idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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11,901 | Splitting Time Series Data into Train/Test/Validation Sets | I think the most complete way to leverage your time-series data for training/validation/testing/prediction is this:
Is the picture self explanatory? If not, please comment and I will add more text... | Splitting Time Series Data into Train/Test/Validation Sets | I think the most complete way to leverage your time-series data for training/validation/testing/prediction is this:
Is the picture self explanatory? If not, please comment and I will add more text... | Splitting Time Series Data into Train/Test/Validation Sets
I think the most complete way to leverage your time-series data for training/validation/testing/prediction is this:
Is the picture self explanatory? If not, please comment and I will add more text... | Splitting Time Series Data into Train/Test/Validation Sets
I think the most complete way to leverage your time-series data for training/validation/testing/prediction is this:
Is the picture self explanatory? If not, please comment and I will add more text... |
11,902 | Splitting Time Series Data into Train/Test/Validation Sets | "walk-forward"
In the following, "validation set" was replaced with "testing set" to be aligned with the naming in this Q/A.
Instead of creating only one set of a training/testing set, you could create more of such sets.
The first training set could be, say, 6 months data (first semester of 2015) and the testing set wo... | Splitting Time Series Data into Train/Test/Validation Sets | "walk-forward"
In the following, "validation set" was replaced with "testing set" to be aligned with the naming in this Q/A.
Instead of creating only one set of a training/testing set, you could creat | Splitting Time Series Data into Train/Test/Validation Sets
"walk-forward"
In the following, "validation set" was replaced with "testing set" to be aligned with the naming in this Q/A.
Instead of creating only one set of a training/testing set, you could create more of such sets.
The first training set could be, say, 6 ... | Splitting Time Series Data into Train/Test/Validation Sets
"walk-forward"
In the following, "validation set" was replaced with "testing set" to be aligned with the naming in this Q/A.
Instead of creating only one set of a training/testing set, you could creat |
11,903 | What is happening here, when I use squared loss in logistic regression setting? | It seems like you've fixed the issue in your particular example but I think it's still worth a more careful study of the difference between least squares and maximum likelihood logistic regression.
Let's get some notation. Let $L_S(y_i, \hat y_i) = \frac 12(y_i - \hat y_i)^2$ and $L_L(y_i, \hat y_i) = y_i \log \hat y_i... | What is happening here, when I use squared loss in logistic regression setting? | It seems like you've fixed the issue in your particular example but I think it's still worth a more careful study of the difference between least squares and maximum likelihood logistic regression.
Le | What is happening here, when I use squared loss in logistic regression setting?
It seems like you've fixed the issue in your particular example but I think it's still worth a more careful study of the difference between least squares and maximum likelihood logistic regression.
Let's get some notation. Let $L_S(y_i, \ha... | What is happening here, when I use squared loss in logistic regression setting?
It seems like you've fixed the issue in your particular example but I think it's still worth a more careful study of the difference between least squares and maximum likelihood logistic regression.
Le |
11,904 | What is happening here, when I use squared loss in logistic regression setting? | I would thank to thank @whuber and @Chaconne for help. Especially @Chaconne, this derivation is what I wished to have for years.
The problem IS in the optimization part. If we set the random seed to 1, the default BFGS will not work. But if we change the algorithm and change the max iteration number it will work again.... | What is happening here, when I use squared loss in logistic regression setting? | I would thank to thank @whuber and @Chaconne for help. Especially @Chaconne, this derivation is what I wished to have for years.
The problem IS in the optimization part. If we set the random seed to 1 | What is happening here, when I use squared loss in logistic regression setting?
I would thank to thank @whuber and @Chaconne for help. Especially @Chaconne, this derivation is what I wished to have for years.
The problem IS in the optimization part. If we set the random seed to 1, the default BFGS will not work. But if... | What is happening here, when I use squared loss in logistic regression setting?
I would thank to thank @whuber and @Chaconne for help. Especially @Chaconne, this derivation is what I wished to have for years.
The problem IS in the optimization part. If we set the random seed to 1 |
11,905 | Computing percentile rank in R [closed] | Given a vector of raw data values, a simple function might look like
perc.rank <- function(x, xo) length(x[x <= xo])/length(x)*100
where x0 is the value for which we want the percentile rank, given the vector x, as suggested on R-bloggers.
However, it might easily be vectorized as
perc.rank <- function(x) trunc(rank... | Computing percentile rank in R [closed] | Given a vector of raw data values, a simple function might look like
perc.rank <- function(x, xo) length(x[x <= xo])/length(x)*100
where x0 is the value for which we want the percentile rank, given | Computing percentile rank in R [closed]
Given a vector of raw data values, a simple function might look like
perc.rank <- function(x, xo) length(x[x <= xo])/length(x)*100
where x0 is the value for which we want the percentile rank, given the vector x, as suggested on R-bloggers.
However, it might easily be vectorize... | Computing percentile rank in R [closed]
Given a vector of raw data values, a simple function might look like
perc.rank <- function(x, xo) length(x[x <= xo])/length(x)*100
where x0 is the value for which we want the percentile rank, given |
11,906 | Computing percentile rank in R [closed] | If your original data.frame is called dfr and the variable of interest is called myvar, you can use dfr$myrank<-rank(dfr$myvar) for normal ranks, or dfr$myrank<-rank(dfr$myvar)/length(myvar) for percentile ranks.
Oh well. If you really want it the Excel way (may not be the simplest solution, but I had some fun using ne... | Computing percentile rank in R [closed] | If your original data.frame is called dfr and the variable of interest is called myvar, you can use dfr$myrank<-rank(dfr$myvar) for normal ranks, or dfr$myrank<-rank(dfr$myvar)/length(myvar) for perce | Computing percentile rank in R [closed]
If your original data.frame is called dfr and the variable of interest is called myvar, you can use dfr$myrank<-rank(dfr$myvar) for normal ranks, or dfr$myrank<-rank(dfr$myvar)/length(myvar) for percentile ranks.
Oh well. If you really want it the Excel way (may not be the simple... | Computing percentile rank in R [closed]
If your original data.frame is called dfr and the variable of interest is called myvar, you can use dfr$myrank<-rank(dfr$myvar) for normal ranks, or dfr$myrank<-rank(dfr$myvar)/length(myvar) for perce |
11,907 | Computing percentile rank in R [closed] | A problem with the presented answer is that it will not work properly, when you have NAs.
In this case, another possibility (inspired by the function from chl♦) is:
perc.rank <- function(x) trunc(rank(x,na.last = NA))/sum(!is.na(x))
quant <- function (x, p.ile) {
x[which.min(x = abs(perc.rank(x-(p.ile/100))))... | Computing percentile rank in R [closed] | A problem with the presented answer is that it will not work properly, when you have NAs.
In this case, another possibility (inspired by the function from chl♦) is:
perc.rank <- function(x) trunc( | Computing percentile rank in R [closed]
A problem with the presented answer is that it will not work properly, when you have NAs.
In this case, another possibility (inspired by the function from chl♦) is:
perc.rank <- function(x) trunc(rank(x,na.last = NA))/sum(!is.na(x))
quant <- function (x, p.ile) {
x[whic... | Computing percentile rank in R [closed]
A problem with the presented answer is that it will not work properly, when you have NAs.
In this case, another possibility (inspired by the function from chl♦) is:
perc.rank <- function(x) trunc( |
11,908 | Why do we do matching for causal inference vs regressing on confounders? | As I see it, there are two related reasons to consider matching instead of regression. The first is assumptions about functional form, and the second is about proving to your audience that functional form assumptions do not affect the resulting effect estimate. The first is a statistical matter and the second is episte... | Why do we do matching for causal inference vs regressing on confounders? | As I see it, there are two related reasons to consider matching instead of regression. The first is assumptions about functional form, and the second is about proving to your audience that functional | Why do we do matching for causal inference vs regressing on confounders?
As I see it, there are two related reasons to consider matching instead of regression. The first is assumptions about functional form, and the second is about proving to your audience that functional form assumptions do not affect the resulting ef... | Why do we do matching for causal inference vs regressing on confounders?
As I see it, there are two related reasons to consider matching instead of regression. The first is assumptions about functional form, and the second is about proving to your audience that functional |
11,909 | Distribution that has a range from 0 to 1 and with peak between them? | One possible choice is the beta distribution, but re-parametrized in terms of mean $\mu$ and precision $\phi$, that is, "for fixed $\mu$, the larger the value of $\phi$, the smaller the variance of $y$" (see Ferrari, and Cribari-Neto, 2004). The probability density function is constructed by replacing the standard para... | Distribution that has a range from 0 to 1 and with peak between them? | One possible choice is the beta distribution, but re-parametrized in terms of mean $\mu$ and precision $\phi$, that is, "for fixed $\mu$, the larger the value of $\phi$, the smaller the variance of $y | Distribution that has a range from 0 to 1 and with peak between them?
One possible choice is the beta distribution, but re-parametrized in terms of mean $\mu$ and precision $\phi$, that is, "for fixed $\mu$, the larger the value of $\phi$, the smaller the variance of $y$" (see Ferrari, and Cribari-Neto, 2004). The prob... | Distribution that has a range from 0 to 1 and with peak between them?
One possible choice is the beta distribution, but re-parametrized in terms of mean $\mu$ and precision $\phi$, that is, "for fixed $\mu$, the larger the value of $\phi$, the smaller the variance of $y |
11,910 | Distribution that has a range from 0 to 1 and with peak between them? | I transform to create this kind of variable. Start with a random variable, x, which has support on the whole real line (like normal), and then transform it to make a new random variable $y=\frac{exp(x)}{1+exp(x)}$. Presto, you have a random variable distributed on the unit interval. Since this particular transformat... | Distribution that has a range from 0 to 1 and with peak between them? | I transform to create this kind of variable. Start with a random variable, x, which has support on the whole real line (like normal), and then transform it to make a new random variable $y=\frac{exp( | Distribution that has a range from 0 to 1 and with peak between them?
I transform to create this kind of variable. Start with a random variable, x, which has support on the whole real line (like normal), and then transform it to make a new random variable $y=\frac{exp(x)}{1+exp(x)}$. Presto, you have a random variabl... | Distribution that has a range from 0 to 1 and with peak between them?
I transform to create this kind of variable. Start with a random variable, x, which has support on the whole real line (like normal), and then transform it to make a new random variable $y=\frac{exp( |
11,911 | Distribution that has a range from 0 to 1 and with peak between them? | This answer is for you if you do not know what your mean/maximum will be and you want your program to be able to handle any mean and freely set variance.
Disclaimer: I am not a Mathematician, my answer works but the explanations might be incomplete/incorrect and not mathematically specific.
All of the comments and answ... | Distribution that has a range from 0 to 1 and with peak between them? | This answer is for you if you do not know what your mean/maximum will be and you want your program to be able to handle any mean and freely set variance.
Disclaimer: I am not a Mathematician, my answe | Distribution that has a range from 0 to 1 and with peak between them?
This answer is for you if you do not know what your mean/maximum will be and you want your program to be able to handle any mean and freely set variance.
Disclaimer: I am not a Mathematician, my answer works but the explanations might be incomplete/i... | Distribution that has a range from 0 to 1 and with peak between them?
This answer is for you if you do not know what your mean/maximum will be and you want your program to be able to handle any mean and freely set variance.
Disclaimer: I am not a Mathematician, my answe |
11,912 | Distribution that has a range from 0 to 1 and with peak between them? | If somebody is interested in the solution I used in Python for generating a random value close to the given number as a parameter. My solution exist of four stages. Each stage the chance that the generated number is closer to the given number is bigger.
I know the solution is not as beautiful as using one distribution ... | Distribution that has a range from 0 to 1 and with peak between them? | If somebody is interested in the solution I used in Python for generating a random value close to the given number as a parameter. My solution exist of four stages. Each stage the chance that the gene | Distribution that has a range from 0 to 1 and with peak between them?
If somebody is interested in the solution I used in Python for generating a random value close to the given number as a parameter. My solution exist of four stages. Each stage the chance that the generated number is closer to the given number is bigg... | Distribution that has a range from 0 to 1 and with peak between them?
If somebody is interested in the solution I used in Python for generating a random value close to the given number as a parameter. My solution exist of four stages. Each stage the chance that the gene |
11,913 | Distribution that has a range from 0 to 1 and with peak between them? | You might want to take a look at 'Johnson curves'. See N.L. Johnson: Systems of Frequency Curves generated by methods of translation. 1949 Biometrika Volume 36 pp 149-176. R has support for fitting them to arbitrary curves. In particular his SB (bounded) curves might be useful.
It's 40 years since I used them, but the... | Distribution that has a range from 0 to 1 and with peak between them? | You might want to take a look at 'Johnson curves'. See N.L. Johnson: Systems of Frequency Curves generated by methods of translation. 1949 Biometrika Volume 36 pp 149-176. R has support for fitting th | Distribution that has a range from 0 to 1 and with peak between them?
You might want to take a look at 'Johnson curves'. See N.L. Johnson: Systems of Frequency Curves generated by methods of translation. 1949 Biometrika Volume 36 pp 149-176. R has support for fitting them to arbitrary curves. In particular his SB (boun... | Distribution that has a range from 0 to 1 and with peak between them?
You might want to take a look at 'Johnson curves'. See N.L. Johnson: Systems of Frequency Curves generated by methods of translation. 1949 Biometrika Volume 36 pp 149-176. R has support for fitting th |
11,914 | What statistical model or algorithm could be used to solve the John Snow Cholera problem? | Not to give a complete or authoritative answer, but just to stimulate ideas, I will report on a quick analysis I made for a lab exercise in a spatial stats course I was teaching ten years ago. The purpose was to see what effect an accurate accounting of likely travel pathways (on foot), compared to using Euclidean dis... | What statistical model or algorithm could be used to solve the John Snow Cholera problem? | Not to give a complete or authoritative answer, but just to stimulate ideas, I will report on a quick analysis I made for a lab exercise in a spatial stats course I was teaching ten years ago. The pu | What statistical model or algorithm could be used to solve the John Snow Cholera problem?
Not to give a complete or authoritative answer, but just to stimulate ideas, I will report on a quick analysis I made for a lab exercise in a spatial stats course I was teaching ten years ago. The purpose was to see what effect a... | What statistical model or algorithm could be used to solve the John Snow Cholera problem?
Not to give a complete or authoritative answer, but just to stimulate ideas, I will report on a quick analysis I made for a lab exercise in a spatial stats course I was teaching ten years ago. The pu |
11,915 | What statistical model or algorithm could be used to solve the John Snow Cholera problem? | In [1,§3.2], David Freedman suggests an essentially negative answer to your question. That is, no (mere) statistical model or algorithm could solve John Snow's problem. Snow's problem was to develop a critical argument supporting his theory that cholera is a water-borne infectious disease, against the prevailing miasma... | What statistical model or algorithm could be used to solve the John Snow Cholera problem? | In [1,§3.2], David Freedman suggests an essentially negative answer to your question. That is, no (mere) statistical model or algorithm could solve John Snow's problem. Snow's problem was to develop a | What statistical model or algorithm could be used to solve the John Snow Cholera problem?
In [1,§3.2], David Freedman suggests an essentially negative answer to your question. That is, no (mere) statistical model or algorithm could solve John Snow's problem. Snow's problem was to develop a critical argument supporting ... | What statistical model or algorithm could be used to solve the John Snow Cholera problem?
In [1,§3.2], David Freedman suggests an essentially negative answer to your question. That is, no (mere) statistical model or algorithm could solve John Snow's problem. Snow's problem was to develop a |
11,916 | How does bootstrapping in R actually work? | There are several "flavours" or forms of the bootstrap (e.g. non-parametric, parametric, residual resampling and many more). The bootstrap in the example is called a non-parametric bootstrap, or case resampling (see here, here, here and here for applications in regression). The basic idea is that you treat your sample ... | How does bootstrapping in R actually work? | There are several "flavours" or forms of the bootstrap (e.g. non-parametric, parametric, residual resampling and many more). The bootstrap in the example is called a non-parametric bootstrap, or case | How does bootstrapping in R actually work?
There are several "flavours" or forms of the bootstrap (e.g. non-parametric, parametric, residual resampling and many more). The bootstrap in the example is called a non-parametric bootstrap, or case resampling (see here, here, here and here for applications in regression). Th... | How does bootstrapping in R actually work?
There are several "flavours" or forms of the bootstrap (e.g. non-parametric, parametric, residual resampling and many more). The bootstrap in the example is called a non-parametric bootstrap, or case |
11,917 | How does bootstrapping in R actually work? | You should focus on the function that is passed to boot as the "statistic" parameter and notice how it is constructed.
f <- function(data, i) {
require(pscl)
m <- zeroinfl(count ~ child + camper | persons,
data = data[i, ], dist = "negbin",
start = list(count = c(1.3711, -1.5152, 0.879), zero = c(1.6028, -1... | How does bootstrapping in R actually work? | You should focus on the function that is passed to boot as the "statistic" parameter and notice how it is constructed.
f <- function(data, i) {
require(pscl)
m <- zeroinfl(count ~ child + camper | | How does bootstrapping in R actually work?
You should focus on the function that is passed to boot as the "statistic" parameter and notice how it is constructed.
f <- function(data, i) {
require(pscl)
m <- zeroinfl(count ~ child + camper | persons,
data = data[i, ], dist = "negbin",
start = list(count = c(1... | How does bootstrapping in R actually work?
You should focus on the function that is passed to boot as the "statistic" parameter and notice how it is constructed.
f <- function(data, i) {
require(pscl)
m <- zeroinfl(count ~ child + camper | |
11,918 | PCA of non-Gaussian data | You have a couple of good answers here already (+1 to both @Cam.Davidson.Pilon & @MichaelChernick). Let me throw out a couple of points that help me to think about this issue.
First, PCA operates over the correlation matrix. Thus, it seems to me the important question is whether it makes sense to use a correlation ... | PCA of non-Gaussian data | You have a couple of good answers here already (+1 to both @Cam.Davidson.Pilon & @MichaelChernick). Let me throw out a couple of points that help me to think about this issue.
First, PCA operates o | PCA of non-Gaussian data
You have a couple of good answers here already (+1 to both @Cam.Davidson.Pilon & @MichaelChernick). Let me throw out a couple of points that help me to think about this issue.
First, PCA operates over the correlation matrix. Thus, it seems to me the important question is whether it makes se... | PCA of non-Gaussian data
You have a couple of good answers here already (+1 to both @Cam.Davidson.Pilon & @MichaelChernick). Let me throw out a couple of points that help me to think about this issue.
First, PCA operates o |
11,919 | PCA of non-Gaussian data | I can give a partial solution and show an answer for your second paragraph third question, relating to whether the new data is correlated. The short answer is no, the data in the new space is not correlated. To see, consider $w_1$ and $w_2$ as two unique principle components. Then $Xw_1$ and $Xw_2$ are two dimensions i... | PCA of non-Gaussian data | I can give a partial solution and show an answer for your second paragraph third question, relating to whether the new data is correlated. The short answer is no, the data in the new space is not corr | PCA of non-Gaussian data
I can give a partial solution and show an answer for your second paragraph third question, relating to whether the new data is correlated. The short answer is no, the data in the new space is not correlated. To see, consider $w_1$ and $w_2$ as two unique principle components. Then $Xw_1$ and $X... | PCA of non-Gaussian data
I can give a partial solution and show an answer for your second paragraph third question, relating to whether the new data is correlated. The short answer is no, the data in the new space is not corr |
11,920 | PCA of non-Gaussian data | There is no linearity or normality assumed in PCA. The idea is just decomposing the variation in a p-dimensional dataset into orthogonal components that are ordered according to amount of variance explained. | PCA of non-Gaussian data | There is no linearity or normality assumed in PCA. The idea is just decomposing the variation in a p-dimensional dataset into orthogonal components that are ordered according to amount of variance ex | PCA of non-Gaussian data
There is no linearity or normality assumed in PCA. The idea is just decomposing the variation in a p-dimensional dataset into orthogonal components that are ordered according to amount of variance explained. | PCA of non-Gaussian data
There is no linearity or normality assumed in PCA. The idea is just decomposing the variation in a p-dimensional dataset into orthogonal components that are ordered according to amount of variance ex |
11,921 | PCA of non-Gaussian data | Reading page 7 here:
http://www.cs.princeton.edu/picasso/mats/PCA-Tutorial-Intuition_jp.pdf
they note that PCA assumes that the distribution of whatever we are explaining can be described by a mean (of zero) and variance alone, which they say can only be the Normal distribution.
(Basically in addition to Cam's answer, ... | PCA of non-Gaussian data | Reading page 7 here:
http://www.cs.princeton.edu/picasso/mats/PCA-Tutorial-Intuition_jp.pdf
they note that PCA assumes that the distribution of whatever we are explaining can be described by a mean (o | PCA of non-Gaussian data
Reading page 7 here:
http://www.cs.princeton.edu/picasso/mats/PCA-Tutorial-Intuition_jp.pdf
they note that PCA assumes that the distribution of whatever we are explaining can be described by a mean (of zero) and variance alone, which they say can only be the Normal distribution.
(Basically in a... | PCA of non-Gaussian data
Reading page 7 here:
http://www.cs.princeton.edu/picasso/mats/PCA-Tutorial-Intuition_jp.pdf
they note that PCA assumes that the distribution of whatever we are explaining can be described by a mean (o |
11,922 | PCA of non-Gaussian data | As far as I know, PCA doesn't assume normality of data. But if it is normally distributed (in more general sense, symmetrically distributed), then the result is more robust. As other people say, the key is that PCA is based on Pearson correlation coefficient matrix, of which estimation is affected by outliers and skewe... | PCA of non-Gaussian data | As far as I know, PCA doesn't assume normality of data. But if it is normally distributed (in more general sense, symmetrically distributed), then the result is more robust. As other people say, the k | PCA of non-Gaussian data
As far as I know, PCA doesn't assume normality of data. But if it is normally distributed (in more general sense, symmetrically distributed), then the result is more robust. As other people say, the key is that PCA is based on Pearson correlation coefficient matrix, of which estimation is affec... | PCA of non-Gaussian data
As far as I know, PCA doesn't assume normality of data. But if it is normally distributed (in more general sense, symmetrically distributed), then the result is more robust. As other people say, the k |
11,923 | PCA of non-Gaussian data | Agreed with others who said data should be "Normally" distributed. Any distribution will overlap with a normal distribution if you transform it. If your distribution is not normal, the results you will get will be inferior compared to the case when it is normal, as stated by some here...
You can transform your distrib... | PCA of non-Gaussian data | Agreed with others who said data should be "Normally" distributed. Any distribution will overlap with a normal distribution if you transform it. If your distribution is not normal, the results you wil | PCA of non-Gaussian data
Agreed with others who said data should be "Normally" distributed. Any distribution will overlap with a normal distribution if you transform it. If your distribution is not normal, the results you will get will be inferior compared to the case when it is normal, as stated by some here...
You c... | PCA of non-Gaussian data
Agreed with others who said data should be "Normally" distributed. Any distribution will overlap with a normal distribution if you transform it. If your distribution is not normal, the results you wil |
11,924 | Calculating statistical power | This isn't an answer you are going to want to hear, I am afraid, but I am going to say it anyway: try to resist the temptation of online calculators (and save your money before purchasing proprietary calculators).
Here are some of the reasons why: 1) online calculators all use different notation and are often poorly do... | Calculating statistical power | This isn't an answer you are going to want to hear, I am afraid, but I am going to say it anyway: try to resist the temptation of online calculators (and save your money before purchasing proprietary | Calculating statistical power
This isn't an answer you are going to want to hear, I am afraid, but I am going to say it anyway: try to resist the temptation of online calculators (and save your money before purchasing proprietary calculators).
Here are some of the reasons why: 1) online calculators all use different no... | Calculating statistical power
This isn't an answer you are going to want to hear, I am afraid, but I am going to say it anyway: try to resist the temptation of online calculators (and save your money before purchasing proprietary |
11,925 | Introduction to measure theory | For a really short introduction (seven page pdf), there's also this, intended to allow you to follow papers that use a bit of measure theory :
A Measure Theory Tutorial (Measure Theory for Dummies). Maya R. Gupta.
Dept of Electrical Engineering, University of Washington, 2006. (archive.org copy)
The author gives some r... | Introduction to measure theory | For a really short introduction (seven page pdf), there's also this, intended to allow you to follow papers that use a bit of measure theory :
A Measure Theory Tutorial (Measure Theory for Dummies). M | Introduction to measure theory
For a really short introduction (seven page pdf), there's also this, intended to allow you to follow papers that use a bit of measure theory :
A Measure Theory Tutorial (Measure Theory for Dummies). Maya R. Gupta.
Dept of Electrical Engineering, University of Washington, 2006. (archive.or... | Introduction to measure theory
For a really short introduction (seven page pdf), there's also this, intended to allow you to follow papers that use a bit of measure theory :
A Measure Theory Tutorial (Measure Theory for Dummies). M |
11,926 | Introduction to measure theory | After some research, I ended up buying this when I thought I needed to know something about measure-theoretic probability:
Jeffrey Rosenthal. A First Look at Rigorous Probability Theory. World Scientific 2007. ISBN 9789812703712.
I haven't read much of it, however, as my personal experience is in accord with Stephen ... | Introduction to measure theory | After some research, I ended up buying this when I thought I needed to know something about measure-theoretic probability:
Jeffrey Rosenthal. A First Look at Rigorous Probability Theory. World Scien | Introduction to measure theory
After some research, I ended up buying this when I thought I needed to know something about measure-theoretic probability:
Jeffrey Rosenthal. A First Look at Rigorous Probability Theory. World Scientific 2007. ISBN 9789812703712.
I haven't read much of it, however, as my personal experi... | Introduction to measure theory
After some research, I ended up buying this when I thought I needed to know something about measure-theoretic probability:
Jeffrey Rosenthal. A First Look at Rigorous Probability Theory. World Scien |
11,927 | Introduction to measure theory | Personally, I've found Kolmogorov's original Foundations of the Theory of Probability to be fairly readable, at least compared to most measure theory texts. Although it obviously doesn't contain any later work, it does give you an idea of most of the important concepts (sets of measure zero, conditional expectation, et... | Introduction to measure theory | Personally, I've found Kolmogorov's original Foundations of the Theory of Probability to be fairly readable, at least compared to most measure theory texts. Although it obviously doesn't contain any l | Introduction to measure theory
Personally, I've found Kolmogorov's original Foundations of the Theory of Probability to be fairly readable, at least compared to most measure theory texts. Although it obviously doesn't contain any later work, it does give you an idea of most of the important concepts (sets of measure ze... | Introduction to measure theory
Personally, I've found Kolmogorov's original Foundations of the Theory of Probability to be fairly readable, at least compared to most measure theory texts. Although it obviously doesn't contain any l |
11,928 | Introduction to measure theory | Outline of Lebesgue Theory: A Heuristic Introduction by Robert E. Wernikoff. For engineers this is easily the best introduction. | Introduction to measure theory | Outline of Lebesgue Theory: A Heuristic Introduction by Robert E. Wernikoff. For engineers this is easily the best introduction. | Introduction to measure theory
Outline of Lebesgue Theory: A Heuristic Introduction by Robert E. Wernikoff. For engineers this is easily the best introduction. | Introduction to measure theory
Outline of Lebesgue Theory: A Heuristic Introduction by Robert E. Wernikoff. For engineers this is easily the best introduction. |
11,929 | Introduction to measure theory | Jumping straight into non-parametric Bayesian analysis is quite a big first leap! Maybe get a bit of parametric Bayes under your belt first?
Three books which you may find useful from the Bayesian part of things are:
1) Probability Theory: The Logic of Science by E. T. Jaynes, Edited by G. L. Bretthorst (2003)
2) Baye... | Introduction to measure theory | Jumping straight into non-parametric Bayesian analysis is quite a big first leap! Maybe get a bit of parametric Bayes under your belt first?
Three books which you may find useful from the Bayesian pa | Introduction to measure theory
Jumping straight into non-parametric Bayesian analysis is quite a big first leap! Maybe get a bit of parametric Bayes under your belt first?
Three books which you may find useful from the Bayesian part of things are:
1) Probability Theory: The Logic of Science by E. T. Jaynes, Edited by ... | Introduction to measure theory
Jumping straight into non-parametric Bayesian analysis is quite a big first leap! Maybe get a bit of parametric Bayes under your belt first?
Three books which you may find useful from the Bayesian pa |
11,930 | Algorithms to compute the running median? | #Edit:
As @Hunaphu's points out (and @whuber below in his answer) the original answer I gave to the OP (below) is wrong. It is indeed quicker to first sort the initial batch and then keep updating the median up or down (depending on whether a new data points falls to the left or to the right of the current median).
It... | Algorithms to compute the running median? | #Edit:
As @Hunaphu's points out (and @whuber below in his answer) the original answer I gave to the OP (below) is wrong. It is indeed quicker to first sort the initial batch and then keep updating the | Algorithms to compute the running median?
#Edit:
As @Hunaphu's points out (and @whuber below in his answer) the original answer I gave to the OP (below) is wrong. It is indeed quicker to first sort the initial batch and then keep updating the median up or down (depending on whether a new data points falls to the left o... | Algorithms to compute the running median?
#Edit:
As @Hunaphu's points out (and @whuber below in his answer) the original answer I gave to the OP (below) is wrong. It is indeed quicker to first sort the initial batch and then keep updating the |
11,931 | Algorithms to compute the running median? | If you're willing to tolerate an approximation, there are other methods. For example, one approximation is a value whose rank is within some (user specified) distance from the true median. For example, the median has (normalized) rank 0.5, and if you specify an error term of 10%, you'd want an answer that has rank betw... | Algorithms to compute the running median? | If you're willing to tolerate an approximation, there are other methods. For example, one approximation is a value whose rank is within some (user specified) distance from the true median. For example | Algorithms to compute the running median?
If you're willing to tolerate an approximation, there are other methods. For example, one approximation is a value whose rank is within some (user specified) distance from the true median. For example, the median has (normalized) rank 0.5, and if you specify an error term of 10... | Algorithms to compute the running median?
If you're willing to tolerate an approximation, there are other methods. For example, one approximation is a value whose rank is within some (user specified) distance from the true median. For example |
11,932 | Algorithms to compute the running median? | Here is an article describing one possible algorithm. Source code included and a quite serious application (gravitational wave detection based on laser interferometry), so you can expect it to be well tested. | Algorithms to compute the running median? | Here is an article describing one possible algorithm. Source code included and a quite serious application (gravitational wave detection based on laser interferometry), so you can expect it to be well | Algorithms to compute the running median?
Here is an article describing one possible algorithm. Source code included and a quite serious application (gravitational wave detection based on laser interferometry), so you can expect it to be well tested. | Algorithms to compute the running median?
Here is an article describing one possible algorithm. Source code included and a quite serious application (gravitational wave detection based on laser interferometry), so you can expect it to be well |
11,933 | Algorithms to compute the running median? | If you maintain a length-k window of data as a sorted doubly linked list then, by means of a binary search (to insert each new element as it gets shifted into the window) and a circular array of pointers (to immediately locate elements that need to be deleted), each shift of the window requires O(log(k)) effort for ins... | Algorithms to compute the running median? | If you maintain a length-k window of data as a sorted doubly linked list then, by means of a binary search (to insert each new element as it gets shifted into the window) and a circular array of point | Algorithms to compute the running median?
If you maintain a length-k window of data as a sorted doubly linked list then, by means of a binary search (to insert each new element as it gets shifted into the window) and a circular array of pointers (to immediately locate elements that need to be deleted), each shift of th... | Algorithms to compute the running median?
If you maintain a length-k window of data as a sorted doubly linked list then, by means of a binary search (to insert each new element as it gets shifted into the window) and a circular array of point |
11,934 | Algorithms to compute the running median? | Here is a solution O(1) for finding current median, and O(log n) for adding a new number
http://www.dsalgo.com/RunningMedian.php | Algorithms to compute the running median? | Here is a solution O(1) for finding current median, and O(log n) for adding a new number
http://www.dsalgo.com/RunningMedian.php | Algorithms to compute the running median?
Here is a solution O(1) for finding current median, and O(log n) for adding a new number
http://www.dsalgo.com/RunningMedian.php | Algorithms to compute the running median?
Here is a solution O(1) for finding current median, and O(log n) for adding a new number
http://www.dsalgo.com/RunningMedian.php |
11,935 | Algorithms to compute the running median? | As you mentioned sorting would be O(n·log n) for a window of length n. Doing this moving adds another l=vectorlength making the total cost O(l·n·log n).
The simplest way to push this is by keeping an ordered list of the last n elements in memory when moving from one window to the next one. As removing/inserting one ele... | Algorithms to compute the running median? | As you mentioned sorting would be O(n·log n) for a window of length n. Doing this moving adds another l=vectorlength making the total cost O(l·n·log n).
The simplest way to push this is by keeping an | Algorithms to compute the running median?
As you mentioned sorting would be O(n·log n) for a window of length n. Doing this moving adds another l=vectorlength making the total cost O(l·n·log n).
The simplest way to push this is by keeping an ordered list of the last n elements in memory when moving from one window to t... | Algorithms to compute the running median?
As you mentioned sorting would be O(n·log n) for a window of length n. Doing this moving adds another l=vectorlength making the total cost O(l·n·log n).
The simplest way to push this is by keeping an |
11,936 | Algorithms to compute the running median? | If you can live with an estimate instead of the true median, the Remedian Algorithm (PDF) is one-pass with low storage requirements and well defined accuracy.
The remedian with base b proceeds by computing medians of groups of b observations, and then medians of these medians, until only a single estimate remains. Thi... | Algorithms to compute the running median? | If you can live with an estimate instead of the true median, the Remedian Algorithm (PDF) is one-pass with low storage requirements and well defined accuracy.
The remedian with base b proceeds by com | Algorithms to compute the running median?
If you can live with an estimate instead of the true median, the Remedian Algorithm (PDF) is one-pass with low storage requirements and well defined accuracy.
The remedian with base b proceeds by computing medians of groups of b observations, and then medians of these medians,... | Algorithms to compute the running median?
If you can live with an estimate instead of the true median, the Remedian Algorithm (PDF) is one-pass with low storage requirements and well defined accuracy.
The remedian with base b proceeds by com |
11,937 | Algorithms to compute the running median? | I used this RunningStats C++ Library in an embedded application. It is the most simple running stats library I have found yet.
From the link:
The code is an extension of the method of Knuth and Welford for
computing standard deviation in one pass through the data. It computes
skewness and kurtosis as well with a s... | Algorithms to compute the running median? | I used this RunningStats C++ Library in an embedded application. It is the most simple running stats library I have found yet.
From the link:
The code is an extension of the method of Knuth and Welfo | Algorithms to compute the running median?
I used this RunningStats C++ Library in an embedded application. It is the most simple running stats library I have found yet.
From the link:
The code is an extension of the method of Knuth and Welford for
computing standard deviation in one pass through the data. It compute... | Algorithms to compute the running median?
I used this RunningStats C++ Library in an embedded application. It is the most simple running stats library I have found yet.
From the link:
The code is an extension of the method of Knuth and Welfo |
11,938 | Zero correlation of all functions of random variables implying independence | Using indicator functions of measurable sets like$$f(x)=\mathbb I_A(x)\quad g(x)=\mathbb I_B(x)$$leads to$$\text{cov}(f(X),g(Y))=\mathbb P(X\in A,Y\in B)-\mathbb P(X\in A)\mathbb P(Y\in B)$$therefore implying independence. As shown in the following snapshot of A. Dembo's probability course, proving the result for indic... | Zero correlation of all functions of random variables implying independence | Using indicator functions of measurable sets like$$f(x)=\mathbb I_A(x)\quad g(x)=\mathbb I_B(x)$$leads to$$\text{cov}(f(X),g(Y))=\mathbb P(X\in A,Y\in B)-\mathbb P(X\in A)\mathbb P(Y\in B)$$therefore | Zero correlation of all functions of random variables implying independence
Using indicator functions of measurable sets like$$f(x)=\mathbb I_A(x)\quad g(x)=\mathbb I_B(x)$$leads to$$\text{cov}(f(X),g(Y))=\mathbb P(X\in A,Y\in B)-\mathbb P(X\in A)\mathbb P(Y\in B)$$therefore implying independence. As shown in the follo... | Zero correlation of all functions of random variables implying independence
Using indicator functions of measurable sets like$$f(x)=\mathbb I_A(x)\quad g(x)=\mathbb I_B(x)$$leads to$$\text{cov}(f(X),g(Y))=\mathbb P(X\in A,Y\in B)-\mathbb P(X\in A)\mathbb P(Y\in B)$$therefore |
11,939 | Zero correlation of all functions of random variables implying independence | @Xi'an gives probably the simplest set of functions $f,\,g$ that will work. Here's a more general argument:
It is sufficient to show that the characteristic function $E[\exp(itX+iSY)]$ factors into $E[\exp(itX)]E[\exp(iSY)]$, because characteristic functions determine distributions.
Therefore, it is sufficient to show... | Zero correlation of all functions of random variables implying independence | @Xi'an gives probably the simplest set of functions $f,\,g$ that will work. Here's a more general argument:
It is sufficient to show that the characteristic function $E[\exp(itX+iSY)]$ factors into $ | Zero correlation of all functions of random variables implying independence
@Xi'an gives probably the simplest set of functions $f,\,g$ that will work. Here's a more general argument:
It is sufficient to show that the characteristic function $E[\exp(itX+iSY)]$ factors into $E[\exp(itX)]E[\exp(iSY)]$, because character... | Zero correlation of all functions of random variables implying independence
@Xi'an gives probably the simplest set of functions $f,\,g$ that will work. Here's a more general argument:
It is sufficient to show that the characteristic function $E[\exp(itX+iSY)]$ factors into $ |
11,940 | Zero correlation of all functions of random variables implying independence | Any continuous random variable can be mapped into a uniform [0,1] random variable using the cumulative distribution function. If the variables are independent, then the joint distribution on the 1x1 square will be the product of the two uniform margins and so uniform too. For the variables to be dependent, the joint di... | Zero correlation of all functions of random variables implying independence | Any continuous random variable can be mapped into a uniform [0,1] random variable using the cumulative distribution function. If the variables are independent, then the joint distribution on the 1x1 s | Zero correlation of all functions of random variables implying independence
Any continuous random variable can be mapped into a uniform [0,1] random variable using the cumulative distribution function. If the variables are independent, then the joint distribution on the 1x1 square will be the product of the two uniform... | Zero correlation of all functions of random variables implying independence
Any continuous random variable can be mapped into a uniform [0,1] random variable using the cumulative distribution function. If the variables are independent, then the joint distribution on the 1x1 s |
11,941 | Zero correlation of all functions of random variables implying independence | If $\text{Corr}\left(f(X),g(Y)\right)=0$ for all possible functions $f(\cdot)$ and $g(\cdot)$, then $X$ and $Y$ are independent.
In the ref that I have the opposite is affirmed. If $X$ and $Y$ are independent we have that:
$E[f(X)]E[g(Y)]-E[f(X)g(Y)]=0$ (then $corr[f(X),g(Y)]=0$)
for any $f()$ and $g()$.
In words, we... | Zero correlation of all functions of random variables implying independence | If $\text{Corr}\left(f(X),g(Y)\right)=0$ for all possible functions $f(\cdot)$ and $g(\cdot)$, then $X$ and $Y$ are independent.
In the ref that I have the opposite is affirmed. If $X$ and $Y$ are in | Zero correlation of all functions of random variables implying independence
If $\text{Corr}\left(f(X),g(Y)\right)=0$ for all possible functions $f(\cdot)$ and $g(\cdot)$, then $X$ and $Y$ are independent.
In the ref that I have the opposite is affirmed. If $X$ and $Y$ are independent we have that:
$E[f(X)]E[g(Y)]-E[f(... | Zero correlation of all functions of random variables implying independence
If $\text{Corr}\left(f(X),g(Y)\right)=0$ for all possible functions $f(\cdot)$ and $g(\cdot)$, then $X$ and $Y$ are independent.
In the ref that I have the opposite is affirmed. If $X$ and $Y$ are in |
11,942 | Zero correlation of all functions of random variables implying independence | Two variables being dependent means that there is some value(s) of one variable that make some value(s) of the other variable more likely (the general statement is that it changes the probability, but WLOG we can assume that it increases the probability). And if that is the cases, then clearly there is positive correla... | Zero correlation of all functions of random variables implying independence | Two variables being dependent means that there is some value(s) of one variable that make some value(s) of the other variable more likely (the general statement is that it changes the probability, but | Zero correlation of all functions of random variables implying independence
Two variables being dependent means that there is some value(s) of one variable that make some value(s) of the other variable more likely (the general statement is that it changes the probability, but WLOG we can assume that it increases the pr... | Zero correlation of all functions of random variables implying independence
Two variables being dependent means that there is some value(s) of one variable that make some value(s) of the other variable more likely (the general statement is that it changes the probability, but |
11,943 | Zero correlation of all functions of random variables implying independence | Correlation catches only the linear dependence between two variables.
A and B are dependent but uncorrelated if $A = B^2$ for example
Pure independence implies the stochastic independence, which is that the occurrence of one does not affect the occurrence of the other. Similarly, two random variables are independent if... | Zero correlation of all functions of random variables implying independence | Correlation catches only the linear dependence between two variables.
A and B are dependent but uncorrelated if $A = B^2$ for example
Pure independence implies the stochastic independence, which is th | Zero correlation of all functions of random variables implying independence
Correlation catches only the linear dependence between two variables.
A and B are dependent but uncorrelated if $A = B^2$ for example
Pure independence implies the stochastic independence, which is that the occurrence of one does not affect the... | Zero correlation of all functions of random variables implying independence
Correlation catches only the linear dependence between two variables.
A and B are dependent but uncorrelated if $A = B^2$ for example
Pure independence implies the stochastic independence, which is th |
11,944 | Log-linear regression vs. logistic regression | The name is a bit of a misnomer. Log-linear models were traditionally used for the analysis of data in a contingency table format. While "count data" need not necessarily follow a Poisson distribution, the log-linear model is actually just a Poisson regression model. Hence the "log" name (Poisson regression models cont... | Log-linear regression vs. logistic regression | The name is a bit of a misnomer. Log-linear models were traditionally used for the analysis of data in a contingency table format. While "count data" need not necessarily follow a Poisson distribution | Log-linear regression vs. logistic regression
The name is a bit of a misnomer. Log-linear models were traditionally used for the analysis of data in a contingency table format. While "count data" need not necessarily follow a Poisson distribution, the log-linear model is actually just a Poisson regression model. Hence ... | Log-linear regression vs. logistic regression
The name is a bit of a misnomer. Log-linear models were traditionally used for the analysis of data in a contingency table format. While "count data" need not necessarily follow a Poisson distribution |
11,945 | Log-linear regression vs. logistic regression | I don't think I would call either of them a "simple linear regression model". Although it is possible to use the log or the logit transformations as the link function for a number of different models, these are typically understood to refer to specific models. For example, "logistic regression" is understood to be a ... | Log-linear regression vs. logistic regression | I don't think I would call either of them a "simple linear regression model". Although it is possible to use the log or the logit transformations as the link function for a number of different models | Log-linear regression vs. logistic regression
I don't think I would call either of them a "simple linear regression model". Although it is possible to use the log or the logit transformations as the link function for a number of different models, these are typically understood to refer to specific models. For example... | Log-linear regression vs. logistic regression
I don't think I would call either of them a "simple linear regression model". Although it is possible to use the log or the logit transformations as the link function for a number of different models |
11,946 | Log-linear regression vs. logistic regression | To clarify, a "binary" logistic regression has a dependent variable with two outcomes. My understanding is that there is also the option of using a "multinomial" logistic regression if your dependent, outcome variable has more than 2 categories. See here. | Log-linear regression vs. logistic regression | To clarify, a "binary" logistic regression has a dependent variable with two outcomes. My understanding is that there is also the option of using a "multinomial" logistic regression if your dependent | Log-linear regression vs. logistic regression
To clarify, a "binary" logistic regression has a dependent variable with two outcomes. My understanding is that there is also the option of using a "multinomial" logistic regression if your dependent, outcome variable has more than 2 categories. See here. | Log-linear regression vs. logistic regression
To clarify, a "binary" logistic regression has a dependent variable with two outcomes. My understanding is that there is also the option of using a "multinomial" logistic regression if your dependent |
11,947 | What exactly is a hypothesis space in machine learning? | Lets say you have an unknown target function $f:X \rightarrow Y$ that you are trying to capture by learning. In order to capture the target function you have to come up with some hypotheses, or you may call it candidate models denoted by H $h_1,...,h_n$ where $h \in H$. Here, $H$ as the set of all candidate models is ... | What exactly is a hypothesis space in machine learning? | Lets say you have an unknown target function $f:X \rightarrow Y$ that you are trying to capture by learning. In order to capture the target function you have to come up with some hypotheses, or you ma | What exactly is a hypothesis space in machine learning?
Lets say you have an unknown target function $f:X \rightarrow Y$ that you are trying to capture by learning. In order to capture the target function you have to come up with some hypotheses, or you may call it candidate models denoted by H $h_1,...,h_n$ where $h \... | What exactly is a hypothesis space in machine learning?
Lets say you have an unknown target function $f:X \rightarrow Y$ that you are trying to capture by learning. In order to capture the target function you have to come up with some hypotheses, or you ma |
11,948 | What exactly is a hypothesis space in machine learning? | Suppose an example with four binary features and one binary output variable. Below is a set of observations:
x1 x2 x3 x4 | y
---------------
0 0 0 1 | 0
0 1 0 1 | 0
1 1 0 0 | 1
0 0 1 0 | 1
This set of observations can be used by a machine learning (ML) algorithm to learn a function f that is able to p... | What exactly is a hypothesis space in machine learning? | Suppose an example with four binary features and one binary output variable. Below is a set of observations:
x1 x2 x3 x4 | y
---------------
0 0 0 1 | 0
0 1 0 1 | 0
1 1 0 0 | 1
0 0 1 | What exactly is a hypothesis space in machine learning?
Suppose an example with four binary features and one binary output variable. Below is a set of observations:
x1 x2 x3 x4 | y
---------------
0 0 0 1 | 0
0 1 0 1 | 0
1 1 0 0 | 1
0 0 1 0 | 1
This set of observations can be used by a machine learnin... | What exactly is a hypothesis space in machine learning?
Suppose an example with four binary features and one binary output variable. Below is a set of observations:
x1 x2 x3 x4 | y
---------------
0 0 0 1 | 0
0 1 0 1 | 0
1 1 0 0 | 1
0 0 1 |
11,949 | What exactly is a hypothesis space in machine learning? | The hypothesis space is very relevant to the topic of the so-called Bias-Variance Tradeoff in maximum likelihood. That's if the number of parameters in the model(hypothesis function) is too small for the model to fit the data(indicating underfitting and
that the hypothesis space is too limited), the bias is high; whi... | What exactly is a hypothesis space in machine learning? | The hypothesis space is very relevant to the topic of the so-called Bias-Variance Tradeoff in maximum likelihood. That's if the number of parameters in the model(hypothesis function) is too small for | What exactly is a hypothesis space in machine learning?
The hypothesis space is very relevant to the topic of the so-called Bias-Variance Tradeoff in maximum likelihood. That's if the number of parameters in the model(hypothesis function) is too small for the model to fit the data(indicating underfitting and
that the... | What exactly is a hypothesis space in machine learning?
The hypothesis space is very relevant to the topic of the so-called Bias-Variance Tradeoff in maximum likelihood. That's if the number of parameters in the model(hypothesis function) is too small for |
11,950 | Why does lrtest() not match anova(test="LRT") | The test statistics is derived differently. anova.lmlist uses the scaled difference of the residual sum of squares:
anova(base, full, test="LRT")
# Res.Df RSS Df Sum of Sq Pr(>Chi)
#1 995 330.29
#2 994 330.20 1 0.08786 0.6071
vals <- (sum(residuals(base)^2) - sum(residuals(full)^2)... | Why does lrtest() not match anova(test="LRT") | The test statistics is derived differently. anova.lmlist uses the scaled difference of the residual sum of squares:
anova(base, full, test="LRT")
# Res.Df RSS Df Sum of Sq Pr(>Chi)
#1 995 330.2 | Why does lrtest() not match anova(test="LRT")
The test statistics is derived differently. anova.lmlist uses the scaled difference of the residual sum of squares:
anova(base, full, test="LRT")
# Res.Df RSS Df Sum of Sq Pr(>Chi)
#1 995 330.29
#2 994 330.20 1 0.08786 0.6071
vals <- (s... | Why does lrtest() not match anova(test="LRT")
The test statistics is derived differently. anova.lmlist uses the scaled difference of the residual sum of squares:
anova(base, full, test="LRT")
# Res.Df RSS Df Sum of Sq Pr(>Chi)
#1 995 330.2 |
11,951 | Why does lrtest() not match anova(test="LRT") | As mentioned in the previous answer, the difference comes down to a difference in scaling, i.e., different estimators for the standard deviation of the errors. Sources for the difference are (1) scaling by $n-k$ (the unbiased OLS estimator) vs. scaling by $n$ (the biased ML estimator), and (2) using the estimator under... | Why does lrtest() not match anova(test="LRT") | As mentioned in the previous answer, the difference comes down to a difference in scaling, i.e., different estimators for the standard deviation of the errors. Sources for the difference are (1) scali | Why does lrtest() not match anova(test="LRT")
As mentioned in the previous answer, the difference comes down to a difference in scaling, i.e., different estimators for the standard deviation of the errors. Sources for the difference are (1) scaling by $n-k$ (the unbiased OLS estimator) vs. scaling by $n$ (the biased ML... | Why does lrtest() not match anova(test="LRT")
As mentioned in the previous answer, the difference comes down to a difference in scaling, i.e., different estimators for the standard deviation of the errors. Sources for the difference are (1) scali |
11,952 | Test model coefficient (regression slope) against some value | Here's a broader solution that will work with any package, or even if you only have the regression output (such as from a paper).
Take the coefficient and its standard error.
Compute $t=\frac{\hat{\beta}-\beta_{H_0}}{\text{s.e.}(\hat{\beta})}$. The d.f. for the $t$ are the same as they would be for a test with $H_0: \b... | Test model coefficient (regression slope) against some value | Here's a broader solution that will work with any package, or even if you only have the regression output (such as from a paper).
Take the coefficient and its standard error.
Compute $t=\frac{\hat{\be | Test model coefficient (regression slope) against some value
Here's a broader solution that will work with any package, or even if you only have the regression output (such as from a paper).
Take the coefficient and its standard error.
Compute $t=\frac{\hat{\beta}-\beta_{H_0}}{\text{s.e.}(\hat{\beta})}$. The d.f. for t... | Test model coefficient (regression slope) against some value
Here's a broader solution that will work with any package, or even if you only have the regression output (such as from a paper).
Take the coefficient and its standard error.
Compute $t=\frac{\hat{\be |
11,953 | Test model coefficient (regression slope) against some value | You can use either a simple t-test as proposed by Glen_b, or a more general Wald test.
The Wald test allows to test multiple hypotheses on multiple parameters. It is formulated as: $R\beta=q$ where R selects (a combination of) coefficients, and q indicates the value to be tested against, $\beta$ being the standard re... | Test model coefficient (regression slope) against some value | You can use either a simple t-test as proposed by Glen_b, or a more general Wald test.
The Wald test allows to test multiple hypotheses on multiple parameters. It is formulated as: $R\beta=q$ where R | Test model coefficient (regression slope) against some value
You can use either a simple t-test as proposed by Glen_b, or a more general Wald test.
The Wald test allows to test multiple hypotheses on multiple parameters. It is formulated as: $R\beta=q$ where R selects (a combination of) coefficients, and q indicates ... | Test model coefficient (regression slope) against some value
You can use either a simple t-test as proposed by Glen_b, or a more general Wald test.
The Wald test allows to test multiple hypotheses on multiple parameters. It is formulated as: $R\beta=q$ where R |
11,954 | Test model coefficient (regression slope) against some value | In the end, farly the easiest solution was to do the reparametrization:
gls(I(y - T*x) ~ x, ...) | Test model coefficient (regression slope) against some value | In the end, farly the easiest solution was to do the reparametrization:
gls(I(y - T*x) ~ x, ...) | Test model coefficient (regression slope) against some value
In the end, farly the easiest solution was to do the reparametrization:
gls(I(y - T*x) ~ x, ...) | Test model coefficient (regression slope) against some value
In the end, farly the easiest solution was to do the reparametrization:
gls(I(y - T*x) ~ x, ...) |
11,955 | Motivation of Expectation Maximization algorithm | Likelihood vs. log-likelihood
As has already been said, the $\log$ is introduced in maximum likelihood simply because it is generally easier to optimize sums than products. The reason we don't consider other monotonic functions is that the logarithm is the unique function with the property of turning products into sums... | Motivation of Expectation Maximization algorithm | Likelihood vs. log-likelihood
As has already been said, the $\log$ is introduced in maximum likelihood simply because it is generally easier to optimize sums than products. The reason we don't conside | Motivation of Expectation Maximization algorithm
Likelihood vs. log-likelihood
As has already been said, the $\log$ is introduced in maximum likelihood simply because it is generally easier to optimize sums than products. The reason we don't consider other monotonic functions is that the logarithm is the unique functio... | Motivation of Expectation Maximization algorithm
Likelihood vs. log-likelihood
As has already been said, the $\log$ is introduced in maximum likelihood simply because it is generally easier to optimize sums than products. The reason we don't conside |
11,956 | Motivation of Expectation Maximization algorithm | The EM algorithm has different interpretations and can arise in different forms in different applications.
It all starts with the likelihood function $p(x \vert \theta)$, or equivalently, the log-likelihood function $\log p(x \vert \theta)$ we would like to maximize. (We generally use logarithm as it simplifies the cal... | Motivation of Expectation Maximization algorithm | The EM algorithm has different interpretations and can arise in different forms in different applications.
It all starts with the likelihood function $p(x \vert \theta)$, or equivalently, the log-like | Motivation of Expectation Maximization algorithm
The EM algorithm has different interpretations and can arise in different forms in different applications.
It all starts with the likelihood function $p(x \vert \theta)$, or equivalently, the log-likelihood function $\log p(x \vert \theta)$ we would like to maximize. (We... | Motivation of Expectation Maximization algorithm
The EM algorithm has different interpretations and can arise in different forms in different applications.
It all starts with the likelihood function $p(x \vert \theta)$, or equivalently, the log-like |
11,957 | Motivation of Expectation Maximization algorithm | The paper that I found clarifying with respect to expectation-maximization is Bayesian K-Means as a "Maximization-Expectation" Algorithm (pdf) by Welling and Kurihara.
Suppose we have a probabilistic model $p(x,z,\theta)$ with $x$ observations, $z$ hidden random variables, and a total of $\theta$ parameters. We are gi... | Motivation of Expectation Maximization algorithm | The paper that I found clarifying with respect to expectation-maximization is Bayesian K-Means as a "Maximization-Expectation" Algorithm (pdf) by Welling and Kurihara.
Suppose we have a probabilistic | Motivation of Expectation Maximization algorithm
The paper that I found clarifying with respect to expectation-maximization is Bayesian K-Means as a "Maximization-Expectation" Algorithm (pdf) by Welling and Kurihara.
Suppose we have a probabilistic model $p(x,z,\theta)$ with $x$ observations, $z$ hidden random variabl... | Motivation of Expectation Maximization algorithm
The paper that I found clarifying with respect to expectation-maximization is Bayesian K-Means as a "Maximization-Expectation" Algorithm (pdf) by Welling and Kurihara.
Suppose we have a probabilistic |
11,958 | Motivation of Expectation Maximization algorithm | There is a useful optimisation technique underlying the EM algorithm. However, it's usually expressed in the language of probability theory so it's hard to see that at the core is a method that has nothing to do with probability and expectation.
Consider the problem of maximising $$g(x)=\sum_i\exp(f_i(x))$$ (or equiva... | Motivation of Expectation Maximization algorithm | There is a useful optimisation technique underlying the EM algorithm. However, it's usually expressed in the language of probability theory so it's hard to see that at the core is a method that has no | Motivation of Expectation Maximization algorithm
There is a useful optimisation technique underlying the EM algorithm. However, it's usually expressed in the language of probability theory so it's hard to see that at the core is a method that has nothing to do with probability and expectation.
Consider the problem of ... | Motivation of Expectation Maximization algorithm
There is a useful optimisation technique underlying the EM algorithm. However, it's usually expressed in the language of probability theory so it's hard to see that at the core is a method that has no |
11,959 | Motivation of Expectation Maximization algorithm | As you said, I will not go into technical details. There are quite a few very nice tutorials. One of my favourites are Andrew Ng's lecture notes. Take a look also at the references here.
EM is naturally motivated in mixture models and models with hidden factors in general. Take for example the case of Gaussian mixture... | Motivation of Expectation Maximization algorithm | As you said, I will not go into technical details. There are quite a few very nice tutorials. One of my favourites are Andrew Ng's lecture notes. Take a look also at the references here.
EM is natura | Motivation of Expectation Maximization algorithm
As you said, I will not go into technical details. There are quite a few very nice tutorials. One of my favourites are Andrew Ng's lecture notes. Take a look also at the references here.
EM is naturally motivated in mixture models and models with hidden factors in gener... | Motivation of Expectation Maximization algorithm
As you said, I will not go into technical details. There are quite a few very nice tutorials. One of my favourites are Andrew Ng's lecture notes. Take a look also at the references here.
EM is natura |
11,960 | What is this type of circular-link visualization called? | Take a look at Circos:
Circos is a software package for visualizing data and information. It visualizes data in a circular layout — this makes Circos ideal for exploring relationships between objects or positions.
The flowing data blog also had a post on this that you might find interesting:
Visual Representation of... | What is this type of circular-link visualization called? | Take a look at Circos:
Circos is a software package for visualizing data and information. It visualizes data in a circular layout — this makes Circos ideal for exploring relationships between objects | What is this type of circular-link visualization called?
Take a look at Circos:
Circos is a software package for visualizing data and information. It visualizes data in a circular layout — this makes Circos ideal for exploring relationships between objects or positions.
The flowing data blog also had a post on this t... | What is this type of circular-link visualization called?
Take a look at Circos:
Circos is a software package for visualizing data and information. It visualizes data in a circular layout — this makes Circos ideal for exploring relationships between objects |
11,961 | What is this type of circular-link visualization called? | I found that the dependency graph in Flare is also similar to what I want:
http://flare.prefuse.org/apps/dependency_graph | What is this type of circular-link visualization called? | I found that the dependency graph in Flare is also similar to what I want:
http://flare.prefuse.org/apps/dependency_graph | What is this type of circular-link visualization called?
I found that the dependency graph in Flare is also similar to what I want:
http://flare.prefuse.org/apps/dependency_graph | What is this type of circular-link visualization called?
I found that the dependency graph in Flare is also similar to what I want:
http://flare.prefuse.org/apps/dependency_graph |
11,962 | What is this type of circular-link visualization called? | It is called a Chord diagram.
Now that you know its name you can research for the tool that best suits you. I dont think it is nice to advertise tools. | What is this type of circular-link visualization called? | It is called a Chord diagram.
Now that you know its name you can research for the tool that best suits you. I dont think it is nice to advertise tools. | What is this type of circular-link visualization called?
It is called a Chord diagram.
Now that you know its name you can research for the tool that best suits you. I dont think it is nice to advertise tools. | What is this type of circular-link visualization called?
It is called a Chord diagram.
Now that you know its name you can research for the tool that best suits you. I dont think it is nice to advertise tools. |
11,963 | What is this type of circular-link visualization called? | I would just add:
As you point out, Flare has the dependency graph, which Aleks Jakulin argued was similar but better. This was based originally on the "Hierarchical Edge Bundles:
Visualization of Adjacency Relations in Hierarchical Data" (Holden 2006).
I personally prefer to use Protovis to Flare directly, and you ... | What is this type of circular-link visualization called? | I would just add:
As you point out, Flare has the dependency graph, which Aleks Jakulin argued was similar but better. This was based originally on the "Hierarchical Edge Bundles:
Visualization of Ad | What is this type of circular-link visualization called?
I would just add:
As you point out, Flare has the dependency graph, which Aleks Jakulin argued was similar but better. This was based originally on the "Hierarchical Edge Bundles:
Visualization of Adjacency Relations in Hierarchical Data" (Holden 2006).
I pers... | What is this type of circular-link visualization called?
I would just add:
As you point out, Flare has the dependency graph, which Aleks Jakulin argued was similar but better. This was based originally on the "Hierarchical Edge Bundles:
Visualization of Ad |
11,964 | What is this type of circular-link visualization called? | For the #Rstats crowd there are two other options.
circlize library (package, vignette):
This package aims to implement circos layout in R.
RCircos library (CRAN):
RCircos package provides a simple and flexible way to generate Circos
2D track plot images for genomic data visualization. | What is this type of circular-link visualization called? | For the #Rstats crowd there are two other options.
circlize library (package, vignette):
This package aims to implement circos layout in R.
RCircos library (CRAN):
RCircos package provides a simpl | What is this type of circular-link visualization called?
For the #Rstats crowd there are two other options.
circlize library (package, vignette):
This package aims to implement circos layout in R.
RCircos library (CRAN):
RCircos package provides a simple and flexible way to generate Circos
2D track plot images fo... | What is this type of circular-link visualization called?
For the #Rstats crowd there are two other options.
circlize library (package, vignette):
This package aims to implement circos layout in R.
RCircos library (CRAN):
RCircos package provides a simpl |
11,965 | Loss function autoencoder vs variational-autoencoder or MSE-loss vs binary-cross-entropy-loss | I don't believe there's some kind of deep, meaningful rationale at play here - it's a showcase example running on MNIST, it's pretty error-tolerant.
Optimizing for MSE means your generated output intensities are symmetrically close to the input intensities. A higher-than-training intensity is penalized by the same amo... | Loss function autoencoder vs variational-autoencoder or MSE-loss vs binary-cross-entropy-loss | I don't believe there's some kind of deep, meaningful rationale at play here - it's a showcase example running on MNIST, it's pretty error-tolerant.
Optimizing for MSE means your generated output int | Loss function autoencoder vs variational-autoencoder or MSE-loss vs binary-cross-entropy-loss
I don't believe there's some kind of deep, meaningful rationale at play here - it's a showcase example running on MNIST, it's pretty error-tolerant.
Optimizing for MSE means your generated output intensities are symmetrically... | Loss function autoencoder vs variational-autoencoder or MSE-loss vs binary-cross-entropy-loss
I don't believe there's some kind of deep, meaningful rationale at play here - it's a showcase example running on MNIST, it's pretty error-tolerant.
Optimizing for MSE means your generated output int |
11,966 | Loss function autoencoder vs variational-autoencoder or MSE-loss vs binary-cross-entropy-loss | This discussion suggests that binary cross entropy is used in VAE case mainly for better optimization behavior. Another reason it works well is that MNIST dataset roughly follows multivariate Bernoulli distribution - the pixel values are close to either zero or one and binarization does not change it much. For more in-... | Loss function autoencoder vs variational-autoencoder or MSE-loss vs binary-cross-entropy-loss | This discussion suggests that binary cross entropy is used in VAE case mainly for better optimization behavior. Another reason it works well is that MNIST dataset roughly follows multivariate Bernoull | Loss function autoencoder vs variational-autoencoder or MSE-loss vs binary-cross-entropy-loss
This discussion suggests that binary cross entropy is used in VAE case mainly for better optimization behavior. Another reason it works well is that MNIST dataset roughly follows multivariate Bernoulli distribution - the pixel... | Loss function autoencoder vs variational-autoencoder or MSE-loss vs binary-cross-entropy-loss
This discussion suggests that binary cross entropy is used in VAE case mainly for better optimization behavior. Another reason it works well is that MNIST dataset roughly follows multivariate Bernoull |
11,967 | Loss function autoencoder vs variational-autoencoder or MSE-loss vs binary-cross-entropy-loss | It depends on how you assume the model for the likelihood. In other words, in variational autoencoders you seek to minimize the ELBO (empirical lower bound), which contains $KL(q||p)$ which is managed by the encoder and a second term known as the reconstruction error $E_{q}[log p(x|z)]$ managed by the decoder and requ... | Loss function autoencoder vs variational-autoencoder or MSE-loss vs binary-cross-entropy-loss | It depends on how you assume the model for the likelihood. In other words, in variational autoencoders you seek to minimize the ELBO (empirical lower bound), which contains $KL(q||p)$ which is manage | Loss function autoencoder vs variational-autoencoder or MSE-loss vs binary-cross-entropy-loss
It depends on how you assume the model for the likelihood. In other words, in variational autoencoders you seek to minimize the ELBO (empirical lower bound), which contains $KL(q||p)$ which is managed by the encoder and a sec... | Loss function autoencoder vs variational-autoencoder or MSE-loss vs binary-cross-entropy-loss
It depends on how you assume the model for the likelihood. In other words, in variational autoencoders you seek to minimize the ELBO (empirical lower bound), which contains $KL(q||p)$ which is manage |
11,968 | Zero inflated distributions, what are they really? | fit a logistic regression first calculate the probability of zeroes, and then I could remove all the zeroes, and then fit a regular regression using my choice of distribution (poisson e.g.)
You're absolutely right. This is one way to fit a zero-inflated model (or as Achim Zeileis points out in the comments, this is st... | Zero inflated distributions, what are they really? | fit a logistic regression first calculate the probability of zeroes, and then I could remove all the zeroes, and then fit a regular regression using my choice of distribution (poisson e.g.)
You're ab | Zero inflated distributions, what are they really?
fit a logistic regression first calculate the probability of zeroes, and then I could remove all the zeroes, and then fit a regular regression using my choice of distribution (poisson e.g.)
You're absolutely right. This is one way to fit a zero-inflated model (or as A... | Zero inflated distributions, what are they really?
fit a logistic regression first calculate the probability of zeroes, and then I could remove all the zeroes, and then fit a regular regression using my choice of distribution (poisson e.g.)
You're ab |
11,969 | Zero inflated distributions, what are they really? | The basic idea you describe is a valid approach and it is often called a hurdle model (or two-part model) rather than a zero-inflated model.
However, it is crucial that the model for the non-zero data accounts for having the zeros removed. If you fit a Poisson model to the data without zeros this will almost certainly... | Zero inflated distributions, what are they really? | The basic idea you describe is a valid approach and it is often called a hurdle model (or two-part model) rather than a zero-inflated model.
However, it is crucial that the model for the non-zero dat | Zero inflated distributions, what are they really?
The basic idea you describe is a valid approach and it is often called a hurdle model (or two-part model) rather than a zero-inflated model.
However, it is crucial that the model for the non-zero data accounts for having the zeros removed. If you fit a Poisson model t... | Zero inflated distributions, what are they really?
The basic idea you describe is a valid approach and it is often called a hurdle model (or two-part model) rather than a zero-inflated model.
However, it is crucial that the model for the non-zero dat |
11,970 | Zero inflated distributions, what are they really? | What ssdecontrol said is very correct. But I'd like to add a few cents to the discussion.
I just watched the lecture on Zero Inflated models for count data by Richard McElreath on YouTube.
It makes sense to estimate p while controlling for the variables that are explaining the rate of the pure Poisson model, specially ... | Zero inflated distributions, what are they really? | What ssdecontrol said is very correct. But I'd like to add a few cents to the discussion.
I just watched the lecture on Zero Inflated models for count data by Richard McElreath on YouTube.
It makes se | Zero inflated distributions, what are they really?
What ssdecontrol said is very correct. But I'd like to add a few cents to the discussion.
I just watched the lecture on Zero Inflated models for count data by Richard McElreath on YouTube.
It makes sense to estimate p while controlling for the variables that are explai... | Zero inflated distributions, what are they really?
What ssdecontrol said is very correct. But I'd like to add a few cents to the discussion.
I just watched the lecture on Zero Inflated models for count data by Richard McElreath on YouTube.
It makes se |
11,971 | Can someone explain the importance of mean stationarity in time series? | In the case of time series forecasting, first of all, you need to understand that stationarity is important mostly in the context of ARMA and related models (AR: Auto-Regressive, MA: Moving Average). There are other types of time series forecasting models where stationarity is not a requirement, such as Holt-Winters or... | Can someone explain the importance of mean stationarity in time series? | In the case of time series forecasting, first of all, you need to understand that stationarity is important mostly in the context of ARMA and related models (AR: Auto-Regressive, MA: Moving Average). | Can someone explain the importance of mean stationarity in time series?
In the case of time series forecasting, first of all, you need to understand that stationarity is important mostly in the context of ARMA and related models (AR: Auto-Regressive, MA: Moving Average). There are other types of time series forecasting... | Can someone explain the importance of mean stationarity in time series?
In the case of time series forecasting, first of all, you need to understand that stationarity is important mostly in the context of ARMA and related models (AR: Auto-Regressive, MA: Moving Average). |
11,972 | Can someone explain the importance of mean stationarity in time series? | Stationarity is important because it is a mathematically strong assumption that's still much weaker than independence or finite-range dependence.
In some settings, it's important primarily for the mathematical tractability: it's easier to first find out what is true for stationary time series, then you can work on how ... | Can someone explain the importance of mean stationarity in time series? | Stationarity is important because it is a mathematically strong assumption that's still much weaker than independence or finite-range dependence.
In some settings, it's important primarily for the mat | Can someone explain the importance of mean stationarity in time series?
Stationarity is important because it is a mathematically strong assumption that's still much weaker than independence or finite-range dependence.
In some settings, it's important primarily for the mathematical tractability: it's easier to first fin... | Can someone explain the importance of mean stationarity in time series?
Stationarity is important because it is a mathematically strong assumption that's still much weaker than independence or finite-range dependence.
In some settings, it's important primarily for the mat |
11,973 | Can someone explain the importance of mean stationarity in time series? | First, your mean estimates and your standard errors will be badly biased if you are using any of the inferential tools which assume i.i.d, meaning your results risk being spurious. This can even be true if your data are weakly stationary, but your study period is shorter than the time it takes your series to reach equi... | Can someone explain the importance of mean stationarity in time series? | First, your mean estimates and your standard errors will be badly biased if you are using any of the inferential tools which assume i.i.d, meaning your results risk being spurious. This can even be tr | Can someone explain the importance of mean stationarity in time series?
First, your mean estimates and your standard errors will be badly biased if you are using any of the inferential tools which assume i.i.d, meaning your results risk being spurious. This can even be true if your data are weakly stationary, but your ... | Can someone explain the importance of mean stationarity in time series?
First, your mean estimates and your standard errors will be badly biased if you are using any of the inferential tools which assume i.i.d, meaning your results risk being spurious. This can even be tr |
11,974 | Can someone explain the importance of mean stationarity in time series? | Stationary means that the statistics that describe the random process are constant. ‘A memoryless Markov process’ is another way to say stationary as is saying that the probability generating function has no “feedback” terms, but if you recognized those words you might not be asking this question. FWIW “weakly stationa... | Can someone explain the importance of mean stationarity in time series? | Stationary means that the statistics that describe the random process are constant. ‘A memoryless Markov process’ is another way to say stationary as is saying that the probability generating function | Can someone explain the importance of mean stationarity in time series?
Stationary means that the statistics that describe the random process are constant. ‘A memoryless Markov process’ is another way to say stationary as is saying that the probability generating function has no “feedback” terms, but if you recognized ... | Can someone explain the importance of mean stationarity in time series?
Stationary means that the statistics that describe the random process are constant. ‘A memoryless Markov process’ is another way to say stationary as is saying that the probability generating function |
11,975 | Can someone explain the importance of mean stationarity in time series? | Short and sweet:
The parameters need to be constant. If the series is not stationary, then the parameters that you estimate are going to be functions of time themselves. But the model assumes that they are constants, as such, you will estimate the average parameter value over the time-period. See Skander's answer for w... | Can someone explain the importance of mean stationarity in time series? | Short and sweet:
The parameters need to be constant. If the series is not stationary, then the parameters that you estimate are going to be functions of time themselves. But the model assumes that the | Can someone explain the importance of mean stationarity in time series?
Short and sweet:
The parameters need to be constant. If the series is not stationary, then the parameters that you estimate are going to be functions of time themselves. But the model assumes that they are constants, as such, you will estimate the ... | Can someone explain the importance of mean stationarity in time series?
Short and sweet:
The parameters need to be constant. If the series is not stationary, then the parameters that you estimate are going to be functions of time themselves. But the model assumes that the |
11,976 | 2 Sample Kolmogorov-Smirnov vs. Anderson-Darling vs Cramer-von-Mises | To cut a long story short: Anderson-Darling test is assumed to be more powerful than Kolmogorov-Smirnov test.
Have a glance on this article comparing various tests (of normality, but the results hold for comparing two distribudions) Power Comparisons of Shapiro-Wilk, Kolmogorov-Smirnov, Lilliefors and Anderson-Darling... | 2 Sample Kolmogorov-Smirnov vs. Anderson-Darling vs Cramer-von-Mises | To cut a long story short: Anderson-Darling test is assumed to be more powerful than Kolmogorov-Smirnov test.
Have a glance on this article comparing various tests (of normality, but the results hold | 2 Sample Kolmogorov-Smirnov vs. Anderson-Darling vs Cramer-von-Mises
To cut a long story short: Anderson-Darling test is assumed to be more powerful than Kolmogorov-Smirnov test.
Have a glance on this article comparing various tests (of normality, but the results hold for comparing two distribudions) Power Comparisons... | 2 Sample Kolmogorov-Smirnov vs. Anderson-Darling vs Cramer-von-Mises
To cut a long story short: Anderson-Darling test is assumed to be more powerful than Kolmogorov-Smirnov test.
Have a glance on this article comparing various tests (of normality, but the results hold |
11,977 | 2 Sample Kolmogorov-Smirnov vs. Anderson-Darling vs Cramer-von-Mises | Each of the three tests have better power against different alternatives; but on the other hand, all three exhibit varying degrees of test bias in some situations.
Broadly speaking, the Anderson-Darling test has better power against fatter tails than specified and the Kolmogorov-Smirnov has more power against deviation... | 2 Sample Kolmogorov-Smirnov vs. Anderson-Darling vs Cramer-von-Mises | Each of the three tests have better power against different alternatives; but on the other hand, all three exhibit varying degrees of test bias in some situations.
Broadly speaking, the Anderson-Darli | 2 Sample Kolmogorov-Smirnov vs. Anderson-Darling vs Cramer-von-Mises
Each of the three tests have better power against different alternatives; but on the other hand, all three exhibit varying degrees of test bias in some situations.
Broadly speaking, the Anderson-Darling test has better power against fatter tails than ... | 2 Sample Kolmogorov-Smirnov vs. Anderson-Darling vs Cramer-von-Mises
Each of the three tests have better power against different alternatives; but on the other hand, all three exhibit varying degrees of test bias in some situations.
Broadly speaking, the Anderson-Darli |
11,978 | Why does Central Limit Theorem break down in my simulation? | Let's recall, precisely, what the central limit theorem says.
If $X_1, X_2, \cdots, X_k$ are independent and identically distributed random variables with (shared) mean $\mu$ and standard deviation $\sigma$, then $\frac{X_1 + X_2 + \cdots + X_k}{k\frac{\sigma}{\sqrt{k}}}$ converges in distribution to a standard normal... | Why does Central Limit Theorem break down in my simulation? | Let's recall, precisely, what the central limit theorem says.
If $X_1, X_2, \cdots, X_k$ are independent and identically distributed random variables with (shared) mean $\mu$ and standard deviation $ | Why does Central Limit Theorem break down in my simulation?
Let's recall, precisely, what the central limit theorem says.
If $X_1, X_2, \cdots, X_k$ are independent and identically distributed random variables with (shared) mean $\mu$ and standard deviation $\sigma$, then $\frac{X_1 + X_2 + \cdots + X_k}{k\frac{\sigma... | Why does Central Limit Theorem break down in my simulation?
Let's recall, precisely, what the central limit theorem says.
If $X_1, X_2, \cdots, X_k$ are independent and identically distributed random variables with (shared) mean $\mu$ and standard deviation $ |
11,979 | Why does Central Limit Theorem break down in my simulation? | In general, the size of each sample should be more than $5$ for the CLT approximation to be good. A rule of thumb is a sample of size $30$ or more. But, with the population of your first example, $5$ is OK.
pop <- c(4, 3, 5, 6, 5, 3, 4, 2, 5, 4, 3, 6, 5)
N <- 10^5
n <- 5
x <- matrix(sample(pop, size = N*n, replace = TR... | Why does Central Limit Theorem break down in my simulation? | In general, the size of each sample should be more than $5$ for the CLT approximation to be good. A rule of thumb is a sample of size $30$ or more. But, with the population of your first example, $5$ | Why does Central Limit Theorem break down in my simulation?
In general, the size of each sample should be more than $5$ for the CLT approximation to be good. A rule of thumb is a sample of size $30$ or more. But, with the population of your first example, $5$ is OK.
pop <- c(4, 3, 5, 6, 5, 3, 4, 2, 5, 4, 3, 6, 5)
N <- ... | Why does Central Limit Theorem break down in my simulation?
In general, the size of each sample should be more than $5$ for the CLT approximation to be good. A rule of thumb is a sample of size $30$ or more. But, with the population of your first example, $5$ |
11,980 | Why does Central Limit Theorem break down in my simulation? | I'd just like to explain, using complex cumulant-generating functions, why everyone keeps blaming this on skew.
Let's write the random variable you're sampling as $\mu+\sigma Z$, where $\mu$ is the mean and $\sigma$ the standard deviation so $Z$ has mean $0$ and variance $1$. The cumulant-generating function of $Z$ is ... | Why does Central Limit Theorem break down in my simulation? | I'd just like to explain, using complex cumulant-generating functions, why everyone keeps blaming this on skew.
Let's write the random variable you're sampling as $\mu+\sigma Z$, where $\mu$ is the me | Why does Central Limit Theorem break down in my simulation?
I'd just like to explain, using complex cumulant-generating functions, why everyone keeps blaming this on skew.
Let's write the random variable you're sampling as $\mu+\sigma Z$, where $\mu$ is the mean and $\sigma$ the standard deviation so $Z$ has mean $0$ a... | Why does Central Limit Theorem break down in my simulation?
I'd just like to explain, using complex cumulant-generating functions, why everyone keeps blaming this on skew.
Let's write the random variable you're sampling as $\mu+\sigma Z$, where $\mu$ is the me |
11,981 | Why does Central Limit Theorem break down in my simulation? | Short answer is, you don't have a big enough sample to make central limit theorem apply. | Why does Central Limit Theorem break down in my simulation? | Short answer is, you don't have a big enough sample to make central limit theorem apply. | Why does Central Limit Theorem break down in my simulation?
Short answer is, you don't have a big enough sample to make central limit theorem apply. | Why does Central Limit Theorem break down in my simulation?
Short answer is, you don't have a big enough sample to make central limit theorem apply. |
11,982 | Are heat maps "one of the least effective types of data visualization"? | There is no such thing as a "best" plot for this or for that.
How you plot your data depends on the message you want to convey. Commonly used plots have the advantage that users are more likely to be able to read them. Nevertheless, that does not mean that they are necessarily the best choice.
Regarding heat maps, I've... | Are heat maps "one of the least effective types of data visualization"? | There is no such thing as a "best" plot for this or for that.
How you plot your data depends on the message you want to convey. Commonly used plots have the advantage that users are more likely to be | Are heat maps "one of the least effective types of data visualization"?
There is no such thing as a "best" plot for this or for that.
How you plot your data depends on the message you want to convey. Commonly used plots have the advantage that users are more likely to be able to read them. Nevertheless, that does not m... | Are heat maps "one of the least effective types of data visualization"?
There is no such thing as a "best" plot for this or for that.
How you plot your data depends on the message you want to convey. Commonly used plots have the advantage that users are more likely to be |
11,983 | Are heat maps "one of the least effective types of data visualization"? | Someone can not say Heat Map is the least effective type of visualization. I would rather say it depends on your requirement. In some cases Heat maps are very useful. Let's say you have to make a report on crime in a country state-wise (or city-wise). Here you will have a huge data set which can have time dependencies.... | Are heat maps "one of the least effective types of data visualization"? | Someone can not say Heat Map is the least effective type of visualization. I would rather say it depends on your requirement. In some cases Heat maps are very useful. Let's say you have to make a repo | Are heat maps "one of the least effective types of data visualization"?
Someone can not say Heat Map is the least effective type of visualization. I would rather say it depends on your requirement. In some cases Heat maps are very useful. Let's say you have to make a report on crime in a country state-wise (or city-wis... | Are heat maps "one of the least effective types of data visualization"?
Someone can not say Heat Map is the least effective type of visualization. I would rather say it depends on your requirement. In some cases Heat maps are very useful. Let's say you have to make a repo |
11,984 | Are heat maps "one of the least effective types of data visualization"? | Critique 1 in the original question covers the biggest drawback - that it is difficult for someone reading the heat map to decode the quantitative information that is conveyed. Consider an xy-scatter plot or dot plot, where the underlying quantity is directly related to the distance on the chart - very straightforward ... | Are heat maps "one of the least effective types of data visualization"? | Critique 1 in the original question covers the biggest drawback - that it is difficult for someone reading the heat map to decode the quantitative information that is conveyed. Consider an xy-scatter | Are heat maps "one of the least effective types of data visualization"?
Critique 1 in the original question covers the biggest drawback - that it is difficult for someone reading the heat map to decode the quantitative information that is conveyed. Consider an xy-scatter plot or dot plot, where the underlying quantity ... | Are heat maps "one of the least effective types of data visualization"?
Critique 1 in the original question covers the biggest drawback - that it is difficult for someone reading the heat map to decode the quantitative information that is conveyed. Consider an xy-scatter |
11,985 | Are heat maps "one of the least effective types of data visualization"? | As aforementioned by others, it is really improper to say that heat maps are always ineffective. Actually, they are quite effective in many instances.
For example, if you want to visualize 4D data, it is simple enough to do the first three dimensions in many plotting software. However, the whole concept of 4D is prett... | Are heat maps "one of the least effective types of data visualization"? | As aforementioned by others, it is really improper to say that heat maps are always ineffective. Actually, they are quite effective in many instances.
For example, if you want to visualize 4D data, i | Are heat maps "one of the least effective types of data visualization"?
As aforementioned by others, it is really improper to say that heat maps are always ineffective. Actually, they are quite effective in many instances.
For example, if you want to visualize 4D data, it is simple enough to do the first three dimensi... | Are heat maps "one of the least effective types of data visualization"?
As aforementioned by others, it is really improper to say that heat maps are always ineffective. Actually, they are quite effective in many instances.
For example, if you want to visualize 4D data, i |
11,986 | Are heat maps "one of the least effective types of data visualization"? | By nature, a heat map displays data with two continuous independent variables (or, not quite equivalently, one independent variable from a two-dimensional vector space), and one continuous dependent variable. For data of that type, a heat map is definitely one of the most effective types of data visualisation. Yes, it ... | Are heat maps "one of the least effective types of data visualization"? | By nature, a heat map displays data with two continuous independent variables (or, not quite equivalently, one independent variable from a two-dimensional vector space), and one continuous dependent v | Are heat maps "one of the least effective types of data visualization"?
By nature, a heat map displays data with two continuous independent variables (or, not quite equivalently, one independent variable from a two-dimensional vector space), and one continuous dependent variable. For data of that type, a heat map is de... | Are heat maps "one of the least effective types of data visualization"?
By nature, a heat map displays data with two continuous independent variables (or, not quite equivalently, one independent variable from a two-dimensional vector space), and one continuous dependent v |
11,987 | Are heat maps "one of the least effective types of data visualization"? | Heat maps are great at providing a simplistic view of multiple variables from a time series perspective- the data can be absolute changes over time or standardized using Z scores or other means to examine variables with different measurements intervals or relative changes of subgroups. It does provide a very visually... | Are heat maps "one of the least effective types of data visualization"? | Heat maps are great at providing a simplistic view of multiple variables from a time series perspective- the data can be absolute changes over time or standardized using Z scores or other means to e | Are heat maps "one of the least effective types of data visualization"?
Heat maps are great at providing a simplistic view of multiple variables from a time series perspective- the data can be absolute changes over time or standardized using Z scores or other means to examine variables with different measurements int... | Are heat maps "one of the least effective types of data visualization"?
Heat maps are great at providing a simplistic view of multiple variables from a time series perspective- the data can be absolute changes over time or standardized using Z scores or other means to e |
11,988 | Are heat maps "one of the least effective types of data visualization"? | Heatmaps are advantageous over scatterplots when there are too many data points to view on a scatterplot. This can be mitigated in a scatterplot using translucent data points but beyond a certain threshold it becomes better to summarize the data.
In this blog post a compelling example of scatterplots being hard to int... | Are heat maps "one of the least effective types of data visualization"? | Heatmaps are advantageous over scatterplots when there are too many data points to view on a scatterplot. This can be mitigated in a scatterplot using translucent data points but beyond a certain thre | Are heat maps "one of the least effective types of data visualization"?
Heatmaps are advantageous over scatterplots when there are too many data points to view on a scatterplot. This can be mitigated in a scatterplot using translucent data points but beyond a certain threshold it becomes better to summarize the data.
... | Are heat maps "one of the least effective types of data visualization"?
Heatmaps are advantageous over scatterplots when there are too many data points to view on a scatterplot. This can be mitigated in a scatterplot using translucent data points but beyond a certain thre |
11,989 | How do ensemble methods outperform all their constituents? | It's not guaranteed. As you say, the ensemble could be worse than the individual models. For example, taking the average of the true model and a bad model would give a fairly bad model.
The average of $k$ models is only going to be an improvement if the models are (somewhat) independent of one another. For example, in ... | How do ensemble methods outperform all their constituents? | It's not guaranteed. As you say, the ensemble could be worse than the individual models. For example, taking the average of the true model and a bad model would give a fairly bad model.
The average of | How do ensemble methods outperform all their constituents?
It's not guaranteed. As you say, the ensemble could be worse than the individual models. For example, taking the average of the true model and a bad model would give a fairly bad model.
The average of $k$ models is only going to be an improvement if the models ... | How do ensemble methods outperform all their constituents?
It's not guaranteed. As you say, the ensemble could be worse than the individual models. For example, taking the average of the true model and a bad model would give a fairly bad model.
The average of |
11,990 | How do ensemble methods outperform all their constituents? | In your example, your ensemble of two models could be worse than a single model itself. But your example is artificial, we generally build more than two in our ensemble.
There is no absolute guarantee a ensemble model performs better than an individual model, but if you build many of those, and your individual classif... | How do ensemble methods outperform all their constituents? | In your example, your ensemble of two models could be worse than a single model itself. But your example is artificial, we generally build more than two in our ensemble.
There is no absolute guarante | How do ensemble methods outperform all their constituents?
In your example, your ensemble of two models could be worse than a single model itself. But your example is artificial, we generally build more than two in our ensemble.
There is no absolute guarantee a ensemble model performs better than an individual model, ... | How do ensemble methods outperform all their constituents?
In your example, your ensemble of two models could be worse than a single model itself. But your example is artificial, we generally build more than two in our ensemble.
There is no absolute guarante |
11,991 | How do ensemble methods outperform all their constituents? | I just want to throw something that is seldom discussed in this context, and it should give you food for thought.
Ensemble also works with humans!
It has been observed that averaging human predictions gives better predictions than any individual prediction. This is known as the wisdom of the crowd.
Now, you could argue... | How do ensemble methods outperform all their constituents? | I just want to throw something that is seldom discussed in this context, and it should give you food for thought.
Ensemble also works with humans!
It has been observed that averaging human predictions | How do ensemble methods outperform all their constituents?
I just want to throw something that is seldom discussed in this context, and it should give you food for thought.
Ensemble also works with humans!
It has been observed that averaging human predictions gives better predictions than any individual prediction. Thi... | How do ensemble methods outperform all their constituents?
I just want to throw something that is seldom discussed in this context, and it should give you food for thought.
Ensemble also works with humans!
It has been observed that averaging human predictions |
11,992 | How do ensemble methods outperform all their constituents? | It is actually quite possible for single models to be better than ensembles.
Even if there are no points in your data where some of your models are overestimating and some are underestimating (in that case you might hope that average error would be negated), some of the most popular loss functions (like mean squared lo... | How do ensemble methods outperform all their constituents? | It is actually quite possible for single models to be better than ensembles.
Even if there are no points in your data where some of your models are overestimating and some are underestimating (in that | How do ensemble methods outperform all their constituents?
It is actually quite possible for single models to be better than ensembles.
Even if there are no points in your data where some of your models are overestimating and some are underestimating (in that case you might hope that average error would be negated), so... | How do ensemble methods outperform all their constituents?
It is actually quite possible for single models to be better than ensembles.
Even if there are no points in your data where some of your models are overestimating and some are underestimating (in that |
11,993 | How do ensemble methods outperform all their constituents? | Yes, it might be the case but the idea for ensembling is to train simpler models to avoid over fitting while capturing different characteristics of data from different ensembles. Of course there is no guarantee of an ensemble model to outperform a single model while trained with same training data.
The outperformance ... | How do ensemble methods outperform all their constituents? | Yes, it might be the case but the idea for ensembling is to train simpler models to avoid over fitting while capturing different characteristics of data from different ensembles. Of course there is no | How do ensemble methods outperform all their constituents?
Yes, it might be the case but the idea for ensembling is to train simpler models to avoid over fitting while capturing different characteristics of data from different ensembles. Of course there is no guarantee of an ensemble model to outperform a single model ... | How do ensemble methods outperform all their constituents?
Yes, it might be the case but the idea for ensembling is to train simpler models to avoid over fitting while capturing different characteristics of data from different ensembles. Of course there is no |
11,994 | How do I know my k-means clustering algorithm is suffering from the curse of dimensionality? | It helps to think about what The Curse of Dimensionality is. There are several very good threads on CV that are worth reading. Here is a place to start: Explain “Curse of dimensionality” to a child.
I note that you are interested in how this applies to $k$-means clustering. It is worth being aware that $k$-means ... | How do I know my k-means clustering algorithm is suffering from the curse of dimensionality? | It helps to think about what The Curse of Dimensionality is. There are several very good threads on CV that are worth reading. Here is a place to start: Explain “Curse of dimensionality” to a child | How do I know my k-means clustering algorithm is suffering from the curse of dimensionality?
It helps to think about what The Curse of Dimensionality is. There are several very good threads on CV that are worth reading. Here is a place to start: Explain “Curse of dimensionality” to a child.
I note that you are int... | How do I know my k-means clustering algorithm is suffering from the curse of dimensionality?
It helps to think about what The Curse of Dimensionality is. There are several very good threads on CV that are worth reading. Here is a place to start: Explain “Curse of dimensionality” to a child |
11,995 | How do I know my k-means clustering algorithm is suffering from the curse of dimensionality? | My answer is not limit to K means, but check if we have curse of dimensionality for any distance based methods. K-means is based on a distance measure (for example, Euclidean distance)
Before run the algorithm, we can check the distance metric distribution, i.e., all distance metrics for all pairs in of data. If you ha... | How do I know my k-means clustering algorithm is suffering from the curse of dimensionality? | My answer is not limit to K means, but check if we have curse of dimensionality for any distance based methods. K-means is based on a distance measure (for example, Euclidean distance)
Before run the | How do I know my k-means clustering algorithm is suffering from the curse of dimensionality?
My answer is not limit to K means, but check if we have curse of dimensionality for any distance based methods. K-means is based on a distance measure (for example, Euclidean distance)
Before run the algorithm, we can check the... | How do I know my k-means clustering algorithm is suffering from the curse of dimensionality?
My answer is not limit to K means, but check if we have curse of dimensionality for any distance based methods. K-means is based on a distance measure (for example, Euclidean distance)
Before run the |
11,996 | Sample size too large? [duplicate] | I always thought larger sample sizes were good.
Almost always, though there are situations where they don't help much. However, as sample sizes become quite large, the particular aspects of the problem that are of most concern change.
Then I read something somewhere about how when sample sizes are larger, it's easier... | Sample size too large? [duplicate] | I always thought larger sample sizes were good.
Almost always, though there are situations where they don't help much. However, as sample sizes become quite large, the particular aspects of the probl | Sample size too large? [duplicate]
I always thought larger sample sizes were good.
Almost always, though there are situations where they don't help much. However, as sample sizes become quite large, the particular aspects of the problem that are of most concern change.
Then I read something somewhere about how when s... | Sample size too large? [duplicate]
I always thought larger sample sizes were good.
Almost always, though there are situations where they don't help much. However, as sample sizes become quite large, the particular aspects of the probl |
11,997 | What are the practical uses of Neural ODEs? | TL;DR: For time series and density modeling, neural ODEs offer some benefits that we don't know how to get otherwise. For plain supervised learning, there are potential computational benefits, but for practical purposes they probably aren't worth using yet in that setting.
To answer your first question:
Is there some... | What are the practical uses of Neural ODEs? | TL;DR: For time series and density modeling, neural ODEs offer some benefits that we don't know how to get otherwise. For plain supervised learning, there are potential computational benefits, but fo | What are the practical uses of Neural ODEs?
TL;DR: For time series and density modeling, neural ODEs offer some benefits that we don't know how to get otherwise. For plain supervised learning, there are potential computational benefits, but for practical purposes they probably aren't worth using yet in that setting.
T... | What are the practical uses of Neural ODEs?
TL;DR: For time series and density modeling, neural ODEs offer some benefits that we don't know how to get otherwise. For plain supervised learning, there are potential computational benefits, but fo |
11,998 | Difference between regression analysis and curve fitting | I doubt that there is a clear and consistent distinction across statistically minded sciences and fields between regression and curve-fitting.
Regression without qualification implies linear regression and least-squares estimation. That doesn't rule out other or broader senses: indeed once you allow logit, Poisson, n... | Difference between regression analysis and curve fitting | I doubt that there is a clear and consistent distinction across statistically minded sciences and fields between regression and curve-fitting.
Regression without qualification implies linear regress | Difference between regression analysis and curve fitting
I doubt that there is a clear and consistent distinction across statistically minded sciences and fields between regression and curve-fitting.
Regression without qualification implies linear regression and least-squares estimation. That doesn't rule out other o... | Difference between regression analysis and curve fitting
I doubt that there is a clear and consistent distinction across statistically minded sciences and fields between regression and curve-fitting.
Regression without qualification implies linear regress |
11,999 | Difference between regression analysis and curve fitting | In addition to @NickCox's excellent answer (+1), I wanted to share my subjective impression on this somewhat fuzzy terminology topic. I think that a rather subtle difference between the two terms lies in the following. On one hand, regression often, if not always, implies an analytical solution (reference to regressors... | Difference between regression analysis and curve fitting | In addition to @NickCox's excellent answer (+1), I wanted to share my subjective impression on this somewhat fuzzy terminology topic. I think that a rather subtle difference between the two terms lies | Difference between regression analysis and curve fitting
In addition to @NickCox's excellent answer (+1), I wanted to share my subjective impression on this somewhat fuzzy terminology topic. I think that a rather subtle difference between the two terms lies in the following. On one hand, regression often, if not always... | Difference between regression analysis and curve fitting
In addition to @NickCox's excellent answer (+1), I wanted to share my subjective impression on this somewhat fuzzy terminology topic. I think that a rather subtle difference between the two terms lies |
12,000 | Difference between regression analysis and curve fitting | As there already seems to be an adequate array of explanations of Regression Analysis vs Curve Fitting, I’ll leave that alone. However, there is an additional question buried in the OP’s original question. There’s very little ‘given data’, but he asked if someone could suggest a correlation formula, so I’ll add my 2 ... | Difference between regression analysis and curve fitting | As there already seems to be an adequate array of explanations of Regression Analysis vs Curve Fitting, I’ll leave that alone. However, there is an additional question buried in the OP’s original que | Difference between regression analysis and curve fitting
As there already seems to be an adequate array of explanations of Regression Analysis vs Curve Fitting, I’ll leave that alone. However, there is an additional question buried in the OP’s original question. There’s very little ‘given data’, but he asked if someo... | Difference between regression analysis and curve fitting
As there already seems to be an adequate array of explanations of Regression Analysis vs Curve Fitting, I’ll leave that alone. However, there is an additional question buried in the OP’s original que |
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