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 |
|---|---|---|---|---|---|---|
39,701 | How to prevent collinearity? | The example you mention is a little overly simplified for my taste. But the sentiment is right: correcting for collinearity is not a post-hoc procedure. This is guaranteed to lead to data dredging, since the result of collinearity is variance inflation, and adding or removing factors to get significant results (i.e. fr... | How to prevent collinearity? | The example you mention is a little overly simplified for my taste. But the sentiment is right: correcting for collinearity is not a post-hoc procedure. This is guaranteed to lead to data dredging, si | How to prevent collinearity?
The example you mention is a little overly simplified for my taste. But the sentiment is right: correcting for collinearity is not a post-hoc procedure. This is guaranteed to lead to data dredging, since the result of collinearity is variance inflation, and adding or removing factors to get... | How to prevent collinearity?
The example you mention is a little overly simplified for my taste. But the sentiment is right: correcting for collinearity is not a post-hoc procedure. This is guaranteed to lead to data dredging, si |
39,702 | How to prevent collinearity? | Generally your sample should be a random sample, therefore what you read is the intuitive description of credible randomness. The opposite would be systematic bias like are you only sampling from one town in a country? Or from one family in a village? Or is there a strong time trend and your cross-section is a quasi ti... | How to prevent collinearity? | Generally your sample should be a random sample, therefore what you read is the intuitive description of credible randomness. The opposite would be systematic bias like are you only sampling from one | How to prevent collinearity?
Generally your sample should be a random sample, therefore what you read is the intuitive description of credible randomness. The opposite would be systematic bias like are you only sampling from one town in a country? Or from one family in a village? Or is there a strong time trend and you... | How to prevent collinearity?
Generally your sample should be a random sample, therefore what you read is the intuitive description of credible randomness. The opposite would be systematic bias like are you only sampling from one |
39,703 | How to prevent collinearity? | Remember collinearity is a consequence of having multiple predictor variables that have a large correlation because.... they might have too much in common! And this creates a problem because they make the analysis of the impact on the response very hard to understand since those variables affect significantly the chang... | How to prevent collinearity? | Remember collinearity is a consequence of having multiple predictor variables that have a large correlation because.... they might have too much in common! And this creates a problem because they make | How to prevent collinearity?
Remember collinearity is a consequence of having multiple predictor variables that have a large correlation because.... they might have too much in common! And this creates a problem because they make the analysis of the impact on the response very hard to understand since those variables a... | How to prevent collinearity?
Remember collinearity is a consequence of having multiple predictor variables that have a large correlation because.... they might have too much in common! And this creates a problem because they make |
39,704 | Machine learning for discovering formulas | In addition to nice answer by @DankMasterDan (+1), I would like to share further information on the topic. It seems that an approach that you're looking for is symbolic regression. It seems to be closely associated with and usually is implemented via evolutionary algorithms, such as the most popular genetic programming... | Machine learning for discovering formulas | In addition to nice answer by @DankMasterDan (+1), I would like to share further information on the topic. It seems that an approach that you're looking for is symbolic regression. It seems to be clos | Machine learning for discovering formulas
In addition to nice answer by @DankMasterDan (+1), I would like to share further information on the topic. It seems that an approach that you're looking for is symbolic regression. It seems to be closely associated with and usually is implemented via evolutionary algorithms, su... | Machine learning for discovering formulas
In addition to nice answer by @DankMasterDan (+1), I would like to share further information on the topic. It seems that an approach that you're looking for is symbolic regression. It seems to be clos |
39,705 | Machine learning for discovering formulas | It sounds like your goal is to find an arbitrary function g(:) such that y=g(x).
The answer to your question depends on what you mean by explicit. Specifically, you should note that there are an infinite number of ways to specify any function g(:), for example g(x)=x on -1
If by 'explicit' you mean find a a g*(:) whic... | Machine learning for discovering formulas | It sounds like your goal is to find an arbitrary function g(:) such that y=g(x).
The answer to your question depends on what you mean by explicit. Specifically, you should note that there are an infin | Machine learning for discovering formulas
It sounds like your goal is to find an arbitrary function g(:) such that y=g(x).
The answer to your question depends on what you mean by explicit. Specifically, you should note that there are an infinite number of ways to specify any function g(:), for example g(x)=x on -1
If ... | Machine learning for discovering formulas
It sounds like your goal is to find an arbitrary function g(:) such that y=g(x).
The answer to your question depends on what you mean by explicit. Specifically, you should note that there are an infin |
39,706 | Machine learning for discovering formulas | I strongly prefer Mathematica for such tasks. Given data of the form $mydata = \{ \{ x_1, y_1 \}, \{ x_2, y_2 \}, ... \}$, one searches for the unknown parameters such as $a$, $b$, $c$, and $d$ in a non-linear function of your choice in this way:
NonlinearModelFit[mydata, {a + b x + c x^2 + d Sin[x]}, {a, b, c, d}, x]... | Machine learning for discovering formulas | I strongly prefer Mathematica for such tasks. Given data of the form $mydata = \{ \{ x_1, y_1 \}, \{ x_2, y_2 \}, ... \}$, one searches for the unknown parameters such as $a$, $b$, $c$, and $d$ in a | Machine learning for discovering formulas
I strongly prefer Mathematica for such tasks. Given data of the form $mydata = \{ \{ x_1, y_1 \}, \{ x_2, y_2 \}, ... \}$, one searches for the unknown parameters such as $a$, $b$, $c$, and $d$ in a non-linear function of your choice in this way:
NonlinearModelFit[mydata, {a +... | Machine learning for discovering formulas
I strongly prefer Mathematica for such tasks. Given data of the form $mydata = \{ \{ x_1, y_1 \}, \{ x_2, y_2 \}, ... \}$, one searches for the unknown parameters such as $a$, $b$, $c$, and $d$ in a |
39,707 | Using multiple comparisons corrections in Fisher p-value framework | Following @MichaelLew's answer (+1), I changed my point of view to the opposite one; now I think that $p$-values should NOT be corrected. I have reworked my answer.
To make the discussion more lively, I will refer to the famous XKCD comic where $20$ colours of jelly beans are independently tested to be linked to acne, ... | Using multiple comparisons corrections in Fisher p-value framework | Following @MichaelLew's answer (+1), I changed my point of view to the opposite one; now I think that $p$-values should NOT be corrected. I have reworked my answer.
To make the discussion more lively, | Using multiple comparisons corrections in Fisher p-value framework
Following @MichaelLew's answer (+1), I changed my point of view to the opposite one; now I think that $p$-values should NOT be corrected. I have reworked my answer.
To make the discussion more lively, I will refer to the famous XKCD comic where $20$ col... | Using multiple comparisons corrections in Fisher p-value framework
Following @MichaelLew's answer (+1), I changed my point of view to the opposite one; now I think that $p$-values should NOT be corrected. I have reworked my answer.
To make the discussion more lively, |
39,708 | Using multiple comparisons corrections in Fisher p-value framework | Amoeba's answer is good, but it not the answer that I would give, as he notes.
The answer is, of course, it depends. It depends on whether you want the P-value to be conditioned on the actual results of the particular comparison or to be conditioned additionally on the number of comparisons that you have made. In the f... | Using multiple comparisons corrections in Fisher p-value framework | Amoeba's answer is good, but it not the answer that I would give, as he notes.
The answer is, of course, it depends. It depends on whether you want the P-value to be conditioned on the actual results | Using multiple comparisons corrections in Fisher p-value framework
Amoeba's answer is good, but it not the answer that I would give, as he notes.
The answer is, of course, it depends. It depends on whether you want the P-value to be conditioned on the actual results of the particular comparison or to be conditioned add... | Using multiple comparisons corrections in Fisher p-value framework
Amoeba's answer is good, but it not the answer that I would give, as he notes.
The answer is, of course, it depends. It depends on whether you want the P-value to be conditioned on the actual results |
39,709 | PDF of function of X | Draw a picture.
Although you can apply a standard formula for changes of variable, this one is tricky because the transformation $X\to Y$ is not one-to-one. Often the most convenient and reliable method is to compute the distribution function (CDF) and then differentiate it.
The distribution function of $Y=\sin(X)$ is... | PDF of function of X | Draw a picture.
Although you can apply a standard formula for changes of variable, this one is tricky because the transformation $X\to Y$ is not one-to-one. Often the most convenient and reliable met | PDF of function of X
Draw a picture.
Although you can apply a standard formula for changes of variable, this one is tricky because the transformation $X\to Y$ is not one-to-one. Often the most convenient and reliable method is to compute the distribution function (CDF) and then differentiate it.
The distribution funct... | PDF of function of X
Draw a picture.
Although you can apply a standard formula for changes of variable, this one is tricky because the transformation $X\to Y$ is not one-to-one. Often the most convenient and reliable met |
39,710 | Testing a regression coefficient against 1 rather than 0 | Examine the confidence interval of the slope coefficient. If it includes 1, then we will not reject the null hypothesis stating that the slope is 1. The drawback is that you will not know the p-value other than it has to be smaller than 0.05.
Some software such as Stata allows user to implement customized testing of th... | Testing a regression coefficient against 1 rather than 0 | Examine the confidence interval of the slope coefficient. If it includes 1, then we will not reject the null hypothesis stating that the slope is 1. The drawback is that you will not know the p-value | Testing a regression coefficient against 1 rather than 0
Examine the confidence interval of the slope coefficient. If it includes 1, then we will not reject the null hypothesis stating that the slope is 1. The drawback is that you will not know the p-value other than it has to be smaller than 0.05.
Some software such a... | Testing a regression coefficient against 1 rather than 0
Examine the confidence interval of the slope coefficient. If it includes 1, then we will not reject the null hypothesis stating that the slope is 1. The drawback is that you will not know the p-value |
39,711 | Testing a regression coefficient against 1 rather than 0 | The key is the use of an offset. Offsets are simple algebraic manipulations to a linear model. In this case, fitting the reduced model with an offset is done by fitting an intercept-only model (since the intercept is a free parameter) and specifying offset(mpg) in the options. This is algebraically equivalent to calcul... | Testing a regression coefficient against 1 rather than 0 | The key is the use of an offset. Offsets are simple algebraic manipulations to a linear model. In this case, fitting the reduced model with an offset is done by fitting an intercept-only model (since | Testing a regression coefficient against 1 rather than 0
The key is the use of an offset. Offsets are simple algebraic manipulations to a linear model. In this case, fitting the reduced model with an offset is done by fitting an intercept-only model (since the intercept is a free parameter) and specifying offset(mpg) i... | Testing a regression coefficient against 1 rather than 0
The key is the use of an offset. Offsets are simple algebraic manipulations to a linear model. In this case, fitting the reduced model with an offset is done by fitting an intercept-only model (since |
39,712 | Does k-fold cross validation always imply k uniformly sized subsets? | I didn't meant to imply that the folds should be different sizes in that answer (and I'll update it to match).
Each fold should contain an equal number of observations, or as close to equal as possible. If you want to perform 10-fold cross-validation on $N=101$ observations, one fold will have 11, rather than 10, item... | Does k-fold cross validation always imply k uniformly sized subsets? | I didn't meant to imply that the folds should be different sizes in that answer (and I'll update it to match).
Each fold should contain an equal number of observations, or as close to equal as possib | Does k-fold cross validation always imply k uniformly sized subsets?
I didn't meant to imply that the folds should be different sizes in that answer (and I'll update it to match).
Each fold should contain an equal number of observations, or as close to equal as possible. If you want to perform 10-fold cross-validation... | Does k-fold cross validation always imply k uniformly sized subsets?
I didn't meant to imply that the folds should be different sizes in that answer (and I'll update it to match).
Each fold should contain an equal number of observations, or as close to equal as possib |
39,713 | Does k-fold cross validation always imply k uniformly sized subsets? | Just one caveat to keep an eye on - if the fold sizes are not equal then the average of fold results is not the same as the average over whole dataset. You should weight fold results by fold size to get the correct average.
Suppose you have a dataset $X=\{1,2,3,4,5\}$ and use 2-fold cross-validation. The first fold is ... | Does k-fold cross validation always imply k uniformly sized subsets? | Just one caveat to keep an eye on - if the fold sizes are not equal then the average of fold results is not the same as the average over whole dataset. You should weight fold results by fold size to g | Does k-fold cross validation always imply k uniformly sized subsets?
Just one caveat to keep an eye on - if the fold sizes are not equal then the average of fold results is not the same as the average over whole dataset. You should weight fold results by fold size to get the correct average.
Suppose you have a dataset ... | Does k-fold cross validation always imply k uniformly sized subsets?
Just one caveat to keep an eye on - if the fold sizes are not equal then the average of fold results is not the same as the average over whole dataset. You should weight fold results by fold size to g |
39,714 | Does k-fold cross validation always imply k uniformly sized subsets? | $k$-fold cross-validation will divide your data into $k$ subsets. Then you iterate $k$ times: $i=1,2,...,k$, using the union of subsets except the $i$th subset to train your model. Then testing that model on the $i$th subset. If $k$ is not a divisor of the amount of observations you have in your data set it is impossib... | Does k-fold cross validation always imply k uniformly sized subsets? | $k$-fold cross-validation will divide your data into $k$ subsets. Then you iterate $k$ times: $i=1,2,...,k$, using the union of subsets except the $i$th subset to train your model. Then testing that m | Does k-fold cross validation always imply k uniformly sized subsets?
$k$-fold cross-validation will divide your data into $k$ subsets. Then you iterate $k$ times: $i=1,2,...,k$, using the union of subsets except the $i$th subset to train your model. Then testing that model on the $i$th subset. If $k$ is not a divisor o... | Does k-fold cross validation always imply k uniformly sized subsets?
$k$-fold cross-validation will divide your data into $k$ subsets. Then you iterate $k$ times: $i=1,2,...,k$, using the union of subsets except the $i$th subset to train your model. Then testing that m |
39,715 | How does CCA find a low-dimensional common subspace? | This question was based on a false premise that CCA finds one "common subspace". It does not.
CCA deals with two datasets $X$ and $Y$ of $n$ points each: points from dataset $X$ are $p$-dimensional and live in $\mathbb R^p$ and points from dataset $Y$ are $q$-dimensional and live in $\mathbb R^q$. Let $\mathbf X$ and $... | How does CCA find a low-dimensional common subspace? | This question was based on a false premise that CCA finds one "common subspace". It does not.
CCA deals with two datasets $X$ and $Y$ of $n$ points each: points from dataset $X$ are $p$-dimensional an | How does CCA find a low-dimensional common subspace?
This question was based on a false premise that CCA finds one "common subspace". It does not.
CCA deals with two datasets $X$ and $Y$ of $n$ points each: points from dataset $X$ are $p$-dimensional and live in $\mathbb R^p$ and points from dataset $Y$ are $q$-dimensi... | How does CCA find a low-dimensional common subspace?
This question was based on a false premise that CCA finds one "common subspace". It does not.
CCA deals with two datasets $X$ and $Y$ of $n$ points each: points from dataset $X$ are $p$-dimensional an |
39,716 | Classification score for Random Forest | You typically plot a confusion matrix of your test set (recall and precision), and report an F1 score on them.
If you have your correct labels of your test set in y_test and your predicted labels in pred, then your F1 score is:
from sklearn import metrics
# testing score
score = metrics.f1_score(y_test, pred, pos_label... | Classification score for Random Forest | You typically plot a confusion matrix of your test set (recall and precision), and report an F1 score on them.
If you have your correct labels of your test set in y_test and your predicted labels in p | Classification score for Random Forest
You typically plot a confusion matrix of your test set (recall and precision), and report an F1 score on them.
If you have your correct labels of your test set in y_test and your predicted labels in pred, then your F1 score is:
from sklearn import metrics
# testing score
score = m... | Classification score for Random Forest
You typically plot a confusion matrix of your test set (recall and precision), and report an F1 score on them.
If you have your correct labels of your test set in y_test and your predicted labels in p |
39,717 | How to do MANCOVA in R? | See: http://www.statmethods.net/stats/anova.html
Y <- cbind(VAR1, VAR2, VAR3)
fit <- manova(Y ~ GRP+age+gender)
summary(fit, test="Pillai")
Other test options are "Wilks", "Hotelling-Lawley", and "Roy".
summary.aov(fit) # for univariate statistics.
Following link may be helpful for permutation based multiple comparis... | How to do MANCOVA in R? | See: http://www.statmethods.net/stats/anova.html
Y <- cbind(VAR1, VAR2, VAR3)
fit <- manova(Y ~ GRP+age+gender)
summary(fit, test="Pillai")
Other test options are "Wilks", "Hotelling-Lawley", and "Ro | How to do MANCOVA in R?
See: http://www.statmethods.net/stats/anova.html
Y <- cbind(VAR1, VAR2, VAR3)
fit <- manova(Y ~ GRP+age+gender)
summary(fit, test="Pillai")
Other test options are "Wilks", "Hotelling-Lawley", and "Roy".
summary.aov(fit) # for univariate statistics.
Following link may be helpful for permutation... | How to do MANCOVA in R?
See: http://www.statmethods.net/stats/anova.html
Y <- cbind(VAR1, VAR2, VAR3)
fit <- manova(Y ~ GRP+age+gender)
summary(fit, test="Pillai")
Other test options are "Wilks", "Hotelling-Lawley", and "Ro |
39,718 | Nonstationary panel data, spurious regression | Admittedly a bit confusing wording from Baltagi in this specific excerpt. But unfortunately, the expression "spurious regression" has come to be used in the econometrics literature as a synonym for "non-stationary and non-cointegrated regression"
Let's first attempt to clarify what the "spurious regression phenomenon" ... | Nonstationary panel data, spurious regression | Admittedly a bit confusing wording from Baltagi in this specific excerpt. But unfortunately, the expression "spurious regression" has come to be used in the econometrics literature as a synonym for "n | Nonstationary panel data, spurious regression
Admittedly a bit confusing wording from Baltagi in this specific excerpt. But unfortunately, the expression "spurious regression" has come to be used in the econometrics literature as a synonym for "non-stationary and non-cointegrated regression"
Let's first attempt to clar... | Nonstationary panel data, spurious regression
Admittedly a bit confusing wording from Baltagi in this specific excerpt. But unfortunately, the expression "spurious regression" has come to be used in the econometrics literature as a synonym for "n |
39,719 | Natural example of bad results with a Lehmer Random Number Generator | I finally came up with a question that send Wichman-Hill’s generator off the road. It is not as natural as one may wish but I hope it’s spectacular enough.
Here’s the problem: study the distribution of
$$ X = -10U_1 - 22U_2 + 38U_3 - 3U_4 + U_5 + 4U_6 - 38 U_7$$
with the $U_i$ iid uniform on $(0,1)$.
We will just dra... | Natural example of bad results with a Lehmer Random Number Generator | I finally came up with a question that send Wichman-Hill’s generator off the road. It is not as natural as one may wish but I hope it’s spectacular enough.
Here’s the problem: study the distribution o | Natural example of bad results with a Lehmer Random Number Generator
I finally came up with a question that send Wichman-Hill’s generator off the road. It is not as natural as one may wish but I hope it’s spectacular enough.
Here’s the problem: study the distribution of
$$ X = -10U_1 - 22U_2 + 38U_3 - 3U_4 + U_5 + 4U_... | Natural example of bad results with a Lehmer Random Number Generator
I finally came up with a question that send Wichman-Hill’s generator off the road. It is not as natural as one may wish but I hope it’s spectacular enough.
Here’s the problem: study the distribution o |
39,720 | Natural example of bad results with a Lehmer Random Number Generator | The application most concerned with tiny deviations from correlation is cryptography. The ability to predict a pseudo-random value with better than ordinary accuracy can translate into superior abilities to break encryption schemes.
This can be illustrated with a somewhat artificial example designed to help the intuit... | Natural example of bad results with a Lehmer Random Number Generator | The application most concerned with tiny deviations from correlation is cryptography. The ability to predict a pseudo-random value with better than ordinary accuracy can translate into superior abili | Natural example of bad results with a Lehmer Random Number Generator
The application most concerned with tiny deviations from correlation is cryptography. The ability to predict a pseudo-random value with better than ordinary accuracy can translate into superior abilities to break encryption schemes.
This can be illus... | Natural example of bad results with a Lehmer Random Number Generator
The application most concerned with tiny deviations from correlation is cryptography. The ability to predict a pseudo-random value with better than ordinary accuracy can translate into superior abili |
39,721 | WLLN: can expectation exist but be infinite? | The expectation of a random variable $X: \{\Omega, \frak{S}, \mathbb{P}\}\to \mathbb{R}$ is the Lebesgue integral
$$\mathbb{E}[X] = \int_\Omega X(\omega)d\mathbb{P}(\omega).$$
The Lebesgue integral is constructed in a sequence of steps whereby its domain of application is broadened to encompass an ever wider variety of... | WLLN: can expectation exist but be infinite? | The expectation of a random variable $X: \{\Omega, \frak{S}, \mathbb{P}\}\to \mathbb{R}$ is the Lebesgue integral
$$\mathbb{E}[X] = \int_\Omega X(\omega)d\mathbb{P}(\omega).$$
The Lebesgue integral is | WLLN: can expectation exist but be infinite?
The expectation of a random variable $X: \{\Omega, \frak{S}, \mathbb{P}\}\to \mathbb{R}$ is the Lebesgue integral
$$\mathbb{E}[X] = \int_\Omega X(\omega)d\mathbb{P}(\omega).$$
The Lebesgue integral is constructed in a sequence of steps whereby its domain of application is br... | WLLN: can expectation exist but be infinite?
The expectation of a random variable $X: \{\Omega, \frak{S}, \mathbb{P}\}\to \mathbb{R}$ is the Lebesgue integral
$$\mathbb{E}[X] = \int_\Omega X(\omega)d\mathbb{P}(\omega).$$
The Lebesgue integral is |
39,722 | WLLN: can expectation exist but be infinite? | There are some useful and well-known distributions which have undefined mean. I think one of the most used is Cauchy distribution. See Wikipedia article.
For example the standard Cauchy distribution has pdf
$$ f(x)=\frac{1}{\pi(1+x^2)}$$
So, the mean is
$$ E(x) = \int_{-\infty}^{\infty}x\frac{1}{\pi(1+x^2)}dx = \frac{l... | WLLN: can expectation exist but be infinite? | There are some useful and well-known distributions which have undefined mean. I think one of the most used is Cauchy distribution. See Wikipedia article.
For example the standard Cauchy distribution h | WLLN: can expectation exist but be infinite?
There are some useful and well-known distributions which have undefined mean. I think one of the most used is Cauchy distribution. See Wikipedia article.
For example the standard Cauchy distribution has pdf
$$ f(x)=\frac{1}{\pi(1+x^2)}$$
So, the mean is
$$ E(x) = \int_{-\inf... | WLLN: can expectation exist but be infinite?
There are some useful and well-known distributions which have undefined mean. I think one of the most used is Cauchy distribution. See Wikipedia article.
For example the standard Cauchy distribution h |
39,723 | What does "statistically insignificantly worse" mean? | I've never heard this before, and hope I don't again! They should say something like "the $A$ mean is less than the $B$ mean, but the difference is not statistically significant".
Often in articles you see something like "$\bar y_B - \bar y_A = 1.32$ ($P = 0.236$)." which conveys a lot more information in less space. ... | What does "statistically insignificantly worse" mean? | I've never heard this before, and hope I don't again! They should say something like "the $A$ mean is less than the $B$ mean, but the difference is not statistically significant".
Often in articles y | What does "statistically insignificantly worse" mean?
I've never heard this before, and hope I don't again! They should say something like "the $A$ mean is less than the $B$ mean, but the difference is not statistically significant".
Often in articles you see something like "$\bar y_B - \bar y_A = 1.32$ ($P = 0.236$).... | What does "statistically insignificantly worse" mean?
I've never heard this before, and hope I don't again! They should say something like "the $A$ mean is less than the $B$ mean, but the difference is not statistically significant".
Often in articles y |
39,724 | Control variables- Difference in Difference | There are two reasons for including covariates in a difference in differences regression:
for identification of the treatment effect;
to reduce the error variance (i.e. increase power of statistical tests).
Suppose you want to know the effect of a job market program on employment in a city where this program was rand... | Control variables- Difference in Difference | There are two reasons for including covariates in a difference in differences regression:
for identification of the treatment effect;
to reduce the error variance (i.e. increase power of statistical | Control variables- Difference in Difference
There are two reasons for including covariates in a difference in differences regression:
for identification of the treatment effect;
to reduce the error variance (i.e. increase power of statistical tests).
Suppose you want to know the effect of a job market program on empl... | Control variables- Difference in Difference
There are two reasons for including covariates in a difference in differences regression:
for identification of the treatment effect;
to reduce the error variance (i.e. increase power of statistical |
39,725 | In convolutional neural networks, how to prevent the overfitting? | I would say there might be a bug when calculating the errors when using backpropagation.
Also how big is your data? And how many epochs are you using for your simulation? How is your training being done? I could help you more if i could get more data.
This might help you: http://www.cs.toronto.edu/~hinton/csc2515/notes... | In convolutional neural networks, how to prevent the overfitting? | I would say there might be a bug when calculating the errors when using backpropagation.
Also how big is your data? And how many epochs are you using for your simulation? How is your training being do | In convolutional neural networks, how to prevent the overfitting?
I would say there might be a bug when calculating the errors when using backpropagation.
Also how big is your data? And how many epochs are you using for your simulation? How is your training being done? I could help you more if i could get more data.
Th... | In convolutional neural networks, how to prevent the overfitting?
I would say there might be a bug when calculating the errors when using backpropagation.
Also how big is your data? And how many epochs are you using for your simulation? How is your training being do |
39,726 | In convolutional neural networks, how to prevent the overfitting? | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
Maybe you could try the dropout technique. I have hear... | In convolutional neural networks, how to prevent the overfitting? | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
| In convolutional neural networks, how to prevent the overfitting?
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
... | In convolutional neural networks, how to prevent the overfitting?
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
|
39,727 | What are the Mild Regularity Conditions in the context of GEEs? | Regularity conditions in statistics usually refer to requirements that functions or groups of functions (usually probability density functions) "behave well" in various senses. These are assumptions made in proofs of statements that are thought to hold in most practical cases and often not explicitly mentioned when giv... | What are the Mild Regularity Conditions in the context of GEEs? | Regularity conditions in statistics usually refer to requirements that functions or groups of functions (usually probability density functions) "behave well" in various senses. These are assumptions m | What are the Mild Regularity Conditions in the context of GEEs?
Regularity conditions in statistics usually refer to requirements that functions or groups of functions (usually probability density functions) "behave well" in various senses. These are assumptions made in proofs of statements that are thought to hold in ... | What are the Mild Regularity Conditions in the context of GEEs?
Regularity conditions in statistics usually refer to requirements that functions or groups of functions (usually probability density functions) "behave well" in various senses. These are assumptions m |
39,728 | Existence of fractional moment of cauchy distribution | Let's apply the law of the unconscious statistician, so we want to be able to evaluate
$\int_{-a}^b \frac{x^k}{1+x^2} dx$
in the limit as $a,b$ each $\to\infty$.
As mentioned in comments, for most fractional $k$ there's problems for negative $x$.
Let's step aside from that issue, and just talk about convergence of the... | Existence of fractional moment of cauchy distribution | Let's apply the law of the unconscious statistician, so we want to be able to evaluate
$\int_{-a}^b \frac{x^k}{1+x^2} dx$
in the limit as $a,b$ each $\to\infty$.
As mentioned in comments, for most fr | Existence of fractional moment of cauchy distribution
Let's apply the law of the unconscious statistician, so we want to be able to evaluate
$\int_{-a}^b \frac{x^k}{1+x^2} dx$
in the limit as $a,b$ each $\to\infty$.
As mentioned in comments, for most fractional $k$ there's problems for negative $x$.
Let's step aside f... | Existence of fractional moment of cauchy distribution
Let's apply the law of the unconscious statistician, so we want to be able to evaluate
$\int_{-a}^b \frac{x^k}{1+x^2} dx$
in the limit as $a,b$ each $\to\infty$.
As mentioned in comments, for most fr |
39,729 | Existence of fractional moment of cauchy distribution | To complement @Glen_b's answer, I asked maple for help, and it gives the following answer, which is a complex number since we ask for fractional powers of negative numbers! If such a complex moment is of any use I do not know, probably one would have to take the moments of the positive and negative part separately, as ... | Existence of fractional moment of cauchy distribution | To complement @Glen_b's answer, I asked maple for help, and it gives the following answer, which is a complex number since we ask for fractional powers of negative numbers! If such a complex moment is | Existence of fractional moment of cauchy distribution
To complement @Glen_b's answer, I asked maple for help, and it gives the following answer, which is a complex number since we ask for fractional powers of negative numbers! If such a complex moment is of any use I do not know, probably one would have to take the mom... | Existence of fractional moment of cauchy distribution
To complement @Glen_b's answer, I asked maple for help, and it gives the following answer, which is a complex number since we ask for fractional powers of negative numbers! If such a complex moment is |
39,730 | Existence of fractional moment of cauchy distribution | The fractional moments $E[x^k]$ do exist for $k<1$. You have to be careful with fractional moments of distributions with negative values, of course. The value $x^k$ may end up being a complex number.
The absolute moments $E[|x|^k]$ were studied in Goria, M. N. "Fractional absolute moments of the Cauchy distribution." Q... | Existence of fractional moment of cauchy distribution | The fractional moments $E[x^k]$ do exist for $k<1$. You have to be careful with fractional moments of distributions with negative values, of course. The value $x^k$ may end up being a complex number.
| Existence of fractional moment of cauchy distribution
The fractional moments $E[x^k]$ do exist for $k<1$. You have to be careful with fractional moments of distributions with negative values, of course. The value $x^k$ may end up being a complex number.
The absolute moments $E[|x|^k]$ were studied in Goria, M. N. "Frac... | Existence of fractional moment of cauchy distribution
The fractional moments $E[x^k]$ do exist for $k<1$. You have to be careful with fractional moments of distributions with negative values, of course. The value $x^k$ may end up being a complex number.
|
39,731 | Existence of fractional moment of cauchy distribution | Let $\mu \in \mathbb{R}$ and $\sigma > 0$ be the location and scale parameters of a Cauchy distribution respectively.
Let $r > 0$ and $\theta \in (0, \pi)$ such that $r\exp(i \theta) = \mu +
\sigma i$, where $i$ denotes the imaginary unit.
Let $-1 < \text{Re}(a) < 1$.
Assume that $x^a = |x|^a \text{sign}(x), \ x \... | Existence of fractional moment of cauchy distribution | Let $\mu \in \mathbb{R}$ and $\sigma > 0$ be the location and scale parameters of a Cauchy distribution respectively.
Let $r > 0$ and $\theta \in (0, \pi)$ such that $r\exp(i \theta) = \mu +
\sigma | Existence of fractional moment of cauchy distribution
Let $\mu \in \mathbb{R}$ and $\sigma > 0$ be the location and scale parameters of a Cauchy distribution respectively.
Let $r > 0$ and $\theta \in (0, \pi)$ such that $r\exp(i \theta) = \mu +
\sigma i$, where $i$ denotes the imaginary unit.
Let $-1 < \text{Re}(a)... | Existence of fractional moment of cauchy distribution
Let $\mu \in \mathbb{R}$ and $\sigma > 0$ be the location and scale parameters of a Cauchy distribution respectively.
Let $r > 0$ and $\theta \in (0, \pi)$ such that $r\exp(i \theta) = \mu +
\sigma |
39,732 | Mixing observed and predicted values within explanatory variables - is it ok? | The OP has not specified an estimation procedure, so I will consider the question for the case of linear least-squares regression. I will also ignore the constant term-let's say variables are already centered on their means.
Should we use model 1 to predict 100% of $\hat{y_i}$ and use them on model 2?
If we do that, ... | Mixing observed and predicted values within explanatory variables - is it ok? | The OP has not specified an estimation procedure, so I will consider the question for the case of linear least-squares regression. I will also ignore the constant term-let's say variables are already | Mixing observed and predicted values within explanatory variables - is it ok?
The OP has not specified an estimation procedure, so I will consider the question for the case of linear least-squares regression. I will also ignore the constant term-let's say variables are already centered on their means.
Should we use mo... | Mixing observed and predicted values within explanatory variables - is it ok?
The OP has not specified an estimation procedure, so I will consider the question for the case of linear least-squares regression. I will also ignore the constant term-let's say variables are already |
39,733 | Mixing observed and predicted values within explanatory variables - is it ok? | Using half of the predicted $y$s would mean that you strongly underestimate the variance of $\beta_4$ in model 2 as the prediction would not be accounted for!
What you suggest would be some form of single imputation which in general leads to underestimation of variance. | Mixing observed and predicted values within explanatory variables - is it ok? | Using half of the predicted $y$s would mean that you strongly underestimate the variance of $\beta_4$ in model 2 as the prediction would not be accounted for!
What you suggest would be some form of s | Mixing observed and predicted values within explanatory variables - is it ok?
Using half of the predicted $y$s would mean that you strongly underestimate the variance of $\beta_4$ in model 2 as the prediction would not be accounted for!
What you suggest would be some form of single imputation which in general leads to... | Mixing observed and predicted values within explanatory variables - is it ok?
Using half of the predicted $y$s would mean that you strongly underestimate the variance of $\beta_4$ in model 2 as the prediction would not be accounted for!
What you suggest would be some form of s |
39,734 | Mixing observed and predicted values within explanatory variables - is it ok? | You can think of this in terms of learning a feature of an ensemble in machine learning.
Normally an ensemble would say have 5 models all trained to predict W and then the ensemble model would combine these models to make a better prediction on W. Normally by something simple like a vote. But there is no reason why the... | Mixing observed and predicted values within explanatory variables - is it ok? | You can think of this in terms of learning a feature of an ensemble in machine learning.
Normally an ensemble would say have 5 models all trained to predict W and then the ensemble model would combine | Mixing observed and predicted values within explanatory variables - is it ok?
You can think of this in terms of learning a feature of an ensemble in machine learning.
Normally an ensemble would say have 5 models all trained to predict W and then the ensemble model would combine these models to make a better prediction ... | Mixing observed and predicted values within explanatory variables - is it ok?
You can think of this in terms of learning a feature of an ensemble in machine learning.
Normally an ensemble would say have 5 models all trained to predict W and then the ensemble model would combine |
39,735 | Mixing observed and predicted values within explanatory variables - is it ok? | Nice question. I can’t say I have come across this before but the following paper on mediation, compounding and suppression might be useful. I can’t see how mixing up $y_i$ and $\hat{y_i}$ in model 2 is incorrect for any statistical reason. Whether or not it leads to better prediction would depend on the relationships ... | Mixing observed and predicted values within explanatory variables - is it ok? | Nice question. I can’t say I have come across this before but the following paper on mediation, compounding and suppression might be useful. I can’t see how mixing up $y_i$ and $\hat{y_i}$ in model 2 | Mixing observed and predicted values within explanatory variables - is it ok?
Nice question. I can’t say I have come across this before but the following paper on mediation, compounding and suppression might be useful. I can’t see how mixing up $y_i$ and $\hat{y_i}$ in model 2 is incorrect for any statistical reason. W... | Mixing observed and predicted values within explanatory variables - is it ok?
Nice question. I can’t say I have come across this before but the following paper on mediation, compounding and suppression might be useful. I can’t see how mixing up $y_i$ and $\hat{y_i}$ in model 2 |
39,736 | Mixing observed and predicted values within explanatory variables - is it ok? | The problem that you pose reminds me a bit of the classic problem of fitting multivariate Gaussian mixture models (GMM), which is the archetypal application for the expectation maximization (EM) algorithm.
At a high level, it's instructive to think a little bit about how the EM algorithm solves the GMM fitting problem,... | Mixing observed and predicted values within explanatory variables - is it ok? | The problem that you pose reminds me a bit of the classic problem of fitting multivariate Gaussian mixture models (GMM), which is the archetypal application for the expectation maximization (EM) algor | Mixing observed and predicted values within explanatory variables - is it ok?
The problem that you pose reminds me a bit of the classic problem of fitting multivariate Gaussian mixture models (GMM), which is the archetypal application for the expectation maximization (EM) algorithm.
At a high level, it's instructive to... | Mixing observed and predicted values within explanatory variables - is it ok?
The problem that you pose reminds me a bit of the classic problem of fitting multivariate Gaussian mixture models (GMM), which is the archetypal application for the expectation maximization (EM) algor |
39,737 | What is the difference between multiple regression & mutivariate regression? [duplicate] | "Multiple regression" refers to situations in which you have more than one predictor / explanatory variable ($X$).
"Multivariate regression" refers to situations in which you have more than one response / outcome / dependent variable ($Y$).
It is also possible to have both multiple predictors and multiple responses... | What is the difference between multiple regression & mutivariate regression? [duplicate] | "Multiple regression" refers to situations in which you have more than one predictor / explanatory variable ($X$).
"Multivariate regression" refers to situations in which you have more than one resp | What is the difference between multiple regression & mutivariate regression? [duplicate]
"Multiple regression" refers to situations in which you have more than one predictor / explanatory variable ($X$).
"Multivariate regression" refers to situations in which you have more than one response / outcome / dependent vari... | What is the difference between multiple regression & mutivariate regression? [duplicate]
"Multiple regression" refers to situations in which you have more than one predictor / explanatory variable ($X$).
"Multivariate regression" refers to situations in which you have more than one resp |
39,738 | Practical vs Statistical significance | In a nutshell:
Suppose you are testing the effect of drinking a glass of wine per day on the risk of a heart attack. In layman terms, statistical significance refers to whether drinking affects such risk. Practical significance refers to whether such change in risk is of a relevant magnitude for real life concerns. If ... | Practical vs Statistical significance | In a nutshell:
Suppose you are testing the effect of drinking a glass of wine per day on the risk of a heart attack. In layman terms, statistical significance refers to whether drinking affects such r | Practical vs Statistical significance
In a nutshell:
Suppose you are testing the effect of drinking a glass of wine per day on the risk of a heart attack. In layman terms, statistical significance refers to whether drinking affects such risk. Practical significance refers to whether such change in risk is of a relevant... | Practical vs Statistical significance
In a nutshell:
Suppose you are testing the effect of drinking a glass of wine per day on the risk of a heart attack. In layman terms, statistical significance refers to whether drinking affects such r |
39,739 | Practical vs Statistical significance | This is a large topic but I suggest that the following are key points.
The relation between practical and statistical significance is not well described in terms of relative importance. To think in those terms rather suggests that a researcher has collected some data, used the data to test a hypothesis chosen without ... | Practical vs Statistical significance | This is a large topic but I suggest that the following are key points.
The relation between practical and statistical significance is not well described in terms of relative importance. To think in t | Practical vs Statistical significance
This is a large topic but I suggest that the following are key points.
The relation between practical and statistical significance is not well described in terms of relative importance. To think in those terms rather suggests that a researcher has collected some data, used the dat... | Practical vs Statistical significance
This is a large topic but I suggest that the following are key points.
The relation between practical and statistical significance is not well described in terms of relative importance. To think in t |
39,740 | Practical vs Statistical significance | Some points about the practical importance (I'm trying to avoid significant here) of statistically significant findings that come to my mind:
With increasing sample size, small effects will become statistically significant. Whether they are practically of importance won't change.
This is another way of looking at @Ada... | Practical vs Statistical significance | Some points about the practical importance (I'm trying to avoid significant here) of statistically significant findings that come to my mind:
With increasing sample size, small effects will become st | Practical vs Statistical significance
Some points about the practical importance (I'm trying to avoid significant here) of statistically significant findings that come to my mind:
With increasing sample size, small effects will become statistically significant. Whether they are practically of importance won't change.
... | Practical vs Statistical significance
Some points about the practical importance (I'm trying to avoid significant here) of statistically significant findings that come to my mind:
With increasing sample size, small effects will become st |
39,741 | Practical vs Statistical significance | Statistical significance always becomes more likely the larger the sample size is. This holds since almost no experiment is done exactly under the null hypothesis. Small irrelevant differences can never be ruled out. Consistency of the tests can make such irrelevant differences significant.
Practical relevance depends... | Practical vs Statistical significance | Statistical significance always becomes more likely the larger the sample size is. This holds since almost no experiment is done exactly under the null hypothesis. Small irrelevant differences can nev | Practical vs Statistical significance
Statistical significance always becomes more likely the larger the sample size is. This holds since almost no experiment is done exactly under the null hypothesis. Small irrelevant differences can never be ruled out. Consistency of the tests can make such irrelevant differences sig... | Practical vs Statistical significance
Statistical significance always becomes more likely the larger the sample size is. This holds since almost no experiment is done exactly under the null hypothesis. Small irrelevant differences can nev |
39,742 | Practical vs Statistical significance | Nutshell is being studied in relation to, among other things, prevention of diabetes and obesity.
Say you wish to analyse the difference between rats that get nutshell extract in their feed and rats that do not.
Then the 'effect of the nutshell' is statistically significant if the results are unlikely given the hypot... | Practical vs Statistical significance | Nutshell is being studied in relation to, among other things, prevention of diabetes and obesity.
Say you wish to analyse the difference between rats that get nutshell extract in their feed and rats | Practical vs Statistical significance
Nutshell is being studied in relation to, among other things, prevention of diabetes and obesity.
Say you wish to analyse the difference between rats that get nutshell extract in their feed and rats that do not.
Then the 'effect of the nutshell' is statistically significant if th... | Practical vs Statistical significance
Nutshell is being studied in relation to, among other things, prevention of diabetes and obesity.
Say you wish to analyse the difference between rats that get nutshell extract in their feed and rats |
39,743 | Practical vs Statistical significance | While I agree with the existing answers, I think one nuance hasn't been stressed enough and I will try to illustrate it with an example.
If you increase $n$, the power of your test rises which means that you are better able to detect real effects. If your $n$ is very large, you will be able to detect very small effects... | Practical vs Statistical significance | While I agree with the existing answers, I think one nuance hasn't been stressed enough and I will try to illustrate it with an example.
If you increase $n$, the power of your test rises which means t | Practical vs Statistical significance
While I agree with the existing answers, I think one nuance hasn't been stressed enough and I will try to illustrate it with an example.
If you increase $n$, the power of your test rises which means that you are better able to detect real effects. If your $n$ is very large, you wil... | Practical vs Statistical significance
While I agree with the existing answers, I think one nuance hasn't been stressed enough and I will try to illustrate it with an example.
If you increase $n$, the power of your test rises which means t |
39,744 | Is it possible to combine the F-test and t-test to test for differences in both the variance and the mean? | This problem of detecting a difference in two Normal distributions based on independent random samples from each was solved asymptotically by Pearson and Neyman in 1930 using the likelihood ratio test. (Specifically, the alternative hypothesis is that $\mu_1\ne\mu_2$ or $\sigma_1^2\ne\sigma_2^2.$ Under the null hypoth... | Is it possible to combine the F-test and t-test to test for differences in both the variance and the | This problem of detecting a difference in two Normal distributions based on independent random samples from each was solved asymptotically by Pearson and Neyman in 1930 using the likelihood ratio test | Is it possible to combine the F-test and t-test to test for differences in both the variance and the mean?
This problem of detecting a difference in two Normal distributions based on independent random samples from each was solved asymptotically by Pearson and Neyman in 1930 using the likelihood ratio test. (Specifical... | Is it possible to combine the F-test and t-test to test for differences in both the variance and the
This problem of detecting a difference in two Normal distributions based on independent random samples from each was solved asymptotically by Pearson and Neyman in 1930 using the likelihood ratio test |
39,745 | How do I get the amplitude and phase for sine wave from lm() summary? | The fit is
$$y = 26.9188 + 1.7468\sin(x) + 1.2077\cos(x).$$
Consider a general (non-zero) linear combination $\alpha \sin(x) + \beta\cos(x).$ Viewing $(\alpha, \beta)$ as a vector and writing it in polar coordinates $(r, \phi)$ yields
$$\alpha = r \cos(\phi),\quad \beta = r \sin(\phi), \quad r = \sqrt{\alpha^2+\beta^2}... | How do I get the amplitude and phase for sine wave from lm() summary? | The fit is
$$y = 26.9188 + 1.7468\sin(x) + 1.2077\cos(x).$$
Consider a general (non-zero) linear combination $\alpha \sin(x) + \beta\cos(x).$ Viewing $(\alpha, \beta)$ as a vector and writing it in po | How do I get the amplitude and phase for sine wave from lm() summary?
The fit is
$$y = 26.9188 + 1.7468\sin(x) + 1.2077\cos(x).$$
Consider a general (non-zero) linear combination $\alpha \sin(x) + \beta\cos(x).$ Viewing $(\alpha, \beta)$ as a vector and writing it in polar coordinates $(r, \phi)$ yields
$$\alpha = r \c... | How do I get the amplitude and phase for sine wave from lm() summary?
The fit is
$$y = 26.9188 + 1.7468\sin(x) + 1.2077\cos(x).$$
Consider a general (non-zero) linear combination $\alpha \sin(x) + \beta\cos(x).$ Viewing $(\alpha, \beta)$ as a vector and writing it in po |
39,746 | Different results by using chi square test and logistic regression | A few points:
1) The fact that the independent variables are categorical is irrelevant for the choice of logistic regression.
2) A significant chi-square value means the two variables are associated, but if both are categorical, it's not really correlation. If both variables have only 2 levels, there are analogues of c... | Different results by using chi square test and logistic regression | A few points:
1) The fact that the independent variables are categorical is irrelevant for the choice of logistic regression.
2) A significant chi-square value means the two variables are associated, | Different results by using chi square test and logistic regression
A few points:
1) The fact that the independent variables are categorical is irrelevant for the choice of logistic regression.
2) A significant chi-square value means the two variables are associated, but if both are categorical, it's not really correlat... | Different results by using chi square test and logistic regression
A few points:
1) The fact that the independent variables are categorical is irrelevant for the choice of logistic regression.
2) A significant chi-square value means the two variables are associated, |
39,747 | pattern of ROC curve and choice of AUC | I agree with your concerns.
given that people in reality will seldom choose a FPR cut-off of 0.5 or higher, why people would prefer a ROC curve with FPR ranging from 0 to 1 and use the full AUC value (i.e. calculate the entire area under the ROC curve) instead of just reporting the area made from, say, 0 to 0.25 or to... | pattern of ROC curve and choice of AUC | I agree with your concerns.
given that people in reality will seldom choose a FPR cut-off of 0.5 or higher, why people would prefer a ROC curve with FPR ranging from 0 to 1 and use the full AUC value | pattern of ROC curve and choice of AUC
I agree with your concerns.
given that people in reality will seldom choose a FPR cut-off of 0.5 or higher, why people would prefer a ROC curve with FPR ranging from 0 to 1 and use the full AUC value (i.e. calculate the entire area under the ROC curve) instead of just reporting t... | pattern of ROC curve and choice of AUC
I agree with your concerns.
given that people in reality will seldom choose a FPR cut-off of 0.5 or higher, why people would prefer a ROC curve with FPR ranging from 0 to 1 and use the full AUC value |
39,748 | pattern of ROC curve and choice of AUC | Usually, it will be your application that will determine whether your focus is on precision or recall.
@2
These will be dramatically different in the medical field, where you will often tolerate having a bad precision for the sake of a very good recall, when it comes to prevention, i.e. you prefer to label a lot of he... | pattern of ROC curve and choice of AUC | Usually, it will be your application that will determine whether your focus is on precision or recall.
@2
These will be dramatically different in the medical field, where you will often tolerate havi | pattern of ROC curve and choice of AUC
Usually, it will be your application that will determine whether your focus is on precision or recall.
@2
These will be dramatically different in the medical field, where you will often tolerate having a bad precision for the sake of a very good recall, when it comes to preventio... | pattern of ROC curve and choice of AUC
Usually, it will be your application that will determine whether your focus is on precision or recall.
@2
These will be dramatically different in the medical field, where you will often tolerate havi |
39,749 | pattern of ROC curve and choice of AUC | You didn't state the ultimate goal of the exercise, hence the choice of ROC curves was not well motivated. Many useful things can be done with log-likelihood and Brier scores, as well as with the distribution of predicted risks (ignoring $Y$). The use of cutoffs is questionable. | pattern of ROC curve and choice of AUC | You didn't state the ultimate goal of the exercise, hence the choice of ROC curves was not well motivated. Many useful things can be done with log-likelihood and Brier scores, as well as with the dis | pattern of ROC curve and choice of AUC
You didn't state the ultimate goal of the exercise, hence the choice of ROC curves was not well motivated. Many useful things can be done with log-likelihood and Brier scores, as well as with the distribution of predicted risks (ignoring $Y$). The use of cutoffs is questionable. | pattern of ROC curve and choice of AUC
You didn't state the ultimate goal of the exercise, hence the choice of ROC curves was not well motivated. Many useful things can be done with log-likelihood and Brier scores, as well as with the dis |
39,750 | Whether to transform non-normal independent variables in logistic regression? | Why odds ratios look strange on transformed variables
Transformations change the metric of the variable. Odds ratios are the predicted difference in odds for a one unit increase on the IV holding all other IVs constant. The meaning of one unit will be very different after a square root transformation.
For example, if y... | Whether to transform non-normal independent variables in logistic regression? | Why odds ratios look strange on transformed variables
Transformations change the metric of the variable. Odds ratios are the predicted difference in odds for a one unit increase on the IV holding all | Whether to transform non-normal independent variables in logistic regression?
Why odds ratios look strange on transformed variables
Transformations change the metric of the variable. Odds ratios are the predicted difference in odds for a one unit increase on the IV holding all other IVs constant. The meaning of one uni... | Whether to transform non-normal independent variables in logistic regression?
Why odds ratios look strange on transformed variables
Transformations change the metric of the variable. Odds ratios are the predicted difference in odds for a one unit increase on the IV holding all |
39,751 | Partial derivative of bivariate normal cdf and pdf | \begin{align}
y &= \Phi(x_1,x_2,\rho)
= \int_{-\infty}^{x_1}\left[\int_{-\infty}^{x_2} \phi(a,b,\rho)\,\mathrm
db\right]\,\mathrm da\\
\frac{\partial y}{\partial x_1}
&= \frac{\partial}{\partial x_1}\Phi(x_1,x_2,\rho) = \frac{\partial}{\partial x_1}\int_{-\infty}^{x_1}
\left[\int_{-\infty}^{x_2} \phi(a,b,\rho)\,\mathr... | Partial derivative of bivariate normal cdf and pdf | \begin{align}
y &= \Phi(x_1,x_2,\rho)
= \int_{-\infty}^{x_1}\left[\int_{-\infty}^{x_2} \phi(a,b,\rho)\,\mathrm
db\right]\,\mathrm da\\
\frac{\partial y}{\partial x_1}
&= \frac{\partial}{\partial x_1} | Partial derivative of bivariate normal cdf and pdf
\begin{align}
y &= \Phi(x_1,x_2,\rho)
= \int_{-\infty}^{x_1}\left[\int_{-\infty}^{x_2} \phi(a,b,\rho)\,\mathrm
db\right]\,\mathrm da\\
\frac{\partial y}{\partial x_1}
&= \frac{\partial}{\partial x_1}\Phi(x_1,x_2,\rho) = \frac{\partial}{\partial x_1}\int_{-\infty}^{x_1... | Partial derivative of bivariate normal cdf and pdf
\begin{align}
y &= \Phi(x_1,x_2,\rho)
= \int_{-\infty}^{x_1}\left[\int_{-\infty}^{x_2} \phi(a,b,\rho)\,\mathrm
db\right]\,\mathrm da\\
\frac{\partial y}{\partial x_1}
&= \frac{\partial}{\partial x_1} |
39,752 | Partial derivative of bivariate normal cdf and pdf | While the accepted answer provides great tips for somebody looking to re-derive these quantities, for some work I was doing I actually just needed to know the closed-form partial derivatives of the bivariate normal cdf. Further, the integral for the partial with respect to $\rho$ is non-trivial. Since my google search ... | Partial derivative of bivariate normal cdf and pdf | While the accepted answer provides great tips for somebody looking to re-derive these quantities, for some work I was doing I actually just needed to know the closed-form partial derivatives of the bi | Partial derivative of bivariate normal cdf and pdf
While the accepted answer provides great tips for somebody looking to re-derive these quantities, for some work I was doing I actually just needed to know the closed-form partial derivatives of the bivariate normal cdf. Further, the integral for the partial with respec... | Partial derivative of bivariate normal cdf and pdf
While the accepted answer provides great tips for somebody looking to re-derive these quantities, for some work I was doing I actually just needed to know the closed-form partial derivatives of the bi |
39,753 | Why are Bayesian methods widely considered particularly "convenient"? | In my personal opinion I think that Bayesian methods are extremely convenient in that you need to specify only four main ingredients for solving problems of inference, prediction, and decision making.
These questions encompass almost all of the discipline of statistics: describing a data set $D$, generalizing outward ... | Why are Bayesian methods widely considered particularly "convenient"? | In my personal opinion I think that Bayesian methods are extremely convenient in that you need to specify only four main ingredients for solving problems of inference, prediction, and decision making. | Why are Bayesian methods widely considered particularly "convenient"?
In my personal opinion I think that Bayesian methods are extremely convenient in that you need to specify only four main ingredients for solving problems of inference, prediction, and decision making.
These questions encompass almost all of the disc... | Why are Bayesian methods widely considered particularly "convenient"?
In my personal opinion I think that Bayesian methods are extremely convenient in that you need to specify only four main ingredients for solving problems of inference, prediction, and decision making. |
39,754 | Why are Bayesian methods widely considered particularly "convenient"? | Reasons why I think they're convenient, working in a field that's still somewhat dominated by frequentist statistics, but where a "Bayesian" analysis carry some cachet:
Credible intervals are awesome, in that they can be interpreted the way people really want to interpret confidence intervals from frequentist analysis... | Why are Bayesian methods widely considered particularly "convenient"? | Reasons why I think they're convenient, working in a field that's still somewhat dominated by frequentist statistics, but where a "Bayesian" analysis carry some cachet:
Credible intervals are awesome | Why are Bayesian methods widely considered particularly "convenient"?
Reasons why I think they're convenient, working in a field that's still somewhat dominated by frequentist statistics, but where a "Bayesian" analysis carry some cachet:
Credible intervals are awesome, in that they can be interpreted the way people r... | Why are Bayesian methods widely considered particularly "convenient"?
Reasons why I think they're convenient, working in a field that's still somewhat dominated by frequentist statistics, but where a "Bayesian" analysis carry some cachet:
Credible intervals are awesome |
39,755 | Why are Bayesian methods widely considered particularly "convenient"? | I'm just a rookie in all of this, but it seems to me that the Bayesian "Prior * Likelihood = Posterior" model is simple and flexible, which means "convenient".
For example, your priors are explicitly stated and your procedure does not change because you choose different priors. I could look at your analysis and decide ... | Why are Bayesian methods widely considered particularly "convenient"? | I'm just a rookie in all of this, but it seems to me that the Bayesian "Prior * Likelihood = Posterior" model is simple and flexible, which means "convenient".
For example, your priors are explicitly | Why are Bayesian methods widely considered particularly "convenient"?
I'm just a rookie in all of this, but it seems to me that the Bayesian "Prior * Likelihood = Posterior" model is simple and flexible, which means "convenient".
For example, your priors are explicitly stated and your procedure does not change because ... | Why are Bayesian methods widely considered particularly "convenient"?
I'm just a rookie in all of this, but it seems to me that the Bayesian "Prior * Likelihood = Posterior" model is simple and flexible, which means "convenient".
For example, your priors are explicitly |
39,756 | Unpaired repeated measures data | A simple two-sample t-test would actually be a conservative way of testing for time differences here.
Let's say that $t_{paired}$ is the t-statistic that you would get from a paired t-test on your data, if you knew the pairings, whereas $t_{unpaired}$ is the t-statistic you get from a simple two-group t-test on the dat... | Unpaired repeated measures data | A simple two-sample t-test would actually be a conservative way of testing for time differences here.
Let's say that $t_{paired}$ is the t-statistic that you would get from a paired t-test on your dat | Unpaired repeated measures data
A simple two-sample t-test would actually be a conservative way of testing for time differences here.
Let's say that $t_{paired}$ is the t-statistic that you would get from a paired t-test on your data, if you knew the pairings, whereas $t_{unpaired}$ is the t-statistic you get from a si... | Unpaired repeated measures data
A simple two-sample t-test would actually be a conservative way of testing for time differences here.
Let's say that $t_{paired}$ is the t-statistic that you would get from a paired t-test on your dat |
39,757 | Statistics, Expected values and Philosophy | I think the answer to your question is best answered by focusing on what it is, precisely, that you want to know.
You're correct that the typist's average words-per-minute is only a meaningful inference on that particular typist. But measuring the typist's performance at many intervals will, hopefully, randomly mix in ... | Statistics, Expected values and Philosophy | I think the answer to your question is best answered by focusing on what it is, precisely, that you want to know.
You're correct that the typist's average words-per-minute is only a meaningful inferen | Statistics, Expected values and Philosophy
I think the answer to your question is best answered by focusing on what it is, precisely, that you want to know.
You're correct that the typist's average words-per-minute is only a meaningful inference on that particular typist. But measuring the typist's performance at many ... | Statistics, Expected values and Philosophy
I think the answer to your question is best answered by focusing on what it is, precisely, that you want to know.
You're correct that the typist's average words-per-minute is only a meaningful inferen |
39,758 | Statistics, Expected values and Philosophy | DJE gave a great answer, but I would just add some clarification about which states we can and can't accept.
When you measure the typist's speed, you are really measuring the marginal expected value. For simplicity, let's consider the typist's speed to be in one of two states (fast =1, slow=0) and say we are trying to... | Statistics, Expected values and Philosophy | DJE gave a great answer, but I would just add some clarification about which states we can and can't accept.
When you measure the typist's speed, you are really measuring the marginal expected value. | Statistics, Expected values and Philosophy
DJE gave a great answer, but I would just add some clarification about which states we can and can't accept.
When you measure the typist's speed, you are really measuring the marginal expected value. For simplicity, let's consider the typist's speed to be in one of two states... | Statistics, Expected values and Philosophy
DJE gave a great answer, but I would just add some clarification about which states we can and can't accept.
When you measure the typist's speed, you are really measuring the marginal expected value. |
39,759 | Statistics, Expected values and Philosophy | This question hinges on the probabilistic concept of exchangeability. Consider an experiment that generates a series of outcomes $X_1, X_2, X_3,...$ and suppose that we have "stable conditions", by which we mean that the conditions of the experiment are sufficiently similar in essentials from trial to trial that we ar... | Statistics, Expected values and Philosophy | This question hinges on the probabilistic concept of exchangeability. Consider an experiment that generates a series of outcomes $X_1, X_2, X_3,...$ and suppose that we have "stable conditions", by w | Statistics, Expected values and Philosophy
This question hinges on the probabilistic concept of exchangeability. Consider an experiment that generates a series of outcomes $X_1, X_2, X_3,...$ and suppose that we have "stable conditions", by which we mean that the conditions of the experiment are sufficiently similar i... | Statistics, Expected values and Philosophy
This question hinges on the probabilistic concept of exchangeability. Consider an experiment that generates a series of outcomes $X_1, X_2, X_3,...$ and suppose that we have "stable conditions", by w |
39,760 | Statistics, Expected values and Philosophy | If you consider x to be constant, well the expected value will be x.
If you want to look at the evolution of x you cannot make the hypothesis that x is constant.
My approach would be different.
Suppose now that your x is evolving over time, you have a time series.
To guess the expected value you can build a model. Thi... | Statistics, Expected values and Philosophy | If you consider x to be constant, well the expected value will be x.
If you want to look at the evolution of x you cannot make the hypothesis that x is constant.
My approach would be different.
Suppo | Statistics, Expected values and Philosophy
If you consider x to be constant, well the expected value will be x.
If you want to look at the evolution of x you cannot make the hypothesis that x is constant.
My approach would be different.
Suppose now that your x is evolving over time, you have a time series.
To guess th... | Statistics, Expected values and Philosophy
If you consider x to be constant, well the expected value will be x.
If you want to look at the evolution of x you cannot make the hypothesis that x is constant.
My approach would be different.
Suppo |
39,761 | Statistics, Expected values and Philosophy | When we say "the typist A types $\mu$ words a minute", we mean the typist A in all his/her different (but normal) states. It means, to evaluate the mean $\mu$ you need to measure his/her performance during several regular working days. No typist works with the hand tied behind her/his back. This is not part of their jo... | Statistics, Expected values and Philosophy | When we say "the typist A types $\mu$ words a minute", we mean the typist A in all his/her different (but normal) states. It means, to evaluate the mean $\mu$ you need to measure his/her performance d | Statistics, Expected values and Philosophy
When we say "the typist A types $\mu$ words a minute", we mean the typist A in all his/her different (but normal) states. It means, to evaluate the mean $\mu$ you need to measure his/her performance during several regular working days. No typist works with the hand tied behind... | Statistics, Expected values and Philosophy
When we say "the typist A types $\mu$ words a minute", we mean the typist A in all his/her different (but normal) states. It means, to evaluate the mean $\mu$ you need to measure his/her performance d |
39,762 | Account for spatial autocorrelation with a binomial regression model | If you are happy to assume your binomial responses are coming from a spatially correlated gaussian random field via a logit link, and your non-spatial covariates have the usual log-linear form, then stuff it all into geoRglm:
http://cran.r-project.org/web/packages/geoRglm/vignettes/geoRglmintro.pdf
and once you've got ... | Account for spatial autocorrelation with a binomial regression model | If you are happy to assume your binomial responses are coming from a spatially correlated gaussian random field via a logit link, and your non-spatial covariates have the usual log-linear form, then s | Account for spatial autocorrelation with a binomial regression model
If you are happy to assume your binomial responses are coming from a spatially correlated gaussian random field via a logit link, and your non-spatial covariates have the usual log-linear form, then stuff it all into geoRglm:
http://cran.r-project.org... | Account for spatial autocorrelation with a binomial regression model
If you are happy to assume your binomial responses are coming from a spatially correlated gaussian random field via a logit link, and your non-spatial covariates have the usual log-linear form, then s |
39,763 | Account for spatial autocorrelation with a binomial regression model | It sounds to me like x, y are potential independent variables in your model. The issue is that the binomial regression model you mention assumes that the independent variables are not correlated. Some people add interaction terms to their model to deal with this, but a lot of model interpretability is lost when you do ... | Account for spatial autocorrelation with a binomial regression model | It sounds to me like x, y are potential independent variables in your model. The issue is that the binomial regression model you mention assumes that the independent variables are not correlated. Some | Account for spatial autocorrelation with a binomial regression model
It sounds to me like x, y are potential independent variables in your model. The issue is that the binomial regression model you mention assumes that the independent variables are not correlated. Some people add interaction terms to their model to dea... | Account for spatial autocorrelation with a binomial regression model
It sounds to me like x, y are potential independent variables in your model. The issue is that the binomial regression model you mention assumes that the independent variables are not correlated. Some |
39,764 | Account for spatial autocorrelation with a binomial regression model | I found this tutorial for the spdep package to be quite useful.
In the end, you would want to create spatial weights like this:
us.nb4 <- knearneigh(coordinates(data[,1:2]), k=4)
us.nb4 <- knn2nb(us.nb4)
us.nb4 <- make.sym.nb(us.nb4)
us.wt4 <- nb2listw(us.nb4, style="W")
... which you could use into a Moran eigenvecto... | Account for spatial autocorrelation with a binomial regression model | I found this tutorial for the spdep package to be quite useful.
In the end, you would want to create spatial weights like this:
us.nb4 <- knearneigh(coordinates(data[,1:2]), k=4)
us.nb4 <- knn2nb(us.n | Account for spatial autocorrelation with a binomial regression model
I found this tutorial for the spdep package to be quite useful.
In the end, you would want to create spatial weights like this:
us.nb4 <- knearneigh(coordinates(data[,1:2]), k=4)
us.nb4 <- knn2nb(us.nb4)
us.nb4 <- make.sym.nb(us.nb4)
us.wt4 <- nb2list... | Account for spatial autocorrelation with a binomial regression model
I found this tutorial for the spdep package to be quite useful.
In the end, you would want to create spatial weights like this:
us.nb4 <- knearneigh(coordinates(data[,1:2]), k=4)
us.nb4 <- knn2nb(us.n |
39,765 | Plotting and presenting longitudinal data, options? | Here's one idea for visualizing your data. Using a variation of small multiples, you could have two charts: one showing the variables' mean with a focus on a variable of interest (including SE or SD), with the second showing the focused variables individual observations.
The following chart shows three variables acros... | Plotting and presenting longitudinal data, options? | Here's one idea for visualizing your data. Using a variation of small multiples, you could have two charts: one showing the variables' mean with a focus on a variable of interest (including SE or SD) | Plotting and presenting longitudinal data, options?
Here's one idea for visualizing your data. Using a variation of small multiples, you could have two charts: one showing the variables' mean with a focus on a variable of interest (including SE or SD), with the second showing the focused variables individual observati... | Plotting and presenting longitudinal data, options?
Here's one idea for visualizing your data. Using a variation of small multiples, you could have two charts: one showing the variables' mean with a focus on a variable of interest (including SE or SD) |
39,766 | Plotting and presenting longitudinal data, options? | One often overlooked problem with plotting/analyzing summary (e.g. mean) curves is how to deal with Phase Variation. In an extreme example, one could plot the mean of 2 sin curves that are 180 degrees out of phase. This would of course be a straight line, which clearly doesn't reflect anything interesting about the ind... | Plotting and presenting longitudinal data, options? | One often overlooked problem with plotting/analyzing summary (e.g. mean) curves is how to deal with Phase Variation. In an extreme example, one could plot the mean of 2 sin curves that are 180 degrees | Plotting and presenting longitudinal data, options?
One often overlooked problem with plotting/analyzing summary (e.g. mean) curves is how to deal with Phase Variation. In an extreme example, one could plot the mean of 2 sin curves that are 180 degrees out of phase. This would of course be a straight line, which clearl... | Plotting and presenting longitudinal data, options?
One often overlooked problem with plotting/analyzing summary (e.g. mean) curves is how to deal with Phase Variation. In an extreme example, one could plot the mean of 2 sin curves that are 180 degrees |
39,767 | Matched binomial pairs | I would recommend you to use Generalized Estimating Equations (GEE). This is analogous to Repeated-measures ANOVA but allows for non-continuous or non-normal response because, being a Generalized linear model, it adopts various link functions.
With your example, I'd use binomial distribution with logit link (albeit you... | Matched binomial pairs | I would recommend you to use Generalized Estimating Equations (GEE). This is analogous to Repeated-measures ANOVA but allows for non-continuous or non-normal response because, being a Generalized line | Matched binomial pairs
I would recommend you to use Generalized Estimating Equations (GEE). This is analogous to Repeated-measures ANOVA but allows for non-continuous or non-normal response because, being a Generalized linear model, it adopts various link functions.
With your example, I'd use binomial distribution with... | Matched binomial pairs
I would recommend you to use Generalized Estimating Equations (GEE). This is analogous to Repeated-measures ANOVA but allows for non-continuous or non-normal response because, being a Generalized line |
39,768 | Matched binomial pairs | I don't think fisher exact test is appropriate here is it?
It is saying that pre-test there are 34 points arranged in this manner (343344355), and that post test there are 44 points. The arrangement of those 44 points is consistent with the pattern (marginal) established in the pre-test. It is also saying that each p... | Matched binomial pairs | I don't think fisher exact test is appropriate here is it?
It is saying that pre-test there are 34 points arranged in this manner (343344355), and that post test there are 44 points. The arrangement | Matched binomial pairs
I don't think fisher exact test is appropriate here is it?
It is saying that pre-test there are 34 points arranged in this manner (343344355), and that post test there are 44 points. The arrangement of those 44 points is consistent with the pattern (marginal) established in the pre-test. It is ... | Matched binomial pairs
I don't think fisher exact test is appropriate here is it?
It is saying that pre-test there are 34 points arranged in this manner (343344355), and that post test there are 44 points. The arrangement |
39,769 | Matched binomial pairs | One other option would be run a binomial mixed model. You would need to code the data like this:
result id time
0 1 pre
0 1 pre
1 1 pre
1 1 pre
1 1 pre
1 1 post
1 1 post
1 1 post
1 1 post
1 1 post
With the R package lme4 you co... | Matched binomial pairs | One other option would be run a binomial mixed model. You would need to code the data like this:
result id time
0 1 pre
0 1 pre
1 1 pre
1 1 pre
1 1 pre
| Matched binomial pairs
One other option would be run a binomial mixed model. You would need to code the data like this:
result id time
0 1 pre
0 1 pre
1 1 pre
1 1 pre
1 1 pre
1 1 post
1 1 post
1 1 post
1 1 post
1 1 post
With th... | Matched binomial pairs
One other option would be run a binomial mixed model. You would need to code the data like this:
result id time
0 1 pre
0 1 pre
1 1 pre
1 1 pre
1 1 pre
|
39,770 | How can I interpret coefficients of categorical predictors in the negative binomial regression model? | I'm going to answer this using a Poisson model, which is precisely a negative binomial model without overdispersion, because the math will be simpler. The poisson model predicts the probability of observing $y_i$ to be a particular non-negative discrete number
$$P(y_i|X) = \dfrac{\exp(-\lambda_i)\lambda_i ^{y_i}}{y_i!... | How can I interpret coefficients of categorical predictors in the negative binomial regression model | I'm going to answer this using a Poisson model, which is precisely a negative binomial model without overdispersion, because the math will be simpler. The poisson model predicts the probability of ob | How can I interpret coefficients of categorical predictors in the negative binomial regression model?
I'm going to answer this using a Poisson model, which is precisely a negative binomial model without overdispersion, because the math will be simpler. The poisson model predicts the probability of observing $y_i$ to b... | How can I interpret coefficients of categorical predictors in the negative binomial regression model
I'm going to answer this using a Poisson model, which is precisely a negative binomial model without overdispersion, because the math will be simpler. The poisson model predicts the probability of ob |
39,771 | Examples of drastic improvements when using deep neural networks | "Dramatic" is subjective.
One example where deep networks do better is the MNIST hand-written digit set. Yann LeCun keeps a web page of progress made by various techniques with many useful links. This is a relatively simple classification problem compared with speech recognition and image recognition, and deep network... | Examples of drastic improvements when using deep neural networks | "Dramatic" is subjective.
One example where deep networks do better is the MNIST hand-written digit set. Yann LeCun keeps a web page of progress made by various techniques with many useful links. Thi | Examples of drastic improvements when using deep neural networks
"Dramatic" is subjective.
One example where deep networks do better is the MNIST hand-written digit set. Yann LeCun keeps a web page of progress made by various techniques with many useful links. This is a relatively simple classification problem compare... | Examples of drastic improvements when using deep neural networks
"Dramatic" is subjective.
One example where deep networks do better is the MNIST hand-written digit set. Yann LeCun keeps a web page of progress made by various techniques with many useful links. Thi |
39,772 | Examples of drastic improvements when using deep neural networks | In my opinion, some of the most convincing results from the deep learning community in the past few years have come from the area of automatic speech recognition (ASR).
At this point, ASR has seen about four decades of excellent work from a number of really smart people, so the field has been on something of a plateau ... | Examples of drastic improvements when using deep neural networks | In my opinion, some of the most convincing results from the deep learning community in the past few years have come from the area of automatic speech recognition (ASR).
At this point, ASR has seen abo | Examples of drastic improvements when using deep neural networks
In my opinion, some of the most convincing results from the deep learning community in the past few years have come from the area of automatic speech recognition (ASR).
At this point, ASR has seen about four decades of excellent work from a number of real... | Examples of drastic improvements when using deep neural networks
In my opinion, some of the most convincing results from the deep learning community in the past few years have come from the area of automatic speech recognition (ASR).
At this point, ASR has seen abo |
39,773 | Conditional Expectation of Multivariate Distributions | Try to build your intuition with particular cases first. Suppose that $X\in\{x_1,\dots,x_m\}$ with pmf $p_X$ and $Y\in\{y_1,\dots,y_n\}$ with pmf $p_Y$, such that $p_Y(y_i)>0$, for $i=1,\dots,n$. Let $p_{X,Y}$ be the joint pmf of $X$ and $Y$. The conditional pmf of $X$ given $Y$ is defined as
$$
p_{X\mid Y}(x_i\mid y... | Conditional Expectation of Multivariate Distributions | Try to build your intuition with particular cases first. Suppose that $X\in\{x_1,\dots,x_m\}$ with pmf $p_X$ and $Y\in\{y_1,\dots,y_n\}$ with pmf $p_Y$, such that $p_Y(y_i)>0$, for $i=1,\dots,n$. Let | Conditional Expectation of Multivariate Distributions
Try to build your intuition with particular cases first. Suppose that $X\in\{x_1,\dots,x_m\}$ with pmf $p_X$ and $Y\in\{y_1,\dots,y_n\}$ with pmf $p_Y$, such that $p_Y(y_i)>0$, for $i=1,\dots,n$. Let $p_{X,Y}$ be the joint pmf of $X$ and $Y$. The conditional pmf of ... | Conditional Expectation of Multivariate Distributions
Try to build your intuition with particular cases first. Suppose that $X\in\{x_1,\dots,x_m\}$ with pmf $p_X$ and $Y\in\{y_1,\dots,y_n\}$ with pmf $p_Y$, such that $p_Y(y_i)>0$, for $i=1,\dots,n$. Let |
39,774 | Maximising the correlation between vectors vs minimising the angle between them | It is often useful to geometrically represent random variables $X_{1}, \ldots, X_{p}$ (theoretical or empirical data) as vectors $\bf{x}_{1}, \ldots, \bf{x}_{p}$ such that their standard deviations $\sigma(X_{i})$ equal their lengths $||\bf{x}_{i}||$, and their correlations $\rho(X_{i}, X_{j})$ equal the cosine of thei... | Maximising the correlation between vectors vs minimising the angle between them | It is often useful to geometrically represent random variables $X_{1}, \ldots, X_{p}$ (theoretical or empirical data) as vectors $\bf{x}_{1}, \ldots, \bf{x}_{p}$ such that their standard deviations $\ | Maximising the correlation between vectors vs minimising the angle between them
It is often useful to geometrically represent random variables $X_{1}, \ldots, X_{p}$ (theoretical or empirical data) as vectors $\bf{x}_{1}, \ldots, \bf{x}_{p}$ such that their standard deviations $\sigma(X_{i})$ equal their lengths $||\bf... | Maximising the correlation between vectors vs minimising the angle between them
It is often useful to geometrically represent random variables $X_{1}, \ldots, X_{p}$ (theoretical or empirical data) as vectors $\bf{x}_{1}, \ldots, \bf{x}_{p}$ such that their standard deviations $\ |
39,775 | Maximising the correlation between vectors vs minimising the angle between them | Since you ask for a reference, Statistics methods: the geometric approach explains this and many other properties by visualization in geometric space. For teaching purposes, it can also be useful because you can explain deep concepts to people with a weak background in calculus.
@caracal's answer is very comprehensive.... | Maximising the correlation between vectors vs minimising the angle between them | Since you ask for a reference, Statistics methods: the geometric approach explains this and many other properties by visualization in geometric space. For teaching purposes, it can also be useful beca | Maximising the correlation between vectors vs minimising the angle between them
Since you ask for a reference, Statistics methods: the geometric approach explains this and many other properties by visualization in geometric space. For teaching purposes, it can also be useful because you can explain deep concepts to peo... | Maximising the correlation between vectors vs minimising the angle between them
Since you ask for a reference, Statistics methods: the geometric approach explains this and many other properties by visualization in geometric space. For teaching purposes, it can also be useful beca |
39,776 | How to statistically describe chain-like patterns in bivariate data? | The correlation between X and Y measures the presence or absence of a linear relationship between them. If y=aX+B -- a pure line with no scatter and no error - the correlation will be 1 (if a>0) and -1 (if a < 0). It is not a general measure of causality or relatedness.
Your second scatter plot shows no linearity at al... | How to statistically describe chain-like patterns in bivariate data? | The correlation between X and Y measures the presence or absence of a linear relationship between them. If y=aX+B -- a pure line with no scatter and no error - the correlation will be 1 (if a>0) and - | How to statistically describe chain-like patterns in bivariate data?
The correlation between X and Y measures the presence or absence of a linear relationship between them. If y=aX+B -- a pure line with no scatter and no error - the correlation will be 1 (if a>0) and -1 (if a < 0). It is not a general measure of causal... | How to statistically describe chain-like patterns in bivariate data?
The correlation between X and Y measures the presence or absence of a linear relationship between them. If y=aX+B -- a pure line with no scatter and no error - the correlation will be 1 (if a>0) and - |
39,777 | How to statistically describe chain-like patterns in bivariate data? | The pattern you describe is completely uncorrelated but can be picked up with some information theoretic measure such as mutual information. There are a number of packages implementing it, e.g. entropy and infotheo.
There is also a quite recent dependency measure called MIC, implemented in java with an R wrapper that y... | How to statistically describe chain-like patterns in bivariate data? | The pattern you describe is completely uncorrelated but can be picked up with some information theoretic measure such as mutual information. There are a number of packages implementing it, e.g. entrop | How to statistically describe chain-like patterns in bivariate data?
The pattern you describe is completely uncorrelated but can be picked up with some information theoretic measure such as mutual information. There are a number of packages implementing it, e.g. entropy and infotheo.
There is also a quite recent depend... | How to statistically describe chain-like patterns in bivariate data?
The pattern you describe is completely uncorrelated but can be picked up with some information theoretic measure such as mutual information. There are a number of packages implementing it, e.g. entrop |
39,778 | Jonckheere-Terpstra interpretation | First, one note. Like Kruskal-Wallis, Jonckheere-Terpstra is generally not a test of medians. It is a test of distributional "locations", or stochastic prevalence. It can give significant result even if medians are equal.
Now, for your test (let us honour your medians as locations). The test is highly significant becau... | Jonckheere-Terpstra interpretation | First, one note. Like Kruskal-Wallis, Jonckheere-Terpstra is generally not a test of medians. It is a test of distributional "locations", or stochastic prevalence. It can give significant result even | Jonckheere-Terpstra interpretation
First, one note. Like Kruskal-Wallis, Jonckheere-Terpstra is generally not a test of medians. It is a test of distributional "locations", or stochastic prevalence. It can give significant result even if medians are equal.
Now, for your test (let us honour your medians as locations). T... | Jonckheere-Terpstra interpretation
First, one note. Like Kruskal-Wallis, Jonckheere-Terpstra is generally not a test of medians. It is a test of distributional "locations", or stochastic prevalence. It can give significant result even |
39,779 | Jonckheere-Terpstra interpretation | The J-T test combines all the comparisons into a single test so it doesn't really make sense to extract a specific conclusion about one comparison. Specifically, the J-T test statistic is the sum of a set of two-sample rank-sum statistics. For your data, the reversal in trend between levels 3 and 4 will reduce the J-T ... | Jonckheere-Terpstra interpretation | The J-T test combines all the comparisons into a single test so it doesn't really make sense to extract a specific conclusion about one comparison. Specifically, the J-T test statistic is the sum of a | Jonckheere-Terpstra interpretation
The J-T test combines all the comparisons into a single test so it doesn't really make sense to extract a specific conclusion about one comparison. Specifically, the J-T test statistic is the sum of a set of two-sample rank-sum statistics. For your data, the reversal in trend between ... | Jonckheere-Terpstra interpretation
The J-T test combines all the comparisons into a single test so it doesn't really make sense to extract a specific conclusion about one comparison. Specifically, the J-T test statistic is the sum of a |
39,780 | How to determine whether data is slightly or extremely non-normally distributed? | The sample skewness $$\gamma=\frac{\sum_{i=1}^n(x_i-\bar{x})^3}{\Big(\sum_{i=1}^n(x_i-\bar{x})^2\Big)^{3/2}}$$ and the sample (excess) kurtosis $$\kappa=\frac{\sum_{i=1}^n(x_i-\bar{x})^4}{\Big(\sum_{i=1}^n(x_i-\bar{x})^2\Big)^{2}}-3$$ are often used as measures of non-normality.
The sample skewness measures the asymmet... | How to determine whether data is slightly or extremely non-normally distributed? | The sample skewness $$\gamma=\frac{\sum_{i=1}^n(x_i-\bar{x})^3}{\Big(\sum_{i=1}^n(x_i-\bar{x})^2\Big)^{3/2}}$$ and the sample (excess) kurtosis $$\kappa=\frac{\sum_{i=1}^n(x_i-\bar{x})^4}{\Big(\sum_{i | How to determine whether data is slightly or extremely non-normally distributed?
The sample skewness $$\gamma=\frac{\sum_{i=1}^n(x_i-\bar{x})^3}{\Big(\sum_{i=1}^n(x_i-\bar{x})^2\Big)^{3/2}}$$ and the sample (excess) kurtosis $$\kappa=\frac{\sum_{i=1}^n(x_i-\bar{x})^4}{\Big(\sum_{i=1}^n(x_i-\bar{x})^2\Big)^{2}}-3$$ are ... | How to determine whether data is slightly or extremely non-normally distributed?
The sample skewness $$\gamma=\frac{\sum_{i=1}^n(x_i-\bar{x})^3}{\Big(\sum_{i=1}^n(x_i-\bar{x})^2\Big)^{3/2}}$$ and the sample (excess) kurtosis $$\kappa=\frac{\sum_{i=1}^n(x_i-\bar{x})^4}{\Big(\sum_{i |
39,781 | How to determine whether data is slightly or extremely non-normally distributed? | I think the other answers really address methods for deciding non-normality. But I think the OP asks a different question. Basically he is asking about how to decide once normality is rejected how do you determine the severity? If it is mild perhaps the deviation can be ignored. Skewness and kurtosis can be looked ... | How to determine whether data is slightly or extremely non-normally distributed? | I think the other answers really address methods for deciding non-normality. But I think the OP asks a different question. Basically he is asking about how to decide once normality is rejected how d | How to determine whether data is slightly or extremely non-normally distributed?
I think the other answers really address methods for deciding non-normality. But I think the OP asks a different question. Basically he is asking about how to decide once normality is rejected how do you determine the severity? If it is... | How to determine whether data is slightly or extremely non-normally distributed?
I think the other answers really address methods for deciding non-normality. But I think the OP asks a different question. Basically he is asking about how to decide once normality is rejected how d |
39,782 | How to determine whether data is slightly or extremely non-normally distributed? | Although a wikipedia link might be not considered extremely helpful, the list of methods for testing normality is quite long.
The methods range from (already mentioned) histograms and qq-Plots if you want to stay on the graphical side over more lets say "empirical tests" (multiple sigma events in relation to sample siz... | How to determine whether data is slightly or extremely non-normally distributed? | Although a wikipedia link might be not considered extremely helpful, the list of methods for testing normality is quite long.
The methods range from (already mentioned) histograms and qq-Plots if you | How to determine whether data is slightly or extremely non-normally distributed?
Although a wikipedia link might be not considered extremely helpful, the list of methods for testing normality is quite long.
The methods range from (already mentioned) histograms and qq-Plots if you want to stay on the graphical side over... | How to determine whether data is slightly or extremely non-normally distributed?
Although a wikipedia link might be not considered extremely helpful, the list of methods for testing normality is quite long.
The methods range from (already mentioned) histograms and qq-Plots if you |
39,783 | How to determine whether data is slightly or extremely non-normally distributed? | The Skewness of the Normal distribution is 0. The Kurtosis of the Normal distribution is 0. Those two statistics are concrete measures of distribution characteristics as opposed to subjective plot interpretation. Of course the question remaining is how far from Normal your distribution is for $n$ points and some value ... | How to determine whether data is slightly or extremely non-normally distributed? | The Skewness of the Normal distribution is 0. The Kurtosis of the Normal distribution is 0. Those two statistics are concrete measures of distribution characteristics as opposed to subjective plot int | How to determine whether data is slightly or extremely non-normally distributed?
The Skewness of the Normal distribution is 0. The Kurtosis of the Normal distribution is 0. Those two statistics are concrete measures of distribution characteristics as opposed to subjective plot interpretation. Of course the question rem... | How to determine whether data is slightly or extremely non-normally distributed?
The Skewness of the Normal distribution is 0. The Kurtosis of the Normal distribution is 0. Those two statistics are concrete measures of distribution characteristics as opposed to subjective plot int |
39,784 | How to determine whether data is slightly or extremely non-normally distributed? | Here I found some rules of thumb on how to evaluate.
If skewness is:
less than −1 or greater than +1, the distribution is highly skewed.
between −1 and −½ or between +½ and +1, the distribution is moderately skewed.
between −½ and +½, the distribution is approximately symmetric. | How to determine whether data is slightly or extremely non-normally distributed? | Here I found some rules of thumb on how to evaluate.
If skewness is:
less than −1 or greater than +1, the distribution is highly skewed.
between −1 and −½ or between +½ and +1, the distribution is | How to determine whether data is slightly or extremely non-normally distributed?
Here I found some rules of thumb on how to evaluate.
If skewness is:
less than −1 or greater than +1, the distribution is highly skewed.
between −1 and −½ or between +½ and +1, the distribution is moderately skewed.
between −½ and +½... | How to determine whether data is slightly or extremely non-normally distributed?
Here I found some rules of thumb on how to evaluate.
If skewness is:
less than −1 or greater than +1, the distribution is highly skewed.
between −1 and −½ or between +½ and +1, the distribution is |
39,785 | Is it okay to compare fitted distributions with the AIC? | You have to penalize the model for number of parameters. Let's say you had 30 data points and a model to fit it to that takes 29 parameters to define it. You could fit the data perfectly. But, that's not a terribly fair way to compare it to a uniform distribution with far fewer parameters.
The paper you cite mention... | Is it okay to compare fitted distributions with the AIC? | You have to penalize the model for number of parameters. Let's say you had 30 data points and a model to fit it to that takes 29 parameters to define it. You could fit the data perfectly. But, that | Is it okay to compare fitted distributions with the AIC?
You have to penalize the model for number of parameters. Let's say you had 30 data points and a model to fit it to that takes 29 parameters to define it. You could fit the data perfectly. But, that's not a terribly fair way to compare it to a uniform distribut... | Is it okay to compare fitted distributions with the AIC?
You have to penalize the model for number of parameters. Let's say you had 30 data points and a model to fit it to that takes 29 parameters to define it. You could fit the data perfectly. But, that |
39,786 | Is it okay to compare fitted distributions with the AIC? | I'd go further and say it is probably the most widely accepted method for comparing distributions. But you should really use the corrected AIC, which has a piece added to it to adjust for small sample sizes. See Burnham and Anderson 2002, for example.
This site will take a set of numbers and do the comparisons for you,... | Is it okay to compare fitted distributions with the AIC? | I'd go further and say it is probably the most widely accepted method for comparing distributions. But you should really use the corrected AIC, which has a piece added to it to adjust for small sample | Is it okay to compare fitted distributions with the AIC?
I'd go further and say it is probably the most widely accepted method for comparing distributions. But you should really use the corrected AIC, which has a piece added to it to adjust for small sample sizes. See Burnham and Anderson 2002, for example.
This site w... | Is it okay to compare fitted distributions with the AIC?
I'd go further and say it is probably the most widely accepted method for comparing distributions. But you should really use the corrected AIC, which has a piece added to it to adjust for small sample |
39,787 | How to interpret the confidence interval of a variance F-test using R? | The rejection region for a test and a confidence interval are different things. The rejection region is the region where you reject the null hypothesis that the ratio of variances equals $1$. A $100(1-α)\%$ confidence interval is an interval that has the property that in repeated sampling would include the true param... | How to interpret the confidence interval of a variance F-test using R? | The rejection region for a test and a confidence interval are different things. The rejection region is the region where you reject the null hypothesis that the ratio of variances equals $1$. A $100 | How to interpret the confidence interval of a variance F-test using R?
The rejection region for a test and a confidence interval are different things. The rejection region is the region where you reject the null hypothesis that the ratio of variances equals $1$. A $100(1-α)\%$ confidence interval is an interval that ... | How to interpret the confidence interval of a variance F-test using R?
The rejection region for a test and a confidence interval are different things. The rejection region is the region where you reject the null hypothesis that the ratio of variances equals $1$. A $100 |
39,788 | How to interpret the confidence interval of a variance F-test using R? | Your method using qf computes the rejection region that you would compare the ratio of the 2 variance to. Using the central F is the correct thing to do because we calculate the rejection region assuming the null hypothesis is true and if the null (that the variances are equal) is true then we have a central F distrib... | How to interpret the confidence interval of a variance F-test using R? | Your method using qf computes the rejection region that you would compare the ratio of the 2 variance to. Using the central F is the correct thing to do because we calculate the rejection region assu | How to interpret the confidence interval of a variance F-test using R?
Your method using qf computes the rejection region that you would compare the ratio of the 2 variance to. Using the central F is the correct thing to do because we calculate the rejection region assuming the null hypothesis is true and if the null ... | How to interpret the confidence interval of a variance F-test using R?
Your method using qf computes the rejection region that you would compare the ratio of the 2 variance to. Using the central F is the correct thing to do because we calculate the rejection region assu |
39,789 | Testing whether two regression coefficients are significantly different | CHCH's answer is interesting. But would it be simpler to use Fisher's Z transformation and the corresponding difference formula to compare the standardized regression coefficients of the two IVs? | Testing whether two regression coefficients are significantly different | CHCH's answer is interesting. But would it be simpler to use Fisher's Z transformation and the corresponding difference formula to compare the standardized regression coefficients of the two IVs? | Testing whether two regression coefficients are significantly different
CHCH's answer is interesting. But would it be simpler to use Fisher's Z transformation and the corresponding difference formula to compare the standardized regression coefficients of the two IVs? | Testing whether two regression coefficients are significantly different
CHCH's answer is interesting. But would it be simpler to use Fisher's Z transformation and the corresponding difference formula to compare the standardized regression coefficients of the two IVs? |
39,790 | Testing whether two regression coefficients are significantly different | If you have the estimated covariance matrix for the coefficients, then you can construct the t-test as follows. Let the hypothesis, in its general form, be $R^T\beta = b$, and $\widehat{\Sigma} = \hat{\sigma}^2(X^TX)^{-1}$ be the estimated covariance matrix of the coefficients. In your case, assuming the test is that... | Testing whether two regression coefficients are significantly different | If you have the estimated covariance matrix for the coefficients, then you can construct the t-test as follows. Let the hypothesis, in its general form, be $R^T\beta = b$, and $\widehat{\Sigma} = \ha | Testing whether two regression coefficients are significantly different
If you have the estimated covariance matrix for the coefficients, then you can construct the t-test as follows. Let the hypothesis, in its general form, be $R^T\beta = b$, and $\widehat{\Sigma} = \hat{\sigma}^2(X^TX)^{-1}$ be the estimated covaria... | Testing whether two regression coefficients are significantly different
If you have the estimated covariance matrix for the coefficients, then you can construct the t-test as follows. Let the hypothesis, in its general form, be $R^T\beta = b$, and $\widehat{\Sigma} = \ha |
39,791 | Testing whether two regression coefficients are significantly different | I believe the correct approach here is to compare the fit of a model where IV(a) and IV(b) are allowed to vary - that is, your present model - with the fit of a model where IV(a) and IV(b) are fit to the same value (in which case the mediator is just an average of the two). The two models can be compared using a Chi-S... | Testing whether two regression coefficients are significantly different | I believe the correct approach here is to compare the fit of a model where IV(a) and IV(b) are allowed to vary - that is, your present model - with the fit of a model where IV(a) and IV(b) are fit to | Testing whether two regression coefficients are significantly different
I believe the correct approach here is to compare the fit of a model where IV(a) and IV(b) are allowed to vary - that is, your present model - with the fit of a model where IV(a) and IV(b) are fit to the same value (in which case the mediator is ju... | Testing whether two regression coefficients are significantly different
I believe the correct approach here is to compare the fit of a model where IV(a) and IV(b) are allowed to vary - that is, your present model - with the fit of a model where IV(a) and IV(b) are fit to |
39,792 | Improving recall in a neural network | Your second question has been answered; as such I will attempt to answer your first question "Is there anything else that I can do?":
As time is the commodity of most value, I would recommend spending time on identifying the cause rather than randomly changing things on gut feel (precision and recall do not always answ... | Improving recall in a neural network | Your second question has been answered; as such I will attempt to answer your first question "Is there anything else that I can do?":
As time is the commodity of most value, I would recommend spending | Improving recall in a neural network
Your second question has been answered; as such I will attempt to answer your first question "Is there anything else that I can do?":
As time is the commodity of most value, I would recommend spending time on identifying the cause rather than randomly changing things on gut feel (pr... | Improving recall in a neural network
Your second question has been answered; as such I will attempt to answer your first question "Is there anything else that I can do?":
As time is the commodity of most value, I would recommend spending |
39,793 | Improving recall in a neural network | The part of your loss function related to the prediction accuracy is:
sum(sum(y1.*log(r) + (1-y1).*log(1-r)))
Assuming that y1(n) == 1 indicates that test case n is a positive example.
Changing this to:
sum(sum( POS_WEIGHT * (y1 .* log(r)) + (1-y1).*log(1-r)))
will increase the penalty associated with getting a pos... | Improving recall in a neural network | The part of your loss function related to the prediction accuracy is:
sum(sum(y1.*log(r) + (1-y1).*log(1-r)))
Assuming that y1(n) == 1 indicates that test case n is a positive example.
Changing this | Improving recall in a neural network
The part of your loss function related to the prediction accuracy is:
sum(sum(y1.*log(r) + (1-y1).*log(1-r)))
Assuming that y1(n) == 1 indicates that test case n is a positive example.
Changing this to:
sum(sum( POS_WEIGHT * (y1 .* log(r)) + (1-y1).*log(1-r)))
will increase the ... | Improving recall in a neural network
The part of your loss function related to the prediction accuracy is:
sum(sum(y1.*log(r) + (1-y1).*log(1-r)))
Assuming that y1(n) == 1 indicates that test case n is a positive example.
Changing this |
39,794 | Why are samples within a cluster less informative than randomly chosen ones from entire population? | Think of a typical clustering situation - a personal interview household survey where the primary sampling unit is the neighborhood or street, for logistic and cost reasons (a simple random sample of households over a nation or even a city is rarely practicable). Obviously sample subjects in the same street do not hav... | Why are samples within a cluster less informative than randomly chosen ones from entire population? | Think of a typical clustering situation - a personal interview household survey where the primary sampling unit is the neighborhood or street, for logistic and cost reasons (a simple random sample of | Why are samples within a cluster less informative than randomly chosen ones from entire population?
Think of a typical clustering situation - a personal interview household survey where the primary sampling unit is the neighborhood or street, for logistic and cost reasons (a simple random sample of households over a na... | Why are samples within a cluster less informative than randomly chosen ones from entire population?
Think of a typical clustering situation - a personal interview household survey where the primary sampling unit is the neighborhood or street, for logistic and cost reasons (a simple random sample of |
39,795 | Why are samples within a cluster less informative than randomly chosen ones from entire population? | Because if you sample the cluster you just get information about the samples within the cluster. Samples within the cluster are more similar than random samples would be, else they would not be put in the same cluster.
The assumption is that when you cluster your data, the clusters are driven by one or more covariate... | Why are samples within a cluster less informative than randomly chosen ones from entire population? | Because if you sample the cluster you just get information about the samples within the cluster. Samples within the cluster are more similar than random samples would be, else they would not be put in | Why are samples within a cluster less informative than randomly chosen ones from entire population?
Because if you sample the cluster you just get information about the samples within the cluster. Samples within the cluster are more similar than random samples would be, else they would not be put in the same cluster. ... | Why are samples within a cluster less informative than randomly chosen ones from entire population?
Because if you sample the cluster you just get information about the samples within the cluster. Samples within the cluster are more similar than random samples would be, else they would not be put in |
39,796 | Why are samples within a cluster less informative than randomly chosen ones from entire population? | If you can go through the mathematics of cluster sampling, just follow an explanation of the variance of the total for a cluster survey. See e.g. p. 174 of Lohr's 2nd edition (open the amazon look inside and type "icc" to search for it; the first reference on p. 174 gives you ANOVA table for cluster sampling in a balan... | Why are samples within a cluster less informative than randomly chosen ones from entire population? | If you can go through the mathematics of cluster sampling, just follow an explanation of the variance of the total for a cluster survey. See e.g. p. 174 of Lohr's 2nd edition (open the amazon look ins | Why are samples within a cluster less informative than randomly chosen ones from entire population?
If you can go through the mathematics of cluster sampling, just follow an explanation of the variance of the total for a cluster survey. See e.g. p. 174 of Lohr's 2nd edition (open the amazon look inside and type "icc" t... | Why are samples within a cluster less informative than randomly chosen ones from entire population?
If you can go through the mathematics of cluster sampling, just follow an explanation of the variance of the total for a cluster survey. See e.g. p. 174 of Lohr's 2nd edition (open the amazon look ins |
39,797 | Betweenness centrality applied to Amazon books graph | The difference between in-degree centrality and closeness centrality - or really any other centrality measure - the answer is that you're identifying different things.
Currently I'm working on betweenness centrality, and it yields quite interesting results, often contradicting degree centrality. But how would you inte... | Betweenness centrality applied to Amazon books graph | The difference between in-degree centrality and closeness centrality - or really any other centrality measure - the answer is that you're identifying different things.
Currently I'm working on betwee | Betweenness centrality applied to Amazon books graph
The difference between in-degree centrality and closeness centrality - or really any other centrality measure - the answer is that you're identifying different things.
Currently I'm working on betweenness centrality, and it yields quite interesting results, often co... | Betweenness centrality applied to Amazon books graph
The difference between in-degree centrality and closeness centrality - or really any other centrality measure - the answer is that you're identifying different things.
Currently I'm working on betwee |
39,798 | Betweenness centrality applied to Amazon books graph | I have spent a fair amount of time looking at social networks (e.g., networks of players in Facebook social games) which involved frequent calculation and comparison of these three measures of Centrality (degree centrality, betweenness centrality, and closeness centrality).
For what it's worth, here's my interpretation... | Betweenness centrality applied to Amazon books graph | I have spent a fair amount of time looking at social networks (e.g., networks of players in Facebook social games) which involved frequent calculation and comparison of these three measures of Central | Betweenness centrality applied to Amazon books graph
I have spent a fair amount of time looking at social networks (e.g., networks of players in Facebook social games) which involved frequent calculation and comparison of these three measures of Centrality (degree centrality, betweenness centrality, and closeness centr... | Betweenness centrality applied to Amazon books graph
I have spent a fair amount of time looking at social networks (e.g., networks of players in Facebook social games) which involved frequent calculation and comparison of these three measures of Central |
39,799 | Choosing between best two attributes with the same information gain when building decision tree | You could look ahead at the information gain of the remaining attributes after a split and select based on that. In general though, if you're using information gain as your splitting criterion, it will be the only thing to look at. | Choosing between best two attributes with the same information gain when building decision tree | You could look ahead at the information gain of the remaining attributes after a split and select based on that. In general though, if you're using information gain as your splitting criterion, it wil | Choosing between best two attributes with the same information gain when building decision tree
You could look ahead at the information gain of the remaining attributes after a split and select based on that. In general though, if you're using information gain as your splitting criterion, it will be the only thing to l... | Choosing between best two attributes with the same information gain when building decision tree
You could look ahead at the information gain of the remaining attributes after a split and select based on that. In general though, if you're using information gain as your splitting criterion, it wil |
39,800 | Choosing between best two attributes with the same information gain when building decision tree | The answer is simply that the first predictor (as found from left to right in the original data frame) is selected. See this thread for the proof. So, to sort everything out:
Will there be any difference between choosing any of the two
attributes to be a tree node?
No, selecting one or the other makes absolutely no... | Choosing between best two attributes with the same information gain when building decision tree | The answer is simply that the first predictor (as found from left to right in the original data frame) is selected. See this thread for the proof. So, to sort everything out:
Will there be any differ | Choosing between best two attributes with the same information gain when building decision tree
The answer is simply that the first predictor (as found from left to right in the original data frame) is selected. See this thread for the proof. So, to sort everything out:
Will there be any difference between choosing an... | Choosing between best two attributes with the same information gain when building decision tree
The answer is simply that the first predictor (as found from left to right in the original data frame) is selected. See this thread for the proof. So, to sort everything out:
Will there be any differ |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.