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 |
|---|---|---|---|---|---|---|
15,001 | Modern Use Cases of Restricted Boltzmann Machines (RBM's)? | I recently found this paper on "Boltzmann Encoded Adversarial Machines" which integrates RBMs with CNNs as a generative model.
The authors show it is mathematically "better" in some ways, and show some toy examples where BEAM seems far more capable of accurately learning the data distribution compared to other GAN mod... | Modern Use Cases of Restricted Boltzmann Machines (RBM's)? | I recently found this paper on "Boltzmann Encoded Adversarial Machines" which integrates RBMs with CNNs as a generative model.
The authors show it is mathematically "better" in some ways, and show so | Modern Use Cases of Restricted Boltzmann Machines (RBM's)?
I recently found this paper on "Boltzmann Encoded Adversarial Machines" which integrates RBMs with CNNs as a generative model.
The authors show it is mathematically "better" in some ways, and show some toy examples where BEAM seems far more capable of accurate... | Modern Use Cases of Restricted Boltzmann Machines (RBM's)?
I recently found this paper on "Boltzmann Encoded Adversarial Machines" which integrates RBMs with CNNs as a generative model.
The authors show it is mathematically "better" in some ways, and show so |
15,002 | How can I 'dodge' the position of geom_point in ggplot2? | The group should = INDEX instead of ntrunc in the aes.
plot = ggplot(data, aes(x=ntrunc, y=beta_best, group=INDEX, colour=INDEX)) +
geom_point(aes(shape=detectable), na.rm=TRUE, position="dodge") +
geom_errorbar(aes(x=ntrunc, ymax=beta_high, ymin=beta_low), na.rm=TRUE, position="dodge")
The plot looks better no... | How can I 'dodge' the position of geom_point in ggplot2? | The group should = INDEX instead of ntrunc in the aes.
plot = ggplot(data, aes(x=ntrunc, y=beta_best, group=INDEX, colour=INDEX)) +
geom_point(aes(shape=detectable), na.rm=TRUE, position="dodge") | How can I 'dodge' the position of geom_point in ggplot2?
The group should = INDEX instead of ntrunc in the aes.
plot = ggplot(data, aes(x=ntrunc, y=beta_best, group=INDEX, colour=INDEX)) +
geom_point(aes(shape=detectable), na.rm=TRUE, position="dodge") +
geom_errorbar(aes(x=ntrunc, ymax=beta_high, ymin=beta_low)... | How can I 'dodge' the position of geom_point in ggplot2?
The group should = INDEX instead of ntrunc in the aes.
plot = ggplot(data, aes(x=ntrunc, y=beta_best, group=INDEX, colour=INDEX)) +
geom_point(aes(shape=detectable), na.rm=TRUE, position="dodge") |
15,003 | Understanding d-separation theory in causal Bayesian networks | Is it not intuitive that you cannot reason from cause to unobserved effect to another cause? If the rain (B) and the sprinkler (D) are causes of the wet ground (C), then can you argue that seeing rain implies that the ground is probably wet, and continue to reason that the sprinkler must be on since the ground is wet?... | Understanding d-separation theory in causal Bayesian networks | Is it not intuitive that you cannot reason from cause to unobserved effect to another cause? If the rain (B) and the sprinkler (D) are causes of the wet ground (C), then can you argue that seeing rai | Understanding d-separation theory in causal Bayesian networks
Is it not intuitive that you cannot reason from cause to unobserved effect to another cause? If the rain (B) and the sprinkler (D) are causes of the wet ground (C), then can you argue that seeing rain implies that the ground is probably wet, and continue to... | Understanding d-separation theory in causal Bayesian networks
Is it not intuitive that you cannot reason from cause to unobserved effect to another cause? If the rain (B) and the sprinkler (D) are causes of the wet ground (C), then can you argue that seeing rai |
15,004 | Understanding d-separation theory in causal Bayesian networks | Let's forget about X for a moment and consider just the collider of B, C and D. The reason that the v-structure can block the path between B and D is that, in general, if you have two independent random variables (B and D) that affect the same outcome (C), then knowing the outcome can allow you to draw conclusions abou... | Understanding d-separation theory in causal Bayesian networks | Let's forget about X for a moment and consider just the collider of B, C and D. The reason that the v-structure can block the path between B and D is that, in general, if you have two independent rand | Understanding d-separation theory in causal Bayesian networks
Let's forget about X for a moment and consider just the collider of B, C and D. The reason that the v-structure can block the path between B and D is that, in general, if you have two independent random variables (B and D) that affect the same outcome (C), t... | Understanding d-separation theory in causal Bayesian networks
Let's forget about X for a moment and consider just the collider of B, C and D. The reason that the v-structure can block the path between B and D is that, in general, if you have two independent rand |
15,005 | Understanding d-separation theory in causal Bayesian networks | Well, up to this point, everything is OK for me since the flow of the
information occurs according to intuitive cause-effect relationships.
But I don't get the special behavior of so called "V-structures" or
"Colliders" in this scheme.
Then the hard nut to crack here is the v-structure. I'd like to illustrate th... | Understanding d-separation theory in causal Bayesian networks | Well, up to this point, everything is OK for me since the flow of the
information occurs according to intuitive cause-effect relationships.
But I don't get the special behavior of so called "V-str | Understanding d-separation theory in causal Bayesian networks
Well, up to this point, everything is OK for me since the flow of the
information occurs according to intuitive cause-effect relationships.
But I don't get the special behavior of so called "V-structures" or
"Colliders" in this scheme.
Then the hard n... | Understanding d-separation theory in causal Bayesian networks
Well, up to this point, everything is OK for me since the flow of the
information occurs according to intuitive cause-effect relationships.
But I don't get the special behavior of so called "V-str |
15,006 | Quiz: Tell the classifier by its decision boundary | Really like this question!
First thing that comes to mind is the division between linear and non-linear classifiers. Three classifiers are linear (linear svm, perceptron and logistic regression) and three plots show a linear decision boundary (A, B, C). So lets start with those.
Linear
The most sallient linear plot i... | Quiz: Tell the classifier by its decision boundary | Really like this question!
First thing that comes to mind is the division between linear and non-linear classifiers. Three classifiers are linear (linear svm, perceptron and logistic regression) and | Quiz: Tell the classifier by its decision boundary
Really like this question!
First thing that comes to mind is the division between linear and non-linear classifiers. Three classifiers are linear (linear svm, perceptron and logistic regression) and three plots show a linear decision boundary (A, B, C). So lets start ... | Quiz: Tell the classifier by its decision boundary
Really like this question!
First thing that comes to mind is the division between linear and non-linear classifiers. Three classifiers are linear (linear svm, perceptron and logistic regression) and |
15,007 | What is the difference between regular PCA and probabilistic PCA? | The goal of PPCA is not to give better results than PCA, but to permit a broad range of future extensions and analysis. The paper states some of the advantages clearly in the introduction, ie/eg:
"the definition of a likelihood measure enables a comparison with other probabilistic techniques, while facilitating statist... | What is the difference between regular PCA and probabilistic PCA? | The goal of PPCA is not to give better results than PCA, but to permit a broad range of future extensions and analysis. The paper states some of the advantages clearly in the introduction, ie/eg:
"the | What is the difference between regular PCA and probabilistic PCA?
The goal of PPCA is not to give better results than PCA, but to permit a broad range of future extensions and analysis. The paper states some of the advantages clearly in the introduction, ie/eg:
"the definition of a likelihood measure enables a comparis... | What is the difference between regular PCA and probabilistic PCA?
The goal of PPCA is not to give better results than PCA, but to permit a broad range of future extensions and analysis. The paper states some of the advantages clearly in the introduction, ie/eg:
"the |
15,008 | What is shrinkage? | In 1961 James and Stein published an article called "Estimation with Quadratic Loss" https://projecteuclid.org/download/pdf_1/euclid.bsmsp/1200512173 . While it doesn't specifically coin the term shrinkage, they discuss minimax estimators for high dimensional (actually even for a 3 parameter location) statistics that h... | What is shrinkage? | In 1961 James and Stein published an article called "Estimation with Quadratic Loss" https://projecteuclid.org/download/pdf_1/euclid.bsmsp/1200512173 . While it doesn't specifically coin the term shri | What is shrinkage?
In 1961 James and Stein published an article called "Estimation with Quadratic Loss" https://projecteuclid.org/download/pdf_1/euclid.bsmsp/1200512173 . While it doesn't specifically coin the term shrinkage, they discuss minimax estimators for high dimensional (actually even for a 3 parameter location... | What is shrinkage?
In 1961 James and Stein published an article called "Estimation with Quadratic Loss" https://projecteuclid.org/download/pdf_1/euclid.bsmsp/1200512173 . While it doesn't specifically coin the term shri |
15,009 | What is shrinkage? | This is about regularization. Suppose you would like to fit a curve and you use a square loss function (you can pick different). By fit you would like to recover the parameters that govern the process which generated that curve. Now imagine that you would like to fit this curve using 100th polynomial (just for example)... | What is shrinkage? | This is about regularization. Suppose you would like to fit a curve and you use a square loss function (you can pick different). By fit you would like to recover the parameters that govern the process | What is shrinkage?
This is about regularization. Suppose you would like to fit a curve and you use a square loss function (you can pick different). By fit you would like to recover the parameters that govern the process which generated that curve. Now imagine that you would like to fit this curve using 100th polynomial... | What is shrinkage?
This is about regularization. Suppose you would like to fit a curve and you use a square loss function (you can pick different). By fit you would like to recover the parameters that govern the process |
15,010 | Is accuracy = 1- test error rate | In principle, accuracy is the fraction of properly predicted cases.
This is the same as 1 - the fraction of misclassified cases or 1 - the *error* (rate).
Both terms may be sometimes used in a more vague way, however, and cover different things like class-balanced error/accuracy or even F-score or AUROC -- it is alway... | Is accuracy = 1- test error rate | In principle, accuracy is the fraction of properly predicted cases.
This is the same as 1 - the fraction of misclassified cases or 1 - the *error* (rate).
Both terms may be sometimes used in a more v | Is accuracy = 1- test error rate
In principle, accuracy is the fraction of properly predicted cases.
This is the same as 1 - the fraction of misclassified cases or 1 - the *error* (rate).
Both terms may be sometimes used in a more vague way, however, and cover different things like class-balanced error/accuracy or eve... | Is accuracy = 1- test error rate
In principle, accuracy is the fraction of properly predicted cases.
This is the same as 1 - the fraction of misclassified cases or 1 - the *error* (rate).
Both terms may be sometimes used in a more v |
15,011 | Is accuracy = 1- test error rate | @mbq answered:
"1-the fraction of misclassified cases, that is error(rate)"
However, it seems wrong as misclassification and error are the same thing. See below (from http://www.dataschool.io/simple-guide-to-confusion-matrix-terminology/):
Accuracy: Overall, how often is the classifier correct?
(TP+TN)/total = (100+... | Is accuracy = 1- test error rate | @mbq answered:
"1-the fraction of misclassified cases, that is error(rate)"
However, it seems wrong as misclassification and error are the same thing. See below (from http://www.dataschool.io/simpl | Is accuracy = 1- test error rate
@mbq answered:
"1-the fraction of misclassified cases, that is error(rate)"
However, it seems wrong as misclassification and error are the same thing. See below (from http://www.dataschool.io/simple-guide-to-confusion-matrix-terminology/):
Accuracy: Overall, how often is the classifi... | Is accuracy = 1- test error rate
@mbq answered:
"1-the fraction of misclassified cases, that is error(rate)"
However, it seems wrong as misclassification and error are the same thing. See below (from http://www.dataschool.io/simpl |
15,012 | Outlier detection in very small sets | Outliers in small samples can always be very tricky to detect. In most cases actually I would advocate that if you feel that your data are not bluntly corrupted, an "outlierish" value might not be problematic and its exclusion might be unreasonable. Probably using robust statistical techniques will be more sensible and... | Outlier detection in very small sets | Outliers in small samples can always be very tricky to detect. In most cases actually I would advocate that if you feel that your data are not bluntly corrupted, an "outlierish" value might not be pro | Outlier detection in very small sets
Outliers in small samples can always be very tricky to detect. In most cases actually I would advocate that if you feel that your data are not bluntly corrupted, an "outlierish" value might not be problematic and its exclusion might be unreasonable. Probably using robust statistical... | Outlier detection in very small sets
Outliers in small samples can always be very tricky to detect. In most cases actually I would advocate that if you feel that your data are not bluntly corrupted, an "outlierish" value might not be pro |
15,013 | Outlier detection in very small sets | Point the first - it may be worth going back to rgb color. It's rarely good to throw away data, and the magnitude of the rgb vector isn't the only way to represent brightness - perceived brightness is different, as is value in HSV.
But putting that to one side and dealing with the data you do have, have you considered ... | Outlier detection in very small sets | Point the first - it may be worth going back to rgb color. It's rarely good to throw away data, and the magnitude of the rgb vector isn't the only way to represent brightness - perceived brightness is | Outlier detection in very small sets
Point the first - it may be worth going back to rgb color. It's rarely good to throw away data, and the magnitude of the rgb vector isn't the only way to represent brightness - perceived brightness is different, as is value in HSV.
But putting that to one side and dealing with the d... | Outlier detection in very small sets
Point the first - it may be worth going back to rgb color. It's rarely good to throw away data, and the magnitude of the rgb vector isn't the only way to represent brightness - perceived brightness is |
15,014 | Outlier detection in very small sets | Dixon's Q-test for outliers in very small datasets seems fits well to this kind of situation:
http://en.wikipedia.org/wiki/Dixon%27s_Q_test
http://www.chem.uoa.gr/applets/AppletQtest/Text_Qtest2.htm | Outlier detection in very small sets | Dixon's Q-test for outliers in very small datasets seems fits well to this kind of situation:
http://en.wikipedia.org/wiki/Dixon%27s_Q_test
http://www.chem.uoa.gr/applets/AppletQtest/Text_Qtest2.htm | Outlier detection in very small sets
Dixon's Q-test for outliers in very small datasets seems fits well to this kind of situation:
http://en.wikipedia.org/wiki/Dixon%27s_Q_test
http://www.chem.uoa.gr/applets/AppletQtest/Text_Qtest2.htm | Outlier detection in very small sets
Dixon's Q-test for outliers in very small datasets seems fits well to this kind of situation:
http://en.wikipedia.org/wiki/Dixon%27s_Q_test
http://www.chem.uoa.gr/applets/AppletQtest/Text_Qtest2.htm |
15,015 | Problem defining ARIMA order | How do I select the best ARIMA model (by trying all different orders and checking the best MASE/MAPE/MSE? where the selection of performance measurement can be a discussion in it's own..)
Out of sample risk estimates are the gold standard for performance evaluation, and therefore for model selection. Ideally, you cro... | Problem defining ARIMA order | How do I select the best ARIMA model (by trying all different orders and checking the best MASE/MAPE/MSE? where the selection of performance measurement can be a discussion in it's own..)
Out of sam | Problem defining ARIMA order
How do I select the best ARIMA model (by trying all different orders and checking the best MASE/MAPE/MSE? where the selection of performance measurement can be a discussion in it's own..)
Out of sample risk estimates are the gold standard for performance evaluation, and therefore for mode... | Problem defining ARIMA order
How do I select the best ARIMA model (by trying all different orders and checking the best MASE/MAPE/MSE? where the selection of performance measurement can be a discussion in it's own..)
Out of sam |
15,016 | Generating random samples from a custom distribution | It looks like you figured out that your code works, but @Aniko pointed out that you could improve its efficiency. Your biggest speed gain would probably come from pre-allocating memory for z so that you're not growing it inside a loop. Something like z <- rep(NA, nsamples) should do the trick. You may get a small speed... | Generating random samples from a custom distribution | It looks like you figured out that your code works, but @Aniko pointed out that you could improve its efficiency. Your biggest speed gain would probably come from pre-allocating memory for z so that y | Generating random samples from a custom distribution
It looks like you figured out that your code works, but @Aniko pointed out that you could improve its efficiency. Your biggest speed gain would probably come from pre-allocating memory for z so that you're not growing it inside a loop. Something like z <- rep(NA, nsa... | Generating random samples from a custom distribution
It looks like you figured out that your code works, but @Aniko pointed out that you could improve its efficiency. Your biggest speed gain would probably come from pre-allocating memory for z so that y |
15,017 | Median of Medians calculation | The median of medians is not the same as the median of the raw scores. A simple case of this is that when you have an odd number of sales, the median is the middle value; when you have an even number of sales, the median is commonly taken as the average between those two values. A more "real world" challenge to this i... | Median of Medians calculation | The median of medians is not the same as the median of the raw scores. A simple case of this is that when you have an odd number of sales, the median is the middle value; when you have an even number | Median of Medians calculation
The median of medians is not the same as the median of the raw scores. A simple case of this is that when you have an odd number of sales, the median is the middle value; when you have an even number of sales, the median is commonly taken as the average between those two values. A more "r... | Median of Medians calculation
The median of medians is not the same as the median of the raw scores. A simple case of this is that when you have an odd number of sales, the median is the middle value; when you have an even number |
15,018 | Using R and plm to estimate fixed-effects models that include interactions with time | Try using
fe3 <- plm(y ~ year * const, index = c('ID', 'year'), data = tmp)
instead. It even works if you are redundantly including time fixed effects in the * interaction (because time is being fixed effect-ed out):
fe4 <- plm(y ~ year * const, index = c('ID', 'year'), data = tmp, effect = "twoway") | Using R and plm to estimate fixed-effects models that include interactions with time | Try using
fe3 <- plm(y ~ year * const, index = c('ID', 'year'), data = tmp)
instead. It even works if you are redundantly including time fixed effects in the * interaction (because time is being fixe | Using R and plm to estimate fixed-effects models that include interactions with time
Try using
fe3 <- plm(y ~ year * const, index = c('ID', 'year'), data = tmp)
instead. It even works if you are redundantly including time fixed effects in the * interaction (because time is being fixed effect-ed out):
fe4 <- plm(y ~ ye... | Using R and plm to estimate fixed-effects models that include interactions with time
Try using
fe3 <- plm(y ~ year * const, index = c('ID', 'year'), data = tmp)
instead. It even works if you are redundantly including time fixed effects in the * interaction (because time is being fixe |
15,019 | What is the frequentist take on the voltmeter story? | In frequentist inference, we want to determine how frequently something would have happened if a given stochastic process were repeatedly realized. That is the starting point for the theory of p-values, confidence intervals, and the like. However, in many applied projects, the "given" process is not really given, and t... | What is the frequentist take on the voltmeter story? | In frequentist inference, we want to determine how frequently something would have happened if a given stochastic process were repeatedly realized. That is the starting point for the theory of p-value | What is the frequentist take on the voltmeter story?
In frequentist inference, we want to determine how frequently something would have happened if a given stochastic process were repeatedly realized. That is the starting point for the theory of p-values, confidence intervals, and the like. However, in many applied pro... | What is the frequentist take on the voltmeter story?
In frequentist inference, we want to determine how frequently something would have happened if a given stochastic process were repeatedly realized. That is the starting point for the theory of p-value |
15,020 | What is the frequentist take on the voltmeter story? | There seems a logical fallacy. Whether or not the 1000 volt meter was working, the engineer says "if any readings would have been over 100, I would have used the other meter." But how would he know that the voltage was >100 without having used the 1000 volt meter?
I don't think this puzzle is well-enough formulated t... | What is the frequentist take on the voltmeter story? | There seems a logical fallacy. Whether or not the 1000 volt meter was working, the engineer says "if any readings would have been over 100, I would have used the other meter." But how would he know | What is the frequentist take on the voltmeter story?
There seems a logical fallacy. Whether or not the 1000 volt meter was working, the engineer says "if any readings would have been over 100, I would have used the other meter." But how would he know that the voltage was >100 without having used the 1000 volt meter?
... | What is the frequentist take on the voltmeter story?
There seems a logical fallacy. Whether or not the 1000 volt meter was working, the engineer says "if any readings would have been over 100, I would have used the other meter." But how would he know |
15,021 | What are "coefficients of linear discriminants" in LDA? | If you multiply each value of LDA1 (the first linear discriminant) by the corresponding elements of the predictor variables and sum them ($-0.6420190\times$Lag1$+ -0.5135293\times$Lag2) you get a score for each respondent. This score along the the prior are used to compute the posterior probability of class membership ... | What are "coefficients of linear discriminants" in LDA? | If you multiply each value of LDA1 (the first linear discriminant) by the corresponding elements of the predictor variables and sum them ($-0.6420190\times$Lag1$+ -0.5135293\times$Lag2) you get a scor | What are "coefficients of linear discriminants" in LDA?
If you multiply each value of LDA1 (the first linear discriminant) by the corresponding elements of the predictor variables and sum them ($-0.6420190\times$Lag1$+ -0.5135293\times$Lag2) you get a score for each respondent. This score along the the prior are used t... | What are "coefficients of linear discriminants" in LDA?
If you multiply each value of LDA1 (the first linear discriminant) by the corresponding elements of the predictor variables and sum them ($-0.6420190\times$Lag1$+ -0.5135293\times$Lag2) you get a scor |
15,022 | What are "coefficients of linear discriminants" in LDA? | Discriminant in the context of ISLR, 4.6.3 Linear Discriminant Analysis, pp161-162 is, as I understand, the value of
\begin{equation}
\hat\delta_2(\vec x) - \hat\delta_1(\vec x) = {\vec x}^T\hat\Sigma^{-1}\Bigl(\vec{\hat\mu}_2 - \vec{\hat\mu}_1\Bigr) - \frac{1}{2}\Bigl(\vec{\hat\mu}_2 + \vec{\hat\mu}_1\Bigr)^T\hat\Sig... | What are "coefficients of linear discriminants" in LDA? | Discriminant in the context of ISLR, 4.6.3 Linear Discriminant Analysis, pp161-162 is, as I understand, the value of
\begin{equation}
\hat\delta_2(\vec x) - \hat\delta_1(\vec x) = {\vec x}^T\hat\Sigm | What are "coefficients of linear discriminants" in LDA?
Discriminant in the context of ISLR, 4.6.3 Linear Discriminant Analysis, pp161-162 is, as I understand, the value of
\begin{equation}
\hat\delta_2(\vec x) - \hat\delta_1(\vec x) = {\vec x}^T\hat\Sigma^{-1}\Bigl(\vec{\hat\mu}_2 - \vec{\hat\mu}_1\Bigr) - \frac{1}{2... | What are "coefficients of linear discriminants" in LDA?
Discriminant in the context of ISLR, 4.6.3 Linear Discriminant Analysis, pp161-162 is, as I understand, the value of
\begin{equation}
\hat\delta_2(\vec x) - \hat\delta_1(\vec x) = {\vec x}^T\hat\Sigm |
15,023 | What are "coefficients of linear discriminants" in LDA? | The theory behind this function is "Fisher's Method for Discriminating among Several Population". I recommend chapter 11.6 in applied multivariate statistical analysis(ISBN: 9780134995397) for reference. | What are "coefficients of linear discriminants" in LDA? | The theory behind this function is "Fisher's Method for Discriminating among Several Population". I recommend chapter 11.6 in applied multivariate statistical analysis(ISBN: 9780134995397) for referen | What are "coefficients of linear discriminants" in LDA?
The theory behind this function is "Fisher's Method for Discriminating among Several Population". I recommend chapter 11.6 in applied multivariate statistical analysis(ISBN: 9780134995397) for reference. | What are "coefficients of linear discriminants" in LDA?
The theory behind this function is "Fisher's Method for Discriminating among Several Population". I recommend chapter 11.6 in applied multivariate statistical analysis(ISBN: 9780134995397) for referen |
15,024 | Choosing seasonal decomposition method | If you are willing to learn to understand the diagnostics, X12-ARIMA provides a boatload of diagnostics that range from (ASCII) graphs to rule-of-thumb indicators. Learning and understanding the diagnostics is something of an education in time series and seasonal adjustment.
On the other hand, X12-ARIMA software is a o... | Choosing seasonal decomposition method | If you are willing to learn to understand the diagnostics, X12-ARIMA provides a boatload of diagnostics that range from (ASCII) graphs to rule-of-thumb indicators. Learning and understanding the diagn | Choosing seasonal decomposition method
If you are willing to learn to understand the diagnostics, X12-ARIMA provides a boatload of diagnostics that range from (ASCII) graphs to rule-of-thumb indicators. Learning and understanding the diagnostics is something of an education in time series and seasonal adjustment.
On th... | Choosing seasonal decomposition method
If you are willing to learn to understand the diagnostics, X12-ARIMA provides a boatload of diagnostics that range from (ASCII) graphs to rule-of-thumb indicators. Learning and understanding the diagn |
15,025 | Choosing seasonal decomposition method | That's an answer for question 2.
STL: http://www.wessa.net/download/stl.pdf
X-12-ARIMA (and much more): http://www.census.gov/srd/www/sapaper/sapaper.html | Choosing seasonal decomposition method | That's an answer for question 2.
STL: http://www.wessa.net/download/stl.pdf
X-12-ARIMA (and much more): http://www.census.gov/srd/www/sapaper/sapaper.html | Choosing seasonal decomposition method
That's an answer for question 2.
STL: http://www.wessa.net/download/stl.pdf
X-12-ARIMA (and much more): http://www.census.gov/srd/www/sapaper/sapaper.html | Choosing seasonal decomposition method
That's an answer for question 2.
STL: http://www.wessa.net/download/stl.pdf
X-12-ARIMA (and much more): http://www.census.gov/srd/www/sapaper/sapaper.html |
15,026 | Robust PCA vs. robust Mahalanobis distance for outlier detection | This paper compares some methods in this area. They refer to the Robust PCA approach you linked to as "PCP" (principal components pursuit) and the family of methods you linked to for robust covariance estimation as M-estimators.
They argue that
PCP is designed for uniformly corrupted coordinates of data, instead of c... | Robust PCA vs. robust Mahalanobis distance for outlier detection | This paper compares some methods in this area. They refer to the Robust PCA approach you linked to as "PCP" (principal components pursuit) and the family of methods you linked to for robust covarianc | Robust PCA vs. robust Mahalanobis distance for outlier detection
This paper compares some methods in this area. They refer to the Robust PCA approach you linked to as "PCP" (principal components pursuit) and the family of methods you linked to for robust covariance estimation as M-estimators.
They argue that
PCP is d... | Robust PCA vs. robust Mahalanobis distance for outlier detection
This paper compares some methods in this area. They refer to the Robust PCA approach you linked to as "PCP" (principal components pursuit) and the family of methods you linked to for robust covarianc |
15,027 | Mean(scores) vs Score(concatenation) in cross validation | The described difference is IMHO bogus.
You'll observe it only if the distribution of truely positive cases (i.e. reference method says it is a positive case) is very unequal over the folds (as in the example) and the number of relevant test cases (the denominator of the performance measure we're talking about, here th... | Mean(scores) vs Score(concatenation) in cross validation | The described difference is IMHO bogus.
You'll observe it only if the distribution of truely positive cases (i.e. reference method says it is a positive case) is very unequal over the folds (as in the | Mean(scores) vs Score(concatenation) in cross validation
The described difference is IMHO bogus.
You'll observe it only if the distribution of truely positive cases (i.e. reference method says it is a positive case) is very unequal over the folds (as in the example) and the number of relevant test cases (the denominato... | Mean(scores) vs Score(concatenation) in cross validation
The described difference is IMHO bogus.
You'll observe it only if the distribution of truely positive cases (i.e. reference method says it is a positive case) is very unequal over the folds (as in the |
15,028 | Mean(scores) vs Score(concatenation) in cross validation | You should do score(concatenation). It is a common misconception in the field that mean(scores) is the best way. It can introduce more bias into your estimate, especially on rare classes, as in your case. Here is a paper backing this up:
http://www.kdd.org/exploration_files/v12-1-p49-forman-sigkdd.pdf
In the paper, the... | Mean(scores) vs Score(concatenation) in cross validation | You should do score(concatenation). It is a common misconception in the field that mean(scores) is the best way. It can introduce more bias into your estimate, especially on rare classes, as in your c | Mean(scores) vs Score(concatenation) in cross validation
You should do score(concatenation). It is a common misconception in the field that mean(scores) is the best way. It can introduce more bias into your estimate, especially on rare classes, as in your case. Here is a paper backing this up:
http://www.kdd.org/explor... | Mean(scores) vs Score(concatenation) in cross validation
You should do score(concatenation). It is a common misconception in the field that mean(scores) is the best way. It can introduce more bias into your estimate, especially on rare classes, as in your c |
15,029 | Out-of-core data analysis options | if you're maxing out at 500,000 records x 2,000 variables, i would spend a little more money on RAM for your laptop and be done with it. if you have 16GB, you can probably read the data set you're describing into R directly. and at that point, you'll be able to do far more - and very quickly.. but you say that's not ... | Out-of-core data analysis options | if you're maxing out at 500,000 records x 2,000 variables, i would spend a little more money on RAM for your laptop and be done with it. if you have 16GB, you can probably read the data set you're de | Out-of-core data analysis options
if you're maxing out at 500,000 records x 2,000 variables, i would spend a little more money on RAM for your laptop and be done with it. if you have 16GB, you can probably read the data set you're describing into R directly. and at that point, you'll be able to do far more - and very... | Out-of-core data analysis options
if you're maxing out at 500,000 records x 2,000 variables, i would spend a little more money on RAM for your laptop and be done with it. if you have 16GB, you can probably read the data set you're de |
15,030 | Out-of-core data analysis options | Maybe it is not so much about the applications/problems you are aiming for, and its characteristics, but more about the algorithms and variants you are using. More concretely, in order to handle big data, many variants based on stochastic gradient descent of popular algorithms, like SVM, have appear which are able to h... | Out-of-core data analysis options | Maybe it is not so much about the applications/problems you are aiming for, and its characteristics, but more about the algorithms and variants you are using. More concretely, in order to handle big d | Out-of-core data analysis options
Maybe it is not so much about the applications/problems you are aiming for, and its characteristics, but more about the algorithms and variants you are using. More concretely, in order to handle big data, many variants based on stochastic gradient descent of popular algorithms, like SV... | Out-of-core data analysis options
Maybe it is not so much about the applications/problems you are aiming for, and its characteristics, but more about the algorithms and variants you are using. More concretely, in order to handle big d |
15,031 | Out-of-core data analysis options | You already seem comfortable with SAS, and your datasets are small enough to fit in RAM, but maybe you can't fit enough RAM into your laptop. If you don't mind sticking with SAS, how about you just connect to SAS running remotely on a computer with lots of RAM? I have no idea how that works, but these links might get y... | Out-of-core data analysis options | You already seem comfortable with SAS, and your datasets are small enough to fit in RAM, but maybe you can't fit enough RAM into your laptop. If you don't mind sticking with SAS, how about you just co | Out-of-core data analysis options
You already seem comfortable with SAS, and your datasets are small enough to fit in RAM, but maybe you can't fit enough RAM into your laptop. If you don't mind sticking with SAS, how about you just connect to SAS running remotely on a computer with lots of RAM? I have no idea how that ... | Out-of-core data analysis options
You already seem comfortable with SAS, and your datasets are small enough to fit in RAM, but maybe you can't fit enough RAM into your laptop. If you don't mind sticking with SAS, how about you just co |
15,032 | Out-of-core data analysis options | Graphchi is excellent, and can handle huge datasets. It's a bit of a pain to work with, but it can handle graphical and non-graphical data. | Out-of-core data analysis options | Graphchi is excellent, and can handle huge datasets. It's a bit of a pain to work with, but it can handle graphical and non-graphical data. | Out-of-core data analysis options
Graphchi is excellent, and can handle huge datasets. It's a bit of a pain to work with, but it can handle graphical and non-graphical data. | Out-of-core data analysis options
Graphchi is excellent, and can handle huge datasets. It's a bit of a pain to work with, but it can handle graphical and non-graphical data. |
15,033 | Out-of-core data analysis options | I recently came across SFrames and GraphLab Create.
These are libraries for Python that offer the kind of functionality you seem to be looking for
From the Pypi site: "SFrame is an scalable, out-of-core dataframe, which allows you to work with datasets that are larger than the amount of RAM on your system." So think ... | Out-of-core data analysis options | I recently came across SFrames and GraphLab Create.
These are libraries for Python that offer the kind of functionality you seem to be looking for
From the Pypi site: "SFrame is an scalable, out-of- | Out-of-core data analysis options
I recently came across SFrames and GraphLab Create.
These are libraries for Python that offer the kind of functionality you seem to be looking for
From the Pypi site: "SFrame is an scalable, out-of-core dataframe, which allows you to work with datasets that are larger than the amount... | Out-of-core data analysis options
I recently came across SFrames and GraphLab Create.
These are libraries for Python that offer the kind of functionality you seem to be looking for
From the Pypi site: "SFrame is an scalable, out-of- |
15,034 | Out-of-core data analysis options | Have you considered a "Real", non-interpreted language like Fortran?
It seems like the suggestions so far are either very vendor dependent or interpreted. Interpreted methods are notoriously bad at memory intense applications. MatLab may be much higher level of a language than "C" but the memory handling optimization... | Out-of-core data analysis options | Have you considered a "Real", non-interpreted language like Fortran?
It seems like the suggestions so far are either very vendor dependent or interpreted. Interpreted methods are notoriously bad at m | Out-of-core data analysis options
Have you considered a "Real", non-interpreted language like Fortran?
It seems like the suggestions so far are either very vendor dependent or interpreted. Interpreted methods are notoriously bad at memory intense applications. MatLab may be much higher level of a language than "C" bu... | Out-of-core data analysis options
Have you considered a "Real", non-interpreted language like Fortran?
It seems like the suggestions so far are either very vendor dependent or interpreted. Interpreted methods are notoriously bad at m |
15,035 | Speed, computational expenses of PCA, LASSO, elastic net | Group 1:
The complexity/speed of group 1. seems not too difficult to figure out if brute force algorithms are used (although there may be more efficient alternatives such as the "leaps and bounds" algorithm). For example, full subset selection will require $2^K$ regressions to be fit given a pool of $K$ candidate featu... | Speed, computational expenses of PCA, LASSO, elastic net | Group 1:
The complexity/speed of group 1. seems not too difficult to figure out if brute force algorithms are used (although there may be more efficient alternatives such as the "leaps and bounds" alg | Speed, computational expenses of PCA, LASSO, elastic net
Group 1:
The complexity/speed of group 1. seems not too difficult to figure out if brute force algorithms are used (although there may be more efficient alternatives such as the "leaps and bounds" algorithm). For example, full subset selection will require $2^K$ ... | Speed, computational expenses of PCA, LASSO, elastic net
Group 1:
The complexity/speed of group 1. seems not too difficult to figure out if brute force algorithms are used (although there may be more efficient alternatives such as the "leaps and bounds" alg |
15,036 | Speed, computational expenses of PCA, LASSO, elastic net | It's only for one part of question 2 on group 3 above (namely PLS), but may be informative nonetheless: Srinivasan et al (2010, technical report; see https://www.umiacs.umd.edu/~balajiv/Papers/UMD_CS_TR_Pls_Gpu.pdf) did some measurements on PLS using the NIPALS algorithm - stating that time (and space) complexity of th... | Speed, computational expenses of PCA, LASSO, elastic net | It's only for one part of question 2 on group 3 above (namely PLS), but may be informative nonetheless: Srinivasan et al (2010, technical report; see https://www.umiacs.umd.edu/~balajiv/Papers/UMD_CS_ | Speed, computational expenses of PCA, LASSO, elastic net
It's only for one part of question 2 on group 3 above (namely PLS), but may be informative nonetheless: Srinivasan et al (2010, technical report; see https://www.umiacs.umd.edu/~balajiv/Papers/UMD_CS_TR_Pls_Gpu.pdf) did some measurements on PLS using the NIPALS a... | Speed, computational expenses of PCA, LASSO, elastic net
It's only for one part of question 2 on group 3 above (namely PLS), but may be informative nonetheless: Srinivasan et al (2010, technical report; see https://www.umiacs.umd.edu/~balajiv/Papers/UMD_CS_ |
15,037 | Rare event logistic regression bias: how to simulate the underestimated p's with a minimal example? | This is an interesting question - I'm have done a few simulations that I post below in the hope that this stimulates further discussion.
First of all, a few general comments:
The paper you cite is about rare-event bias. What was not clear to me before (also with respect to comments that were made above) is if there is... | Rare event logistic regression bias: how to simulate the underestimated p's with a minimal example? | This is an interesting question - I'm have done a few simulations that I post below in the hope that this stimulates further discussion.
First of all, a few general comments:
The paper you cite is ab | Rare event logistic regression bias: how to simulate the underestimated p's with a minimal example?
This is an interesting question - I'm have done a few simulations that I post below in the hope that this stimulates further discussion.
First of all, a few general comments:
The paper you cite is about rare-event bias.... | Rare event logistic regression bias: how to simulate the underestimated p's with a minimal example?
This is an interesting question - I'm have done a few simulations that I post below in the hope that this stimulates further discussion.
First of all, a few general comments:
The paper you cite is ab |
15,038 | Rare event logistic regression bias: how to simulate the underestimated p's with a minimal example? | Figure 7 in the paper seems to most-directly address the question of bias in the predictions. I don't fully understand the figure (specifically, the interpretation "estimated event probabilities are too small" seems like an oversimplification) but I managed to reproduce something similar to it based on their terse desc... | Rare event logistic regression bias: how to simulate the underestimated p's with a minimal example? | Figure 7 in the paper seems to most-directly address the question of bias in the predictions. I don't fully understand the figure (specifically, the interpretation "estimated event probabilities are t | Rare event logistic regression bias: how to simulate the underestimated p's with a minimal example?
Figure 7 in the paper seems to most-directly address the question of bias in the predictions. I don't fully understand the figure (specifically, the interpretation "estimated event probabilities are too small" seems like... | Rare event logistic regression bias: how to simulate the underestimated p's with a minimal example?
Figure 7 in the paper seems to most-directly address the question of bias in the predictions. I don't fully understand the figure (specifically, the interpretation "estimated event probabilities are t |
15,039 | Rare event logistic regression bias: how to simulate the underestimated p's with a minimal example? | Rare events bias only occurs when there are regressors. It won't occur in an intercept-only model like the one simulated here. See this post for details:
http://statisticalhorizons.com/linear-vs-logistic#comment-276108 | Rare event logistic regression bias: how to simulate the underestimated p's with a minimal example? | Rare events bias only occurs when there are regressors. It won't occur in an intercept-only model like the one simulated here. See this post for details:
http://statisticalhorizons.com/linear-vs-logi | Rare event logistic regression bias: how to simulate the underestimated p's with a minimal example?
Rare events bias only occurs when there are regressors. It won't occur in an intercept-only model like the one simulated here. See this post for details:
http://statisticalhorizons.com/linear-vs-logistic#comment-276108 | Rare event logistic regression bias: how to simulate the underestimated p's with a minimal example?
Rare events bias only occurs when there are regressors. It won't occur in an intercept-only model like the one simulated here. See this post for details:
http://statisticalhorizons.com/linear-vs-logi |
15,040 | Bayesian network inference using pymc (Beginner's confusion) | Take a look at a post in Healthy Algorithm:
http://healthyalgorithms.com/2011/11/23/causal-modeling-in-python-bayesian-networks-in-pymc/
also in PyMC's totorial:
http://pymc-devs.github.io/pymc/tutorial.html
Maybe you would try the following code clip (assuming you have imported pymc as mc):
A = mc.Normal('A', mu_A, ta... | Bayesian network inference using pymc (Beginner's confusion) | Take a look at a post in Healthy Algorithm:
http://healthyalgorithms.com/2011/11/23/causal-modeling-in-python-bayesian-networks-in-pymc/
also in PyMC's totorial:
http://pymc-devs.github.io/pymc/tutori | Bayesian network inference using pymc (Beginner's confusion)
Take a look at a post in Healthy Algorithm:
http://healthyalgorithms.com/2011/11/23/causal-modeling-in-python-bayesian-networks-in-pymc/
also in PyMC's totorial:
http://pymc-devs.github.io/pymc/tutorial.html
Maybe you would try the following code clip (assumi... | Bayesian network inference using pymc (Beginner's confusion)
Take a look at a post in Healthy Algorithm:
http://healthyalgorithms.com/2011/11/23/causal-modeling-in-python-bayesian-networks-in-pymc/
also in PyMC's totorial:
http://pymc-devs.github.io/pymc/tutori |
15,041 | Two worlds collide: Using ML for complex survey data | Update May 2022: In terms of accounting for survey weights, there's a nice pair of recent (2020?) articles on arXiv by Dagdoug, Goga, and Haziza. They list many ML-flavored methods and discuss how they have been / could be modified to incorporate weights, including kNN, splines, trees, random forests, XGBoost, BART, Cu... | Two worlds collide: Using ML for complex survey data | Update May 2022: In terms of accounting for survey weights, there's a nice pair of recent (2020?) articles on arXiv by Dagdoug, Goga, and Haziza. They list many ML-flavored methods and discuss how the | Two worlds collide: Using ML for complex survey data
Update May 2022: In terms of accounting for survey weights, there's a nice pair of recent (2020?) articles on arXiv by Dagdoug, Goga, and Haziza. They list many ML-flavored methods and discuss how they have been / could be modified to incorporate weights, including k... | Two worlds collide: Using ML for complex survey data
Update May 2022: In terms of accounting for survey weights, there's a nice pair of recent (2020?) articles on arXiv by Dagdoug, Goga, and Haziza. They list many ML-flavored methods and discuss how the |
15,042 | Two worlds collide: Using ML for complex survey data | R package glmertree allows for fitting decision trees to multilevel data. It allows for specifying a random effects structure, and partitioning the dataset into subgroups using predictors. (The method can correct for the level at which partitioning variables are measured through a cluster argument)
For further referenc... | Two worlds collide: Using ML for complex survey data | R package glmertree allows for fitting decision trees to multilevel data. It allows for specifying a random effects structure, and partitioning the dataset into subgroups using predictors. (The method | Two worlds collide: Using ML for complex survey data
R package glmertree allows for fitting decision trees to multilevel data. It allows for specifying a random effects structure, and partitioning the dataset into subgroups using predictors. (The method can correct for the level at which partitioning variables are meas... | Two worlds collide: Using ML for complex survey data
R package glmertree allows for fitting decision trees to multilevel data. It allows for specifying a random effects structure, and partitioning the dataset into subgroups using predictors. (The method |
15,043 | Bias-variance decomposition | ...the expected [squared error] loss can be decomposed into a squared
bias term (which describes how far the average predictions are from
the true model), a variance term (which describes the spread of the
predictions around the average), and a noise term (which gives the
intrinsic noise of the data).
When loo... | Bias-variance decomposition | ...the expected [squared error] loss can be decomposed into a squared
bias term (which describes how far the average predictions are from
the true model), a variance term (which describes the spre | Bias-variance decomposition
...the expected [squared error] loss can be decomposed into a squared
bias term (which describes how far the average predictions are from
the true model), a variance term (which describes the spread of the
predictions around the average), and a noise term (which gives the
intrinsic n... | Bias-variance decomposition
...the expected [squared error] loss can be decomposed into a squared
bias term (which describes how far the average predictions are from
the true model), a variance term (which describes the spre |
15,044 | Anomaly Detection with Dummy Features (and other Discrete/Categorical Features) | In general, for both discrete* & categorical features, this method isn't particularly amenable to outlier analysis. Since there is no magnitude associated with categorical predictors, we are working with:
Frequency of the category being observed in the global data
Frequency of the category being observed within subspa... | Anomaly Detection with Dummy Features (and other Discrete/Categorical Features) | In general, for both discrete* & categorical features, this method isn't particularly amenable to outlier analysis. Since there is no magnitude associated with categorical predictors, we are working w | Anomaly Detection with Dummy Features (and other Discrete/Categorical Features)
In general, for both discrete* & categorical features, this method isn't particularly amenable to outlier analysis. Since there is no magnitude associated with categorical predictors, we are working with:
Frequency of the category being ob... | Anomaly Detection with Dummy Features (and other Discrete/Categorical Features)
In general, for both discrete* & categorical features, this method isn't particularly amenable to outlier analysis. Since there is no magnitude associated with categorical predictors, we are working w |
15,045 | Anomaly Detection with Dummy Features (and other Discrete/Categorical Features) | Andrew Ng class math handles "discrete" data quite like it handles "non-discrete" data. All we have to do is empirically estimate normal distribution parameters, and it can be perfectly done for discrete data.
If you think about it, machine learning always deals with discrete data anyways: the number of data points is ... | Anomaly Detection with Dummy Features (and other Discrete/Categorical Features) | Andrew Ng class math handles "discrete" data quite like it handles "non-discrete" data. All we have to do is empirically estimate normal distribution parameters, and it can be perfectly done for discr | Anomaly Detection with Dummy Features (and other Discrete/Categorical Features)
Andrew Ng class math handles "discrete" data quite like it handles "non-discrete" data. All we have to do is empirically estimate normal distribution parameters, and it can be perfectly done for discrete data.
If you think about it, machine... | Anomaly Detection with Dummy Features (and other Discrete/Categorical Features)
Andrew Ng class math handles "discrete" data quite like it handles "non-discrete" data. All we have to do is empirically estimate normal distribution parameters, and it can be perfectly done for discr |
15,046 | What's the forward stagewise regression algorithm? | They authors do a poor job of explaining the algorithm in their book. If you look at equations 1.6 and 1.7 in their paper, it becomes clearer. The paper has a slightly different formulation (it builds the residual rather than the coefficient vector), but the key point is that it reaches a least squares fit very in ve... | What's the forward stagewise regression algorithm? | They authors do a poor job of explaining the algorithm in their book. If you look at equations 1.6 and 1.7 in their paper, it becomes clearer. The paper has a slightly different formulation (it buil | What's the forward stagewise regression algorithm?
They authors do a poor job of explaining the algorithm in their book. If you look at equations 1.6 and 1.7 in their paper, it becomes clearer. The paper has a slightly different formulation (it builds the residual rather than the coefficient vector), but the key poin... | What's the forward stagewise regression algorithm?
They authors do a poor job of explaining the algorithm in their book. If you look at equations 1.6 and 1.7 in their paper, it becomes clearer. The paper has a slightly different formulation (it buil |
15,047 | Metropolis-Hastings algorithms used in practice | Hybrid Monte Carlo is the standard algorithm used for neural networks. Gibbs sampling for Gaussian process classification (when not using a deterministic approximation instead). | Metropolis-Hastings algorithms used in practice | Hybrid Monte Carlo is the standard algorithm used for neural networks. Gibbs sampling for Gaussian process classification (when not using a deterministic approximation instead). | Metropolis-Hastings algorithms used in practice
Hybrid Monte Carlo is the standard algorithm used for neural networks. Gibbs sampling for Gaussian process classification (when not using a deterministic approximation instead). | Metropolis-Hastings algorithms used in practice
Hybrid Monte Carlo is the standard algorithm used for neural networks. Gibbs sampling for Gaussian process classification (when not using a deterministic approximation instead). |
15,048 | Metropolis-Hastings algorithms used in practice | MH sampling is used when it's difficult to sample from the target distribution (e.g., when the prior isn't conjugate to the likelihood). So you use a proposal distribution to generate samples and accept/reject them based on the acceptance probability. The Gibbs sampling algorithm is a particular instance of MH where th... | Metropolis-Hastings algorithms used in practice | MH sampling is used when it's difficult to sample from the target distribution (e.g., when the prior isn't conjugate to the likelihood). So you use a proposal distribution to generate samples and acce | Metropolis-Hastings algorithms used in practice
MH sampling is used when it's difficult to sample from the target distribution (e.g., when the prior isn't conjugate to the likelihood). So you use a proposal distribution to generate samples and accept/reject them based on the acceptance probability. The Gibbs sampling a... | Metropolis-Hastings algorithms used in practice
MH sampling is used when it's difficult to sample from the target distribution (e.g., when the prior isn't conjugate to the likelihood). So you use a proposal distribution to generate samples and acce |
15,049 | Metropolis-Hastings algorithms used in practice | In physics, statistical physics in particular, Metropolis-type algorithm(s) are used extensively. There are really countless variants of these, and the new ones are being actively developed. It's much too broad topic to give any sort of expanation here, so if you're interested you can start e.g. from these lecture note... | Metropolis-Hastings algorithms used in practice | In physics, statistical physics in particular, Metropolis-type algorithm(s) are used extensively. There are really countless variants of these, and the new ones are being actively developed. It's much | Metropolis-Hastings algorithms used in practice
In physics, statistical physics in particular, Metropolis-type algorithm(s) are used extensively. There are really countless variants of these, and the new ones are being actively developed. It's much too broad topic to give any sort of expanation here, so if you're inter... | Metropolis-Hastings algorithms used in practice
In physics, statistical physics in particular, Metropolis-type algorithm(s) are used extensively. There are really countless variants of these, and the new ones are being actively developed. It's much |
15,050 | Metropolis-Hastings algorithms used in practice | I use a slice sampler - originally proposed by Neal(2003), which I tune through heuristic optimization. | Metropolis-Hastings algorithms used in practice | I use a slice sampler - originally proposed by Neal(2003), which I tune through heuristic optimization. | Metropolis-Hastings algorithms used in practice
I use a slice sampler - originally proposed by Neal(2003), which I tune through heuristic optimization. | Metropolis-Hastings algorithms used in practice
I use a slice sampler - originally proposed by Neal(2003), which I tune through heuristic optimization. |
15,051 | Independence of residuals in a computer-based experiment/simulation? | You are essentially doing some form of cross-validation here for each of your m methods and would then like to see which method performed better. The results between runs will definitely be dependent, since they are based on the same data and you have overlap between your train/test sets. The question is whether this s... | Independence of residuals in a computer-based experiment/simulation? | You are essentially doing some form of cross-validation here for each of your m methods and would then like to see which method performed better. The results between runs will definitely be dependent, | Independence of residuals in a computer-based experiment/simulation?
You are essentially doing some form of cross-validation here for each of your m methods and would then like to see which method performed better. The results between runs will definitely be dependent, since they are based on the same data and you have... | Independence of residuals in a computer-based experiment/simulation?
You are essentially doing some form of cross-validation here for each of your m methods and would then like to see which method performed better. The results between runs will definitely be dependent, |
15,052 | Independence of residuals in a computer-based experiment/simulation? | May not really understand what you have done but
for Run I am assuming that the RMSEP values for that run are correlated to some degree
Yes, that reflects how challenging the test set was in that run
but are uncorrelated between runs
No, given the way you have sampled the test sets some will be more overlapped th... | Independence of residuals in a computer-based experiment/simulation? | May not really understand what you have done but
for Run I am assuming that the RMSEP values for that run are correlated to some degree
Yes, that reflects how challenging the test set was in that r | Independence of residuals in a computer-based experiment/simulation?
May not really understand what you have done but
for Run I am assuming that the RMSEP values for that run are correlated to some degree
Yes, that reflects how challenging the test set was in that run
but are uncorrelated between runs
No, given t... | Independence of residuals in a computer-based experiment/simulation?
May not really understand what you have done but
for Run I am assuming that the RMSEP values for that run are correlated to some degree
Yes, that reflects how challenging the test set was in that r |
15,053 | Multivariant time series in R. How to find lagged correlation and build model for forecasting | You need to use your ACF & PACF behaviours to help you determine which model suits your data better (e.g. an existence of slow decay in ACF plot indicates that differencing might be needed to make the series more stabilized. Your ACF plot obviously shows that some sort of transformation is needed. The fluctuation has t... | Multivariant time series in R. How to find lagged correlation and build model for forecasting | You need to use your ACF & PACF behaviours to help you determine which model suits your data better (e.g. an existence of slow decay in ACF plot indicates that differencing might be needed to make the | Multivariant time series in R. How to find lagged correlation and build model for forecasting
You need to use your ACF & PACF behaviours to help you determine which model suits your data better (e.g. an existence of slow decay in ACF plot indicates that differencing might be needed to make the series more stabilized. Y... | Multivariant time series in R. How to find lagged correlation and build model for forecasting
You need to use your ACF & PACF behaviours to help you determine which model suits your data better (e.g. an existence of slow decay in ACF plot indicates that differencing might be needed to make the |
15,054 | Updating classification probability in logistic regression through time | You can't get there from here. You need to start with a different model. I would keep the weekly snapshots and build a stochastic model around transitions in each student's state variable. Suppose there are 10 weeks, which gives 11 "decision'' points, $t_0, t_1, \ldots, t_n$. The state at $t_i$ is $(Z_i,S_i)$, where $Z... | Updating classification probability in logistic regression through time | You can't get there from here. You need to start with a different model. I would keep the weekly snapshots and build a stochastic model around transitions in each student's state variable. Suppose the | Updating classification probability in logistic regression through time
You can't get there from here. You need to start with a different model. I would keep the weekly snapshots and build a stochastic model around transitions in each student's state variable. Suppose there are 10 weeks, which gives 11 "decision'' poin... | Updating classification probability in logistic regression through time
You can't get there from here. You need to start with a different model. I would keep the weekly snapshots and build a stochastic model around transitions in each student's state variable. Suppose the |
15,055 | Updating classification probability in logistic regression through time | When I train predictive models for a similar type of deployment, I make sure my datasets have some sort of Term_End_Date so I can derrive the length of time left until the term ends. This will probably end up being a significant predictor in your model.
Regarding the question of correlated observations, I suppose it m... | Updating classification probability in logistic regression through time | When I train predictive models for a similar type of deployment, I make sure my datasets have some sort of Term_End_Date so I can derrive the length of time left until the term ends. This will probabl | Updating classification probability in logistic regression through time
When I train predictive models for a similar type of deployment, I make sure my datasets have some sort of Term_End_Date so I can derrive the length of time left until the term ends. This will probably end up being a significant predictor in your m... | Updating classification probability in logistic regression through time
When I train predictive models for a similar type of deployment, I make sure my datasets have some sort of Term_End_Date so I can derrive the length of time left until the term ends. This will probabl |
15,056 | Distribution of $\frac{\sum_{i=1}^n X_iY_i}{\sum_{i=1}^n X_i^2}$ where $X_i,Y_i$s are i.i.d Normal variables | Although this is a conditional argument as well, using the characteristic function is faster:
\begin{align*}
\mathbb E\left[\exp\left\{ \iota t\sum_i Y_i X_i\Big/{\sum_j X_j^2}\right\}\right] &=
\mathbb E\left[\left.\mathbb E\left[\exp\left\{\iota t Y_i X_i\Big/{\sum_j X_j^2}\right\}\right]\,\right|\,\mathbf X \right]\... | Distribution of $\frac{\sum_{i=1}^n X_iY_i}{\sum_{i=1}^n X_i^2}$ where $X_i,Y_i$s are i.i.d Normal v | Although this is a conditional argument as well, using the characteristic function is faster:
\begin{align*}
\mathbb E\left[\exp\left\{ \iota t\sum_i Y_i X_i\Big/{\sum_j X_j^2}\right\}\right] &=
\math | Distribution of $\frac{\sum_{i=1}^n X_iY_i}{\sum_{i=1}^n X_i^2}$ where $X_i,Y_i$s are i.i.d Normal variables
Although this is a conditional argument as well, using the characteristic function is faster:
\begin{align*}
\mathbb E\left[\exp\left\{ \iota t\sum_i Y_i X_i\Big/{\sum_j X_j^2}\right\}\right] &=
\mathbb E\left[\... | Distribution of $\frac{\sum_{i=1}^n X_iY_i}{\sum_{i=1}^n X_i^2}$ where $X_i,Y_i$s are i.i.d Normal v
Although this is a conditional argument as well, using the characteristic function is faster:
\begin{align*}
\mathbb E\left[\exp\left\{ \iota t\sum_i Y_i X_i\Big/{\sum_j X_j^2}\right\}\right] &=
\math |
15,057 | Understanding Gaussian Process Regression via infinite dimensional basis function view | Here are a few remarks. Perhaps someone else can fill in the details.
1) Basis representations are always a good idea. It's hard to avoid them if you want to actually do something computational with your covariance function. The basis expansion can give you an approximation to the kernel and something to work with. The... | Understanding Gaussian Process Regression via infinite dimensional basis function view | Here are a few remarks. Perhaps someone else can fill in the details.
1) Basis representations are always a good idea. It's hard to avoid them if you want to actually do something computational with y | Understanding Gaussian Process Regression via infinite dimensional basis function view
Here are a few remarks. Perhaps someone else can fill in the details.
1) Basis representations are always a good idea. It's hard to avoid them if you want to actually do something computational with your covariance function. The basi... | Understanding Gaussian Process Regression via infinite dimensional basis function view
Here are a few remarks. Perhaps someone else can fill in the details.
1) Basis representations are always a good idea. It's hard to avoid them if you want to actually do something computational with y |
15,058 | Are neural networks consistent estimators? | Some details must be defined before the question can be answered.
There are different sorts of neuron and network connections, and these need specifying. There are also different measures of how well a learnt function approximates the function to be learned.
The universal approximation theorem assumes compact support, ... | Are neural networks consistent estimators? | Some details must be defined before the question can be answered.
There are different sorts of neuron and network connections, and these need specifying. There are also different measures of how well | Are neural networks consistent estimators?
Some details must be defined before the question can be answered.
There are different sorts of neuron and network connections, and these need specifying. There are also different measures of how well a learnt function approximates the function to be learned.
The universal appr... | Are neural networks consistent estimators?
Some details must be defined before the question can be answered.
There are different sorts of neuron and network connections, and these need specifying. There are also different measures of how well |
15,059 | Are neural networks consistent estimators? | TL;DR SGD works great on some problems because the problems it works great on possess significant symmetry, redundancy and smoothness. For such problems a greedy general-purpose algorithm exists, that finds a global or almost global minimum given finite noisy data and relatively small number of iterations. But, of cour... | Are neural networks consistent estimators? | TL;DR SGD works great on some problems because the problems it works great on possess significant symmetry, redundancy and smoothness. For such problems a greedy general-purpose algorithm exists, that | Are neural networks consistent estimators?
TL;DR SGD works great on some problems because the problems it works great on possess significant symmetry, redundancy and smoothness. For such problems a greedy general-purpose algorithm exists, that finds a global or almost global minimum given finite noisy data and relative... | Are neural networks consistent estimators?
TL;DR SGD works great on some problems because the problems it works great on possess significant symmetry, redundancy and smoothness. For such problems a greedy general-purpose algorithm exists, that |
15,060 | Is bootstrap problematic in small samples? | My short answer would be: Yes, if samples are very small, this can definitely be a problem since the sample may not contain enough information to get a good estimate of the desired population parameter. This problem affects all statistical methods, not just the bootstrap.
The good news, however, is that ‘small’ may be ... | Is bootstrap problematic in small samples? | My short answer would be: Yes, if samples are very small, this can definitely be a problem since the sample may not contain enough information to get a good estimate of the desired population paramete | Is bootstrap problematic in small samples?
My short answer would be: Yes, if samples are very small, this can definitely be a problem since the sample may not contain enough information to get a good estimate of the desired population parameter. This problem affects all statistical methods, not just the bootstrap.
The ... | Is bootstrap problematic in small samples?
My short answer would be: Yes, if samples are very small, this can definitely be a problem since the sample may not contain enough information to get a good estimate of the desired population paramete |
15,061 | Caret - Repeated K-fold cross-validation vs Nested K-fold cross validation, repeated n-times | There's nothing wrong with the (nested) algorithm presented, and in fact, it would likely perform well with decent robustness for the bias-variance problem on different data sets. You never said, however, that the reader should assume the features you were using are the most "optimal", so if that's unknown, there are ... | Caret - Repeated K-fold cross-validation vs Nested K-fold cross validation, repeated n-times | There's nothing wrong with the (nested) algorithm presented, and in fact, it would likely perform well with decent robustness for the bias-variance problem on different data sets. You never said, how | Caret - Repeated K-fold cross-validation vs Nested K-fold cross validation, repeated n-times
There's nothing wrong with the (nested) algorithm presented, and in fact, it would likely perform well with decent robustness for the bias-variance problem on different data sets. You never said, however, that the reader shoul... | Caret - Repeated K-fold cross-validation vs Nested K-fold cross validation, repeated n-times
There's nothing wrong with the (nested) algorithm presented, and in fact, it would likely perform well with decent robustness for the bias-variance problem on different data sets. You never said, how |
15,062 | Cheat Sheet ANOVA Alphabet Soup & Regression Equivalents | Nice list, Antoni. Here are some minor suggestions:
One-Way ANOVA: IV is a FACTOR with 3 or more levels. You could also add an Example Data: mtcars to this entry. (Similarly, you could add *Example Data" statements to all of your entries, to make it clearer what data sets you are using.)
Two-Way Anova: Why not use IV1... | Cheat Sheet ANOVA Alphabet Soup & Regression Equivalents | Nice list, Antoni. Here are some minor suggestions:
One-Way ANOVA: IV is a FACTOR with 3 or more levels. You could also add an Example Data: mtcars to this entry. (Similarly, you could add *Example Da | Cheat Sheet ANOVA Alphabet Soup & Regression Equivalents
Nice list, Antoni. Here are some minor suggestions:
One-Way ANOVA: IV is a FACTOR with 3 or more levels. You could also add an Example Data: mtcars to this entry. (Similarly, you could add *Example Data" statements to all of your entries, to make it clearer what ... | Cheat Sheet ANOVA Alphabet Soup & Regression Equivalents
Nice list, Antoni. Here are some minor suggestions:
One-Way ANOVA: IV is a FACTOR with 3 or more levels. You could also add an Example Data: mtcars to this entry. (Similarly, you could add *Example Da |
15,063 | Stability of cross-validation in Bayesian models | I don't know if this qualifies as a comment or as an answer. I'm putting here because it feels like an answer.
In k-fold cross-validation you are partitioning your data into k groups. If you are covering even the "basics" then you are uniformly randomly selecting members for each of the k bins.
When I speak of data, ... | Stability of cross-validation in Bayesian models | I don't know if this qualifies as a comment or as an answer. I'm putting here because it feels like an answer.
In k-fold cross-validation you are partitioning your data into k groups. If you are cov | Stability of cross-validation in Bayesian models
I don't know if this qualifies as a comment or as an answer. I'm putting here because it feels like an answer.
In k-fold cross-validation you are partitioning your data into k groups. If you are covering even the "basics" then you are uniformly randomly selecting membe... | Stability of cross-validation in Bayesian models
I don't know if this qualifies as a comment or as an answer. I'm putting here because it feels like an answer.
In k-fold cross-validation you are partitioning your data into k groups. If you are cov |
15,064 | Stability of cross-validation in Bayesian models | It may not be a complete answer, but if 0 is NOT in the 95% CI for several differences it is quite safe to say that they are not identical at a 0.05 level. | Stability of cross-validation in Bayesian models | It may not be a complete answer, but if 0 is NOT in the 95% CI for several differences it is quite safe to say that they are not identical at a 0.05 level. | Stability of cross-validation in Bayesian models
It may not be a complete answer, but if 0 is NOT in the 95% CI for several differences it is quite safe to say that they are not identical at a 0.05 level. | Stability of cross-validation in Bayesian models
It may not be a complete answer, but if 0 is NOT in the 95% CI for several differences it is quite safe to say that they are not identical at a 0.05 level. |
15,065 | If variable kernel widths are often good for kernel regression, why are they generally not good for kernel density estimation? | There seem to be two different questions here, which I'll try to split:
1) how is KS, kernel smoothing, different from KDE, kernel density estimation ?
Well, say I have an estimator / smoother / interpolator
est( xi, fi -> gridj, estj )
and also happen to know the "real" densityf() at the xi. Then running
est( x, den... | If variable kernel widths are often good for kernel regression, why are they generally not good for | There seem to be two different questions here, which I'll try to split:
1) how is KS, kernel smoothing, different from KDE, kernel density estimation ?
Well, say I have an estimator / smoother / inter | If variable kernel widths are often good for kernel regression, why are they generally not good for kernel density estimation?
There seem to be two different questions here, which I'll try to split:
1) how is KS, kernel smoothing, different from KDE, kernel density estimation ?
Well, say I have an estimator / smoother ... | If variable kernel widths are often good for kernel regression, why are they generally not good for
There seem to be two different questions here, which I'll try to split:
1) how is KS, kernel smoothing, different from KDE, kernel density estimation ?
Well, say I have an estimator / smoother / inter |
15,066 | If variable kernel widths are often good for kernel regression, why are they generally not good for kernel density estimation? | Kernel density estimation means integration over a local (fuzzy) window, and kernel smoothing means averaging over a local (fuzzy) window.
Kernel smoothing:
$ \tilde y(x) \propto \frac 1 {\rho(x)} \sum K(||x-x_i||)\,y_i $.
Kernel density estimation:
$\rho(x) \propto \sum K(||x-x_i||) $.
How are these the same?
Consider... | If variable kernel widths are often good for kernel regression, why are they generally not good for | Kernel density estimation means integration over a local (fuzzy) window, and kernel smoothing means averaging over a local (fuzzy) window.
Kernel smoothing:
$ \tilde y(x) \propto \frac 1 {\rho(x)} \su | If variable kernel widths are often good for kernel regression, why are they generally not good for kernel density estimation?
Kernel density estimation means integration over a local (fuzzy) window, and kernel smoothing means averaging over a local (fuzzy) window.
Kernel smoothing:
$ \tilde y(x) \propto \frac 1 {\rho(... | If variable kernel widths are often good for kernel regression, why are they generally not good for
Kernel density estimation means integration over a local (fuzzy) window, and kernel smoothing means averaging over a local (fuzzy) window.
Kernel smoothing:
$ \tilde y(x) \propto \frac 1 {\rho(x)} \su |
15,067 | Are categorical variables standardized differently in penalized regression? [duplicate] | I think the main point is what you want to do with the model.
There is not a single answer to whether you should standardize none, some or all of variables. It depends on what you want your model for.
Using the z-score of the predictors (what you call standardizing), puts all the predictors in the same scale, but make... | Are categorical variables standardized differently in penalized regression? [duplicate] | I think the main point is what you want to do with the model.
There is not a single answer to whether you should standardize none, some or all of variables. It depends on what you want your model for | Are categorical variables standardized differently in penalized regression? [duplicate]
I think the main point is what you want to do with the model.
There is not a single answer to whether you should standardize none, some or all of variables. It depends on what you want your model for.
Using the z-score of the predi... | Are categorical variables standardized differently in penalized regression? [duplicate]
I think the main point is what you want to do with the model.
There is not a single answer to whether you should standardize none, some or all of variables. It depends on what you want your model for |
15,068 | Does a "Normal Distribution" need to have mean=median=mode? | A problem with your discussion with the professor is one of terminology, there's a misunderstanding that is getting in the way of conveying a potentially useful idea. In different places, you both make errors.
So the first thing to address: it's important to be pretty clear about what a distribution is.
A normal distri... | Does a "Normal Distribution" need to have mean=median=mode? | A problem with your discussion with the professor is one of terminology, there's a misunderstanding that is getting in the way of conveying a potentially useful idea. In different places, you both mak | Does a "Normal Distribution" need to have mean=median=mode?
A problem with your discussion with the professor is one of terminology, there's a misunderstanding that is getting in the way of conveying a potentially useful idea. In different places, you both make errors.
So the first thing to address: it's important to b... | Does a "Normal Distribution" need to have mean=median=mode?
A problem with your discussion with the professor is one of terminology, there's a misunderstanding that is getting in the way of conveying a potentially useful idea. In different places, you both mak |
15,069 | Does a "Normal Distribution" need to have mean=median=mode? | You're missing the point and probably are also being "difficult," which is not appreciated in the industry. She's showing you a toy example, to train you in assessment of normality of a data set, which is to say whether the data set comes from a normal distribution. Looking at distribution moments is one way to check t... | Does a "Normal Distribution" need to have mean=median=mode? | You're missing the point and probably are also being "difficult," which is not appreciated in the industry. She's showing you a toy example, to train you in assessment of normality of a data set, whic | Does a "Normal Distribution" need to have mean=median=mode?
You're missing the point and probably are also being "difficult," which is not appreciated in the industry. She's showing you a toy example, to train you in assessment of normality of a data set, which is to say whether the data set comes from a normal distrib... | Does a "Normal Distribution" need to have mean=median=mode?
You're missing the point and probably are also being "difficult," which is not appreciated in the industry. She's showing you a toy example, to train you in assessment of normality of a data set, whic |
15,070 | Does a "Normal Distribution" need to have mean=median=mode? | The teacher is clearly out of his/her element, and probably should not be teaching statistics. It seems worse to me to teach something wrong than to not teach it at all.
These issues could all be cleared up easily if the distinction between "data" and "process that produced the data" were made more clearly. Data targ... | Does a "Normal Distribution" need to have mean=median=mode? | The teacher is clearly out of his/her element, and probably should not be teaching statistics. It seems worse to me to teach something wrong than to not teach it at all.
These issues could all be cle | Does a "Normal Distribution" need to have mean=median=mode?
The teacher is clearly out of his/her element, and probably should not be teaching statistics. It seems worse to me to teach something wrong than to not teach it at all.
These issues could all be cleared up easily if the distinction between "data" and "proces... | Does a "Normal Distribution" need to have mean=median=mode?
The teacher is clearly out of his/her element, and probably should not be teaching statistics. It seems worse to me to teach something wrong than to not teach it at all.
These issues could all be cle |
15,071 | Does a "Normal Distribution" need to have mean=median=mode? | I'm an engineer, so in my world, the applied statistician is what I see most, and get the most concrete value. If you are going to work in applied, then you need to be solidly grounded in practice over theory: whether or not it is elegant, the aircraft has to fly and not crash.
When I think about this question the... | Does a "Normal Distribution" need to have mean=median=mode? | I'm an engineer, so in my world, the applied statistician is what I see most, and get the most concrete value. If you are going to work in applied, then you need to be solidly grounded in practice ov | Does a "Normal Distribution" need to have mean=median=mode?
I'm an engineer, so in my world, the applied statistician is what I see most, and get the most concrete value. If you are going to work in applied, then you need to be solidly grounded in practice over theory: whether or not it is elegant, the aircraft has to... | Does a "Normal Distribution" need to have mean=median=mode?
I'm an engineer, so in my world, the applied statistician is what I see most, and get the most concrete value. If you are going to work in applied, then you need to be solidly grounded in practice ov |
15,072 | Does a "Normal Distribution" need to have mean=median=mode? | In medical statistics, we only ever comment on the shapes and seeming of distributions. The fact that no discrete finite sample can ever be normal is irrelevant and pedantic. I would mark you wrong for that.
If a distribution looks "mostly" normal, we are comfortable with calling it normal. When I describe distribution... | Does a "Normal Distribution" need to have mean=median=mode? | In medical statistics, we only ever comment on the shapes and seeming of distributions. The fact that no discrete finite sample can ever be normal is irrelevant and pedantic. I would mark you wrong fo | Does a "Normal Distribution" need to have mean=median=mode?
In medical statistics, we only ever comment on the shapes and seeming of distributions. The fact that no discrete finite sample can ever be normal is irrelevant and pedantic. I would mark you wrong for that.
If a distribution looks "mostly" normal, we are comf... | Does a "Normal Distribution" need to have mean=median=mode?
In medical statistics, we only ever comment on the shapes and seeming of distributions. The fact that no discrete finite sample can ever be normal is irrelevant and pedantic. I would mark you wrong fo |
15,073 | Does a "Normal Distribution" need to have mean=median=mode? | I think you and your professor are talking in different context. Equality of mean = median = mode is characteristics of theoretical distribution and this is not the only characteristics. You can not say that if for any distribution above property hold then distribution is normal. T-distribution is also symmetric but it... | Does a "Normal Distribution" need to have mean=median=mode? | I think you and your professor are talking in different context. Equality of mean = median = mode is characteristics of theoretical distribution and this is not the only characteristics. You can not s | Does a "Normal Distribution" need to have mean=median=mode?
I think you and your professor are talking in different context. Equality of mean = median = mode is characteristics of theoretical distribution and this is not the only characteristics. You can not say that if for any distribution above property hold then dis... | Does a "Normal Distribution" need to have mean=median=mode?
I think you and your professor are talking in different context. Equality of mean = median = mode is characteristics of theoretical distribution and this is not the only characteristics. You can not s |
15,074 | Does a "Normal Distribution" need to have mean=median=mode? | For practical purposes, underlying processes such as this one are usually finely approximated by normal distribution without anyone raising an eyebrow.
However, if you wanted to be pedantic the underlying process in this case can't be normally distributed, because it can't produce negative values (number of falls can't... | Does a "Normal Distribution" need to have mean=median=mode? | For practical purposes, underlying processes such as this one are usually finely approximated by normal distribution without anyone raising an eyebrow.
However, if you wanted to be pedantic the underl | Does a "Normal Distribution" need to have mean=median=mode?
For practical purposes, underlying processes such as this one are usually finely approximated by normal distribution without anyone raising an eyebrow.
However, if you wanted to be pedantic the underlying process in this case can't be normally distributed, bec... | Does a "Normal Distribution" need to have mean=median=mode?
For practical purposes, underlying processes such as this one are usually finely approximated by normal distribution without anyone raising an eyebrow.
However, if you wanted to be pedantic the underl |
15,075 | Why is correlation only defined between two variables? | Pearson correlation is defined as a measure of the linear relationship between two variables.
For other relationships, like multidimensional relationships, we use other names. For instance:
one could use the eigenvalues of a principal component analysis to express a degree of correlation in a multivariate case.
Anothe... | Why is correlation only defined between two variables? | Pearson correlation is defined as a measure of the linear relationship between two variables.
For other relationships, like multidimensional relationships, we use other names. For instance:
one could | Why is correlation only defined between two variables?
Pearson correlation is defined as a measure of the linear relationship between two variables.
For other relationships, like multidimensional relationships, we use other names. For instance:
one could use the eigenvalues of a principal component analysis to express... | Why is correlation only defined between two variables?
Pearson correlation is defined as a measure of the linear relationship between two variables.
For other relationships, like multidimensional relationships, we use other names. For instance:
one could |
15,076 | Why is correlation only defined between two variables? | In a sense, correlation is defined between more than two variables, through a correlation matrix. This is not a single number of course, but that is only natural given that it is describing correlation between several pairs of variables. This situation is analogous to many types of measurement in multivariate analysi... | Why is correlation only defined between two variables? | In a sense, correlation is defined between more than two variables, through a correlation matrix. This is not a single number of course, but that is only natural given that it is describing correlati | Why is correlation only defined between two variables?
In a sense, correlation is defined between more than two variables, through a correlation matrix. This is not a single number of course, but that is only natural given that it is describing correlation between several pairs of variables. This situation is analogo... | Why is correlation only defined between two variables?
In a sense, correlation is defined between more than two variables, through a correlation matrix. This is not a single number of course, but that is only natural given that it is describing correlati |
15,077 | Why is correlation only defined between two variables? | why do we only evaluate the correlation between two variables and not more than two variables?
It can be more than 2 variables. Three point correlation function (3PC) is used in cosmology, The Three-Point Correlation Function in Cosmology. It is formed for variables $x$, $y$ and $z$ with the following approximation wi... | Why is correlation only defined between two variables? | why do we only evaluate the correlation between two variables and not more than two variables?
It can be more than 2 variables. Three point correlation function (3PC) is used in cosmology, The Three- | Why is correlation only defined between two variables?
why do we only evaluate the correlation between two variables and not more than two variables?
It can be more than 2 variables. Three point correlation function (3PC) is used in cosmology, The Three-Point Correlation Function in Cosmology. It is formed for variabl... | Why is correlation only defined between two variables?
why do we only evaluate the correlation between two variables and not more than two variables?
It can be more than 2 variables. Three point correlation function (3PC) is used in cosmology, The Three- |
15,078 | Why is correlation only defined between two variables? | Such a statistic would be hard to define and interpret. Say you have the variables $A$, $B$, and $C$. The pairwise correlation between $A$ and $B$ is close to $+1$ and the pairwise correlation between $B$ and $C$ is close to $-1$. What should the single number correlation between the three variables be? High, low, or m... | Why is correlation only defined between two variables? | Such a statistic would be hard to define and interpret. Say you have the variables $A$, $B$, and $C$. The pairwise correlation between $A$ and $B$ is close to $+1$ and the pairwise correlation between | Why is correlation only defined between two variables?
Such a statistic would be hard to define and interpret. Say you have the variables $A$, $B$, and $C$. The pairwise correlation between $A$ and $B$ is close to $+1$ and the pairwise correlation between $B$ and $C$ is close to $-1$. What should the single number corr... | Why is correlation only defined between two variables?
Such a statistic would be hard to define and interpret. Say you have the variables $A$, $B$, and $C$. The pairwise correlation between $A$ and $B$ is close to $+1$ and the pairwise correlation between |
15,079 | Why is correlation only defined between two variables? | Correlations between multiple variables can be defined as a joint cumulant. In physics we call this a "connected correlation function". In statistics, one would call these quantities covariances instead of correlations as it's customary to normalize correlations so that they are between -1 and 1.
The connected correlat... | Why is correlation only defined between two variables? | Correlations between multiple variables can be defined as a joint cumulant. In physics we call this a "connected correlation function". In statistics, one would call these quantities covariances inste | Why is correlation only defined between two variables?
Correlations between multiple variables can be defined as a joint cumulant. In physics we call this a "connected correlation function". In statistics, one would call these quantities covariances instead of correlations as it's customary to normalize correlations so... | Why is correlation only defined between two variables?
Correlations between multiple variables can be defined as a joint cumulant. In physics we call this a "connected correlation function". In statistics, one would call these quantities covariances inste |
15,080 | Why is correlation only defined between two variables? | Main Answer
Why is correlation only defined between two variables?
Your professor likely meant Pearson's correlation as presented in the standard material you are required to learn. It is a definition used in the context of conventional (or at least introductory) statistics, and is certainly defined between only two ... | Why is correlation only defined between two variables? | Main Answer
Why is correlation only defined between two variables?
Your professor likely meant Pearson's correlation as presented in the standard material you are required to learn. It is a definiti | Why is correlation only defined between two variables?
Main Answer
Why is correlation only defined between two variables?
Your professor likely meant Pearson's correlation as presented in the standard material you are required to learn. It is a definition used in the context of conventional (or at least introductory)... | Why is correlation only defined between two variables?
Main Answer
Why is correlation only defined between two variables?
Your professor likely meant Pearson's correlation as presented in the standard material you are required to learn. It is a definiti |
15,081 | Why is correlation only defined between two variables? | One of the interpretations of Pearson's correlation coefficient is the proportionate reduction of error (PRE): Assume a variable vector $y$, about which nothing further is known. Then, if you have to predict a missing $y_i$, your best estimator would be the arithmetic mean $\bar{y}$, and the error would be $E_1 = SS_{t... | Why is correlation only defined between two variables? | One of the interpretations of Pearson's correlation coefficient is the proportionate reduction of error (PRE): Assume a variable vector $y$, about which nothing further is known. Then, if you have to | Why is correlation only defined between two variables?
One of the interpretations of Pearson's correlation coefficient is the proportionate reduction of error (PRE): Assume a variable vector $y$, about which nothing further is known. Then, if you have to predict a missing $y_i$, your best estimator would be the arithme... | Why is correlation only defined between two variables?
One of the interpretations of Pearson's correlation coefficient is the proportionate reduction of error (PRE): Assume a variable vector $y$, about which nothing further is known. Then, if you have to |
15,082 | A term for "number of columns" of a matrix | There is a concept of wide and narrow data, so maybe you could use the term „width“ for the number of columns after you define it in order to avoid the ambiguity. | A term for "number of columns" of a matrix | There is a concept of wide and narrow data, so maybe you could use the term „width“ for the number of columns after you define it in order to avoid the ambiguity. | A term for "number of columns" of a matrix
There is a concept of wide and narrow data, so maybe you could use the term „width“ for the number of columns after you define it in order to avoid the ambiguity. | A term for "number of columns" of a matrix
There is a concept of wide and narrow data, so maybe you could use the term „width“ for the number of columns after you define it in order to avoid the ambiguity. |
15,083 | A term for "number of columns" of a matrix | Let's review your objectives:
You want a short, meaningful term.
You want it to be memorable and readable, rather than some clunky abstract mathematical or computerese construction like "let $\mathbb{A}\in\operatorname{Mat}(n,p)$" or even "$\mathbb{A}\in\mathbb{R}^{n\times p}.$"
You want to be able to specify the numb... | A term for "number of columns" of a matrix | Let's review your objectives:
You want a short, meaningful term.
You want it to be memorable and readable, rather than some clunky abstract mathematical or computerese construction like "let $\mathbb | A term for "number of columns" of a matrix
Let's review your objectives:
You want a short, meaningful term.
You want it to be memorable and readable, rather than some clunky abstract mathematical or computerese construction like "let $\mathbb{A}\in\operatorname{Mat}(n,p)$" or even "$\mathbb{A}\in\mathbb{R}^{n\times p}... | A term for "number of columns" of a matrix
Let's review your objectives:
You want a short, meaningful term.
You want it to be memorable and readable, rather than some clunky abstract mathematical or computerese construction like "let $\mathbb |
15,084 | A term for "number of columns" of a matrix | Personally I would denote the matrix as $$X \in \mathbb{R}^{n \times p}$$ and use $p$ as a reference (assuming your matrix is composed of real values!).
Also note that the notation p >> n is quite widely used to describe the 'short and wide' datasets, e.g. datasets where the number of rows (observations) is significant... | A term for "number of columns" of a matrix | Personally I would denote the matrix as $$X \in \mathbb{R}^{n \times p}$$ and use $p$ as a reference (assuming your matrix is composed of real values!).
Also note that the notation p >> n is quite wid | A term for "number of columns" of a matrix
Personally I would denote the matrix as $$X \in \mathbb{R}^{n \times p}$$ and use $p$ as a reference (assuming your matrix is composed of real values!).
Also note that the notation p >> n is quite widely used to describe the 'short and wide' datasets, e.g. datasets where the n... | A term for "number of columns" of a matrix
Personally I would denote the matrix as $$X \in \mathbb{R}^{n \times p}$$ and use $p$ as a reference (assuming your matrix is composed of real values!).
Also note that the notation p >> n is quite wid |
15,085 | A term for "number of columns" of a matrix | I propose you do as Tukey would have done and invent a word. It is of course OK to define new terminology as long as we are explicit about it. As you say it might not gain immediate traction, but it would still work within the scope of your paper. My personal suggestion is
columnity [n.] of A: the extent to which A is... | A term for "number of columns" of a matrix | I propose you do as Tukey would have done and invent a word. It is of course OK to define new terminology as long as we are explicit about it. As you say it might not gain immediate traction, but it w | A term for "number of columns" of a matrix
I propose you do as Tukey would have done and invent a word. It is of course OK to define new terminology as long as we are explicit about it. As you say it might not gain immediate traction, but it would still work within the scope of your paper. My personal suggestion is
co... | A term for "number of columns" of a matrix
I propose you do as Tukey would have done and invent a word. It is of course OK to define new terminology as long as we are explicit about it. As you say it might not gain immediate traction, but it w |
15,086 | A term for "number of columns" of a matrix | I like "width", as suggested by aivanov. It is difficult to be more specific, without being longer and without using several words. If several words are ok, then we are back to "number of columns".
An alternative is to reformulate: Instead of saying:
$A$ is a matrix of width 3.
or
The number of columns of $A$ is 3... | A term for "number of columns" of a matrix | I like "width", as suggested by aivanov. It is difficult to be more specific, without being longer and without using several words. If several words are ok, then we are back to "number of columns".
| A term for "number of columns" of a matrix
I like "width", as suggested by aivanov. It is difficult to be more specific, without being longer and without using several words. If several words are ok, then we are back to "number of columns".
An alternative is to reformulate: Instead of saying:
$A$ is a matrix of widt... | A term for "number of columns" of a matrix
I like "width", as suggested by aivanov. It is difficult to be more specific, without being longer and without using several words. If several words are ok, then we are back to "number of columns".
|
15,087 | A term for "number of columns" of a matrix | It's not clear why it's important to have only a single-word term.
I'd say that for most purposes don't be afraid of three shortish words: "number of columns"; the very term you began with, which served to perfectly convey the idea you asked about.
It is a mere 5 syllables, it's not a strain to say or write.
A term co... | A term for "number of columns" of a matrix | It's not clear why it's important to have only a single-word term.
I'd say that for most purposes don't be afraid of three shortish words: "number of columns"; the very term you began with, which serv | A term for "number of columns" of a matrix
It's not clear why it's important to have only a single-word term.
I'd say that for most purposes don't be afraid of three shortish words: "number of columns"; the very term you began with, which served to perfectly convey the idea you asked about.
It is a mere 5 syllables, it... | A term for "number of columns" of a matrix
It's not clear why it's important to have only a single-word term.
I'd say that for most purposes don't be afraid of three shortish words: "number of columns"; the very term you began with, which serv |
15,088 | A term for "number of columns" of a matrix | It seems like mostly a specific language (English) problem. In German language this would be much less problematic. The term 'spaltenanzahl' is not a strange word and regularly used. So you may consider introducing 'column-count' or 'column count' (while column-number would be ambiguous), or accept 'number of columns' ... | A term for "number of columns" of a matrix | It seems like mostly a specific language (English) problem. In German language this would be much less problematic. The term 'spaltenanzahl' is not a strange word and regularly used. So you may consid | A term for "number of columns" of a matrix
It seems like mostly a specific language (English) problem. In German language this would be much less problematic. The term 'spaltenanzahl' is not a strange word and regularly used. So you may consider introducing 'column-count' or 'column count' (while column-number would be... | A term for "number of columns" of a matrix
It seems like mostly a specific language (English) problem. In German language this would be much less problematic. The term 'spaltenanzahl' is not a strange word and regularly used. So you may consid |
15,089 | A term for "number of columns" of a matrix | I always recommend avoiding to talk about matrices at all. Most applications that deal with matrices are in principle not interested in matrices at all, but rather in linear mappings between vector spaces. The basis-expanded representation of a mapping $\mathbb{R}^n \to \mathbb{R}^m$ is an $n\times m$ matrix, thus the ... | A term for "number of columns" of a matrix | I always recommend avoiding to talk about matrices at all. Most applications that deal with matrices are in principle not interested in matrices at all, but rather in linear mappings between vector sp | A term for "number of columns" of a matrix
I always recommend avoiding to talk about matrices at all. Most applications that deal with matrices are in principle not interested in matrices at all, but rather in linear mappings between vector spaces. The basis-expanded representation of a mapping $\mathbb{R}^n \to \mathb... | A term for "number of columns" of a matrix
I always recommend avoiding to talk about matrices at all. Most applications that deal with matrices are in principle not interested in matrices at all, but rather in linear mappings between vector sp |
15,090 | A term for "number of columns" of a matrix | go for width \ height as mentioned
its pretty clear what you mean and even a child knows what those words mean
(providing the array is always represented from the same viewpoint)
Of course if you go into arrays of more than 3 dimensions (height, width, depth) it gets a little tricky and is probably better to use matrix... | A term for "number of columns" of a matrix | go for width \ height as mentioned
its pretty clear what you mean and even a child knows what those words mean
(providing the array is always represented from the same viewpoint)
Of course if you go i | A term for "number of columns" of a matrix
go for width \ height as mentioned
its pretty clear what you mean and even a child knows what those words mean
(providing the array is always represented from the same viewpoint)
Of course if you go into arrays of more than 3 dimensions (height, width, depth) it gets a little ... | A term for "number of columns" of a matrix
go for width \ height as mentioned
its pretty clear what you mean and even a child knows what those words mean
(providing the array is always represented from the same viewpoint)
Of course if you go i |
15,091 | A term for "number of columns" of a matrix | There does exist and English word columnarity which means the property of being columnar. So saying a matrix of columnarity 3 would seem quite natural. | A term for "number of columns" of a matrix | There does exist and English word columnarity which means the property of being columnar. So saying a matrix of columnarity 3 would seem quite natural. | A term for "number of columns" of a matrix
There does exist and English word columnarity which means the property of being columnar. So saying a matrix of columnarity 3 would seem quite natural. | A term for "number of columns" of a matrix
There does exist and English word columnarity which means the property of being columnar. So saying a matrix of columnarity 3 would seem quite natural. |
15,092 | A term for "number of columns" of a matrix | I am guessing that you use your matrix for representing data. Usually, columns represent the different features and rows are different data points, as the data store in the figure below (ref).
This then extends to the the dimension of useful matrices, e. g. for mixing these features into a new dimension.
In that conte... | A term for "number of columns" of a matrix | I am guessing that you use your matrix for representing data. Usually, columns represent the different features and rows are different data points, as the data store in the figure below (ref).
This t | A term for "number of columns" of a matrix
I am guessing that you use your matrix for representing data. Usually, columns represent the different features and rows are different data points, as the data store in the figure below (ref).
This then extends to the the dimension of useful matrices, e. g. for mixing these f... | A term for "number of columns" of a matrix
I am guessing that you use your matrix for representing data. Usually, columns represent the different features and rows are different data points, as the data store in the figure below (ref).
This t |
15,093 | Why do we need an estimator to be consistent? | If the estimator is not consistent, it won't converge to the true value in probability. In other words, there is always a probability that your estimator and true value will have a difference, no matter how many data points you have. This is actually bad, because even if you collect immense amount of data, your estimat... | Why do we need an estimator to be consistent? | If the estimator is not consistent, it won't converge to the true value in probability. In other words, there is always a probability that your estimator and true value will have a difference, no matt | Why do we need an estimator to be consistent?
If the estimator is not consistent, it won't converge to the true value in probability. In other words, there is always a probability that your estimator and true value will have a difference, no matter how many data points you have. This is actually bad, because even if yo... | Why do we need an estimator to be consistent?
If the estimator is not consistent, it won't converge to the true value in probability. In other words, there is always a probability that your estimator and true value will have a difference, no matt |
15,094 | Why do we need an estimator to be consistent? | Consider $n = 10\,000$ observations from the standard Cauchy distribution,
which is the same as Student's t distribution with 1 degree of freedom.
The tails of this distribution are sufficiently heavy that it has no
mean; the distribution is centered at its median $\eta = 0.$
A sequence of sample means $A_j = \frac 1j ... | Why do we need an estimator to be consistent? | Consider $n = 10\,000$ observations from the standard Cauchy distribution,
which is the same as Student's t distribution with 1 degree of freedom.
The tails of this distribution are sufficiently heavy | Why do we need an estimator to be consistent?
Consider $n = 10\,000$ observations from the standard Cauchy distribution,
which is the same as Student's t distribution with 1 degree of freedom.
The tails of this distribution are sufficiently heavy that it has no
mean; the distribution is centered at its median $\eta = 0... | Why do we need an estimator to be consistent?
Consider $n = 10\,000$ observations from the standard Cauchy distribution,
which is the same as Student's t distribution with 1 degree of freedom.
The tails of this distribution are sufficiently heavy |
15,095 | Why do we need an estimator to be consistent? | @BruceET has already given an excellent technical answer, but I'd like to add a point about the interpretation of it all though.
One of the fundamental concepts in statistics is that as our sample size increases, we can reach more precise conclusions about our underlying distribution. You could think of it as the notio... | Why do we need an estimator to be consistent? | @BruceET has already given an excellent technical answer, but I'd like to add a point about the interpretation of it all though.
One of the fundamental concepts in statistics is that as our sample siz | Why do we need an estimator to be consistent?
@BruceET has already given an excellent technical answer, but I'd like to add a point about the interpretation of it all though.
One of the fundamental concepts in statistics is that as our sample size increases, we can reach more precise conclusions about our underlying di... | Why do we need an estimator to be consistent?
@BruceET has already given an excellent technical answer, but I'd like to add a point about the interpretation of it all though.
One of the fundamental concepts in statistics is that as our sample siz |
15,096 | Why do we need an estimator to be consistent? | A really simple of example of why it's important to think of consistency, which I don't think gets enough attention, is that of an over-simplified model.
As a theoretical example, suppose you wanted to fit a linear regression model on some data, in which the true effects were actually non-linear. Then your predictions... | Why do we need an estimator to be consistent? | A really simple of example of why it's important to think of consistency, which I don't think gets enough attention, is that of an over-simplified model.
As a theoretical example, suppose you wanted | Why do we need an estimator to be consistent?
A really simple of example of why it's important to think of consistency, which I don't think gets enough attention, is that of an over-simplified model.
As a theoretical example, suppose you wanted to fit a linear regression model on some data, in which the true effects w... | Why do we need an estimator to be consistent?
A really simple of example of why it's important to think of consistency, which I don't think gets enough attention, is that of an over-simplified model.
As a theoretical example, suppose you wanted |
15,097 | What do/did you do to remember Bayes' rule? | It may help to recall that it follows from the definition of conditional probability:
$$p(a|b) = \frac{p(a,b)}{p(b)}$$
$$p(a,b) = p(a|b)p(b) = p(b|a)p(a)$$
$$p(a|b) = \frac{p(b|a)p(a)}{p(b)}$$
In other words, if you remember how joint probabilities factor into conditional ones, you can always derive Bayes rule, should ... | What do/did you do to remember Bayes' rule? | It may help to recall that it follows from the definition of conditional probability:
$$p(a|b) = \frac{p(a,b)}{p(b)}$$
$$p(a,b) = p(a|b)p(b) = p(b|a)p(a)$$
$$p(a|b) = \frac{p(b|a)p(a)}{p(b)}$$
In othe | What do/did you do to remember Bayes' rule?
It may help to recall that it follows from the definition of conditional probability:
$$p(a|b) = \frac{p(a,b)}{p(b)}$$
$$p(a,b) = p(a|b)p(b) = p(b|a)p(a)$$
$$p(a|b) = \frac{p(b|a)p(a)}{p(b)}$$
In other words, if you remember how joint probabilities factor into conditional one... | What do/did you do to remember Bayes' rule?
It may help to recall that it follows from the definition of conditional probability:
$$p(a|b) = \frac{p(a,b)}{p(b)}$$
$$p(a,b) = p(a|b)p(b) = p(b|a)p(a)$$
$$p(a|b) = \frac{p(b|a)p(a)}{p(b)}$$
In othe |
15,098 | What do/did you do to remember Bayes' rule? | A simple way that has helped my students is to write $P(A \cap B)$ in two different ways as conditional probabilities:
$P(A \cap B)=P(A|B)P(B)$
and
$P(A \cap B)=P(B|A)P(A)$
Then
$P(A|B)P(B)=P(B|A)P(A)$
and
$P(B|A)=\frac{P(A|B)P(B)}{P(A)}$ | What do/did you do to remember Bayes' rule? | A simple way that has helped my students is to write $P(A \cap B)$ in two different ways as conditional probabilities:
$P(A \cap B)=P(A|B)P(B)$
and
$P(A \cap B)=P(B|A)P(A)$
Then
$P(A|B)P(B)=P(B|A)P(A | What do/did you do to remember Bayes' rule?
A simple way that has helped my students is to write $P(A \cap B)$ in two different ways as conditional probabilities:
$P(A \cap B)=P(A|B)P(B)$
and
$P(A \cap B)=P(B|A)P(A)$
Then
$P(A|B)P(B)=P(B|A)P(A)$
and
$P(B|A)=\frac{P(A|B)P(B)}{P(A)}$ | What do/did you do to remember Bayes' rule?
A simple way that has helped my students is to write $P(A \cap B)$ in two different ways as conditional probabilities:
$P(A \cap B)=P(A|B)P(B)$
and
$P(A \cap B)=P(B|A)P(A)$
Then
$P(A|B)P(B)=P(B|A)P(A |
15,099 | What do/did you do to remember Bayes' rule? | I worry about understanding the concept behind the formula. Once you have understood a concept, the underlying simple formula is stuck in your mind. Sorry for the stand-offish answer, but that's it. | What do/did you do to remember Bayes' rule? | I worry about understanding the concept behind the formula. Once you have understood a concept, the underlying simple formula is stuck in your mind. Sorry for the stand-offish answer, but that's it. | What do/did you do to remember Bayes' rule?
I worry about understanding the concept behind the formula. Once you have understood a concept, the underlying simple formula is stuck in your mind. Sorry for the stand-offish answer, but that's it. | What do/did you do to remember Bayes' rule?
I worry about understanding the concept behind the formula. Once you have understood a concept, the underlying simple formula is stuck in your mind. Sorry for the stand-offish answer, but that's it. |
15,100 | What do/did you do to remember Bayes' rule? | I personally think this for is just easier to remember:$$P(A|B)P(B)=P(B|A)P(A)$$ | What do/did you do to remember Bayes' rule? | I personally think this for is just easier to remember:$$P(A|B)P(B)=P(B|A)P(A)$$ | What do/did you do to remember Bayes' rule?
I personally think this for is just easier to remember:$$P(A|B)P(B)=P(B|A)P(A)$$ | What do/did you do to remember Bayes' rule?
I personally think this for is just easier to remember:$$P(A|B)P(B)=P(B|A)P(A)$$ |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.