{3}{5} \max(x_i)$ (the sample maximum is a sufficient statistic f |
8,561 | How can a statistician who has the data for a non-normal distribution guess better than one who only has the mean? | The sum of observations is not sufficient for estimating the mean of a uniform
population. The midrange has a smaller expectation of absolute error.
Approximation by simulation in R:
set.seed(2021)
a = replicate(10^6, mean(runif(5)))
mr = replicate(10^6, mean(range(runif(5))))
mean(a); mean(mr)
[1]... | How can a statistician who has the data for a non-normal distribution guess better than one who only | The sum of observations is not sufficient for estimating the mean of a uniform
population. The midrange has a smaller expectation of absolute error.
Approximation by simulation in R:
set.seed(2021 | How can a statistician who has the data for a non-normal distribution guess better than one who only has the mean?
The sum of observations is not sufficient for estimating the mean of a uniform
population. The midrange has a smaller expectation of absolute error.
Approximation by simulation in R:
set.seed(2021)
... | How can a statistician who has the data for a non-normal distribution guess better than one who only
The sum of observations is not sufficient for estimating the mean of a uniform
population. The midrange has a smaller expectation of absolute error.
Approximation by simulation in R:
set.seed(2021 |
8,562 | How can a statistician who has the data for a non-normal distribution guess better than one who only has the mean? | It might be worth adding that while you can often do better for low-dimensional parametric families, you can't do better if the distribution is completely unknown (or completely unknown apart from knowing it has a finite mean). The mean is the only estimator of the mean that works over all distributions. | How can a statistician who has the data for a non-normal distribution guess better than one who only | It might be worth adding that while you can often do better for low-dimensional parametric families, you can't do better if the distribution is completely unknown (or completely unknown apart from kno | How can a statistician who has the data for a non-normal distribution guess better than one who only has the mean?
It might be worth adding that while you can often do better for low-dimensional parametric families, you can't do better if the distribution is completely unknown (or completely unknown apart from knowing ... | How can a statistician who has the data for a non-normal distribution guess better than one who only
It might be worth adding that while you can often do better for low-dimensional parametric families, you can't do better if the distribution is completely unknown (or completely unknown apart from kno |
8,563 | Why are random walks intercorrelated? | Your independent processes are not correlated! If $X_t$ and $Y_t$ are independent random walks:
A correlation coefficient unconditional on time does not exist. (Don't talk about $\operatorname{Corr}(X, Y)$.)
For any time $t$, $\operatorname{Corr}(X_t, Y_t)$ is indeed 0.
But sample statistics based upon time-series av... | Why are random walks intercorrelated? | Your independent processes are not correlated! If $X_t$ and $Y_t$ are independent random walks:
A correlation coefficient unconditional on time does not exist. (Don't talk about $\operatorname{Corr}( | Why are random walks intercorrelated?
Your independent processes are not correlated! If $X_t$ and $Y_t$ are independent random walks:
A correlation coefficient unconditional on time does not exist. (Don't talk about $\operatorname{Corr}(X, Y)$.)
For any time $t$, $\operatorname{Corr}(X_t, Y_t)$ is indeed 0.
But sampl... | Why are random walks intercorrelated?
Your independent processes are not correlated! If $X_t$ and $Y_t$ are independent random walks:
A correlation coefficient unconditional on time does not exist. (Don't talk about $\operatorname{Corr}( |
8,564 | Why are random walks intercorrelated? | The math needed to obtain an exact result is messy, but we can derive an exact value for the expected squared correlation coefficient relatively painlessly. It helps explain why a value near $1/2$ keeps showing up and why increasing the length $n$ of the random walk won't change things.
There is potential for confusio... | Why are random walks intercorrelated? | The math needed to obtain an exact result is messy, but we can derive an exact value for the expected squared correlation coefficient relatively painlessly. It helps explain why a value near $1/2$ ke | Why are random walks intercorrelated?
The math needed to obtain an exact result is messy, but we can derive an exact value for the expected squared correlation coefficient relatively painlessly. It helps explain why a value near $1/2$ keeps showing up and why increasing the length $n$ of the random walk won't change t... | Why are random walks intercorrelated?
The math needed to obtain an exact result is messy, but we can derive an exact value for the expected squared correlation coefficient relatively painlessly. It helps explain why a value near $1/2$ ke |
8,565 | What is the probability that this person is female? | Many people find it helpful to think in terms of a "population," subgroups within it, and proportions (rather than probabilities). This lends itself to visual reasoning.
I will explain the figures in detail, but the intention is that a quick comparison of the two figures should immediately and convincingly indicate ho... | What is the probability that this person is female? | Many people find it helpful to think in terms of a "population," subgroups within it, and proportions (rather than probabilities). This lends itself to visual reasoning.
I will explain the figures in | What is the probability that this person is female?
Many people find it helpful to think in terms of a "population," subgroups within it, and proportions (rather than probabilities). This lends itself to visual reasoning.
I will explain the figures in detail, but the intention is that a quick comparison of the two fig... | What is the probability that this person is female?
Many people find it helpful to think in terms of a "population," subgroups within it, and proportions (rather than probabilities). This lends itself to visual reasoning.
I will explain the figures in |
8,566 | What is the probability that this person is female? | This is a question of conditional probability. You know that the person has long hair and blood type Ax3 . Let$$\ \ \ \ \ A =\{\text{'The person has long hair'}\}\\
\ \ \ \ \ \ \ \ \ \ \ \ \ \ B = \{\text{'The person has blood type Ax3'}\} \\
C =\{\text{'The person is female'}\}.$$
So you seek $P(C|A\ \text{and}\ B)$... | What is the probability that this person is female? | This is a question of conditional probability. You know that the person has long hair and blood type Ax3 . Let$$\ \ \ \ \ A =\{\text{'The person has long hair'}\}\\
\ \ \ \ \ \ \ \ \ \ \ \ \ \ B = \ | What is the probability that this person is female?
This is a question of conditional probability. You know that the person has long hair and blood type Ax3 . Let$$\ \ \ \ \ A =\{\text{'The person has long hair'}\}\\
\ \ \ \ \ \ \ \ \ \ \ \ \ \ B = \{\text{'The person has blood type Ax3'}\} \\
C =\{\text{'The person ... | What is the probability that this person is female?
This is a question of conditional probability. You know that the person has long hair and blood type Ax3 . Let$$\ \ \ \ \ A =\{\text{'The person has long hair'}\}\\
\ \ \ \ \ \ \ \ \ \ \ \ \ \ B = \ |
8,567 | What is the probability that this person is female? | Fascinating discussion ! I am wondering if we specified P(A) and P(B) as well whether the ranges of P(C| A,B) will not be much narrower than the full interval [0,1], simply because of the many constraints we have.
Sticking to the notation introduced above:
A = the event that the person has long hair
B = the event that ... | What is the probability that this person is female? | Fascinating discussion ! I am wondering if we specified P(A) and P(B) as well whether the ranges of P(C| A,B) will not be much narrower than the full interval [0,1], simply because of the many constra | What is the probability that this person is female?
Fascinating discussion ! I am wondering if we specified P(A) and P(B) as well whether the ranges of P(C| A,B) will not be much narrower than the full interval [0,1], simply because of the many constraints we have.
Sticking to the notation introduced above:
A = the eve... | What is the probability that this person is female?
Fascinating discussion ! I am wondering if we specified P(A) and P(B) as well whether the ranges of P(C| A,B) will not be much narrower than the full interval [0,1], simply because of the many constra |
8,568 | What is the probability that this person is female? | Make the hypotheses is that the person behind a curtain is a woman.
We area given 2 pieces of evidence, namely:
Evidence 1: We know the person has long hair (and we're told that 90% of all people with long hair are female)
Evidence 2: We know the person has a rare blood type AX3 (and we're told that 80% of all people w... | What is the probability that this person is female? | Make the hypotheses is that the person behind a curtain is a woman.
We area given 2 pieces of evidence, namely:
Evidence 1: We know the person has long hair (and we're told that 90% of all people with | What is the probability that this person is female?
Make the hypotheses is that the person behind a curtain is a woman.
We area given 2 pieces of evidence, namely:
Evidence 1: We know the person has long hair (and we're told that 90% of all people with long hair are female)
Evidence 2: We know the person has a rare blo... | What is the probability that this person is female?
Make the hypotheses is that the person behind a curtain is a woman.
We area given 2 pieces of evidence, namely:
Evidence 1: We know the person has long hair (and we're told that 90% of all people with |
8,569 | What is the probability that this person is female? | Question Restatement and Generalisation
$A$, $B$, and $C$ are binary unknowns whose possible values are $0$ and $1$. Let $Z_i$ stand for the proposition, "The value of $Z$ is $i$". Also let $(X | Y)$ stand for "The probability that $X$, given that $Y$". What is $(A_a | B_b C_c I)$, given that
$(A_{a_1} | B_{b_1} I) = ... | What is the probability that this person is female? | Question Restatement and Generalisation
$A$, $B$, and $C$ are binary unknowns whose possible values are $0$ and $1$. Let $Z_i$ stand for the proposition, "The value of $Z$ is $i$". Also let $(X | Y)$ | What is the probability that this person is female?
Question Restatement and Generalisation
$A$, $B$, and $C$ are binary unknowns whose possible values are $0$ and $1$. Let $Z_i$ stand for the proposition, "The value of $Z$ is $i$". Also let $(X | Y)$ stand for "The probability that $X$, given that $Y$". What is $(A_a ... | What is the probability that this person is female?
Question Restatement and Generalisation
$A$, $B$, and $C$ are binary unknowns whose possible values are $0$ and $1$. Let $Z_i$ stand for the proposition, "The value of $Z$ is $i$". Also let $(X | Y)$ |
8,570 | What is the probability that this person is female? | I believe now that, if we assume a ratio of men and women in the population at large, then there is a single indisputable answer.
A = the event that the person has long hair
B = the event that the person has blood type AX3
C = the event that person is female
P(C|A) = 0.9
P(C|B) = 0.8
P(C) = 0.5 (i.e. let's assume an e... | What is the probability that this person is female? | I believe now that, if we assume a ratio of men and women in the population at large, then there is a single indisputable answer.
A = the event that the person has long hair
B = the event that the per | What is the probability that this person is female?
I believe now that, if we assume a ratio of men and women in the population at large, then there is a single indisputable answer.
A = the event that the person has long hair
B = the event that the person has blood type AX3
C = the event that person is female
P(C|A) = ... | What is the probability that this person is female?
I believe now that, if we assume a ratio of men and women in the population at large, then there is a single indisputable answer.
A = the event that the person has long hair
B = the event that the per |
8,571 | What is the probability that this person is female? | Note: In order to get a definitive answer, the below answers assume that the probability of a person, a long-haired man, and a long-haired women having AX3 are approximately the same. If more accuracy is desired, this should be verified.
You start out with the knowledge that the person has long hair, so at this point... | What is the probability that this person is female? | Note: In order to get a definitive answer, the below answers assume that the probability of a person, a long-haired man, and a long-haired women having AX3 are approximately the same. If more accura | What is the probability that this person is female?
Note: In order to get a definitive answer, the below answers assume that the probability of a person, a long-haired man, and a long-haired women having AX3 are approximately the same. If more accuracy is desired, this should be verified.
You start out with the knowl... | What is the probability that this person is female?
Note: In order to get a definitive answer, the below answers assume that the probability of a person, a long-haired man, and a long-haired women having AX3 are approximately the same. If more accura |
8,572 | What is the probability that this person is female? | 98% Female, simple interpolation. First premise 90% female, leaves 10%, second premise only leaves 2% of the existing 10%, hence 98% female | What is the probability that this person is female? | 98% Female, simple interpolation. First premise 90% female, leaves 10%, second premise only leaves 2% of the existing 10%, hence 98% female | What is the probability that this person is female?
98% Female, simple interpolation. First premise 90% female, leaves 10%, second premise only leaves 2% of the existing 10%, hence 98% female | What is the probability that this person is female?
98% Female, simple interpolation. First premise 90% female, leaves 10%, second premise only leaves 2% of the existing 10%, hence 98% female |
8,573 | One-vs-All and One-vs-One in svm? | The difference is the number of classifiers you have to learn, which strongly correlates with the decision boundary they create.
Assume you have $N$ different classes. One vs all will train one classifier per class in total $N$ classifiers. For class $i$ it will assume $i$-labels as positive and the rest as negative. T... | One-vs-All and One-vs-One in svm? | The difference is the number of classifiers you have to learn, which strongly correlates with the decision boundary they create.
Assume you have $N$ different classes. One vs all will train one classi | One-vs-All and One-vs-One in svm?
The difference is the number of classifiers you have to learn, which strongly correlates with the decision boundary they create.
Assume you have $N$ different classes. One vs all will train one classifier per class in total $N$ classifiers. For class $i$ it will assume $i$-labels as po... | One-vs-All and One-vs-One in svm?
The difference is the number of classifiers you have to learn, which strongly correlates with the decision boundary they create.
Assume you have $N$ different classes. One vs all will train one classi |
8,574 | Strategies for teaching the sampling distribution | In my opinion, sampling distributions are the key idea of statistics 101. You might as well skip the course as skip that issue. However, I am very familiar with the fact that students just don't get it, seemingly no matter what you do. I have a series of strategies. These can take up a lot of time, but I recommend ... | Strategies for teaching the sampling distribution | In my opinion, sampling distributions are the key idea of statistics 101. You might as well skip the course as skip that issue. However, I am very familiar with the fact that students just don't get | Strategies for teaching the sampling distribution
In my opinion, sampling distributions are the key idea of statistics 101. You might as well skip the course as skip that issue. However, I am very familiar with the fact that students just don't get it, seemingly no matter what you do. I have a series of strategies. ... | Strategies for teaching the sampling distribution
In my opinion, sampling distributions are the key idea of statistics 101. You might as well skip the course as skip that issue. However, I am very familiar with the fact that students just don't get |
8,575 | Strategies for teaching the sampling distribution | I have had some luck with reminding students that the sampling distribution is the distribution of the test statistic based on a random sample. I have students think about what would happen in the sampling process itself was biased - focusing on extreme cases. For example, what would the "sampling distribution" look li... | Strategies for teaching the sampling distribution | I have had some luck with reminding students that the sampling distribution is the distribution of the test statistic based on a random sample. I have students think about what would happen in the sam | Strategies for teaching the sampling distribution
I have had some luck with reminding students that the sampling distribution is the distribution of the test statistic based on a random sample. I have students think about what would happen in the sampling process itself was biased - focusing on extreme cases. For examp... | Strategies for teaching the sampling distribution
I have had some luck with reminding students that the sampling distribution is the distribution of the test statistic based on a random sample. I have students think about what would happen in the sam |
8,576 | Strategies for teaching the sampling distribution | I start back with the teaching of probability. I don't go into a lot of the formal definitions and rules (just not enough time), but show probability by simulation. The Monty Hall problem is a great example to use, I show through simulation (and then follow-up with the logic) that the strategy to switch gives a highe... | Strategies for teaching the sampling distribution | I start back with the teaching of probability. I don't go into a lot of the formal definitions and rules (just not enough time), but show probability by simulation. The Monty Hall problem is a great | Strategies for teaching the sampling distribution
I start back with the teaching of probability. I don't go into a lot of the formal definitions and rules (just not enough time), but show probability by simulation. The Monty Hall problem is a great example to use, I show through simulation (and then follow-up with th... | Strategies for teaching the sampling distribution
I start back with the teaching of probability. I don't go into a lot of the formal definitions and rules (just not enough time), but show probability by simulation. The Monty Hall problem is a great |
8,577 | Strategies for teaching the sampling distribution | This is a very important and well-thought out issue on your part. I do think the concept of the sampling distribution is very basic to understanding inference and definitely should be taught.
I have taught many introductory statistics courses, particularly in biostatistics. I teach the concept of sampling distributio... | Strategies for teaching the sampling distribution | This is a very important and well-thought out issue on your part. I do think the concept of the sampling distribution is very basic to understanding inference and definitely should be taught.
I have | Strategies for teaching the sampling distribution
This is a very important and well-thought out issue on your part. I do think the concept of the sampling distribution is very basic to understanding inference and definitely should be taught.
I have taught many introductory statistics courses, particularly in biostatis... | Strategies for teaching the sampling distribution
This is a very important and well-thought out issue on your part. I do think the concept of the sampling distribution is very basic to understanding inference and definitely should be taught.
I have |
8,578 | Strategies for teaching the sampling distribution | I think it would be good to put a 'population' of numbers in a bag ( ranging for example from 1-10). You could make your own tiles, or use coins, playing cards etc.
Get students to sit in groups (5 or more) and each picks a number out of the bag. Each group then calculates the mean value for their group. Tell them t... | Strategies for teaching the sampling distribution | I think it would be good to put a 'population' of numbers in a bag ( ranging for example from 1-10). You could make your own tiles, or use coins, playing cards etc.
Get students to sit in groups (5 o | Strategies for teaching the sampling distribution
I think it would be good to put a 'population' of numbers in a bag ( ranging for example from 1-10). You could make your own tiles, or use coins, playing cards etc.
Get students to sit in groups (5 or more) and each picks a number out of the bag. Each group then calc... | Strategies for teaching the sampling distribution
I think it would be good to put a 'population' of numbers in a bag ( ranging for example from 1-10). You could make your own tiles, or use coins, playing cards etc.
Get students to sit in groups (5 o |
8,579 | How can you account for COVID-19 in your models? | We do forecasting for retail: supermarkets, drugstores etc. We add predictors to explain our sales time series, specifically different predictors for different phases of the lockdowns.
On the one hand, that will cleanse the time series, so we don't misinterpret higher sales of cat litter boxes as a seasonal effect that... | How can you account for COVID-19 in your models? | We do forecasting for retail: supermarkets, drugstores etc. We add predictors to explain our sales time series, specifically different predictors for different phases of the lockdowns.
On the one hand | How can you account for COVID-19 in your models?
We do forecasting for retail: supermarkets, drugstores etc. We add predictors to explain our sales time series, specifically different predictors for different phases of the lockdowns.
On the one hand, that will cleanse the time series, so we don't misinterpret higher sa... | How can you account for COVID-19 in your models?
We do forecasting for retail: supermarkets, drugstores etc. We add predictors to explain our sales time series, specifically different predictors for different phases of the lockdowns.
On the one hand |
8,580 | How can you account for COVID-19 in your models? | That's an interesting question and I'm sure that there are dozens of different approaches. This is a "there is no wrong answer" type of question.
From my perspective, I've been dealing with the Covid-19 when I think about revenue, which is almost as seeing the sales (as shown by Stephan), but not entirely, since there ... | How can you account for COVID-19 in your models? | That's an interesting question and I'm sure that there are dozens of different approaches. This is a "there is no wrong answer" type of question.
From my perspective, I've been dealing with the Covid- | How can you account for COVID-19 in your models?
That's an interesting question and I'm sure that there are dozens of different approaches. This is a "there is no wrong answer" type of question.
From my perspective, I've been dealing with the Covid-19 when I think about revenue, which is almost as seeing the sales (as ... | How can you account for COVID-19 in your models?
That's an interesting question and I'm sure that there are dozens of different approaches. This is a "there is no wrong answer" type of question.
From my perspective, I've been dealing with the Covid- |
8,581 | How can you account for COVID-19 in your models? | I work for a large airline in the revenue and pricing area where we forecast revenue and bookings and other things. We tried 2 approaches. One was effectively scaling from pre-covid data. We tried predicting a lower quantile instead of the mean and having a dynamic scaling factor from 2019. This worked ok. What has wor... | How can you account for COVID-19 in your models? | I work for a large airline in the revenue and pricing area where we forecast revenue and bookings and other things. We tried 2 approaches. One was effectively scaling from pre-covid data. We tried pre | How can you account for COVID-19 in your models?
I work for a large airline in the revenue and pricing area where we forecast revenue and bookings and other things. We tried 2 approaches. One was effectively scaling from pre-covid data. We tried predicting a lower quantile instead of the mean and having a dynamic scali... | How can you account for COVID-19 in your models?
I work for a large airline in the revenue and pricing area where we forecast revenue and bookings and other things. We tried 2 approaches. One was effectively scaling from pre-covid data. We tried pre |
8,582 | How can you account for COVID-19 in your models? | I hope I can tell some interesting stories here just as the others:
I worked on a project for a pharmaceutical company, which wanted to have their dementia and cold cough products to be modeled, especially during coronavirus/COVID-19 infection. For the dementia product, we already saw a decreasing trend that were alrea... | How can you account for COVID-19 in your models? | I hope I can tell some interesting stories here just as the others:
I worked on a project for a pharmaceutical company, which wanted to have their dementia and cold cough products to be modeled, espec | How can you account for COVID-19 in your models?
I hope I can tell some interesting stories here just as the others:
I worked on a project for a pharmaceutical company, which wanted to have their dementia and cold cough products to be modeled, especially during coronavirus/COVID-19 infection. For the dementia product, ... | How can you account for COVID-19 in your models?
I hope I can tell some interesting stories here just as the others:
I worked on a project for a pharmaceutical company, which wanted to have their dementia and cold cough products to be modeled, espec |
8,583 | How can you account for COVID-19 in your models? | Other answers here give some good advice. However, I just wanted to add that economic models should usually be able to incorporate generic "shocks" that affect one or more of the variables of interest. How you incorporat this really depends on what you are interested in explaining, but often the "shocks" will be trea... | How can you account for COVID-19 in your models? | Other answers here give some good advice. However, I just wanted to add that economic models should usually be able to incorporate generic "shocks" that affect one or more of the variables of interes | How can you account for COVID-19 in your models?
Other answers here give some good advice. However, I just wanted to add that economic models should usually be able to incorporate generic "shocks" that affect one or more of the variables of interest. How you incorporat this really depends on what you are interested i... | How can you account for COVID-19 in your models?
Other answers here give some good advice. However, I just wanted to add that economic models should usually be able to incorporate generic "shocks" that affect one or more of the variables of interes |
8,584 | How to perform dimensionality reduction with PCA in R | I believe what you are getting at in your question concerns data truncation using a smaller number of principal components (PC). For such operations, I think the function prcompis more illustrative in that it is easier to visualize the matrix multiplication used in reconstruction.
First, give a synthetic dataset, Xt, y... | How to perform dimensionality reduction with PCA in R | I believe what you are getting at in your question concerns data truncation using a smaller number of principal components (PC). For such operations, I think the function prcompis more illustrative in | How to perform dimensionality reduction with PCA in R
I believe what you are getting at in your question concerns data truncation using a smaller number of principal components (PC). For such operations, I think the function prcompis more illustrative in that it is easier to visualize the matrix multiplication used in ... | How to perform dimensionality reduction with PCA in R
I believe what you are getting at in your question concerns data truncation using a smaller number of principal components (PC). For such operations, I think the function prcompis more illustrative in |
8,585 | How to perform dimensionality reduction with PCA in R | These other answers are very good and detailed, but I'm wondering if you're actually asking a much more basic question: what do you do once you have your PCs?
Each PC simply becomes a new variable. Say PC1 accounts for 60 % of the total variation and PC2 accounts for 30 %. As that's 90 % of the total variation accounte... | How to perform dimensionality reduction with PCA in R | These other answers are very good and detailed, but I'm wondering if you're actually asking a much more basic question: what do you do once you have your PCs?
Each PC simply becomes a new variable. Sa | How to perform dimensionality reduction with PCA in R
These other answers are very good and detailed, but I'm wondering if you're actually asking a much more basic question: what do you do once you have your PCs?
Each PC simply becomes a new variable. Say PC1 accounts for 60 % of the total variation and PC2 accounts fo... | How to perform dimensionality reduction with PCA in R
These other answers are very good and detailed, but I'm wondering if you're actually asking a much more basic question: what do you do once you have your PCs?
Each PC simply becomes a new variable. Sa |
8,586 | How to perform dimensionality reduction with PCA in R | I believe your original question stems from being a bit uncertain about what PCA is doing. Principal Component Analysis allows you to identify the principal mode of variation in your sample. Those modes are emperically calculated as the eigenvectors of your sample's covariance matrix (the "loadings"). Subsequently thos... | How to perform dimensionality reduction with PCA in R | I believe your original question stems from being a bit uncertain about what PCA is doing. Principal Component Analysis allows you to identify the principal mode of variation in your sample. Those mod | How to perform dimensionality reduction with PCA in R
I believe your original question stems from being a bit uncertain about what PCA is doing. Principal Component Analysis allows you to identify the principal mode of variation in your sample. Those modes are emperically calculated as the eigenvectors of your sample's... | How to perform dimensionality reduction with PCA in R
I believe your original question stems from being a bit uncertain about what PCA is doing. Principal Component Analysis allows you to identify the principal mode of variation in your sample. Those mod |
8,587 | How to perform dimensionality reduction with PCA in R | After doing the PCA then you may select the first two components and plot.. You can see the variation of the components using a scree plot in R. Also using summary function with loadings=T you can fins the variation of features with the components.
You can also look at this http://www.statmethods.net/advstats/factor.ht... | How to perform dimensionality reduction with PCA in R | After doing the PCA then you may select the first two components and plot.. You can see the variation of the components using a scree plot in R. Also using summary function with loadings=T you can fin | How to perform dimensionality reduction with PCA in R
After doing the PCA then you may select the first two components and plot.. You can see the variation of the components using a scree plot in R. Also using summary function with loadings=T you can fins the variation of features with the components.
You can also look... | How to perform dimensionality reduction with PCA in R
After doing the PCA then you may select the first two components and plot.. You can see the variation of the components using a scree plot in R. Also using summary function with loadings=T you can fin |
8,588 | About CNN, kernels and scale/rotation invariance | 1) The features extracted using CNN are scale and rotation invariant?
A feature in itself in a CNN is not scale or rotation invariant. For more details, see: Deep Learning. Ian Goodfellow and Yoshua Bengio and Aaron Courville. 2016: http://egrcc.github.io/docs/dl/deeplearningbook-convnets.pdf ; http://www.deeplearning... | About CNN, kernels and scale/rotation invariance | 1) The features extracted using CNN are scale and rotation invariant?
A feature in itself in a CNN is not scale or rotation invariant. For more details, see: Deep Learning. Ian Goodfellow and Yoshua | About CNN, kernels and scale/rotation invariance
1) The features extracted using CNN are scale and rotation invariant?
A feature in itself in a CNN is not scale or rotation invariant. For more details, see: Deep Learning. Ian Goodfellow and Yoshua Bengio and Aaron Courville. 2016: http://egrcc.github.io/docs/dl/deeple... | About CNN, kernels and scale/rotation invariance
1) The features extracted using CNN are scale and rotation invariant?
A feature in itself in a CNN is not scale or rotation invariant. For more details, see: Deep Learning. Ian Goodfellow and Yoshua |
8,589 | About CNN, kernels and scale/rotation invariance | I think there are a couple of things confusing you, so first things first.
Given a signal $x[n]$, and a kernel (also called a filter) $h[n]$, then the convolution of $x[n]$ with $h[n]$ is written as $y[n] = (x \star h)[n]$, and is computed via a sliding dot-product, mathematically given by:
$$
y[n] = \sum_{m=-\infty}^... | About CNN, kernels and scale/rotation invariance | I think there are a couple of things confusing you, so first things first.
Given a signal $x[n]$, and a kernel (also called a filter) $h[n]$, then the convolution of $x[n]$ with $h[n]$ is written as | About CNN, kernels and scale/rotation invariance
I think there are a couple of things confusing you, so first things first.
Given a signal $x[n]$, and a kernel (also called a filter) $h[n]$, then the convolution of $x[n]$ with $h[n]$ is written as $y[n] = (x \star h)[n]$, and is computed via a sliding dot-product, mat... | About CNN, kernels and scale/rotation invariance
I think there are a couple of things confusing you, so first things first.
Given a signal $x[n]$, and a kernel (also called a filter) $h[n]$, then the convolution of $x[n]$ with $h[n]$ is written as |
8,590 | About CNN, kernels and scale/rotation invariance | Many authors including Geoffrey Hinton (who proposes Capsule net) try to solve the issue, but qualitatively. We try to address this issue quantitatively. By having all convolution kernels be symmetric (dihedral symmetry of order 8 [Dih4] or 90-degree increment rotation symmetric, et al) in the CNN, we would provide a p... | About CNN, kernels and scale/rotation invariance | Many authors including Geoffrey Hinton (who proposes Capsule net) try to solve the issue, but qualitatively. We try to address this issue quantitatively. By having all convolution kernels be symmetric | About CNN, kernels and scale/rotation invariance
Many authors including Geoffrey Hinton (who proposes Capsule net) try to solve the issue, but qualitatively. We try to address this issue quantitatively. By having all convolution kernels be symmetric (dihedral symmetry of order 8 [Dih4] or 90-degree increment rotation s... | About CNN, kernels and scale/rotation invariance
Many authors including Geoffrey Hinton (who proposes Capsule net) try to solve the issue, but qualitatively. We try to address this issue quantitatively. By having all convolution kernels be symmetric |
8,591 | About CNN, kernels and scale/rotation invariance | I think max pooling can reserve translational and rotational invariances only for translations and rotations smaller than the stride size. If greater, no invariance | About CNN, kernels and scale/rotation invariance | I think max pooling can reserve translational and rotational invariances only for translations and rotations smaller than the stride size. If greater, no invariance | About CNN, kernels and scale/rotation invariance
I think max pooling can reserve translational and rotational invariances only for translations and rotations smaller than the stride size. If greater, no invariance | About CNN, kernels and scale/rotation invariance
I think max pooling can reserve translational and rotational invariances only for translations and rotations smaller than the stride size. If greater, no invariance |
8,592 | How to calculate the prediction interval for an OLS multiple regression? | Take a regression model with $N$ observations and $k$ regressors:
$$\mathbf{y=X\beta+u} \newcommand{\Var}{\rm Var}$$
Given a vector $\mathbf{x_0}$, the predicted value for that observation would be
$$E[y \vert \mathbf{x_0}]=\hat y_0 = \mathbf{x_0} \hat \beta.$$
A consistent estimator of the variance of this prediction ... | How to calculate the prediction interval for an OLS multiple regression? | Take a regression model with $N$ observations and $k$ regressors:
$$\mathbf{y=X\beta+u} \newcommand{\Var}{\rm Var}$$
Given a vector $\mathbf{x_0}$, the predicted value for that observation would be
$$ | How to calculate the prediction interval for an OLS multiple regression?
Take a regression model with $N$ observations and $k$ regressors:
$$\mathbf{y=X\beta+u} \newcommand{\Var}{\rm Var}$$
Given a vector $\mathbf{x_0}$, the predicted value for that observation would be
$$E[y \vert \mathbf{x_0}]=\hat y_0 = \mathbf{x_0}... | How to calculate the prediction interval for an OLS multiple regression?
Take a regression model with $N$ observations and $k$ regressors:
$$\mathbf{y=X\beta+u} \newcommand{\Var}{\rm Var}$$
Given a vector $\mathbf{x_0}$, the predicted value for that observation would be
$$ |
8,593 | Can overfitting and underfitting occur simultaneously? | Your reasoning makes sense to me.
Here is an extremely simple example. Suppose that $X$ consists of only two columns $x_1$ and $x_2$, and the true DGP is
$$ y=\beta_1x_1+\beta_2x_2+\epsilon $$
with nonzero $\beta_1$ and $\beta_2$, and noise $\epsilon$.
Next, assume that $Z$ contains columns $x_1, x_1^2, x_1^3, \dots$ -... | Can overfitting and underfitting occur simultaneously? | Your reasoning makes sense to me.
Here is an extremely simple example. Suppose that $X$ consists of only two columns $x_1$ and $x_2$, and the true DGP is
$$ y=\beta_1x_1+\beta_2x_2+\epsilon $$
with no | Can overfitting and underfitting occur simultaneously?
Your reasoning makes sense to me.
Here is an extremely simple example. Suppose that $X$ consists of only two columns $x_1$ and $x_2$, and the true DGP is
$$ y=\beta_1x_1+\beta_2x_2+\epsilon $$
with nonzero $\beta_1$ and $\beta_2$, and noise $\epsilon$.
Next, assume... | Can overfitting and underfitting occur simultaneously?
Your reasoning makes sense to me.
Here is an extremely simple example. Suppose that $X$ consists of only two columns $x_1$ and $x_2$, and the true DGP is
$$ y=\beta_1x_1+\beta_2x_2+\epsilon $$
with no |
8,594 | Can overfitting and underfitting occur simultaneously? | I like the idea of having a bad fit of the deterministic part and also overly fitting the noise as being both overfitting and underfitting, but that is not how I view those terminologies.
I consider the issue of overfitting versus underfitting as related to the trade-off between bias and variance. Sure you can have sit... | Can overfitting and underfitting occur simultaneously? | I like the idea of having a bad fit of the deterministic part and also overly fitting the noise as being both overfitting and underfitting, but that is not how I view those terminologies.
I consider t | Can overfitting and underfitting occur simultaneously?
I like the idea of having a bad fit of the deterministic part and also overly fitting the noise as being both overfitting and underfitting, but that is not how I view those terminologies.
I consider the issue of overfitting versus underfitting as related to the tra... | Can overfitting and underfitting occur simultaneously?
I like the idea of having a bad fit of the deterministic part and also overly fitting the noise as being both overfitting and underfitting, but that is not how I view those terminologies.
I consider t |
8,595 | Can degrees of freedom be a non-integer number? | Degrees of freedom are non-integer in a number of contexts. Indeed in a few circumstances you can establish that the degrees of freedom to fit the data for some particular models must be between some value $k$ and $k+1$.
We usually think of degrees of freedom as the number of free parameters, but there are situations w... | Can degrees of freedom be a non-integer number? | Degrees of freedom are non-integer in a number of contexts. Indeed in a few circumstances you can establish that the degrees of freedom to fit the data for some particular models must be between some | Can degrees of freedom be a non-integer number?
Degrees of freedom are non-integer in a number of contexts. Indeed in a few circumstances you can establish that the degrees of freedom to fit the data for some particular models must be between some value $k$ and $k+1$.
We usually think of degrees of freedom as the numbe... | Can degrees of freedom be a non-integer number?
Degrees of freedom are non-integer in a number of contexts. Indeed in a few circumstances you can establish that the degrees of freedom to fit the data for some particular models must be between some |
8,596 | Should I make decisions based on micro-averaged or macro-averaged evaluation measures? | If you think all the labels are more or less equally sized (have roughly the same number of instances), use any.
If you think there are labels with more instances than others and if you want to bias your metric towards the most populated ones, use micromedia.
If you think there are labels with more instances than othe... | Should I make decisions based on micro-averaged or macro-averaged evaluation measures? | If you think all the labels are more or less equally sized (have roughly the same number of instances), use any.
If you think there are labels with more instances than others and if you want to bias y | Should I make decisions based on micro-averaged or macro-averaged evaluation measures?
If you think all the labels are more or less equally sized (have roughly the same number of instances), use any.
If you think there are labels with more instances than others and if you want to bias your metric towards the most popul... | Should I make decisions based on micro-averaged or macro-averaged evaluation measures?
If you think all the labels are more or less equally sized (have roughly the same number of instances), use any.
If you think there are labels with more instances than others and if you want to bias y |
8,597 | Why is it necessary to sample from the posterior distribution if we already KNOW the posterior distribution? | This question has likely been considered already on this forum.
When you state that you "have the posterior distribution", what exactly do you mean? "Having" an available$-$in the sense I can compute it everywhere$-$function of $\theta$ that I know to be proportional to the posterior density, namely$$\pi(\theta|x) \pro... | Why is it necessary to sample from the posterior distribution if we already KNOW the posterior distr | This question has likely been considered already on this forum.
When you state that you "have the posterior distribution", what exactly do you mean? "Having" an available$-$in the sense I can compute | Why is it necessary to sample from the posterior distribution if we already KNOW the posterior distribution?
This question has likely been considered already on this forum.
When you state that you "have the posterior distribution", what exactly do you mean? "Having" an available$-$in the sense I can compute it everywhe... | Why is it necessary to sample from the posterior distribution if we already KNOW the posterior distr
This question has likely been considered already on this forum.
When you state that you "have the posterior distribution", what exactly do you mean? "Having" an available$-$in the sense I can compute |
8,598 | Why is it necessary to sample from the posterior distribution if we already KNOW the posterior distribution? | Yes you might have an analytical posterior distribution. But the core of Bayesian analysis is to marginalize over the posterior distribution of parameters so that you get a better prediction result both in terms of accuracy and generalization capability. Basically, you want to obtain a predictive distribution which has... | Why is it necessary to sample from the posterior distribution if we already KNOW the posterior distr | Yes you might have an analytical posterior distribution. But the core of Bayesian analysis is to marginalize over the posterior distribution of parameters so that you get a better prediction result bo | Why is it necessary to sample from the posterior distribution if we already KNOW the posterior distribution?
Yes you might have an analytical posterior distribution. But the core of Bayesian analysis is to marginalize over the posterior distribution of parameters so that you get a better prediction result both in terms... | Why is it necessary to sample from the posterior distribution if we already KNOW the posterior distr
Yes you might have an analytical posterior distribution. But the core of Bayesian analysis is to marginalize over the posterior distribution of parameters so that you get a better prediction result bo |
8,599 | Why is it necessary to sample from the posterior distribution if we already KNOW the posterior distribution? | A short answer:
Sampling is not only used to estimate a distribution function*, it is also used to perform computations with a density function and MCMC is just one of many ways of sampling. Often such computations are a way of Monte Carlo integration.
Computing a posterior average, a 95% highest density interval, marg... | Why is it necessary to sample from the posterior distribution if we already KNOW the posterior distr | A short answer:
Sampling is not only used to estimate a distribution function*, it is also used to perform computations with a density function and MCMC is just one of many ways of sampling. Often suc | Why is it necessary to sample from the posterior distribution if we already KNOW the posterior distribution?
A short answer:
Sampling is not only used to estimate a distribution function*, it is also used to perform computations with a density function and MCMC is just one of many ways of sampling. Often such computati... | Why is it necessary to sample from the posterior distribution if we already KNOW the posterior distr
A short answer:
Sampling is not only used to estimate a distribution function*, it is also used to perform computations with a density function and MCMC is just one of many ways of sampling. Often suc |
8,600 | XGBoost vs Python Sklearn gradient boosted trees | You are correct, XGBoost ('eXtreme Gradient Boosting') and sklearn's GradientBoost are fundamentally the same as they are both gradient boosting implementations.
However, there are very significant differences under the hood in a practical sense. XGBoost is a lot faster (see http://machinelearningmastery.com/gentle-int... | XGBoost vs Python Sklearn gradient boosted trees | You are correct, XGBoost ('eXtreme Gradient Boosting') and sklearn's GradientBoost are fundamentally the same as they are both gradient boosting implementations.
However, there are very significant di | XGBoost vs Python Sklearn gradient boosted trees
You are correct, XGBoost ('eXtreme Gradient Boosting') and sklearn's GradientBoost are fundamentally the same as they are both gradient boosting implementations.
However, there are very significant differences under the hood in a practical sense. XGBoost is a lot faster ... | XGBoost vs Python Sklearn gradient boosted trees
You are correct, XGBoost ('eXtreme Gradient Boosting') and sklearn's GradientBoost are fundamentally the same as they are both gradient boosting implementations.
However, there are very significant di |
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