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 |
|---|---|---|---|---|---|---|
7,301 | Variable importance from SVM | If you use l-1 penalty on the weight vector, it does automatic feature selection as the weights corresponding to irrelevant attributes are automatically set to zero. See this paper. The (absolute) magnitude of each non-zero weights can give an idea about the importance of the corresponding attribute.
Also look at this ... | Variable importance from SVM | If you use l-1 penalty on the weight vector, it does automatic feature selection as the weights corresponding to irrelevant attributes are automatically set to zero. See this paper. The (absolute) mag | Variable importance from SVM
If you use l-1 penalty on the weight vector, it does automatic feature selection as the weights corresponding to irrelevant attributes are automatically set to zero. See this paper. The (absolute) magnitude of each non-zero weights can give an idea about the importance of the corresponding ... | Variable importance from SVM
If you use l-1 penalty on the weight vector, it does automatic feature selection as the weights corresponding to irrelevant attributes are automatically set to zero. See this paper. The (absolute) mag |
7,302 | Variable importance from SVM | Isabelle Guyon, André Elisseeff, "An Introduction to Variable and Feature Selection", JMLR, 3(Mar):1157-1182, 2003. http://jmlr.csail.mit.edu/papers/v3/guyon03a.html
is well worth reading, it will give a good overview of approaches and issues. The one thing I would add is that feature selection doesn't necessarily imp... | Variable importance from SVM | Isabelle Guyon, André Elisseeff, "An Introduction to Variable and Feature Selection", JMLR, 3(Mar):1157-1182, 2003. http://jmlr.csail.mit.edu/papers/v3/guyon03a.html
is well worth reading, it will giv | Variable importance from SVM
Isabelle Guyon, André Elisseeff, "An Introduction to Variable and Feature Selection", JMLR, 3(Mar):1157-1182, 2003. http://jmlr.csail.mit.edu/papers/v3/guyon03a.html
is well worth reading, it will give a good overview of approaches and issues. The one thing I would add is that feature sele... | Variable importance from SVM
Isabelle Guyon, André Elisseeff, "An Introduction to Variable and Feature Selection", JMLR, 3(Mar):1157-1182, 2003. http://jmlr.csail.mit.edu/papers/v3/guyon03a.html
is well worth reading, it will giv |
7,303 | Variable importance from SVM | If you use R, the variable importance can be calculated with Importance method in rminer package. This is my sample code:
library(rminer)
M <- fit(y~., data=train, model="svm", kpar=list(sigma=0.10), C=2)
svm.imp <- Importance(M, data=train)
In detail, refer to the following link https://cran.r-project.org/web/package... | Variable importance from SVM | If you use R, the variable importance can be calculated with Importance method in rminer package. This is my sample code:
library(rminer)
M <- fit(y~., data=train, model="svm", kpar=list(sigma=0.10), | Variable importance from SVM
If you use R, the variable importance can be calculated with Importance method in rminer package. This is my sample code:
library(rminer)
M <- fit(y~., data=train, model="svm", kpar=list(sigma=0.10), C=2)
svm.imp <- Importance(M, data=train)
In detail, refer to the following link https://c... | Variable importance from SVM
If you use R, the variable importance can be calculated with Importance method in rminer package. This is my sample code:
library(rminer)
M <- fit(y~., data=train, model="svm", kpar=list(sigma=0.10), |
7,304 | Are the digits of $\pi$ statistically random? | The US National Institute of Standard has put together a battery of tests that a (pseudo-)random number generator must pass to be considered adequate, see http://csrc.nist.gov/groups/ST/toolkit/rng/stats_tests.html. There are also tests known as the Diehard suite of tests, which overlap somewhat with NIST tests. Develo... | Are the digits of $\pi$ statistically random? | The US National Institute of Standard has put together a battery of tests that a (pseudo-)random number generator must pass to be considered adequate, see http://csrc.nist.gov/groups/ST/toolkit/rng/st | Are the digits of $\pi$ statistically random?
The US National Institute of Standard has put together a battery of tests that a (pseudo-)random number generator must pass to be considered adequate, see http://csrc.nist.gov/groups/ST/toolkit/rng/stats_tests.html. There are also tests known as the Diehard suite of tests, ... | Are the digits of $\pi$ statistically random?
The US National Institute of Standard has put together a battery of tests that a (pseudo-)random number generator must pass to be considered adequate, see http://csrc.nist.gov/groups/ST/toolkit/rng/st |
7,305 | Are the digits of $\pi$ statistically random? | Answering just the first of your questions: "What tests would you apply to determine if this [sequence] is truly random?"
How about treating it as a time-series, and checking for auto-correlations? Here is some R code. First some test data (first 1000 digits):
digits_string="14159265358979323846264338327950288419716939... | Are the digits of $\pi$ statistically random? | Answering just the first of your questions: "What tests would you apply to determine if this [sequence] is truly random?"
How about treating it as a time-series, and checking for auto-correlations? He | Are the digits of $\pi$ statistically random?
Answering just the first of your questions: "What tests would you apply to determine if this [sequence] is truly random?"
How about treating it as a time-series, and checking for auto-correlations? Here is some R code. First some test data (first 1000 digits):
digits_string... | Are the digits of $\pi$ statistically random?
Answering just the first of your questions: "What tests would you apply to determine if this [sequence] is truly random?"
How about treating it as a time-series, and checking for auto-correlations? He |
7,306 | Are the digits of $\pi$ statistically random? | It's a strange question. Numbers aren't random.
As a time series of base 10 digits, $\pi$ is completely fixed.
If you are talking about randomly selecting an index for the time series, and picking that number, sure it's random. But so is the boring, rational number $0.1212121212\ldots$. In both cases, the "randomness" ... | Are the digits of $\pi$ statistically random? | It's a strange question. Numbers aren't random.
As a time series of base 10 digits, $\pi$ is completely fixed.
If you are talking about randomly selecting an index for the time series, and picking tha | Are the digits of $\pi$ statistically random?
It's a strange question. Numbers aren't random.
As a time series of base 10 digits, $\pi$ is completely fixed.
If you are talking about randomly selecting an index for the time series, and picking that number, sure it's random. But so is the boring, rational number $0.12121... | Are the digits of $\pi$ statistically random?
It's a strange question. Numbers aren't random.
As a time series of base 10 digits, $\pi$ is completely fixed.
If you are talking about randomly selecting an index for the time series, and picking tha |
7,307 | When is t-SNE misleading? | T-Sne is a reduction technique that maintains the small scale structure (i.e. what is particularly close to what) of the space, which makes it very good at visualizing data separability. This means that T-Sne is particularly useful for early visualization geared at understanding the degree of data separability. Other t... | When is t-SNE misleading? | T-Sne is a reduction technique that maintains the small scale structure (i.e. what is particularly close to what) of the space, which makes it very good at visualizing data separability. This means th | When is t-SNE misleading?
T-Sne is a reduction technique that maintains the small scale structure (i.e. what is particularly close to what) of the space, which makes it very good at visualizing data separability. This means that T-Sne is particularly useful for early visualization geared at understanding the degree of ... | When is t-SNE misleading?
T-Sne is a reduction technique that maintains the small scale structure (i.e. what is particularly close to what) of the space, which makes it very good at visualizing data separability. This means th |
7,308 | When is t-SNE misleading? | Out of the box, tSNE has a few hyperparameters, the main one being perplexity. Remember that heuristically, perplexity defines a notion of similarity for tSNE and a universal perplexity is used for all data-points. You could try generating a labelled dataset where each cluster has wildly different perplexity. This can ... | When is t-SNE misleading? | Out of the box, tSNE has a few hyperparameters, the main one being perplexity. Remember that heuristically, perplexity defines a notion of similarity for tSNE and a universal perplexity is used for al | When is t-SNE misleading?
Out of the box, tSNE has a few hyperparameters, the main one being perplexity. Remember that heuristically, perplexity defines a notion of similarity for tSNE and a universal perplexity is used for all data-points. You could try generating a labelled dataset where each cluster has wildly diffe... | When is t-SNE misleading?
Out of the box, tSNE has a few hyperparameters, the main one being perplexity. Remember that heuristically, perplexity defines a notion of similarity for tSNE and a universal perplexity is used for al |
7,309 | Cloud computing platforms for machine learning [closed] | I've not used these firms, but these are just some of the options. However, setting up on EC2 is very simple. At least after you've numbed your head by banging it against the wall hard enough and often enough. It also increases your pain threshold. Kids these days have it so much easier. When I was getting started,... | Cloud computing platforms for machine learning [closed] | I've not used these firms, but these are just some of the options. However, setting up on EC2 is very simple. At least after you've numbed your head by banging it against the wall hard enough and of | Cloud computing platforms for machine learning [closed]
I've not used these firms, but these are just some of the options. However, setting up on EC2 is very simple. At least after you've numbed your head by banging it against the wall hard enough and often enough. It also increases your pain threshold. Kids these d... | Cloud computing platforms for machine learning [closed]
I've not used these firms, but these are just some of the options. However, setting up on EC2 is very simple. At least after you've numbed your head by banging it against the wall hard enough and of |
7,310 | Cloud computing platforms for machine learning [closed] | There's also PiCloud for running Python code in parallel on EC2.
From their product page:
PiCloud is a cloud-computing platform that integrates into the Python
Programming Language. It enables you to leverage the computing power
of Amazon Web Services without having to manage, maintain, or
configure virtual serv... | Cloud computing platforms for machine learning [closed] | There's also PiCloud for running Python code in parallel on EC2.
From their product page:
PiCloud is a cloud-computing platform that integrates into the Python
Programming Language. It enables you | Cloud computing platforms for machine learning [closed]
There's also PiCloud for running Python code in parallel on EC2.
From their product page:
PiCloud is a cloud-computing platform that integrates into the Python
Programming Language. It enables you to leverage the computing power
of Amazon Web Services without... | Cloud computing platforms for machine learning [closed]
There's also PiCloud for running Python code in parallel on EC2.
From their product page:
PiCloud is a cloud-computing platform that integrates into the Python
Programming Language. It enables you |
7,311 | Cloud computing platforms for machine learning [closed] | Did you try CloudStat before? Different from other clouds, CloudStat is meant only for R Language users. There is no more setup. you can just login and use up to 7.5 Gb RAM for free.
However, with free account, your analysis will be viewed and used by public.
The option is pay $ 5 per month to make your analysis priv... | Cloud computing platforms for machine learning [closed] | Did you try CloudStat before? Different from other clouds, CloudStat is meant only for R Language users. There is no more setup. you can just login and use up to 7.5 Gb RAM for free.
However, with fr | Cloud computing platforms for machine learning [closed]
Did you try CloudStat before? Different from other clouds, CloudStat is meant only for R Language users. There is no more setup. you can just login and use up to 7.5 Gb RAM for free.
However, with free account, your analysis will be viewed and used by public.
Th... | Cloud computing platforms for machine learning [closed]
Did you try CloudStat before? Different from other clouds, CloudStat is meant only for R Language users. There is no more setup. you can just login and use up to 7.5 Gb RAM for free.
However, with fr |
7,312 | Cloud computing platforms for machine learning [closed] | One cloud computing platform that I can recommend are Backbone who provide a secure productivity enhancing cloud computing platform. | Cloud computing platforms for machine learning [closed] | One cloud computing platform that I can recommend are Backbone who provide a secure productivity enhancing cloud computing platform. | Cloud computing platforms for machine learning [closed]
One cloud computing platform that I can recommend are Backbone who provide a secure productivity enhancing cloud computing platform. | Cloud computing platforms for machine learning [closed]
One cloud computing platform that I can recommend are Backbone who provide a secure productivity enhancing cloud computing platform. |
7,313 | Satterthwaite vs. Kenward-Roger approximations for the degrees of freedom in mixed models | I'm also interested in figuring out what the difference might be. The best I can offer you, for now, is that this blog post suggests that the Kenward-Roger approximation is slightly, but probably not significantly, more conservative than the Satterthwaite approximation. The author also notes that they are both more con... | Satterthwaite vs. Kenward-Roger approximations for the degrees of freedom in mixed models | I'm also interested in figuring out what the difference might be. The best I can offer you, for now, is that this blog post suggests that the Kenward-Roger approximation is slightly, but probably not | Satterthwaite vs. Kenward-Roger approximations for the degrees of freedom in mixed models
I'm also interested in figuring out what the difference might be. The best I can offer you, for now, is that this blog post suggests that the Kenward-Roger approximation is slightly, but probably not significantly, more conservati... | Satterthwaite vs. Kenward-Roger approximations for the degrees of freedom in mixed models
I'm also interested in figuring out what the difference might be. The best I can offer you, for now, is that this blog post suggests that the Kenward-Roger approximation is slightly, but probably not |
7,314 | Satterthwaite vs. Kenward-Roger approximations for the degrees of freedom in mixed models | Another difference between the two methods is described in Luke (2017):
Both the Kenward-Roger (Kenward & Roger, 1997) and Satterthwaite (1941) approaches are used to estimate denominator degrees of freedom for F statistics or degrees of freedom for t statistics. SAS PROC MIXED uses the Satterthwaite approximation (S... | Satterthwaite vs. Kenward-Roger approximations for the degrees of freedom in mixed models | Another difference between the two methods is described in Luke (2017):
Both the Kenward-Roger (Kenward & Roger, 1997) and Satterthwaite (1941) approaches are used to estimate denominator degrees of | Satterthwaite vs. Kenward-Roger approximations for the degrees of freedom in mixed models
Another difference between the two methods is described in Luke (2017):
Both the Kenward-Roger (Kenward & Roger, 1997) and Satterthwaite (1941) approaches are used to estimate denominator degrees of freedom for F statistics or d... | Satterthwaite vs. Kenward-Roger approximations for the degrees of freedom in mixed models
Another difference between the two methods is described in Luke (2017):
Both the Kenward-Roger (Kenward & Roger, 1997) and Satterthwaite (1941) approaches are used to estimate denominator degrees of |
7,315 | Satterthwaite vs. Kenward-Roger approximations for the degrees of freedom in mixed models | "This latest result uses the Satterthwaite method, which is implemented in the lmerTest package. Note that, with this method, not only are the degrees of freedom slightly different, but so are the standard errors. That is because the Kenward-Roger method also entails making a bias adjustment to the covariance matrix of... | Satterthwaite vs. Kenward-Roger approximations for the degrees of freedom in mixed models | "This latest result uses the Satterthwaite method, which is implemented in the lmerTest package. Note that, with this method, not only are the degrees of freedom slightly different, but so are the sta | Satterthwaite vs. Kenward-Roger approximations for the degrees of freedom in mixed models
"This latest result uses the Satterthwaite method, which is implemented in the lmerTest package. Note that, with this method, not only are the degrees of freedom slightly different, but so are the standard errors. That is because ... | Satterthwaite vs. Kenward-Roger approximations for the degrees of freedom in mixed models
"This latest result uses the Satterthwaite method, which is implemented in the lmerTest package. Note that, with this method, not only are the degrees of freedom slightly different, but so are the sta |
7,316 | Free data set for very high dimensional classification [closed] | Dorothea
n=1950
p=100000 (0.1M, half is artificially added noise)
k=2 (~10x unbalanced)
From NIPS2003. | Free data set for very high dimensional classification [closed] | Dorothea
n=1950
p=100000 (0.1M, half is artificially added noise)
k=2 (~10x unbalanced)
From NIPS2003. | Free data set for very high dimensional classification [closed]
Dorothea
n=1950
p=100000 (0.1M, half is artificially added noise)
k=2 (~10x unbalanced)
From NIPS2003. | Free data set for very high dimensional classification [closed]
Dorothea
n=1950
p=100000 (0.1M, half is artificially added noise)
k=2 (~10x unbalanced)
From NIPS2003. |
7,317 | Free data set for very high dimensional classification [closed] | Gisette
n=13500
p=5000 (half is artificially added noise)
k=2 (balanced)
From NIPS2003. | Free data set for very high dimensional classification [closed] | Gisette
n=13500
p=5000 (half is artificially added noise)
k=2 (balanced)
From NIPS2003. | Free data set for very high dimensional classification [closed]
Gisette
n=13500
p=5000 (half is artificially added noise)
k=2 (balanced)
From NIPS2003. | Free data set for very high dimensional classification [closed]
Gisette
n=13500
p=5000 (half is artificially added noise)
k=2 (balanced)
From NIPS2003. |
7,318 | Free data set for very high dimensional classification [closed] | Dexter
n=2600
p=20000 (10k+53 is artificial noise)
k=2 (balanced)
From NIPS2003. | Free data set for very high dimensional classification [closed] | Dexter
n=2600
p=20000 (10k+53 is artificial noise)
k=2 (balanced)
From NIPS2003. | Free data set for very high dimensional classification [closed]
Dexter
n=2600
p=20000 (10k+53 is artificial noise)
k=2 (balanced)
From NIPS2003. | Free data set for very high dimensional classification [closed]
Dexter
n=2600
p=20000 (10k+53 is artificial noise)
k=2 (balanced)
From NIPS2003. |
7,319 | Free data set for very high dimensional classification [closed] | Arcene
n=900
p=10000 (3k is artificially added noise)
k=2 (~balanced)
From NIPS2003. | Free data set for very high dimensional classification [closed] | Arcene
n=900
p=10000 (3k is artificially added noise)
k=2 (~balanced)
From NIPS2003. | Free data set for very high dimensional classification [closed]
Arcene
n=900
p=10000 (3k is artificially added noise)
k=2 (~balanced)
From NIPS2003. | Free data set for very high dimensional classification [closed]
Arcene
n=900
p=10000 (3k is artificially added noise)
k=2 (~balanced)
From NIPS2003. |
7,320 | Free data set for very high dimensional classification [closed] | Prostate (gene expression array)
k=2
n=48+52
p=6033
Available via (among other) R package spls
name of the dataset: prostate
error rate = 3/102 (see here) also I think there are paper which show 1/102 error rate. I would say this is an easy test case. | Free data set for very high dimensional classification [closed] | Prostate (gene expression array)
k=2
n=48+52
p=6033
Available via (among other) R package spls
name of the dataset: prostate
error rate = 3/102 (see here) also I think there are paper which sho | Free data set for very high dimensional classification [closed]
Prostate (gene expression array)
k=2
n=48+52
p=6033
Available via (among other) R package spls
name of the dataset: prostate
error rate = 3/102 (see here) also I think there are paper which show 1/102 error rate. I would say this is an easy test cas... | Free data set for very high dimensional classification [closed]
Prostate (gene expression array)
k=2
n=48+52
p=6033
Available via (among other) R package spls
name of the dataset: prostate
error rate = 3/102 (see here) also I think there are paper which sho |
7,321 | Probability inequalities | Using the Chernoff bound you suggested for some $s\le 1/(2\sigma^2)$ that will be specified later,
\[
P[X>t] \le \exp(-st) \exp\Big(-(N/2) \log(1-\sigma^4s^2) \Big) \le \exp(-st + \sigma^4s^2 N)
\]
where the second inequality holds thanks to $-\log(1-x)\le 2x$ for any $x\in(0,1/2)$. Now take $t=\epsilon \sigma^2 N$ a... | Probability inequalities | Using the Chernoff bound you suggested for some $s\le 1/(2\sigma^2)$ that will be specified later,
\[
P[X>t] \le \exp(-st) \exp\Big(-(N/2) \log(1-\sigma^4s^2) \Big) \le \exp(-st + \sigma^4s^2 N)
\]
w | Probability inequalities
Using the Chernoff bound you suggested for some $s\le 1/(2\sigma^2)$ that will be specified later,
\[
P[X>t] \le \exp(-st) \exp\Big(-(N/2) \log(1-\sigma^4s^2) \Big) \le \exp(-st + \sigma^4s^2 N)
\]
where the second inequality holds thanks to $-\log(1-x)\le 2x$ for any $x\in(0,1/2)$. Now take ... | Probability inequalities
Using the Chernoff bound you suggested for some $s\le 1/(2\sigma^2)$ that will be specified later,
\[
P[X>t] \le \exp(-st) \exp\Big(-(N/2) \log(1-\sigma^4s^2) \Big) \le \exp(-st + \sigma^4s^2 N)
\]
w |
7,322 | Probability inequalities | The bound you obtain is of order $e^{-\epsilon}$ as $\epsilon \to \infty$. I don't think you can do much better for general $\epsilon$. From the Wikipedia page on Product Variables the distribution of $w_i v_i$ is $K_0(z)/\pi$ where $K_0$ is a modified Bessel function. From (10.25.3) in the DLMF function list, $K_0(t) ... | Probability inequalities | The bound you obtain is of order $e^{-\epsilon}$ as $\epsilon \to \infty$. I don't think you can do much better for general $\epsilon$. From the Wikipedia page on Product Variables the distribution of | Probability inequalities
The bound you obtain is of order $e^{-\epsilon}$ as $\epsilon \to \infty$. I don't think you can do much better for general $\epsilon$. From the Wikipedia page on Product Variables the distribution of $w_i v_i$ is $K_0(z)/\pi$ where $K_0$ is a modified Bessel function. From (10.25.3) in the DLM... | Probability inequalities
The bound you obtain is of order $e^{-\epsilon}$ as $\epsilon \to \infty$. I don't think you can do much better for general $\epsilon$. From the Wikipedia page on Product Variables the distribution of |
7,323 | Why are there two spellings of "heteroskedastic" or "heteroscedastic"? | Inside this small and vexed question even smaller questions are struggling to get out.
The most detailed discussion to date appears to be
Alfredo R. Paloyo. 2011. When did we begin to spell “heteros*edasticity” correctly? Ruhr Economic Papers 0300.
see here
(a reference I owe to @Andy here in Ten fold chat). I can'... | Why are there two spellings of "heteroskedastic" or "heteroscedastic"? | Inside this small and vexed question even smaller questions are struggling to get out.
The most detailed discussion to date appears to be
Alfredo R. Paloyo. 2011. When did we begin to spell “hetero | Why are there two spellings of "heteroskedastic" or "heteroscedastic"?
Inside this small and vexed question even smaller questions are struggling to get out.
The most detailed discussion to date appears to be
Alfredo R. Paloyo. 2011. When did we begin to spell “heteros*edasticity” correctly? Ruhr Economic Papers 030... | Why are there two spellings of "heteroskedastic" or "heteroscedastic"?
Inside this small and vexed question even smaller questions are struggling to get out.
The most detailed discussion to date appears to be
Alfredo R. Paloyo. 2011. When did we begin to spell “hetero |
7,324 | Why are there two spellings of "heteroskedastic" or "heteroscedastic"? | There is a tradition in English language to use special letters to indicate that a word is of Greek origin (and as all language "rules", it is not absolutely observed). Most of the times for example, when you see "ph" in an English word, it indicates that it has a Greek origin, as in, say, "photograph" which is the tra... | Why are there two spellings of "heteroskedastic" or "heteroscedastic"? | There is a tradition in English language to use special letters to indicate that a word is of Greek origin (and as all language "rules", it is not absolutely observed). Most of the times for example, | Why are there two spellings of "heteroskedastic" or "heteroscedastic"?
There is a tradition in English language to use special letters to indicate that a word is of Greek origin (and as all language "rules", it is not absolutely observed). Most of the times for example, when you see "ph" in an English word, it indicate... | Why are there two spellings of "heteroskedastic" or "heteroscedastic"?
There is a tradition in English language to use special letters to indicate that a word is of Greek origin (and as all language "rules", it is not absolutely observed). Most of the times for example, |
7,325 | Why are there two spellings of "heteroskedastic" or "heteroscedastic"? | In Polish it is "heteroskedastyczność", but sometimes "heteroscedastyczność" is used instead. For examples you can check the book by Andrzej Gałecki and Tomasz Burzykowski, who were born and educated in Poland. They use the "c" form in their book written in English. Notice, however, that the forms used by different aut... | Why are there two spellings of "heteroskedastic" or "heteroscedastic"? | In Polish it is "heteroskedastyczność", but sometimes "heteroscedastyczność" is used instead. For examples you can check the book by Andrzej Gałecki and Tomasz Burzykowski, who were born and educated | Why are there two spellings of "heteroskedastic" or "heteroscedastic"?
In Polish it is "heteroskedastyczność", but sometimes "heteroscedastyczność" is used instead. For examples you can check the book by Andrzej Gałecki and Tomasz Burzykowski, who were born and educated in Poland. They use the "c" form in their book wr... | Why are there two spellings of "heteroskedastic" or "heteroscedastic"?
In Polish it is "heteroskedastyczność", but sometimes "heteroscedastyczność" is used instead. For examples you can check the book by Andrzej Gałecki and Tomasz Burzykowski, who were born and educated |
7,326 | Why are there two spellings of "heteroskedastic" or "heteroscedastic"? | The missing explanation is that letter 'C' was always pronounced as the modern English 'K' in classical Latin, while K itself was actually a redundant letter. A Greek word with the letter Kappa borrowed into Latin, in Roman times, would have always been spelled with a C. Later, in Vulgar Latin and by extension in Frenc... | Why are there two spellings of "heteroskedastic" or "heteroscedastic"? | The missing explanation is that letter 'C' was always pronounced as the modern English 'K' in classical Latin, while K itself was actually a redundant letter. A Greek word with the letter Kappa borrow | Why are there two spellings of "heteroskedastic" or "heteroscedastic"?
The missing explanation is that letter 'C' was always pronounced as the modern English 'K' in classical Latin, while K itself was actually a redundant letter. A Greek word with the letter Kappa borrowed into Latin, in Roman times, would have always ... | Why are there two spellings of "heteroskedastic" or "heteroscedastic"?
The missing explanation is that letter 'C' was always pronounced as the modern English 'K' in classical Latin, while K itself was actually a redundant letter. A Greek word with the letter Kappa borrow |
7,327 | Why are there two spellings of "heteroskedastic" or "heteroscedastic"? | This is a very interesting discussion.
One problem with using the c instead of k is that in the modern Italianized Latin pronunciation, the combination ce (as with ci) yields a "soft c" (/ch/ sound); moreover, the combination sce yields the soft /sh/ sound. So the word heteroscedastic would be pronounced /hetero-sheh-d... | Why are there two spellings of "heteroskedastic" or "heteroscedastic"? | This is a very interesting discussion.
One problem with using the c instead of k is that in the modern Italianized Latin pronunciation, the combination ce (as with ci) yields a "soft c" (/ch/ sound); | Why are there two spellings of "heteroskedastic" or "heteroscedastic"?
This is a very interesting discussion.
One problem with using the c instead of k is that in the modern Italianized Latin pronunciation, the combination ce (as with ci) yields a "soft c" (/ch/ sound); moreover, the combination sce yields the soft /sh... | Why are there two spellings of "heteroskedastic" or "heteroscedastic"?
This is a very interesting discussion.
One problem with using the c instead of k is that in the modern Italianized Latin pronunciation, the combination ce (as with ci) yields a "soft c" (/ch/ sound); |
7,328 | Can AUC-ROC be between 0-0.5? | A perfect predictor gives an AUC-ROC score of 1, a predictor which makes random guesses has an AUC-ROC score of 0.5.
If you get a score of 0 that means the classifier is perfectly incorrect, it is predicting the incorrect choice 100% of the time. If you just changed the prediction of this classifier to the opposite cho... | Can AUC-ROC be between 0-0.5? | A perfect predictor gives an AUC-ROC score of 1, a predictor which makes random guesses has an AUC-ROC score of 0.5.
If you get a score of 0 that means the classifier is perfectly incorrect, it is pre | Can AUC-ROC be between 0-0.5?
A perfect predictor gives an AUC-ROC score of 1, a predictor which makes random guesses has an AUC-ROC score of 0.5.
If you get a score of 0 that means the classifier is perfectly incorrect, it is predicting the incorrect choice 100% of the time. If you just changed the prediction of this ... | Can AUC-ROC be between 0-0.5?
A perfect predictor gives an AUC-ROC score of 1, a predictor which makes random guesses has an AUC-ROC score of 0.5.
If you get a score of 0 that means the classifier is perfectly incorrect, it is pre |
7,329 | Can AUC-ROC be between 0-0.5? | I am sorry, but these answers are dangerously wrong. No, you cannot just flip AUC after you see the data. Imagine you are buying stocks, and you always bought the wrong one, but you said to yourself, then it's ok, because if you were purchasing the opposite of what your model was predicting, then you would make money.
... | Can AUC-ROC be between 0-0.5? | I am sorry, but these answers are dangerously wrong. No, you cannot just flip AUC after you see the data. Imagine you are buying stocks, and you always bought the wrong one, but you said to yourself, | Can AUC-ROC be between 0-0.5?
I am sorry, but these answers are dangerously wrong. No, you cannot just flip AUC after you see the data. Imagine you are buying stocks, and you always bought the wrong one, but you said to yourself, then it's ok, because if you were purchasing the opposite of what your model was predictin... | Can AUC-ROC be between 0-0.5?
I am sorry, but these answers are dangerously wrong. No, you cannot just flip AUC after you see the data. Imagine you are buying stocks, and you always bought the wrong one, but you said to yourself, |
7,330 | Can AUC-ROC be between 0-0.5? | They can, if the system you're analyzing performs below chance level. Trivially, you could easily construct a classifier with 0 AUC by having it always answer opposite to the truth.
In practice of course you train your classifier on some data so values very much smaller than 0.5 would typically indicate an error in yo... | Can AUC-ROC be between 0-0.5? | They can, if the system you're analyzing performs below chance level. Trivially, you could easily construct a classifier with 0 AUC by having it always answer opposite to the truth.
In practice of co | Can AUC-ROC be between 0-0.5?
They can, if the system you're analyzing performs below chance level. Trivially, you could easily construct a classifier with 0 AUC by having it always answer opposite to the truth.
In practice of course you train your classifier on some data so values very much smaller than 0.5 would typ... | Can AUC-ROC be between 0-0.5?
They can, if the system you're analyzing performs below chance level. Trivially, you could easily construct a classifier with 0 AUC by having it always answer opposite to the truth.
In practice of co |
7,331 | Why is Poisson regression used for count data? | Poisson distributed data is intrinsically integer-valued, which makes sense for count data. Ordinary Least Squares (OLS, which you call "linear regression") assumes that true values are normally distributed around the expected value and can take any real value, positive or negative, integer or fractional, whatever. Fin... | Why is Poisson regression used for count data? | Poisson distributed data is intrinsically integer-valued, which makes sense for count data. Ordinary Least Squares (OLS, which you call "linear regression") assumes that true values are normally distr | Why is Poisson regression used for count data?
Poisson distributed data is intrinsically integer-valued, which makes sense for count data. Ordinary Least Squares (OLS, which you call "linear regression") assumes that true values are normally distributed around the expected value and can take any real value, positive or... | Why is Poisson regression used for count data?
Poisson distributed data is intrinsically integer-valued, which makes sense for count data. Ordinary Least Squares (OLS, which you call "linear regression") assumes that true values are normally distr |
7,332 | Why is Poisson regression used for count data? | Essentially, it's because linear and logistic regression make the wrong kinds of assumptions about what count outcomes look like. Imagine your model as a very stupid robot that will relentlessly follow your orders, no matter how nonsensical those orders are; it completely lacks the ability to evaluate what you tell it... | Why is Poisson regression used for count data? | Essentially, it's because linear and logistic regression make the wrong kinds of assumptions about what count outcomes look like. Imagine your model as a very stupid robot that will relentlessly foll | Why is Poisson regression used for count data?
Essentially, it's because linear and logistic regression make the wrong kinds of assumptions about what count outcomes look like. Imagine your model as a very stupid robot that will relentlessly follow your orders, no matter how nonsensical those orders are; it completely... | Why is Poisson regression used for count data?
Essentially, it's because linear and logistic regression make the wrong kinds of assumptions about what count outcomes look like. Imagine your model as a very stupid robot that will relentlessly foll |
7,333 | Why is Poisson regression used for count data? | Mathematically if you start with the simple assumption that the probability of an event occurring in a defined interval $T = 1$ is $\lambda$ you can show the expected number of events in the interval $T = t$ is is $\lambda.t$, the variance is also $\lambda.t$ and the probability distribution is
$$p(N=n) = \frac{(\lam... | Why is Poisson regression used for count data? | Mathematically if you start with the simple assumption that the probability of an event occurring in a defined interval $T = 1$ is $\lambda$ you can show the expected number of events in the interval | Why is Poisson regression used for count data?
Mathematically if you start with the simple assumption that the probability of an event occurring in a defined interval $T = 1$ is $\lambda$ you can show the expected number of events in the interval $T = t$ is is $\lambda.t$, the variance is also $\lambda.t$ and the proba... | Why is Poisson regression used for count data?
Mathematically if you start with the simple assumption that the probability of an event occurring in a defined interval $T = 1$ is $\lambda$ you can show the expected number of events in the interval |
7,334 | Why is Poisson regression used for count data? | Others have basically said the same thing I'm going to but I thought I'd add my take on it. It depends on what you're doing exactly but a lot of times we like to conceptualize the problem/data at hand. This is a slightly different approach compared to just building a model that predicts pretty well. If we are trying... | Why is Poisson regression used for count data? | Others have basically said the same thing I'm going to but I thought I'd add my take on it. It depends on what you're doing exactly but a lot of times we like to conceptualize the problem/data at han | Why is Poisson regression used for count data?
Others have basically said the same thing I'm going to but I thought I'd add my take on it. It depends on what you're doing exactly but a lot of times we like to conceptualize the problem/data at hand. This is a slightly different approach compared to just building a mod... | Why is Poisson regression used for count data?
Others have basically said the same thing I'm going to but I thought I'd add my take on it. It depends on what you're doing exactly but a lot of times we like to conceptualize the problem/data at han |
7,335 | Why is Poisson regression used for count data? | My understanding is primarily because counts are always positive and discrete, the Poisson can summarize such data with one parameter. The main catch being that the variance equals the mean. | Why is Poisson regression used for count data? | My understanding is primarily because counts are always positive and discrete, the Poisson can summarize such data with one parameter. The main catch being that the variance equals the mean. | Why is Poisson regression used for count data?
My understanding is primarily because counts are always positive and discrete, the Poisson can summarize such data with one parameter. The main catch being that the variance equals the mean. | Why is Poisson regression used for count data?
My understanding is primarily because counts are always positive and discrete, the Poisson can summarize such data with one parameter. The main catch being that the variance equals the mean. |
7,336 | Changing the scale of a variable to 0-100 | Any variable (univariate distribution) $v$ with observed $min_{old}$ and $max_{old}$ values (or these could be preset potential bounds for values) can be rescaled to range $min_{new}$ to $max_{new}$ by the following formula:
$\frac{max_{new}-min_{new}}{max_{old}-min_{old}}\cdot (v-max_{old})+max_{new}$
or
$\frac{max_{n... | Changing the scale of a variable to 0-100 | Any variable (univariate distribution) $v$ with observed $min_{old}$ and $max_{old}$ values (or these could be preset potential bounds for values) can be rescaled to range $min_{new}$ to $max_{new}$ b | Changing the scale of a variable to 0-100
Any variable (univariate distribution) $v$ with observed $min_{old}$ and $max_{old}$ values (or these could be preset potential bounds for values) can be rescaled to range $min_{new}$ to $max_{new}$ by the following formula:
$\frac{max_{new}-min_{new}}{max_{old}-min_{old}}\cdot... | Changing the scale of a variable to 0-100
Any variable (univariate distribution) $v$ with observed $min_{old}$ and $max_{old}$ values (or these could be preset potential bounds for values) can be rescaled to range $min_{new}$ to $max_{new}$ b |
7,337 | Changing the scale of a variable to 0-100 | For R there is also already available rescale function from scales package, which does exactly what you want and what @AndrewTulloch and @ttnphns described:
library(scales)
rescale(c(-10, -9, -5, 2, 6), to = c(0, 100)) ## Use scales:::rescale() if you have several packages loaded using the same function name
[1] 0.00... | Changing the scale of a variable to 0-100 | For R there is also already available rescale function from scales package, which does exactly what you want and what @AndrewTulloch and @ttnphns described:
library(scales)
rescale(c(-10, -9, -5, 2, 6 | Changing the scale of a variable to 0-100
For R there is also already available rescale function from scales package, which does exactly what you want and what @AndrewTulloch and @ttnphns described:
library(scales)
rescale(c(-10, -9, -5, 2, 6), to = c(0, 100)) ## Use scales:::rescale() if you have several packages load... | Changing the scale of a variable to 0-100
For R there is also already available rescale function from scales package, which does exactly what you want and what @AndrewTulloch and @ttnphns described:
library(scales)
rescale(c(-10, -9, -5, 2, 6 |
7,338 | Changing the scale of a variable to 0-100 | first, lets get some example data:
x <- runif(20, -10, 10)
Here are two functions that will work in R
rescale <- function(x) (x-min(x))/(max(x) - min(x)) * 100
rescale(x)
Or, you could use other transformations. For example, the logit transform was mentioned by @ondrej
plogis(x)*100
or, other transforms:
pnorm(x)*10... | Changing the scale of a variable to 0-100 | first, lets get some example data:
x <- runif(20, -10, 10)
Here are two functions that will work in R
rescale <- function(x) (x-min(x))/(max(x) - min(x)) * 100
rescale(x)
Or, you could use other tra | Changing the scale of a variable to 0-100
first, lets get some example data:
x <- runif(20, -10, 10)
Here are two functions that will work in R
rescale <- function(x) (x-min(x))/(max(x) - min(x)) * 100
rescale(x)
Or, you could use other transformations. For example, the logit transform was mentioned by @ondrej
plogis... | Changing the scale of a variable to 0-100
first, lets get some example data:
x <- runif(20, -10, 10)
Here are two functions that will work in R
rescale <- function(x) (x-min(x))/(max(x) - min(x)) * 100
rescale(x)
Or, you could use other tra |
7,339 | Changing the scale of a variable to 0-100 | Just to add to ttnphnss's answer, to implement this process in Python (for example), this function will do the trick:
from __future__ import division
def rescale(values, new_min = 0, new_max = 100):
output = []
old_min, old_max = min(values), max(values)
for v in values:
new_v = (new_max - new_min... | Changing the scale of a variable to 0-100 | Just to add to ttnphnss's answer, to implement this process in Python (for example), this function will do the trick:
from __future__ import division
def rescale(values, new_min = 0, new_max = 100):
| Changing the scale of a variable to 0-100
Just to add to ttnphnss's answer, to implement this process in Python (for example), this function will do the trick:
from __future__ import division
def rescale(values, new_min = 0, new_max = 100):
output = []
old_min, old_max = min(values), max(values)
for v in ... | Changing the scale of a variable to 0-100
Just to add to ttnphnss's answer, to implement this process in Python (for example), this function will do the trick:
from __future__ import division
def rescale(values, new_min = 0, new_max = 100):
|
7,340 | Changing the scale of a variable to 0-100 | I suggest not to bind the index to 0-100 interval, as it does not improve interpretation, but rather makes it more difficult. If the index constituents can be negative, then it is possible that the index becomes negative, and it reflects what's going on with constituents better than some low value in 0-100 range, in my... | Changing the scale of a variable to 0-100 | I suggest not to bind the index to 0-100 interval, as it does not improve interpretation, but rather makes it more difficult. If the index constituents can be negative, then it is possible that the in | Changing the scale of a variable to 0-100
I suggest not to bind the index to 0-100 interval, as it does not improve interpretation, but rather makes it more difficult. If the index constituents can be negative, then it is possible that the index becomes negative, and it reflects what's going on with constituents better... | Changing the scale of a variable to 0-100
I suggest not to bind the index to 0-100 interval, as it does not improve interpretation, but rather makes it more difficult. If the index constituents can be negative, then it is possible that the in |
7,341 | Changing the scale of a variable to 0-100 | For R with standard packages loaded, you may just use scale() from 'base' package:
x=c(2,4,8,16)
x.scaled = scale(x,FALSE,max(x)) # divide each value in x by max(x)
x.scaled = as.vector(x.scaled)
use 'as.vector()' to retrieve the scaled x as vector. | Changing the scale of a variable to 0-100 | For R with standard packages loaded, you may just use scale() from 'base' package:
x=c(2,4,8,16)
x.scaled = scale(x,FALSE,max(x)) # divide each value in x by max(x)
x.scaled = as.vector(x.scaled)
u | Changing the scale of a variable to 0-100
For R with standard packages loaded, you may just use scale() from 'base' package:
x=c(2,4,8,16)
x.scaled = scale(x,FALSE,max(x)) # divide each value in x by max(x)
x.scaled = as.vector(x.scaled)
use 'as.vector()' to retrieve the scaled x as vector. | Changing the scale of a variable to 0-100
For R with standard packages loaded, you may just use scale() from 'base' package:
x=c(2,4,8,16)
x.scaled = scale(x,FALSE,max(x)) # divide each value in x by max(x)
x.scaled = as.vector(x.scaled)
u |
7,342 | What is the weak side of decision trees? | Here are a couple I can think of:
They can be extremely sensitive to small perturbations in the data: a slight change can result in a drastically different tree.
They can easily overfit. This can be negated by validation methods and pruning, but this is a grey area.
They can have problems out-of-sample prediction (thi... | What is the weak side of decision trees? | Here are a couple I can think of:
They can be extremely sensitive to small perturbations in the data: a slight change can result in a drastically different tree.
They can easily overfit. This can be | What is the weak side of decision trees?
Here are a couple I can think of:
They can be extremely sensitive to small perturbations in the data: a slight change can result in a drastically different tree.
They can easily overfit. This can be negated by validation methods and pruning, but this is a grey area.
They can ha... | What is the weak side of decision trees?
Here are a couple I can think of:
They can be extremely sensitive to small perturbations in the data: a slight change can result in a drastically different tree.
They can easily overfit. This can be |
7,343 | What is the weak side of decision trees? | One disadvantage is that all terms are assumed to interact. That is, you can't have two explanatory variables that behave independently. Every variable in the tree is forced to interact with every variable further up the tree. This is extremely inefficient if there are variables that have no or weak interactions. | What is the weak side of decision trees? | One disadvantage is that all terms are assumed to interact. That is, you can't have two explanatory variables that behave independently. Every variable in the tree is forced to interact with every var | What is the weak side of decision trees?
One disadvantage is that all terms are assumed to interact. That is, you can't have two explanatory variables that behave independently. Every variable in the tree is forced to interact with every variable further up the tree. This is extremely inefficient if there are variables... | What is the weak side of decision trees?
One disadvantage is that all terms are assumed to interact. That is, you can't have two explanatory variables that behave independently. Every variable in the tree is forced to interact with every var |
7,344 | What is the weak side of decision trees? | My answer is directed to CART (the C 4.5/C 5 implementations) though i don't think are limited to it. My guess is that this is what the OP has in mind--it's usually what someone means when they say "Decision Tree."
Limitations of Decision Trees:
Low-Performance
By 'performance' i don't mean resolution, but execution sp... | What is the weak side of decision trees? | My answer is directed to CART (the C 4.5/C 5 implementations) though i don't think are limited to it. My guess is that this is what the OP has in mind--it's usually what someone means when they say "D | What is the weak side of decision trees?
My answer is directed to CART (the C 4.5/C 5 implementations) though i don't think are limited to it. My guess is that this is what the OP has in mind--it's usually what someone means when they say "Decision Tree."
Limitations of Decision Trees:
Low-Performance
By 'performance' ... | What is the weak side of decision trees?
My answer is directed to CART (the C 4.5/C 5 implementations) though i don't think are limited to it. My guess is that this is what the OP has in mind--it's usually what someone means when they say "D |
7,345 | What is the weak side of decision trees? | There are good answers here, but I am surprised that one thing has not been emphasized. CART does not make any distributional assumptions about the data, particularly the response variable. In contrast, OLS regression (for continuous response variables) and logistic regression (for certain categorical response variab... | What is the weak side of decision trees? | There are good answers here, but I am surprised that one thing has not been emphasized. CART does not make any distributional assumptions about the data, particularly the response variable. In contr | What is the weak side of decision trees?
There are good answers here, but I am surprised that one thing has not been emphasized. CART does not make any distributional assumptions about the data, particularly the response variable. In contrast, OLS regression (for continuous response variables) and logistic regression... | What is the weak side of decision trees?
There are good answers here, but I am surprised that one thing has not been emphasized. CART does not make any distributional assumptions about the data, particularly the response variable. In contr |
7,346 | I know the 95% confidence interval for ln(x), do I also know the 95% confidence interval of x? | That is a 95% confidence interval for $x$, but not the 95% confidence interval. For any continuous strictly-monotonic transformation, your method is a legitimate way to get a confidence interval for the transformed value. (For monotonically decreasing functions, you reverse the bounds.) The other excellent answer by... | I know the 95% confidence interval for ln(x), do I also know the 95% confidence interval of x? | That is a 95% confidence interval for $x$, but not the 95% confidence interval. For any continuous strictly-monotonic transformation, your method is a legitimate way to get a confidence interval for | I know the 95% confidence interval for ln(x), do I also know the 95% confidence interval of x?
That is a 95% confidence interval for $x$, but not the 95% confidence interval. For any continuous strictly-monotonic transformation, your method is a legitimate way to get a confidence interval for the transformed value. (... | I know the 95% confidence interval for ln(x), do I also know the 95% confidence interval of x?
That is a 95% confidence interval for $x$, but not the 95% confidence interval. For any continuous strictly-monotonic transformation, your method is a legitimate way to get a confidence interval for |
7,347 | I know the 95% confidence interval for ln(x), do I also know the 95% confidence interval of x? | You can easily show that this is the case.
Let $Y\equiv \log(X)$. Then, the $\alpha$-quantile of $Y$ is $y\in\mathbb{R}$, such that $\mathbb{P}[Y \leq y] = \alpha$. Similarly, the $\alpha$-quantile of $X$ is $x \in \mathbb{R}^+$, such that $\mathbb{P}[X \leq x] = \alpha$, or, $\mathbb{P}[\log(X) \leq y] = \alpha$, or, ... | I know the 95% confidence interval for ln(x), do I also know the 95% confidence interval of x? | You can easily show that this is the case.
Let $Y\equiv \log(X)$. Then, the $\alpha$-quantile of $Y$ is $y\in\mathbb{R}$, such that $\mathbb{P}[Y \leq y] = \alpha$. Similarly, the $\alpha$-quantile of | I know the 95% confidence interval for ln(x), do I also know the 95% confidence interval of x?
You can easily show that this is the case.
Let $Y\equiv \log(X)$. Then, the $\alpha$-quantile of $Y$ is $y\in\mathbb{R}$, such that $\mathbb{P}[Y \leq y] = \alpha$. Similarly, the $\alpha$-quantile of $X$ is $x \in \mathbb{R}... | I know the 95% confidence interval for ln(x), do I also know the 95% confidence interval of x?
You can easily show that this is the case.
Let $Y\equiv \log(X)$. Then, the $\alpha$-quantile of $Y$ is $y\in\mathbb{R}$, such that $\mathbb{P}[Y \leq y] = \alpha$. Similarly, the $\alpha$-quantile of |
7,348 | I know the 95% confidence interval for ln(x), do I also know the 95% confidence interval of x? | Confidence intervals do not change when you transform the parameters (with a monotonic transformation)
Confidence intervals are based on probabilities conditional on the parameters, and do not transform if you transform the parameters. Unlike (Bayesian) probabilities of the parameters (on which credible intervals are b... | I know the 95% confidence interval for ln(x), do I also know the 95% confidence interval of x? | Confidence intervals do not change when you transform the parameters (with a monotonic transformation)
Confidence intervals are based on probabilities conditional on the parameters, and do not transfo | I know the 95% confidence interval for ln(x), do I also know the 95% confidence interval of x?
Confidence intervals do not change when you transform the parameters (with a monotonic transformation)
Confidence intervals are based on probabilities conditional on the parameters, and do not transform if you transform the p... | I know the 95% confidence interval for ln(x), do I also know the 95% confidence interval of x?
Confidence intervals do not change when you transform the parameters (with a monotonic transformation)
Confidence intervals are based on probabilities conditional on the parameters, and do not transfo |
7,349 | How to generate numbers based on an arbitrary discrete distribution? | One of the best algorithms for sampling from a discrete distribution is the alias method.
The alias method (efficiently) precomputes a two-dimensional data structure to partition a rectangle into areas proportional to the probabilities.
In this schematic from the referenced site, a rectangle of unit height has been ... | How to generate numbers based on an arbitrary discrete distribution? | One of the best algorithms for sampling from a discrete distribution is the alias method.
The alias method (efficiently) precomputes a two-dimensional data structure to partition a rectangle into area | How to generate numbers based on an arbitrary discrete distribution?
One of the best algorithms for sampling from a discrete distribution is the alias method.
The alias method (efficiently) precomputes a two-dimensional data structure to partition a rectangle into areas proportional to the probabilities.
In this sch... | How to generate numbers based on an arbitrary discrete distribution?
One of the best algorithms for sampling from a discrete distribution is the alias method.
The alias method (efficiently) precomputes a two-dimensional data structure to partition a rectangle into area |
7,350 | How to generate numbers based on an arbitrary discrete distribution? | You can do this easily in R, just specify the size you need:
sample(x=c(1,2,3), size=1000, replace=TRUE, prob=c(.04,.50,.46)) | How to generate numbers based on an arbitrary discrete distribution? | You can do this easily in R, just specify the size you need:
sample(x=c(1,2,3), size=1000, replace=TRUE, prob=c(.04,.50,.46)) | How to generate numbers based on an arbitrary discrete distribution?
You can do this easily in R, just specify the size you need:
sample(x=c(1,2,3), size=1000, replace=TRUE, prob=c(.04,.50,.46)) | How to generate numbers based on an arbitrary discrete distribution?
You can do this easily in R, just specify the size you need:
sample(x=c(1,2,3), size=1000, replace=TRUE, prob=c(.04,.50,.46)) |
7,351 | How to generate numbers based on an arbitrary discrete distribution? | In your example, say you draw your pseudorandom Uniform[0,1] value and call it U. Then output:
1 if U<0.04
2 if U>=0.04 and U<0.54
3 if U>=0.54
If the % specified are a, b, ..., simply output
value 1 if U
value 2 if U>=a and U<(a+b)
etc.
Essentially, we are mapping the % into subsets of [0,1], and we know the probabi... | How to generate numbers based on an arbitrary discrete distribution? | In your example, say you draw your pseudorandom Uniform[0,1] value and call it U. Then output:
1 if U<0.04
2 if U>=0.04 and U<0.54
3 if U>=0.54
If the % specified are a, b, ..., simply output
value 1 | How to generate numbers based on an arbitrary discrete distribution?
In your example, say you draw your pseudorandom Uniform[0,1] value and call it U. Then output:
1 if U<0.04
2 if U>=0.04 and U<0.54
3 if U>=0.54
If the % specified are a, b, ..., simply output
value 1 if U
value 2 if U>=a and U<(a+b)
etc.
Essentially... | How to generate numbers based on an arbitrary discrete distribution?
In your example, say you draw your pseudorandom Uniform[0,1] value and call it U. Then output:
1 if U<0.04
2 if U>=0.04 and U<0.54
3 if U>=0.54
If the % specified are a, b, ..., simply output
value 1 |
7,352 | How to generate numbers based on an arbitrary discrete distribution? | Suppose there are $m$ possible discrete outcomes. You divide up the interval $[0,1]$ into subintervals based on the cumulative probability mass function, $F$, to give the partitioned $(0,1)$ interval
$$ I_{1} \cup I_{2} \cup \cdots \cup I_{m}$$
where $I_{j} = (F(j-1), F(j))$ and $F(0) \equiv 0$. In your example $m =... | How to generate numbers based on an arbitrary discrete distribution? | Suppose there are $m$ possible discrete outcomes. You divide up the interval $[0,1]$ into subintervals based on the cumulative probability mass function, $F$, to give the partitioned $(0,1)$ interval | How to generate numbers based on an arbitrary discrete distribution?
Suppose there are $m$ possible discrete outcomes. You divide up the interval $[0,1]$ into subintervals based on the cumulative probability mass function, $F$, to give the partitioned $(0,1)$ interval
$$ I_{1} \cup I_{2} \cup \cdots \cup I_{m}$$
whe... | How to generate numbers based on an arbitrary discrete distribution?
Suppose there are $m$ possible discrete outcomes. You divide up the interval $[0,1]$ into subintervals based on the cumulative probability mass function, $F$, to give the partitioned $(0,1)$ interval |
7,353 | How to generate numbers based on an arbitrary discrete distribution? | One simple algorithm is to start with your uniform random number and in a loop first subtract off the first probability, if the result is negative then you return the first value, if still positive then you go to the next iteration and subtract off the next probability, check if negative, etc.
This is nice in that the ... | How to generate numbers based on an arbitrary discrete distribution? | One simple algorithm is to start with your uniform random number and in a loop first subtract off the first probability, if the result is negative then you return the first value, if still positive th | How to generate numbers based on an arbitrary discrete distribution?
One simple algorithm is to start with your uniform random number and in a loop first subtract off the first probability, if the result is negative then you return the first value, if still positive then you go to the next iteration and subtract off th... | How to generate numbers based on an arbitrary discrete distribution?
One simple algorithm is to start with your uniform random number and in a loop first subtract off the first probability, if the result is negative then you return the first value, if still positive th |
7,354 | How to generate numbers based on an arbitrary discrete distribution? | First of all, let me draw your attention to a python library with ready-to-use classes for either integer or floating point random number generation that follow arbitrary distribution.
Generally speaking there are several approaches to this problem. Some are linear in time, but require large memory storage, some run i... | How to generate numbers based on an arbitrary discrete distribution? | First of all, let me draw your attention to a python library with ready-to-use classes for either integer or floating point random number generation that follow arbitrary distribution.
Generally spea | How to generate numbers based on an arbitrary discrete distribution?
First of all, let me draw your attention to a python library with ready-to-use classes for either integer or floating point random number generation that follow arbitrary distribution.
Generally speaking there are several approaches to this problem. ... | How to generate numbers based on an arbitrary discrete distribution?
First of all, let me draw your attention to a python library with ready-to-use classes for either integer or floating point random number generation that follow arbitrary distribution.
Generally spea |
7,355 | How to generate numbers based on an arbitrary discrete distribution? | I had the same problem. Given a set where each item has a probability and whose items' probabilities sum up to one, I wanted to draw a sample efficiently, i.e. without sorting anything and without repeatedly iterating over the set.
The following function draws the lowest of $N$ uniformly distributed random numbers with... | How to generate numbers based on an arbitrary discrete distribution? | I had the same problem. Given a set where each item has a probability and whose items' probabilities sum up to one, I wanted to draw a sample efficiently, i.e. without sorting anything and without rep | How to generate numbers based on an arbitrary discrete distribution?
I had the same problem. Given a set where each item has a probability and whose items' probabilities sum up to one, I wanted to draw a sample efficiently, i.e. without sorting anything and without repeatedly iterating over the set.
The following funct... | How to generate numbers based on an arbitrary discrete distribution?
I had the same problem. Given a set where each item has a probability and whose items' probabilities sum up to one, I wanted to draw a sample efficiently, i.e. without sorting anything and without rep |
7,356 | How to determine the confidence of a neural network prediction? | It sounds like you are looking for a prediction-interval, i.e., an interval that contains a prespecified percentage of future realizations. (Look at the tag wikis for prediction-interval and confidence-interval for the difference.)
Your best bet is likely to work directly with NN architectures that do not output single... | How to determine the confidence of a neural network prediction? | It sounds like you are looking for a prediction-interval, i.e., an interval that contains a prespecified percentage of future realizations. (Look at the tag wikis for prediction-interval and confidenc | How to determine the confidence of a neural network prediction?
It sounds like you are looking for a prediction-interval, i.e., an interval that contains a prespecified percentage of future realizations. (Look at the tag wikis for prediction-interval and confidence-interval for the difference.)
Your best bet is likely ... | How to determine the confidence of a neural network prediction?
It sounds like you are looking for a prediction-interval, i.e., an interval that contains a prespecified percentage of future realizations. (Look at the tag wikis for prediction-interval and confidenc |
7,357 | How to determine the confidence of a neural network prediction? | I'm not sure you can compute a confidence interval for a single prediction, but you can indeed compute a confidence interval for error rate of the whole dataset (you can generalize for accuracy and whatever other measure you are assessing).
If $e$ is your error rate while classifying some data $S$ of size $n$, a 95% co... | How to determine the confidence of a neural network prediction? | I'm not sure you can compute a confidence interval for a single prediction, but you can indeed compute a confidence interval for error rate of the whole dataset (you can generalize for accuracy and wh | How to determine the confidence of a neural network prediction?
I'm not sure you can compute a confidence interval for a single prediction, but you can indeed compute a confidence interval for error rate of the whole dataset (you can generalize for accuracy and whatever other measure you are assessing).
If $e$ is your ... | How to determine the confidence of a neural network prediction?
I'm not sure you can compute a confidence interval for a single prediction, but you can indeed compute a confidence interval for error rate of the whole dataset (you can generalize for accuracy and wh |
7,358 | How to determine the confidence of a neural network prediction? | In terms of directly outputting prediction intervals, there's a 2011 paper 'Comprehensive Review of Neural Network-Based Prediction Intervals'
They compare four approaches:
1: Delta method
2: Bayesian method
3: Mean variance estimation
4: Bootstrap
The same authors went on to develop Lower Upper Bound Estimation Method... | How to determine the confidence of a neural network prediction? | In terms of directly outputting prediction intervals, there's a 2011 paper 'Comprehensive Review of Neural Network-Based Prediction Intervals'
They compare four approaches:
1: Delta method
2: Bayesian | How to determine the confidence of a neural network prediction?
In terms of directly outputting prediction intervals, there's a 2011 paper 'Comprehensive Review of Neural Network-Based Prediction Intervals'
They compare four approaches:
1: Delta method
2: Bayesian method
3: Mean variance estimation
4: Bootstrap
The sam... | How to determine the confidence of a neural network prediction?
In terms of directly outputting prediction intervals, there's a 2011 paper 'Comprehensive Review of Neural Network-Based Prediction Intervals'
They compare four approaches:
1: Delta method
2: Bayesian |
7,359 | How to determine the confidence of a neural network prediction? | I don't know of any method to do that in an exact way.
A work-around could be to assume that you have gaussian noise and make the Neural Network predict a mean $\mu$ and variance $\sigma$. For the cost function you can use the NLPD (negative log probability density). For datapoint $(x_i,y_i)$ that will be $-\log N(y_... | How to determine the confidence of a neural network prediction? | I don't know of any method to do that in an exact way.
A work-around could be to assume that you have gaussian noise and make the Neural Network predict a mean $\mu$ and variance $\sigma$. For the c | How to determine the confidence of a neural network prediction?
I don't know of any method to do that in an exact way.
A work-around could be to assume that you have gaussian noise and make the Neural Network predict a mean $\mu$ and variance $\sigma$. For the cost function you can use the NLPD (negative log probabil... | How to determine the confidence of a neural network prediction?
I don't know of any method to do that in an exact way.
A work-around could be to assume that you have gaussian noise and make the Neural Network predict a mean $\mu$ and variance $\sigma$. For the c |
7,360 | How to determine the confidence of a neural network prediction? | There are actually ways of doing this using dropout. Run the evaluation with dropout enabled (it's usually disabled for evaluation but turned on when training), and run the evaluation several times.
The result distribution from multiple different runs can be used as confidence intervals.
See the paper "Dropout as a Ba... | How to determine the confidence of a neural network prediction? | There are actually ways of doing this using dropout. Run the evaluation with dropout enabled (it's usually disabled for evaluation but turned on when training), and run the evaluation several times.
| How to determine the confidence of a neural network prediction?
There are actually ways of doing this using dropout. Run the evaluation with dropout enabled (it's usually disabled for evaluation but turned on when training), and run the evaluation several times.
The result distribution from multiple different runs can... | How to determine the confidence of a neural network prediction?
There are actually ways of doing this using dropout. Run the evaluation with dropout enabled (it's usually disabled for evaluation but turned on when training), and run the evaluation several times.
|
7,361 | How to determine the confidence of a neural network prediction? | Prediction intervals (PI) in non parametric regression & classification problems, such as neural nets, SVMs, random forests, etc. are difficult to construct. I'd love to hear other opinions on this.
However, as far as I know, Conformal Prediction (CP) is the only principled method for building calibrated PI for predic... | How to determine the confidence of a neural network prediction? | Prediction intervals (PI) in non parametric regression & classification problems, such as neural nets, SVMs, random forests, etc. are difficult to construct. I'd love to hear other opinions on this.
| How to determine the confidence of a neural network prediction?
Prediction intervals (PI) in non parametric regression & classification problems, such as neural nets, SVMs, random forests, etc. are difficult to construct. I'd love to hear other opinions on this.
However, as far as I know, Conformal Prediction (CP) is ... | How to determine the confidence of a neural network prediction?
Prediction intervals (PI) in non parametric regression & classification problems, such as neural nets, SVMs, random forests, etc. are difficult to construct. I'd love to hear other opinions on this.
|
7,362 | How to determine the confidence of a neural network prediction? | I have not heard of any method that gives a confidence interval for a neural network prediction. Despite a lack of formal methodology, it seems like it might be feasible to construct one. I have never attempted this due to the compute power that would be needed and I make no claims on this working for certain, but one ... | How to determine the confidence of a neural network prediction? | I have not heard of any method that gives a confidence interval for a neural network prediction. Despite a lack of formal methodology, it seems like it might be feasible to construct one. I have never | How to determine the confidence of a neural network prediction?
I have not heard of any method that gives a confidence interval for a neural network prediction. Despite a lack of formal methodology, it seems like it might be feasible to construct one. I have never attempted this due to the compute power that would be n... | How to determine the confidence of a neural network prediction?
I have not heard of any method that gives a confidence interval for a neural network prediction. Despite a lack of formal methodology, it seems like it might be feasible to construct one. I have never |
7,363 | How to determine the confidence of a neural network prediction? | This article is an interesting presentation by Yarin Gal of a technique based on dropout:
http://mlg.eng.cam.ac.uk/yarin/blog_3d801aa532c1ce.html
Archived version: https://web.archive.org/web/20210422213844/http://mlg.eng.cam.ac.uk/yarin/blog_3d801aa532c1ce.html | How to determine the confidence of a neural network prediction? | This article is an interesting presentation by Yarin Gal of a technique based on dropout:
http://mlg.eng.cam.ac.uk/yarin/blog_3d801aa532c1ce.html
Archived version: https://web.archive.org/web/20210422 | How to determine the confidence of a neural network prediction?
This article is an interesting presentation by Yarin Gal of a technique based on dropout:
http://mlg.eng.cam.ac.uk/yarin/blog_3d801aa532c1ce.html
Archived version: https://web.archive.org/web/20210422213844/http://mlg.eng.cam.ac.uk/yarin/blog_3d801aa532c1c... | How to determine the confidence of a neural network prediction?
This article is an interesting presentation by Yarin Gal of a technique based on dropout:
http://mlg.eng.cam.ac.uk/yarin/blog_3d801aa532c1ce.html
Archived version: https://web.archive.org/web/20210422 |
7,364 | How to determine the confidence of a neural network prediction? | Work in Progress...
There has been a lot of work on predictive intervals for neural nets going back over the years:
The simplest approach (Nix and Weigend, 1994) is to train a second neural network to predict the mean-squared error of the first. Regression networks trained to minimise the mean-squared error learn the ... | How to determine the confidence of a neural network prediction? | Work in Progress...
There has been a lot of work on predictive intervals for neural nets going back over the years:
The simplest approach (Nix and Weigend, 1994) is to train a second neural network to | How to determine the confidence of a neural network prediction?
Work in Progress...
There has been a lot of work on predictive intervals for neural nets going back over the years:
The simplest approach (Nix and Weigend, 1994) is to train a second neural network to predict the mean-squared error of the first. Regressio... | How to determine the confidence of a neural network prediction?
Work in Progress...
There has been a lot of work on predictive intervals for neural nets going back over the years:
The simplest approach (Nix and Weigend, 1994) is to train a second neural network to |
7,365 | How to determine the confidence of a neural network prediction? | I find that a simple method is MC dropout. In prediction you duplicate the case and expand that into a batch and enable the dropout, then you will obtain multiple outputs for the same input but with different dropped parameters. You get multiple outputs through one forward pass(and only one model) and then get a distri... | How to determine the confidence of a neural network prediction? | I find that a simple method is MC dropout. In prediction you duplicate the case and expand that into a batch and enable the dropout, then you will obtain multiple outputs for the same input but with d | How to determine the confidence of a neural network prediction?
I find that a simple method is MC dropout. In prediction you duplicate the case and expand that into a batch and enable the dropout, then you will obtain multiple outputs for the same input but with different dropped parameters. You get multiple outputs th... | How to determine the confidence of a neural network prediction?
I find that a simple method is MC dropout. In prediction you duplicate the case and expand that into a batch and enable the dropout, then you will obtain multiple outputs for the same input but with d |
7,366 | How to determine the confidence of a neural network prediction? | There is no way, all ML models is not about phenomen understanding, it's interpolation methods with hope "that it works". Start with such questions confidence, robustnes to noise there is no answers.
So to derive something please use various applied and fundamental science:
Use control (and make assumption about dyna... | How to determine the confidence of a neural network prediction? | There is no way, all ML models is not about phenomen understanding, it's interpolation methods with hope "that it works". Start with such questions confidence, robustnes to noise there is no answers. | How to determine the confidence of a neural network prediction?
There is no way, all ML models is not about phenomen understanding, it's interpolation methods with hope "that it works". Start with such questions confidence, robustnes to noise there is no answers.
So to derive something please use various applied and f... | How to determine the confidence of a neural network prediction?
There is no way, all ML models is not about phenomen understanding, it's interpolation methods with hope "that it works". Start with such questions confidence, robustnes to noise there is no answers. |
7,367 | Interpretation of Shapiro-Wilk test | No - you cannot say "the sample has a normal distribution" or "the sample comes from a population which has a normal distribution", but only "you cannot reject the hypothesis that the sample comes from a population which has a normal distribution".
In fact the sample does not have a normal distribution (see the qqplot ... | Interpretation of Shapiro-Wilk test | No - you cannot say "the sample has a normal distribution" or "the sample comes from a population which has a normal distribution", but only "you cannot reject the hypothesis that the sample comes fro | Interpretation of Shapiro-Wilk test
No - you cannot say "the sample has a normal distribution" or "the sample comes from a population which has a normal distribution", but only "you cannot reject the hypothesis that the sample comes from a population which has a normal distribution".
In fact the sample does not have a ... | Interpretation of Shapiro-Wilk test
No - you cannot say "the sample has a normal distribution" or "the sample comes from a population which has a normal distribution", but only "you cannot reject the hypothesis that the sample comes fro |
7,368 | Interpretation of Shapiro-Wilk test | Failing to reject a null hypothesis is an indication that the sample you have is too small to pick up whatever deviations from normality you have - but your sample is so small that even quite substantial deviations from normality likely won't be detected.
However a hypothesis test is pretty much beside the point in mos... | Interpretation of Shapiro-Wilk test | Failing to reject a null hypothesis is an indication that the sample you have is too small to pick up whatever deviations from normality you have - but your sample is so small that even quite substant | Interpretation of Shapiro-Wilk test
Failing to reject a null hypothesis is an indication that the sample you have is too small to pick up whatever deviations from normality you have - but your sample is so small that even quite substantial deviations from normality likely won't be detected.
However a hypothesis test is... | Interpretation of Shapiro-Wilk test
Failing to reject a null hypothesis is an indication that the sample you have is too small to pick up whatever deviations from normality you have - but your sample is so small that even quite substant |
7,369 | Interpretation of Shapiro-Wilk test | Considering that you are pretty new to statistics, I suspect that you are thinking about this because these are residuals of an estimate of a mean and you want to know whether the assumption of normality is valid for confidence estimates using a $t$-distribution.
$t$-tests are quite robust to violations of this assumpt... | Interpretation of Shapiro-Wilk test | Considering that you are pretty new to statistics, I suspect that you are thinking about this because these are residuals of an estimate of a mean and you want to know whether the assumption of normal | Interpretation of Shapiro-Wilk test
Considering that you are pretty new to statistics, I suspect that you are thinking about this because these are residuals of an estimate of a mean and you want to know whether the assumption of normality is valid for confidence estimates using a $t$-distribution.
$t$-tests are quite ... | Interpretation of Shapiro-Wilk test
Considering that you are pretty new to statistics, I suspect that you are thinking about this because these are residuals of an estimate of a mean and you want to know whether the assumption of normal |
7,370 | Interpretation of Shapiro-Wilk test | As Henry already said you can't say it's normal. Just try to run the following command in R several times:
shapiro.test(runif(9))
This will test the sample of 9 numbers from uniform distribution. Many times the p-value will be much larger than 0.05 - which means that you cannot conclude that the distribution is norma... | Interpretation of Shapiro-Wilk test | As Henry already said you can't say it's normal. Just try to run the following command in R several times:
shapiro.test(runif(9))
This will test the sample of 9 numbers from uniform distribution. Ma | Interpretation of Shapiro-Wilk test
As Henry already said you can't say it's normal. Just try to run the following command in R several times:
shapiro.test(runif(9))
This will test the sample of 9 numbers from uniform distribution. Many times the p-value will be much larger than 0.05 - which means that you cannot con... | Interpretation of Shapiro-Wilk test
As Henry already said you can't say it's normal. Just try to run the following command in R several times:
shapiro.test(runif(9))
This will test the sample of 9 numbers from uniform distribution. Ma |
7,371 | Interpretation of Shapiro-Wilk test | I was also looking on how to properly interpret W value in Shapiro-Wilk test and according to Emil O. W. Kirkegaard's article "W values from the Shapiro-Wilk test visualized with different datasets" it's very difficult to say anything about the normality of a distribution looking at W value alone.
As he states in concl... | Interpretation of Shapiro-Wilk test | I was also looking on how to properly interpret W value in Shapiro-Wilk test and according to Emil O. W. Kirkegaard's article "W values from the Shapiro-Wilk test visualized with different datasets" i | Interpretation of Shapiro-Wilk test
I was also looking on how to properly interpret W value in Shapiro-Wilk test and according to Emil O. W. Kirkegaard's article "W values from the Shapiro-Wilk test visualized with different datasets" it's very difficult to say anything about the normality of a distribution looking at ... | Interpretation of Shapiro-Wilk test
I was also looking on how to properly interpret W value in Shapiro-Wilk test and according to Emil O. W. Kirkegaard's article "W values from the Shapiro-Wilk test visualized with different datasets" i |
7,372 | Interpretation of Shapiro-Wilk test | One important issue not mentioned by previous answer are the test limitations:
The test has limitations, most importantly that the test has a bias by sample size. The larger the sample, the more likely you’ll get a statistically significant result.
To answer the original question (very small sample size): see the fo... | Interpretation of Shapiro-Wilk test | One important issue not mentioned by previous answer are the test limitations:
The test has limitations, most importantly that the test has a bias by sample size. The larger the sample, the more lik | Interpretation of Shapiro-Wilk test
One important issue not mentioned by previous answer are the test limitations:
The test has limitations, most importantly that the test has a bias by sample size. The larger the sample, the more likely you’ll get a statistically significant result.
To answer the original question ... | Interpretation of Shapiro-Wilk test
One important issue not mentioned by previous answer are the test limitations:
The test has limitations, most importantly that the test has a bias by sample size. The larger the sample, the more lik |
7,373 | How to perform orthogonal regression (total least squares) via PCA? | Ordinary least squares vs. total least squares
Let's first consider the simplest case of only one predictor (independent) variable $x$. For simplicity, let both $x$ and $y$ be centered, i.e. intercept is always zero. The difference between standard OLS regression and "orthogonal" TLS regression is clearly shown on this... | How to perform orthogonal regression (total least squares) via PCA? | Ordinary least squares vs. total least squares
Let's first consider the simplest case of only one predictor (independent) variable $x$. For simplicity, let both $x$ and $y$ be centered, i.e. intercept | How to perform orthogonal regression (total least squares) via PCA?
Ordinary least squares vs. total least squares
Let's first consider the simplest case of only one predictor (independent) variable $x$. For simplicity, let both $x$ and $y$ be centered, i.e. intercept is always zero. The difference between standard OLS... | How to perform orthogonal regression (total least squares) via PCA?
Ordinary least squares vs. total least squares
Let's first consider the simplest case of only one predictor (independent) variable $x$. For simplicity, let both $x$ and $y$ be centered, i.e. intercept |
7,374 | How to perform orthogonal regression (total least squares) via PCA? | Based on the naive GNU Octave implementation found here, something like this might (grain of salt, it's late) work.
tls <- function(A, b){
n <- ncol(A)
C <- cbind(A, b)
V <- svd(C)$v
VAB <- V[1:n, (n+1):ncol(V)]
VBB <- V[(n+1):nrow(V), (n+1):ncol(V)]
return(-VAB/VBB)
} | How to perform orthogonal regression (total least squares) via PCA? | Based on the naive GNU Octave implementation found here, something like this might (grain of salt, it's late) work.
tls <- function(A, b){
n <- ncol(A)
C <- cbind(A, b)
V <- svd(C)$v
VAB <- | How to perform orthogonal regression (total least squares) via PCA?
Based on the naive GNU Octave implementation found here, something like this might (grain of salt, it's late) work.
tls <- function(A, b){
n <- ncol(A)
C <- cbind(A, b)
V <- svd(C)$v
VAB <- V[1:n, (n+1):ncol(V)]
VBB <- V[(n+1):nrow(V), (n+1... | How to perform orthogonal regression (total least squares) via PCA?
Based on the naive GNU Octave implementation found here, something like this might (grain of salt, it's late) work.
tls <- function(A, b){
n <- ncol(A)
C <- cbind(A, b)
V <- svd(C)$v
VAB <- |
7,375 | How to perform orthogonal regression (total least squares) via PCA? | princomp is running principal component analysis instead of total least squares regression. As far as I know there is no R function nor package that does TLS; at most there is Deming regression in MethComp.
Yet, please treat this as a suggestion that it is most likely not worth it. | How to perform orthogonal regression (total least squares) via PCA? | princomp is running principal component analysis instead of total least squares regression. As far as I know there is no R function nor package that does TLS; at most there is Deming regression in Met | How to perform orthogonal regression (total least squares) via PCA?
princomp is running principal component analysis instead of total least squares regression. As far as I know there is no R function nor package that does TLS; at most there is Deming regression in MethComp.
Yet, please treat this as a suggestion that i... | How to perform orthogonal regression (total least squares) via PCA?
princomp is running principal component analysis instead of total least squares regression. As far as I know there is no R function nor package that does TLS; at most there is Deming regression in Met |
7,376 | Calculate Transition Matrix (Markov) in R | I am not immediately aware of a "built-in" function (e.g., in base or similar), but we can do this very easily and efficiently in a couple of lines of code.
Here is a function that takes a matrix (not a data frame) as an input and produces either the transition counts (prob=FALSE) or, by default (prob=TRUE), the estima... | Calculate Transition Matrix (Markov) in R | I am not immediately aware of a "built-in" function (e.g., in base or similar), but we can do this very easily and efficiently in a couple of lines of code.
Here is a function that takes a matrix (not | Calculate Transition Matrix (Markov) in R
I am not immediately aware of a "built-in" function (e.g., in base or similar), but we can do this very easily and efficiently in a couple of lines of code.
Here is a function that takes a matrix (not a data frame) as an input and produces either the transition counts (prob=FAL... | Calculate Transition Matrix (Markov) in R
I am not immediately aware of a "built-in" function (e.g., in base or similar), but we can do this very easily and efficiently in a couple of lines of code.
Here is a function that takes a matrix (not |
7,377 | Calculate Transition Matrix (Markov) in R | I have just uploaded a new R package, markovchain, based on S4 programming style. Along with various methods to handle S4 markovchain objects it contains a function to fit a Markov chain from a sequence of states. Have a look at:
library(markovchain)
sequence <- c("a", "b", "a", "a", "a", "a", "b", "a", "b", "a",
... | Calculate Transition Matrix (Markov) in R | I have just uploaded a new R package, markovchain, based on S4 programming style. Along with various methods to handle S4 markovchain objects it contains a function to fit a Markov chain from a sequen | Calculate Transition Matrix (Markov) in R
I have just uploaded a new R package, markovchain, based on S4 programming style. Along with various methods to handle S4 markovchain objects it contains a function to fit a Markov chain from a sequence of states. Have a look at:
library(markovchain)
sequence <- c("a", "b", "a... | Calculate Transition Matrix (Markov) in R
I have just uploaded a new R package, markovchain, based on S4 programming style. Along with various methods to handle S4 markovchain objects it contains a function to fit a Markov chain from a sequen |
7,378 | Pre-training in deep convolutional neural network? | I'm not sure if this exactly answers your question, but from what I understand the reason you don't see people pretraining (I mean this in an unsupervised pretraining sense) conv nets is because there have been various innovations in purely supervised training that have rendered unsupervised pretraining unnecessary (fo... | Pre-training in deep convolutional neural network? | I'm not sure if this exactly answers your question, but from what I understand the reason you don't see people pretraining (I mean this in an unsupervised pretraining sense) conv nets is because there | Pre-training in deep convolutional neural network?
I'm not sure if this exactly answers your question, but from what I understand the reason you don't see people pretraining (I mean this in an unsupervised pretraining sense) conv nets is because there have been various innovations in purely supervised training that hav... | Pre-training in deep convolutional neural network?
I'm not sure if this exactly answers your question, but from what I understand the reason you don't see people pretraining (I mean this in an unsupervised pretraining sense) conv nets is because there |
7,379 | Pre-training in deep convolutional neural network? | As can be understood from the above answers, pre-training was 'fashioned out' when multiple things happened. However, I do want to distill my understanding of it:
Long time ago in 2010, everyone cared about pre-training. Here is a great paper on the subject that I did not see brought up.
Slightly before before Alex Kr... | Pre-training in deep convolutional neural network? | As can be understood from the above answers, pre-training was 'fashioned out' when multiple things happened. However, I do want to distill my understanding of it:
Long time ago in 2010, everyone care | Pre-training in deep convolutional neural network?
As can be understood from the above answers, pre-training was 'fashioned out' when multiple things happened. However, I do want to distill my understanding of it:
Long time ago in 2010, everyone cared about pre-training. Here is a great paper on the subject that I did... | Pre-training in deep convolutional neural network?
As can be understood from the above answers, pre-training was 'fashioned out' when multiple things happened. However, I do want to distill my understanding of it:
Long time ago in 2010, everyone care |
7,380 | Pre-training in deep convolutional neural network? | There are some papers but not as much as autoencoders or RBMs. I think the reason is the time line of NN. Stacked RBM and autoencoder are introduced at 2006 and 2007, respectively. After employment of ReLU at 2009 unsupervised learning is partially abandoned (when there is enough data to learn in direct supervised lear... | Pre-training in deep convolutional neural network? | There are some papers but not as much as autoencoders or RBMs. I think the reason is the time line of NN. Stacked RBM and autoencoder are introduced at 2006 and 2007, respectively. After employment of | Pre-training in deep convolutional neural network?
There are some papers but not as much as autoencoders or RBMs. I think the reason is the time line of NN. Stacked RBM and autoencoder are introduced at 2006 and 2007, respectively. After employment of ReLU at 2009 unsupervised learning is partially abandoned (when ther... | Pre-training in deep convolutional neural network?
There are some papers but not as much as autoencoders or RBMs. I think the reason is the time line of NN. Stacked RBM and autoencoder are introduced at 2006 and 2007, respectively. After employment of |
7,381 | When to log transform a time series before fitting an ARIMA model | Some caveats before to proceed. As I often suggest to my students, use auto.arima() things only as a first approximation to your final result or if you want to have parsimonious model when you check that your rival theory-based model do better.
Data
You have clearly to start from the description of time series data you... | When to log transform a time series before fitting an ARIMA model | Some caveats before to proceed. As I often suggest to my students, use auto.arima() things only as a first approximation to your final result or if you want to have parsimonious model when you check t | When to log transform a time series before fitting an ARIMA model
Some caveats before to proceed. As I often suggest to my students, use auto.arima() things only as a first approximation to your final result or if you want to have parsimonious model when you check that your rival theory-based model do better.
Data
You ... | When to log transform a time series before fitting an ARIMA model
Some caveats before to proceed. As I often suggest to my students, use auto.arima() things only as a first approximation to your final result or if you want to have parsimonious model when you check t |
7,382 | When to log transform a time series before fitting an ARIMA model | Plot a graph of the data against time. If it looks like the variation increases with the level of the series, take logs. Otherwise model the original data. | When to log transform a time series before fitting an ARIMA model | Plot a graph of the data against time. If it looks like the variation increases with the level of the series, take logs. Otherwise model the original data. | When to log transform a time series before fitting an ARIMA model
Plot a graph of the data against time. If it looks like the variation increases with the level of the series, take logs. Otherwise model the original data. | When to log transform a time series before fitting an ARIMA model
Plot a graph of the data against time. If it looks like the variation increases with the level of the series, take logs. Otherwise model the original data. |
7,383 | When to log transform a time series before fitting an ARIMA model | By Their Fruits Ye Shall Know Them
The assumption (to be tested) is that the errors from the model have constant variance. Note this does not mean the errors from an assumed model. When you use a simple graphical analysis you are essentially assuming a linear model in time.
Thus if you have an inadequate model such as ... | When to log transform a time series before fitting an ARIMA model | By Their Fruits Ye Shall Know Them
The assumption (to be tested) is that the errors from the model have constant variance. Note this does not mean the errors from an assumed model. When you use a simp | When to log transform a time series before fitting an ARIMA model
By Their Fruits Ye Shall Know Them
The assumption (to be tested) is that the errors from the model have constant variance. Note this does not mean the errors from an assumed model. When you use a simple graphical analysis you are essentially assuming a l... | When to log transform a time series before fitting an ARIMA model
By Their Fruits Ye Shall Know Them
The assumption (to be tested) is that the errors from the model have constant variance. Note this does not mean the errors from an assumed model. When you use a simp |
7,384 | When to log transform a time series before fitting an ARIMA model | You might want to log-transform series when they are somehow naturally geometric or where the time value of an investment implies that you will be comparing to a minimal risk bond that has a positive return. This will make them more "linearizable", and therefore suitable for a simple differencing recurrence relationshi... | When to log transform a time series before fitting an ARIMA model | You might want to log-transform series when they are somehow naturally geometric or where the time value of an investment implies that you will be comparing to a minimal risk bond that has a positive | When to log transform a time series before fitting an ARIMA model
You might want to log-transform series when they are somehow naturally geometric or where the time value of an investment implies that you will be comparing to a minimal risk bond that has a positive return. This will make them more "linearizable", and t... | When to log transform a time series before fitting an ARIMA model
You might want to log-transform series when they are somehow naturally geometric or where the time value of an investment implies that you will be comparing to a minimal risk bond that has a positive |
7,385 | Expected prediction error - derivation | \begin{align*}
EPE(f) &= \int [y - f(x)]^2 Pr(dx, dy) \\
&= \int [y - f(x)]^2p(x,y)dxdy \\
&= \int_x \int_y [y - f(x)]^2p(x,y)dxdy \\
&= \int_x \int_y [y - f(x)]^2p(x)p(y|x)dxdy \\
&= \int_x\left( \int_y [y - f(x)]^2p(y|x)dy \right)p(x)dx \\
&= \int_x \left( E_{Y|X}([Y - f(X)]^2|X = x) \right) p(x)dx\\
&= E_{X}E_{Y|X}... | Expected prediction error - derivation | \begin{align*}
EPE(f) &= \int [y - f(x)]^2 Pr(dx, dy) \\
&= \int [y - f(x)]^2p(x,y)dxdy \\
&= \int_x \int_y [y - f(x)]^2p(x,y)dxdy \\
&= \int_x \int_y [y - f(x)]^2p(x)p(y|x)dxdy \\
&= \int_x\left( \i | Expected prediction error - derivation
\begin{align*}
EPE(f) &= \int [y - f(x)]^2 Pr(dx, dy) \\
&= \int [y - f(x)]^2p(x,y)dxdy \\
&= \int_x \int_y [y - f(x)]^2p(x,y)dxdy \\
&= \int_x \int_y [y - f(x)]^2p(x)p(y|x)dxdy \\
&= \int_x\left( \int_y [y - f(x)]^2p(y|x)dy \right)p(x)dx \\
&= \int_x \left( E_{Y|X}([Y - f(X)]^2|... | Expected prediction error - derivation
\begin{align*}
EPE(f) &= \int [y - f(x)]^2 Pr(dx, dy) \\
&= \int [y - f(x)]^2p(x,y)dxdy \\
&= \int_x \int_y [y - f(x)]^2p(x,y)dxdy \\
&= \int_x \int_y [y - f(x)]^2p(x)p(y|x)dxdy \\
&= \int_x\left( \i |
7,386 | Expected prediction error - derivation | The equation (2.11) is a consequence of the following little equality. For any two random variables $Z_1$ and $Z_2$, and any function $g$
$$ E_{Z_1, Z_2} (g(Z_1, Z_2)) = E_{Z_2}(E_{Z_1 \mid Z_2}(g(Z_1, Z_2) \mid Z_2)) $$
The notation $E_{Z_1, Z_2}$ is the expectation over the joint distribution. The notation $E_{Z_1 ... | Expected prediction error - derivation | The equation (2.11) is a consequence of the following little equality. For any two random variables $Z_1$ and $Z_2$, and any function $g$
$$ E_{Z_1, Z_2} (g(Z_1, Z_2)) = E_{Z_2}(E_{Z_1 \mid Z_2}(g(Z_ | Expected prediction error - derivation
The equation (2.11) is a consequence of the following little equality. For any two random variables $Z_1$ and $Z_2$, and any function $g$
$$ E_{Z_1, Z_2} (g(Z_1, Z_2)) = E_{Z_2}(E_{Z_1 \mid Z_2}(g(Z_1, Z_2) \mid Z_2)) $$
The notation $E_{Z_1, Z_2}$ is the expectation over the joi... | Expected prediction error - derivation
The equation (2.11) is a consequence of the following little equality. For any two random variables $Z_1$ and $Z_2$, and any function $g$
$$ E_{Z_1, Z_2} (g(Z_1, Z_2)) = E_{Z_2}(E_{Z_1 \mid Z_2}(g(Z_ |
7,387 | Expected prediction error - derivation | I find some parts in this book express in a way that is difficult to understand, especially for those who do not have a strong background in statistics.
I will try to make it simple and hope that you can get rid of confusion.
Claim 1 (Smoothing) $E(X) = E(E(X|Y)),\forall X,Y$
Proof:
Notice that E(Y) is a constant but... | Expected prediction error - derivation | I find some parts in this book express in a way that is difficult to understand, especially for those who do not have a strong background in statistics.
I will try to make it simple and hope that you | Expected prediction error - derivation
I find some parts in this book express in a way that is difficult to understand, especially for those who do not have a strong background in statistics.
I will try to make it simple and hope that you can get rid of confusion.
Claim 1 (Smoothing) $E(X) = E(E(X|Y)),\forall X,Y$
Pro... | Expected prediction error - derivation
I find some parts in this book express in a way that is difficult to understand, especially for those who do not have a strong background in statistics.
I will try to make it simple and hope that you |
7,388 | Expected prediction error - derivation | I found the explanation in the textbook and the other answers here (and Confusion in regression function derivation and Confused by Derivation of Regression Function) inadequate, so I decided to add my own version. I know many readers of the book and this website will not have a background in measure theory but for me ... | Expected prediction error - derivation | I found the explanation in the textbook and the other answers here (and Confusion in regression function derivation and Confused by Derivation of Regression Function) inadequate, so I decided to add m | Expected prediction error - derivation
I found the explanation in the textbook and the other answers here (and Confusion in regression function derivation and Confused by Derivation of Regression Function) inadequate, so I decided to add my own version. I know many readers of the book and this website will not have a b... | Expected prediction error - derivation
I found the explanation in the textbook and the other answers here (and Confusion in regression function derivation and Confused by Derivation of Regression Function) inadequate, so I decided to add m |
7,389 | Expected prediction error - derivation | I will try to explain this as per my understanding.
The main idea of the section 2.4 Statistical Decision Theory is to provide a framework for developing models(e.g. least-squares regression, k-NN).
As a first step(it is what author of this topic is asking about) in that section we consider regression function.
Idea of... | Expected prediction error - derivation | I will try to explain this as per my understanding.
The main idea of the section 2.4 Statistical Decision Theory is to provide a framework for developing models(e.g. least-squares regression, k-NN).
A | Expected prediction error - derivation
I will try to explain this as per my understanding.
The main idea of the section 2.4 Statistical Decision Theory is to provide a framework for developing models(e.g. least-squares regression, k-NN).
As a first step(it is what author of this topic is asking about) in that section w... | Expected prediction error - derivation
I will try to explain this as per my understanding.
The main idea of the section 2.4 Statistical Decision Theory is to provide a framework for developing models(e.g. least-squares regression, k-NN).
A |
7,390 | Difference between binomial, negative binomial and Poisson regression | Only the nature of your data and your question of interest can tell you which of these regressions are best for your situation. So there are no tests that will tell you which one of these methods is the best for you. (Click on the links of the regression methods below to see some worked examples in SPSS.)
If you have ... | Difference between binomial, negative binomial and Poisson regression | Only the nature of your data and your question of interest can tell you which of these regressions are best for your situation. So there are no tests that will tell you which one of these methods is t | Difference between binomial, negative binomial and Poisson regression
Only the nature of your data and your question of interest can tell you which of these regressions are best for your situation. So there are no tests that will tell you which one of these methods is the best for you. (Click on the links of the regres... | Difference between binomial, negative binomial and Poisson regression
Only the nature of your data and your question of interest can tell you which of these regressions are best for your situation. So there are no tests that will tell you which one of these methods is t |
7,391 | Difference between binomial, negative binomial and Poisson regression | This is too long to be a comment, so I will make it an answer.
The distinction between binomial on the whole hand and Poisson and negative binomial on the other is in the nature of the data; tests are irrelevant.
There are widespread myths about the requirements for Poisson regression. Variance equal to mean is chara... | Difference between binomial, negative binomial and Poisson regression | This is too long to be a comment, so I will make it an answer.
The distinction between binomial on the whole hand and Poisson and negative binomial on the other is in the nature of the data; tests ar | Difference between binomial, negative binomial and Poisson regression
This is too long to be a comment, so I will make it an answer.
The distinction between binomial on the whole hand and Poisson and negative binomial on the other is in the nature of the data; tests are irrelevant.
There are widespread myths about th... | Difference between binomial, negative binomial and Poisson regression
This is too long to be a comment, so I will make it an answer.
The distinction between binomial on the whole hand and Poisson and negative binomial on the other is in the nature of the data; tests ar |
7,392 | Difference between binomial, negative binomial and Poisson regression | In SPSS Statistics, the GENLIN command handles Poisson, negative binomial and a bunch of others. (Analyze > Generalized Linear Models). It is part of the Advanced Statistics option. | Difference between binomial, negative binomial and Poisson regression | In SPSS Statistics, the GENLIN command handles Poisson, negative binomial and a bunch of others. (Analyze > Generalized Linear Models). It is part of the Advanced Statistics option. | Difference between binomial, negative binomial and Poisson regression
In SPSS Statistics, the GENLIN command handles Poisson, negative binomial and a bunch of others. (Analyze > Generalized Linear Models). It is part of the Advanced Statistics option. | Difference between binomial, negative binomial and Poisson regression
In SPSS Statistics, the GENLIN command handles Poisson, negative binomial and a bunch of others. (Analyze > Generalized Linear Models). It is part of the Advanced Statistics option. |
7,393 | Difference between binomial, negative binomial and Poisson regression | Poisson/Negative binomial can also be used with a binary outcome with offset equal to one. Of course it necessitates that the data be from a prospective design (cohort, rct, etc). Poisson or NB regression gives the more appropriate effect measure (IRR) versus odds ratio from logistic regression.
NB regression is "safer... | Difference between binomial, negative binomial and Poisson regression | Poisson/Negative binomial can also be used with a binary outcome with offset equal to one. Of course it necessitates that the data be from a prospective design (cohort, rct, etc). Poisson or NB regres | Difference between binomial, negative binomial and Poisson regression
Poisson/Negative binomial can also be used with a binary outcome with offset equal to one. Of course it necessitates that the data be from a prospective design (cohort, rct, etc). Poisson or NB regression gives the more appropriate effect measure (IR... | Difference between binomial, negative binomial and Poisson regression
Poisson/Negative binomial can also be used with a binary outcome with offset equal to one. Of course it necessitates that the data be from a prospective design (cohort, rct, etc). Poisson or NB regres |
7,394 | How can I analytically prove that randomly dividing an amount results in an exponential distribution (of e.g. income and wealth)? | To make the problem simpler, let's consider the case where the allowed values of the share of each person is discrete, e.g., integers. Equivalently, one can also imagine partitioning the "income axis" into equally spaced intervals and approximating all values falling into a given interval by the midpoint.
Denoting the ... | How can I analytically prove that randomly dividing an amount results in an exponential distribution | To make the problem simpler, let's consider the case where the allowed values of the share of each person is discrete, e.g., integers. Equivalently, one can also imagine partitioning the "income axis" | How can I analytically prove that randomly dividing an amount results in an exponential distribution (of e.g. income and wealth)?
To make the problem simpler, let's consider the case where the allowed values of the share of each person is discrete, e.g., integers. Equivalently, one can also imagine partitioning the "in... | How can I analytically prove that randomly dividing an amount results in an exponential distribution
To make the problem simpler, let's consider the case where the allowed values of the share of each person is discrete, e.g., integers. Equivalently, one can also imagine partitioning the "income axis" |
7,395 | How can I analytically prove that randomly dividing an amount results in an exponential distribution (of e.g. income and wealth)? | In fact you can prove it's not actually exponential, almost trivially:
Compute the probability that a given share is greater than $500$ million. Compare with the probability that an exponential random variable is greater than $500$ million.
However, it's not too hard to see that for your uniform-gap example that it sho... | How can I analytically prove that randomly dividing an amount results in an exponential distribution | In fact you can prove it's not actually exponential, almost trivially:
Compute the probability that a given share is greater than $500$ million. Compare with the probability that an exponential random | How can I analytically prove that randomly dividing an amount results in an exponential distribution (of e.g. income and wealth)?
In fact you can prove it's not actually exponential, almost trivially:
Compute the probability that a given share is greater than $500$ million. Compare with the probability that an exponent... | How can I analytically prove that randomly dividing an amount results in an exponential distribution
In fact you can prove it's not actually exponential, almost trivially:
Compute the probability that a given share is greater than $500$ million. Compare with the probability that an exponential random |
7,396 | How can I analytically prove that randomly dividing an amount results in an exponential distribution (of e.g. income and wealth)? | Let's suppose the money is infinitely divisible so we can deal with real numbers rather than integers.
Then the uniform distribution of $t=500000000$ partitioned across $n=10000$ individuals will give a marginal density for each individual $$p(x)=\frac{n-1}{t}\left(1-\frac{x}{t}\right)^{n-2}$$ for $0 \le x \le t$, an... | How can I analytically prove that randomly dividing an amount results in an exponential distribution | Let's suppose the money is infinitely divisible so we can deal with real numbers rather than integers.
Then the uniform distribution of $t=500000000$ partitioned across $n=10000$ individuals will gi | How can I analytically prove that randomly dividing an amount results in an exponential distribution (of e.g. income and wealth)?
Let's suppose the money is infinitely divisible so we can deal with real numbers rather than integers.
Then the uniform distribution of $t=500000000$ partitioned across $n=10000$ individua... | How can I analytically prove that randomly dividing an amount results in an exponential distribution
Let's suppose the money is infinitely divisible so we can deal with real numbers rather than integers.
Then the uniform distribution of $t=500000000$ partitioned across $n=10000$ individuals will gi |
7,397 | How can I analytically prove that randomly dividing an amount results in an exponential distribution (of e.g. income and wealth)? | To say, "suppose you randomly divide 500 million in income among 10,000 people" is insufficiently specific to answer the question. There are many different random process that could be used to allocate a fixed amount of money to a fixed number of people, and each will have its own characteristics for the resulting dist... | How can I analytically prove that randomly dividing an amount results in an exponential distribution | To say, "suppose you randomly divide 500 million in income among 10,000 people" is insufficiently specific to answer the question. There are many different random process that could be used to allocat | How can I analytically prove that randomly dividing an amount results in an exponential distribution (of e.g. income and wealth)?
To say, "suppose you randomly divide 500 million in income among 10,000 people" is insufficiently specific to answer the question. There are many different random process that could be used ... | How can I analytically prove that randomly dividing an amount results in an exponential distribution
To say, "suppose you randomly divide 500 million in income among 10,000 people" is insufficiently specific to answer the question. There are many different random process that could be used to allocat |
7,398 | How can I analytically prove that randomly dividing an amount results in an exponential distribution (of e.g. income and wealth)? | Let me add something regarding your addendum.
In the continuous case, as pointed out by Glen_b and Henry, the exact PDF for the amount each person receives is
\begin{equation}
p(x) = \frac{N-1}{X}\left(1-\frac{x}{X}\right)^{N-2},
\end{equation}
where $N$ is the number of people, and $X$ is the total amount of money.
In... | How can I analytically prove that randomly dividing an amount results in an exponential distribution | Let me add something regarding your addendum.
In the continuous case, as pointed out by Glen_b and Henry, the exact PDF for the amount each person receives is
\begin{equation}
p(x) = \frac{N-1}{X}\lef | How can I analytically prove that randomly dividing an amount results in an exponential distribution (of e.g. income and wealth)?
Let me add something regarding your addendum.
In the continuous case, as pointed out by Glen_b and Henry, the exact PDF for the amount each person receives is
\begin{equation}
p(x) = \frac{N... | How can I analytically prove that randomly dividing an amount results in an exponential distribution
Let me add something regarding your addendum.
In the continuous case, as pointed out by Glen_b and Henry, the exact PDF for the amount each person receives is
\begin{equation}
p(x) = \frac{N-1}{X}\lef |
7,399 | How can I analytically prove that randomly dividing an amount results in an exponential distribution (of e.g. income and wealth)? | Good theoretical analysis done by the upvoted answers.
However, here's my simple, empirical view on why the distribution is exponential.
When you distribute the money randomly, let's consider you do it one-by-one.
Let S be the original sum.
For the first man, you must choose a random amount between 0 and S. Thus, on av... | How can I analytically prove that randomly dividing an amount results in an exponential distribution | Good theoretical analysis done by the upvoted answers.
However, here's my simple, empirical view on why the distribution is exponential.
When you distribute the money randomly, let's consider you do i | How can I analytically prove that randomly dividing an amount results in an exponential distribution (of e.g. income and wealth)?
Good theoretical analysis done by the upvoted answers.
However, here's my simple, empirical view on why the distribution is exponential.
When you distribute the money randomly, let's conside... | How can I analytically prove that randomly dividing an amount results in an exponential distribution
Good theoretical analysis done by the upvoted answers.
However, here's my simple, empirical view on why the distribution is exponential.
When you distribute the money randomly, let's consider you do i |
7,400 | Proof of convergence of k-means | First, there are at most $k^N$ ways to partition $N$ data points into $k$ clusters; each such partition can be called a "clustering". This is a large but finite number. For each iteration of the algorithm, we produce a new clustering based only on the old clustering. Notice that
if the old clustering is the same as t... | Proof of convergence of k-means | First, there are at most $k^N$ ways to partition $N$ data points into $k$ clusters; each such partition can be called a "clustering". This is a large but finite number. For each iteration of the algor | Proof of convergence of k-means
First, there are at most $k^N$ ways to partition $N$ data points into $k$ clusters; each such partition can be called a "clustering". This is a large but finite number. For each iteration of the algorithm, we produce a new clustering based only on the old clustering. Notice that
if the... | Proof of convergence of k-means
First, there are at most $k^N$ ways to partition $N$ data points into $k$ clusters; each such partition can be called a "clustering". This is a large but finite number. For each iteration of the algor |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.