idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
|---|---|---|---|---|---|---|
8,901 | Why are there only $n-1$ principal components for $n$ data if the number of dimensions is $\ge n$? | Consider what PCA does. Put simply, PCA (as most typically run) creates a new coordinate system by:
shifting the origin to the centroid of your data,
squeezes and/or stretches the axes to make them equal in length, and
rotates your axes into a new orientation.
(For more details, see this excellent CV thread: Making ... | Why are there only $n-1$ principal components for $n$ data if the number of dimensions is $\ge n$? | Consider what PCA does. Put simply, PCA (as most typically run) creates a new coordinate system by:
shifting the origin to the centroid of your data,
squeezes and/or stretches the axes to make them | Why are there only $n-1$ principal components for $n$ data if the number of dimensions is $\ge n$?
Consider what PCA does. Put simply, PCA (as most typically run) creates a new coordinate system by:
shifting the origin to the centroid of your data,
squeezes and/or stretches the axes to make them equal in length, and
... | Why are there only $n-1$ principal components for $n$ data if the number of dimensions is $\ge n$?
Consider what PCA does. Put simply, PCA (as most typically run) creates a new coordinate system by:
shifting the origin to the centroid of your data,
squeezes and/or stretches the axes to make them |
8,902 | Why are there only $n-1$ principal components for $n$ data if the number of dimensions is $\ge n$? | Let's say we have a matrix $X=[x_1, x_2, \cdots, x_n]$ , where each $x_i$ is an obervation (sample) from $d$ dimension space, so $X$ is a $d$ by $n$ matrix, and $d > n$.
If we first centered the dataset , we have $\sum\limits_{i=1}^n x_i = 0$, which means: $x_1=-\sum\limits_{i=2}^n x_i$, so the column rank of $X \leq... | Why are there only $n-1$ principal components for $n$ data if the number of dimensions is $\ge n$? | Let's say we have a matrix $X=[x_1, x_2, \cdots, x_n]$ , where each $x_i$ is an obervation (sample) from $d$ dimension space, so $X$ is a $d$ by $n$ matrix, and $d > n$.
If we first centered the data | Why are there only $n-1$ principal components for $n$ data if the number of dimensions is $\ge n$?
Let's say we have a matrix $X=[x_1, x_2, \cdots, x_n]$ , where each $x_i$ is an obervation (sample) from $d$ dimension space, so $X$ is a $d$ by $n$ matrix, and $d > n$.
If we first centered the dataset , we have $\sum\... | Why are there only $n-1$ principal components for $n$ data if the number of dimensions is $\ge n$?
Let's say we have a matrix $X=[x_1, x_2, \cdots, x_n]$ , where each $x_i$ is an obervation (sample) from $d$ dimension space, so $X$ is a $d$ by $n$ matrix, and $d > n$.
If we first centered the data |
8,903 | Difference between rungs two and three in the Ladder of Causation | There is no contradiction between the factual world and the action of interest in the interventional level. For example, smoking until today and being forced to quit smoking starting tomorrow are not in contradiction with each other, even though you could say one “negates” the other. But now imagine the following scena... | Difference between rungs two and three in the Ladder of Causation | There is no contradiction between the factual world and the action of interest in the interventional level. For example, smoking until today and being forced to quit smoking starting tomorrow are not | Difference between rungs two and three in the Ladder of Causation
There is no contradiction between the factual world and the action of interest in the interventional level. For example, smoking until today and being forced to quit smoking starting tomorrow are not in contradiction with each other, even though you coul... | Difference between rungs two and three in the Ladder of Causation
There is no contradiction between the factual world and the action of interest in the interventional level. For example, smoking until today and being forced to quit smoking starting tomorrow are not |
8,904 | Difference between rungs two and three in the Ladder of Causation | Here is the answer Judea Pearl gave on twitter:
Readers ask: Why is intervention (Rung-2) different from
counterfactual (Rung-3)? Doesn't intervening negate some aspects of
the observed world?
Ans. Interventions change but do not contradict the observed world,
because the world before and after the intervention entail... | Difference between rungs two and three in the Ladder of Causation | Here is the answer Judea Pearl gave on twitter:
Readers ask: Why is intervention (Rung-2) different from
counterfactual (Rung-3)? Doesn't intervening negate some aspects of
the observed world?
Ans. I | Difference between rungs two and three in the Ladder of Causation
Here is the answer Judea Pearl gave on twitter:
Readers ask: Why is intervention (Rung-2) different from
counterfactual (Rung-3)? Doesn't intervening negate some aspects of
the observed world?
Ans. Interventions change but do not contradict the observed... | Difference between rungs two and three in the Ladder of Causation
Here is the answer Judea Pearl gave on twitter:
Readers ask: Why is intervention (Rung-2) different from
counterfactual (Rung-3)? Doesn't intervening negate some aspects of
the observed world?
Ans. I |
8,905 | Difference between rungs two and three in the Ladder of Causation | Counterfactual questions are also questions about intervening. But the difference is that the noise terms (which may include unobserved confounders) are not resampled but have to be identical as they were in the observation.
Counterfactuals are computed in SCMs through the following procedure:
Update the noise distrib... | Difference between rungs two and three in the Ladder of Causation | Counterfactual questions are also questions about intervening. But the difference is that the noise terms (which may include unobserved confounders) are not resampled but have to be identical as they | Difference between rungs two and three in the Ladder of Causation
Counterfactual questions are also questions about intervening. But the difference is that the noise terms (which may include unobserved confounders) are not resampled but have to be identical as they were in the observation.
Counterfactuals are computed ... | Difference between rungs two and three in the Ladder of Causation
Counterfactual questions are also questions about intervening. But the difference is that the noise terms (which may include unobserved confounders) are not resampled but have to be identical as they |
8,906 | Difference between rungs two and three in the Ladder of Causation | To add more insight to this question and the other answers:
Intervention: We want to answer/predict what will happen to variable $Z$, if we intervene on a variable $X$ in the present.
Counterfactual: We want to answer/predict what would happen to variable $Z$, had we intervened on a variable $X$ in the past. But the wo... | Difference between rungs two and three in the Ladder of Causation | To add more insight to this question and the other answers:
Intervention: We want to answer/predict what will happen to variable $Z$, if we intervene on a variable $X$ in the present.
Counterfactual: | Difference between rungs two and three in the Ladder of Causation
To add more insight to this question and the other answers:
Intervention: We want to answer/predict what will happen to variable $Z$, if we intervene on a variable $X$ in the present.
Counterfactual: We want to answer/predict what would happen to variabl... | Difference between rungs two and three in the Ladder of Causation
To add more insight to this question and the other answers:
Intervention: We want to answer/predict what will happen to variable $Z$, if we intervene on a variable $X$ in the present.
Counterfactual: |
8,907 | Why are probability distributions denoted with a tilde? | The ~ (tilde) used in that way means "is distributed as". Why? To ask why doesn't make much sense to me, its just a convention. To cite Brian Ripley:
Mathematical conventions are just that, conventions. They differ by
field of mathematics. Don't ask us why matrix rows are numbered down
but graphs are numbered up t... | Why are probability distributions denoted with a tilde? | The ~ (tilde) used in that way means "is distributed as". Why? To ask why doesn't make much sense to me, its just a convention. To cite Brian Ripley:
Mathematical conventions are just that, conventio | Why are probability distributions denoted with a tilde?
The ~ (tilde) used in that way means "is distributed as". Why? To ask why doesn't make much sense to me, its just a convention. To cite Brian Ripley:
Mathematical conventions are just that, conventions. They differ by
field of mathematics. Don't ask us why matr... | Why are probability distributions denoted with a tilde?
The ~ (tilde) used in that way means "is distributed as". Why? To ask why doesn't make much sense to me, its just a convention. To cite Brian Ripley:
Mathematical conventions are just that, conventio |
8,908 | Why are probability distributions denoted with a tilde? | I can't comment on the history, but I believe it might be the following. The ~ symbol is commonly used in mathematics to denote an equivalence relation. In the context of probability theory it is used to denote equivalance in (marginal) distribution. So when we say,
Z ~ N(0,1),
what we mean is that the random variab... | Why are probability distributions denoted with a tilde? | I can't comment on the history, but I believe it might be the following. The ~ symbol is commonly used in mathematics to denote an equivalence relation. In the context of probability theory it is us | Why are probability distributions denoted with a tilde?
I can't comment on the history, but I believe it might be the following. The ~ symbol is commonly used in mathematics to denote an equivalence relation. In the context of probability theory it is used to denote equivalance in (marginal) distribution. So when we... | Why are probability distributions denoted with a tilde?
I can't comment on the history, but I believe it might be the following. The ~ symbol is commonly used in mathematics to denote an equivalence relation. In the context of probability theory it is us |
8,909 | Why would anyone use KNN for regression? | Local methods like K-NN make sense in some situations.
One example that I did in school work had to do with predicting the compressive strength of various mixtures of cement ingredients. All of these ingredients were relatively non-volatile with respect to the response or each other and KNN made reliable predictions o... | Why would anyone use KNN for regression? | Local methods like K-NN make sense in some situations.
One example that I did in school work had to do with predicting the compressive strength of various mixtures of cement ingredients. All of these | Why would anyone use KNN for regression?
Local methods like K-NN make sense in some situations.
One example that I did in school work had to do with predicting the compressive strength of various mixtures of cement ingredients. All of these ingredients were relatively non-volatile with respect to the response or each ... | Why would anyone use KNN for regression?
Local methods like K-NN make sense in some situations.
One example that I did in school work had to do with predicting the compressive strength of various mixtures of cement ingredients. All of these |
8,910 | Why would anyone use KNN for regression? | I don't like to say it but actually the short answer is, that "predicting into the future" is not really possible not with a knn nor with any other currently existing classifier or regressor.
Sure you can extrapolate the line of a linear regression or the hyper plane of an SVM but in the end you don't know what the fu... | Why would anyone use KNN for regression? | I don't like to say it but actually the short answer is, that "predicting into the future" is not really possible not with a knn nor with any other currently existing classifier or regressor.
Sure yo | Why would anyone use KNN for regression?
I don't like to say it but actually the short answer is, that "predicting into the future" is not really possible not with a knn nor with any other currently existing classifier or regressor.
Sure you can extrapolate the line of a linear regression or the hyper plane of an SVM ... | Why would anyone use KNN for regression?
I don't like to say it but actually the short answer is, that "predicting into the future" is not really possible not with a knn nor with any other currently existing classifier or regressor.
Sure yo |
8,911 | Why would anyone use KNN for regression? | First an example for
"How would I predict into the future using a KNN regressor ?".
Problem: predict hours of sunlight tomorrow $sun_{t+1}$
from $sun_t .. sun_{t-6}$ over the last week.
Training data: $sun_t$ (in one city) over the last 10 years, 3650 numbers.
Denote $week_t \equiv sun_t .. sun_{t-6}$
and $tomorrow( we... | Why would anyone use KNN for regression? | First an example for
"How would I predict into the future using a KNN regressor ?".
Problem: predict hours of sunlight tomorrow $sun_{t+1}$
from $sun_t .. sun_{t-6}$ over the last week.
Training data: | Why would anyone use KNN for regression?
First an example for
"How would I predict into the future using a KNN regressor ?".
Problem: predict hours of sunlight tomorrow $sun_{t+1}$
from $sun_t .. sun_{t-6}$ over the last week.
Training data: $sun_t$ (in one city) over the last 10 years, 3650 numbers.
Denote $week_t \eq... | Why would anyone use KNN for regression?
First an example for
"How would I predict into the future using a KNN regressor ?".
Problem: predict hours of sunlight tomorrow $sun_{t+1}$
from $sun_t .. sun_{t-6}$ over the last week.
Training data: |
8,912 | Why would anyone use KNN for regression? | From An Introduction to Statistical Learning, section 3.5:
In a real-life situation in which the true relationship is unknown, one might draw the conclusion that KNN should be favored over linear regression because it will at worst be slightly inferior than linear regression if the true relationship is linear, and m... | Why would anyone use KNN for regression? | From An Introduction to Statistical Learning, section 3.5:
In a real-life situation in which the true relationship is unknown, one might draw the conclusion that KNN should be favored over linear r | Why would anyone use KNN for regression?
From An Introduction to Statistical Learning, section 3.5:
In a real-life situation in which the true relationship is unknown, one might draw the conclusion that KNN should be favored over linear regression because it will at worst be slightly inferior than linear regression ... | Why would anyone use KNN for regression?
From An Introduction to Statistical Learning, section 3.5:
In a real-life situation in which the true relationship is unknown, one might draw the conclusion that KNN should be favored over linear r |
8,913 | Why would anyone use KNN for regression? | Hangyu Tian makes a great point that k-NN regression will not do well when there isn't enough data and method like linear regression that make stronger assumptions may outperform k-NN. However, the amazing thing about k-NN is that you can encode all sorts of interesting assumptions by using different weights. For examp... | Why would anyone use KNN for regression? | Hangyu Tian makes a great point that k-NN regression will not do well when there isn't enough data and method like linear regression that make stronger assumptions may outperform k-NN. However, the am | Why would anyone use KNN for regression?
Hangyu Tian makes a great point that k-NN regression will not do well when there isn't enough data and method like linear regression that make stronger assumptions may outperform k-NN. However, the amazing thing about k-NN is that you can encode all sorts of interesting assumpti... | Why would anyone use KNN for regression?
Hangyu Tian makes a great point that k-NN regression will not do well when there isn't enough data and method like linear regression that make stronger assumptions may outperform k-NN. However, the am |
8,914 | What is the loss function of hard margin SVM? | The hinge loss term $\sum_i\max(0,1-y_i(\mathbf{w}^\intercal \mathbf{x}_i+b))$ in soft margin SVM penalizes misclassifications. In hard margin SVM there are, by definition, no misclassifications.
This indeed means that hard margin SVM tries to minimize $\|\mathbf{w}\|^2$. Due to the formulation of the SVM problem, the ... | What is the loss function of hard margin SVM? | The hinge loss term $\sum_i\max(0,1-y_i(\mathbf{w}^\intercal \mathbf{x}_i+b))$ in soft margin SVM penalizes misclassifications. In hard margin SVM there are, by definition, no misclassifications.
This | What is the loss function of hard margin SVM?
The hinge loss term $\sum_i\max(0,1-y_i(\mathbf{w}^\intercal \mathbf{x}_i+b))$ in soft margin SVM penalizes misclassifications. In hard margin SVM there are, by definition, no misclassifications.
This indeed means that hard margin SVM tries to minimize $\|\mathbf{w}\|^2$. D... | What is the loss function of hard margin SVM?
The hinge loss term $\sum_i\max(0,1-y_i(\mathbf{w}^\intercal \mathbf{x}_i+b))$ in soft margin SVM penalizes misclassifications. In hard margin SVM there are, by definition, no misclassifications.
This |
8,915 | What is the loss function of hard margin SVM? | There's no "loss function" for hard-margin SVMs, but when we're solving soft-margin SVMs, it turns out the loss exists.
Now is the detailed explanation:
When we talk about loss function, what we really mean is a training objective that we want to minimize.
In hard-margin SVM setting, the "objective" is to maximize the ... | What is the loss function of hard margin SVM? | There's no "loss function" for hard-margin SVMs, but when we're solving soft-margin SVMs, it turns out the loss exists.
Now is the detailed explanation:
When we talk about loss function, what we reall | What is the loss function of hard margin SVM?
There's no "loss function" for hard-margin SVMs, but when we're solving soft-margin SVMs, it turns out the loss exists.
Now is the detailed explanation:
When we talk about loss function, what we really mean is a training objective that we want to minimize.
In hard-margin SV... | What is the loss function of hard margin SVM?
There's no "loss function" for hard-margin SVMs, but when we're solving soft-margin SVMs, it turns out the loss exists.
Now is the detailed explanation:
When we talk about loss function, what we reall |
8,916 | What is the loss function of hard margin SVM? | Just to clarify,
$$
\frac{1}{2}\|w\|^2
$$
is minimized subject to the constraint that the points are linearly separable (I.e. one can draw a hyperplane that perfectly separates the two). In other words, the only allowed values of w that we can consider as solutions are those that separate the two sets of points.
Now,... | What is the loss function of hard margin SVM? | Just to clarify,
$$
\frac{1}{2}\|w\|^2
$$
is minimized subject to the constraint that the points are linearly separable (I.e. one can draw a hyperplane that perfectly separates the two). In other wo | What is the loss function of hard margin SVM?
Just to clarify,
$$
\frac{1}{2}\|w\|^2
$$
is minimized subject to the constraint that the points are linearly separable (I.e. one can draw a hyperplane that perfectly separates the two). In other words, the only allowed values of w that we can consider as solutions are th... | What is the loss function of hard margin SVM?
Just to clarify,
$$
\frac{1}{2}\|w\|^2
$$
is minimized subject to the constraint that the points are linearly separable (I.e. one can draw a hyperplane that perfectly separates the two). In other wo |
8,917 | For which distributions are the parameterizations in BUGS and R different? | I don't know of a canned list.
update: this list (plus additional information) is now published as Translating Probability Density Functions: From R to BUGS and Back Again (2013), DS LeBauer, MC Dietze, BM Bolker R Journal 5 (1), 207-209.
Here is my list (edits provided by original questioner):
Normal and log-normal ... | For which distributions are the parameterizations in BUGS and R different? | I don't know of a canned list.
update: this list (plus additional information) is now published as Translating Probability Density Functions: From R to BUGS and Back Again (2013), DS LeBauer, MC Diet | For which distributions are the parameterizations in BUGS and R different?
I don't know of a canned list.
update: this list (plus additional information) is now published as Translating Probability Density Functions: From R to BUGS and Back Again (2013), DS LeBauer, MC Dietze, BM Bolker R Journal 5 (1), 207-209.
Here ... | For which distributions are the parameterizations in BUGS and R different?
I don't know of a canned list.
update: this list (plus additional information) is now published as Translating Probability Density Functions: From R to BUGS and Back Again (2013), DS LeBauer, MC Diet |
8,918 | 2D analog of standard deviation? | One thing you could use is a distance measure from a central point, ${\bf c}=(c_{1},c_{2})$, such as the sample mean of the points $(\overline{x}, \overline{y})$, or perhaps the centroid of the observed points. Then a measure of dispersion would be the average distance from that central point:
$$ \frac{1}{n} \sum_{i=1... | 2D analog of standard deviation? | One thing you could use is a distance measure from a central point, ${\bf c}=(c_{1},c_{2})$, such as the sample mean of the points $(\overline{x}, \overline{y})$, or perhaps the centroid of the observ | 2D analog of standard deviation?
One thing you could use is a distance measure from a central point, ${\bf c}=(c_{1},c_{2})$, such as the sample mean of the points $(\overline{x}, \overline{y})$, or perhaps the centroid of the observed points. Then a measure of dispersion would be the average distance from that central... | 2D analog of standard deviation?
One thing you could use is a distance measure from a central point, ${\bf c}=(c_{1},c_{2})$, such as the sample mean of the points $(\overline{x}, \overline{y})$, or perhaps the centroid of the observ |
8,919 | 2D analog of standard deviation? | A good reference on metrics for the spatial distribution of point patterns is the CrimeStat manual (in particular for this question, Chapter 4 will be of interest). Similar to the metric Macro suggested, the Standard Distance Deviation is similar to a 2D standard deviation (the only difference is that you would divide ... | 2D analog of standard deviation? | A good reference on metrics for the spatial distribution of point patterns is the CrimeStat manual (in particular for this question, Chapter 4 will be of interest). Similar to the metric Macro suggest | 2D analog of standard deviation?
A good reference on metrics for the spatial distribution of point patterns is the CrimeStat manual (in particular for this question, Chapter 4 will be of interest). Similar to the metric Macro suggested, the Standard Distance Deviation is similar to a 2D standard deviation (the only dif... | 2D analog of standard deviation?
A good reference on metrics for the spatial distribution of point patterns is the CrimeStat manual (in particular for this question, Chapter 4 will be of interest). Similar to the metric Macro suggest |
8,920 | 2D analog of standard deviation? | I actually ran into a similar problem recently. It sounds like you want a way to measure how well the points are scattered area-wise. Of course, for a given measurement, you’d have to realize that if all the points are in a straight line, the answer is zero, since there’s no 2 dimensional variety.
From the calculatio... | 2D analog of standard deviation? | I actually ran into a similar problem recently. It sounds like you want a way to measure how well the points are scattered area-wise. Of course, for a given measurement, you’d have to realize that i | 2D analog of standard deviation?
I actually ran into a similar problem recently. It sounds like you want a way to measure how well the points are scattered area-wise. Of course, for a given measurement, you’d have to realize that if all the points are in a straight line, the answer is zero, since there’s no 2 dimensi... | 2D analog of standard deviation?
I actually ran into a similar problem recently. It sounds like you want a way to measure how well the points are scattered area-wise. Of course, for a given measurement, you’d have to realize that i |
8,921 | 2D analog of standard deviation? | I think you should use 'Mahalanobis Distance' rather than Euclidean distance norms, as it takes into account the correlation of the data set and is 'scale-invariant'. Here is the link:
http://en.wikipedia.org/wiki/Mahalanobis_distance
You could also use 'Half-Space Depth'. It is a bit more complicated but shares many a... | 2D analog of standard deviation? | I think you should use 'Mahalanobis Distance' rather than Euclidean distance norms, as it takes into account the correlation of the data set and is 'scale-invariant'. Here is the link:
http://en.wikip | 2D analog of standard deviation?
I think you should use 'Mahalanobis Distance' rather than Euclidean distance norms, as it takes into account the correlation of the data set and is 'scale-invariant'. Here is the link:
http://en.wikipedia.org/wiki/Mahalanobis_distance
You could also use 'Half-Space Depth'. It is a bit m... | 2D analog of standard deviation?
I think you should use 'Mahalanobis Distance' rather than Euclidean distance norms, as it takes into account the correlation of the data set and is 'scale-invariant'. Here is the link:
http://en.wikip |
8,922 | 2D analog of standard deviation? | For this specific example - where there is a predetermined "correct" answer - I would re-work the x/y cooridnates to be polar coordinates around the city they were being asked to mark on the map. The accuracy is then measured agains the radial component (mean, sd, etc.). An "average angle" could also be used to measu... | 2D analog of standard deviation? | For this specific example - where there is a predetermined "correct" answer - I would re-work the x/y cooridnates to be polar coordinates around the city they were being asked to mark on the map. The | 2D analog of standard deviation?
For this specific example - where there is a predetermined "correct" answer - I would re-work the x/y cooridnates to be polar coordinates around the city they were being asked to mark on the map. The accuracy is then measured agains the radial component (mean, sd, etc.). An "average a... | 2D analog of standard deviation?
For this specific example - where there is a predetermined "correct" answer - I would re-work the x/y cooridnates to be polar coordinates around the city they were being asked to mark on the map. The |
8,923 | Is the result of an exam a binomial? | I would agree with your answer. Usually this kind of data would nowadays be modeled with some kind of Item Response Theory model. For example, if you used the Rasch model, then the binary answer $X_{ni}$ would be modeled as
$$
\Pr \{X_{ni}=1\} =\frac{e^{{\beta_n} - {\delta_i}}}{1 + e^{{\beta_n} - {\delta_i}}}
$$
where ... | Is the result of an exam a binomial? | I would agree with your answer. Usually this kind of data would nowadays be modeled with some kind of Item Response Theory model. For example, if you used the Rasch model, then the binary answer $X_{n | Is the result of an exam a binomial?
I would agree with your answer. Usually this kind of data would nowadays be modeled with some kind of Item Response Theory model. For example, if you used the Rasch model, then the binary answer $X_{ni}$ would be modeled as
$$
\Pr \{X_{ni}=1\} =\frac{e^{{\beta_n} - {\delta_i}}}{1 + ... | Is the result of an exam a binomial?
I would agree with your answer. Usually this kind of data would nowadays be modeled with some kind of Item Response Theory model. For example, if you used the Rasch model, then the binary answer $X_{n |
8,924 | Is the result of an exam a binomial? | The answer to this problem depends on the framing of the question and when information is gained. Overall, I tend to agree with the professor but think the explanation of his/her answer is poor and the professor's question should include more information up front.
If you consider an infinite number of potential exam... | Is the result of an exam a binomial? | The answer to this problem depends on the framing of the question and when information is gained. Overall, I tend to agree with the professor but think the explanation of his/her answer is poor and t | Is the result of an exam a binomial?
The answer to this problem depends on the framing of the question and when information is gained. Overall, I tend to agree with the professor but think the explanation of his/her answer is poor and the professor's question should include more information up front.
If you consider... | Is the result of an exam a binomial?
The answer to this problem depends on the framing of the question and when information is gained. Overall, I tend to agree with the professor but think the explanation of his/her answer is poor and t |
8,925 | Is the result of an exam a binomial? | If there are n questions, and I can answer any one question correctly with probability p, and there is enough time to attempt answering all questions, and I did 100 of these tests, then my scores would be normal distributed with a mean of np.
But it's not me repeating the test 100 times, it's 100 different candidates ... | Is the result of an exam a binomial? | If there are n questions, and I can answer any one question correctly with probability p, and there is enough time to attempt answering all questions, and I did 100 of these tests, then my scores woul | Is the result of an exam a binomial?
If there are n questions, and I can answer any one question correctly with probability p, and there is enough time to attempt answering all questions, and I did 100 of these tests, then my scores would be normal distributed with a mean of np.
But it's not me repeating the test 100 ... | Is the result of an exam a binomial?
If there are n questions, and I can answer any one question correctly with probability p, and there is enough time to attempt answering all questions, and I did 100 of these tests, then my scores woul |
8,926 | Is the result of an exam a binomial? | By definition, a binomial distribution is a set of $n$ independent and identically distributed Bernoulli trials. In the case of a multiple choice exam, each of the $n$ questions would be one of the Bernoulli trials.
The issue here arises because we can't reasonably assume that the $n$ questions:
Are identically distri... | Is the result of an exam a binomial? | By definition, a binomial distribution is a set of $n$ independent and identically distributed Bernoulli trials. In the case of a multiple choice exam, each of the $n$ questions would be one of the Be | Is the result of an exam a binomial?
By definition, a binomial distribution is a set of $n$ independent and identically distributed Bernoulli trials. In the case of a multiple choice exam, each of the $n$ questions would be one of the Bernoulli trials.
The issue here arises because we can't reasonably assume that the $... | Is the result of an exam a binomial?
By definition, a binomial distribution is a set of $n$ independent and identically distributed Bernoulli trials. In the case of a multiple choice exam, each of the $n$ questions would be one of the Be |
8,927 | How can stochastic gradient descent avoid the problem of a local minimum? | The stochastic gradient (SG) algorithm behaves like a simulated annealing (SA) algorithm, where the learning rate of the SG is related to the temperature of SA.
The randomness or noise introduced by SG allows to escape from local minima to reach a better minimum. Of course, it depends on how fast you decrease the learn... | How can stochastic gradient descent avoid the problem of a local minimum? | The stochastic gradient (SG) algorithm behaves like a simulated annealing (SA) algorithm, where the learning rate of the SG is related to the temperature of SA.
The randomness or noise introduced by S | How can stochastic gradient descent avoid the problem of a local minimum?
The stochastic gradient (SG) algorithm behaves like a simulated annealing (SA) algorithm, where the learning rate of the SG is related to the temperature of SA.
The randomness or noise introduced by SG allows to escape from local minima to reach ... | How can stochastic gradient descent avoid the problem of a local minimum?
The stochastic gradient (SG) algorithm behaves like a simulated annealing (SA) algorithm, where the learning rate of the SG is related to the temperature of SA.
The randomness or noise introduced by S |
8,928 | How can stochastic gradient descent avoid the problem of a local minimum? | In stochastic gradient descent the parameters are estimated for every observation, as opposed the whole sample in regular gradient descent (batch gradient descent). This is what gives it a lot of randomness. The path of stochastic gradient descent wanders over more places, and thus is more likely to "jump out" of a loc... | How can stochastic gradient descent avoid the problem of a local minimum? | In stochastic gradient descent the parameters are estimated for every observation, as opposed the whole sample in regular gradient descent (batch gradient descent). This is what gives it a lot of rand | How can stochastic gradient descent avoid the problem of a local minimum?
In stochastic gradient descent the parameters are estimated for every observation, as opposed the whole sample in regular gradient descent (batch gradient descent). This is what gives it a lot of randomness. The path of stochastic gradient descen... | How can stochastic gradient descent avoid the problem of a local minimum?
In stochastic gradient descent the parameters are estimated for every observation, as opposed the whole sample in regular gradient descent (batch gradient descent). This is what gives it a lot of rand |
8,929 | How can stochastic gradient descent avoid the problem of a local minimum? | As it was already mentioned in the previous answers, stochastic gradient descent has a much noisier error surface since you are evaluating each sample iteratively. While you are taking a step towards the global minimum in batch gradient descent at every epoch (pass over the training set), the individual steps of your s... | How can stochastic gradient descent avoid the problem of a local minimum? | As it was already mentioned in the previous answers, stochastic gradient descent has a much noisier error surface since you are evaluating each sample iteratively. While you are taking a step towards | How can stochastic gradient descent avoid the problem of a local minimum?
As it was already mentioned in the previous answers, stochastic gradient descent has a much noisier error surface since you are evaluating each sample iteratively. While you are taking a step towards the global minimum in batch gradient descent a... | How can stochastic gradient descent avoid the problem of a local minimum?
As it was already mentioned in the previous answers, stochastic gradient descent has a much noisier error surface since you are evaluating each sample iteratively. While you are taking a step towards |
8,930 | What is the appropriate model for underdispersed count data? | The best --- and standard ways to handle underdispersed Poisson data is by using a generalized Poisson, or perhaps a hurdle model. Three parameter count models can also be used for underdispersed data; eg Faddy-Smith, Waring, Famoye, Conway-Maxwell and other generalized count models. The only drawback with these is int... | What is the appropriate model for underdispersed count data? | The best --- and standard ways to handle underdispersed Poisson data is by using a generalized Poisson, or perhaps a hurdle model. Three parameter count models can also be used for underdispersed data | What is the appropriate model for underdispersed count data?
The best --- and standard ways to handle underdispersed Poisson data is by using a generalized Poisson, or perhaps a hurdle model. Three parameter count models can also be used for underdispersed data; eg Faddy-Smith, Waring, Famoye, Conway-Maxwell and other ... | What is the appropriate model for underdispersed count data?
The best --- and standard ways to handle underdispersed Poisson data is by using a generalized Poisson, or perhaps a hurdle model. Three parameter count models can also be used for underdispersed data |
8,931 | What is the appropriate model for underdispersed count data? | I encountered an under dispersed Poisson once that had to do with frequency at which people would play a social game. It turned out this was due to the extreme regularity with which people would play on Fridays. Removing Friday data gave me the expected overdispersed Poisson. Perhaps you have the option to similarly ed... | What is the appropriate model for underdispersed count data? | I encountered an under dispersed Poisson once that had to do with frequency at which people would play a social game. It turned out this was due to the extreme regularity with which people would play | What is the appropriate model for underdispersed count data?
I encountered an under dispersed Poisson once that had to do with frequency at which people would play a social game. It turned out this was due to the extreme regularity with which people would play on Fridays. Removing Friday data gave me the expected overd... | What is the appropriate model for underdispersed count data?
I encountered an under dispersed Poisson once that had to do with frequency at which people would play a social game. It turned out this was due to the extreme regularity with which people would play |
8,932 | What is the appropriate model for underdispersed count data? | It seems that the solution provided by Joseph Hilbe within the vgam package is no longer available. From the manual of the package: The genpoisson() has been simplified to genpoisson0 by only handling positive parameters, hence only overdispersion relative to the Poisson is accommodated. Some of the reasons for this a... | What is the appropriate model for underdispersed count data? | It seems that the solution provided by Joseph Hilbe within the vgam package is no longer available. From the manual of the package: The genpoisson() has been simplified to genpoisson0 by only handlin | What is the appropriate model for underdispersed count data?
It seems that the solution provided by Joseph Hilbe within the vgam package is no longer available. From the manual of the package: The genpoisson() has been simplified to genpoisson0 by only handling positive parameters, hence only overdispersion relative t... | What is the appropriate model for underdispersed count data?
It seems that the solution provided by Joseph Hilbe within the vgam package is no longer available. From the manual of the package: The genpoisson() has been simplified to genpoisson0 by only handlin |
8,933 | What is the appropriate model for underdispersed count data? | There are situations where underdispersion coalesces with zero-inflation which is typical for preferred children counts by individuals of both sexes. I haven't found a way to capture this to date | What is the appropriate model for underdispersed count data? | There are situations where underdispersion coalesces with zero-inflation which is typical for preferred children counts by individuals of both sexes. I haven't found a way to capture this to date | What is the appropriate model for underdispersed count data?
There are situations where underdispersion coalesces with zero-inflation which is typical for preferred children counts by individuals of both sexes. I haven't found a way to capture this to date | What is the appropriate model for underdispersed count data?
There are situations where underdispersion coalesces with zero-inflation which is typical for preferred children counts by individuals of both sexes. I haven't found a way to capture this to date |
8,934 | Nonlinear vs. generalized linear model: How do you refer to logistic, Poisson, etc. regression? | This is a great question.
We know models such as logistic, Poisson, etc. fall under the umbrella of generalized linear models.
Well, yes and no. Given the context of the question, we must be quite careful to specify what we're talking about -- and "logistic" and "Poisson" alone are insufficient to describe what is i... | Nonlinear vs. generalized linear model: How do you refer to logistic, Poisson, etc. regression? | This is a great question.
We know models such as logistic, Poisson, etc. fall under the umbrella of generalized linear models.
Well, yes and no. Given the context of the question, we must be quite | Nonlinear vs. generalized linear model: How do you refer to logistic, Poisson, etc. regression?
This is a great question.
We know models such as logistic, Poisson, etc. fall under the umbrella of generalized linear models.
Well, yes and no. Given the context of the question, we must be quite careful to specify what ... | Nonlinear vs. generalized linear model: How do you refer to logistic, Poisson, etc. regression?
This is a great question.
We know models such as logistic, Poisson, etc. fall under the umbrella of generalized linear models.
Well, yes and no. Given the context of the question, we must be quite |
8,935 | How to understand output from R's polr function (ordered logistic regression)? | I would suggest you look at books on categorical data analysis (cf. Alan Agresti's Categorical Data Analysis, 2002) for better explanation and understanding of ordered logistic regression. All the questions that you ask are basically answered by a few chapters in such books. If you are only interested in R related exam... | How to understand output from R's polr function (ordered logistic regression)? | I would suggest you look at books on categorical data analysis (cf. Alan Agresti's Categorical Data Analysis, 2002) for better explanation and understanding of ordered logistic regression. All the que | How to understand output from R's polr function (ordered logistic regression)?
I would suggest you look at books on categorical data analysis (cf. Alan Agresti's Categorical Data Analysis, 2002) for better explanation and understanding of ordered logistic regression. All the questions that you ask are basically answere... | How to understand output from R's polr function (ordered logistic regression)?
I would suggest you look at books on categorical data analysis (cf. Alan Agresti's Categorical Data Analysis, 2002) for better explanation and understanding of ordered logistic regression. All the que |
8,936 | How to understand output from R's polr function (ordered logistic regression)? | I have greatly enjoyed the conversation here, however I feel that the answers did not correctly address all the (very good) components to the question you put forth. The second half of the example page for polr is all about profiling. A good technical reference here is Venerables and Ripley who discuss profiling and wh... | How to understand output from R's polr function (ordered logistic regression)? | I have greatly enjoyed the conversation here, however I feel that the answers did not correctly address all the (very good) components to the question you put forth. The second half of the example pag | How to understand output from R's polr function (ordered logistic regression)?
I have greatly enjoyed the conversation here, however I feel that the answers did not correctly address all the (very good) components to the question you put forth. The second half of the example page for polr is all about profiling. A good... | How to understand output from R's polr function (ordered logistic regression)?
I have greatly enjoyed the conversation here, however I feel that the answers did not correctly address all the (very good) components to the question you put forth. The second half of the example pag |
8,937 | How to understand output from R's polr function (ordered logistic regression)? | To 'test' (i.e., evaluate) the proportional odds assumption in R, you can use residuals.lrm() in Frank Harrell Jr.'s Design package. If you type ?residuals.lrm , there is a quick-to-replicate example of how Frank Harrell recommends evaluating the proportional odds assumption (i.e., visually, rather than by a push-butto... | How to understand output from R's polr function (ordered logistic regression)? | To 'test' (i.e., evaluate) the proportional odds assumption in R, you can use residuals.lrm() in Frank Harrell Jr.'s Design package. If you type ?residuals.lrm , there is a quick-to-replicate example | How to understand output from R's polr function (ordered logistic regression)?
To 'test' (i.e., evaluate) the proportional odds assumption in R, you can use residuals.lrm() in Frank Harrell Jr.'s Design package. If you type ?residuals.lrm , there is a quick-to-replicate example of how Frank Harrell recommends evaluatin... | How to understand output from R's polr function (ordered logistic regression)?
To 'test' (i.e., evaluate) the proportional odds assumption in R, you can use residuals.lrm() in Frank Harrell Jr.'s Design package. If you type ?residuals.lrm , there is a quick-to-replicate example |
8,938 | Theoretical motivation for using log-likelihood vs likelihood | It's really just a convenience for loglikelihood, nothing more.
I mean the convenience of the sums vs. products: $\ln (\prod_i x_i) =\sum_i\ln x_i$, the sums are easier to deal with in many respects, such as differentialtion or integration. It's not a convenience for only exponential families, I'm trying to say.
When y... | Theoretical motivation for using log-likelihood vs likelihood | It's really just a convenience for loglikelihood, nothing more.
I mean the convenience of the sums vs. products: $\ln (\prod_i x_i) =\sum_i\ln x_i$, the sums are easier to deal with in many respects, | Theoretical motivation for using log-likelihood vs likelihood
It's really just a convenience for loglikelihood, nothing more.
I mean the convenience of the sums vs. products: $\ln (\prod_i x_i) =\sum_i\ln x_i$, the sums are easier to deal with in many respects, such as differentialtion or integration. It's not a conven... | Theoretical motivation for using log-likelihood vs likelihood
It's really just a convenience for loglikelihood, nothing more.
I mean the convenience of the sums vs. products: $\ln (\prod_i x_i) =\sum_i\ln x_i$, the sums are easier to deal with in many respects, |
8,939 | Theoretical motivation for using log-likelihood vs likelihood | Log-likelihood's theoretical importance can be seen from (at least) two perspectives: asymptotic likelihood theory and information theory.
The earlier of these (I believe) is the asymptotic theory of log-likelihood. I think information theory got underway well after Fisher set maximum likelihood on its course towards 2... | Theoretical motivation for using log-likelihood vs likelihood | Log-likelihood's theoretical importance can be seen from (at least) two perspectives: asymptotic likelihood theory and information theory.
The earlier of these (I believe) is the asymptotic theory of | Theoretical motivation for using log-likelihood vs likelihood
Log-likelihood's theoretical importance can be seen from (at least) two perspectives: asymptotic likelihood theory and information theory.
The earlier of these (I believe) is the asymptotic theory of log-likelihood. I think information theory got underway we... | Theoretical motivation for using log-likelihood vs likelihood
Log-likelihood's theoretical importance can be seen from (at least) two perspectives: asymptotic likelihood theory and information theory.
The earlier of these (I believe) is the asymptotic theory of |
8,940 | Theoretical motivation for using log-likelihood vs likelihood | Additional point. Some of the commonly used probability distributions (including the normal distribution, the exponential distribution, the Laplace distribution, just to name a few) are log-concave. This means that their logarithm is concave. This makes maximising the log-probability much easier than maximising the ori... | Theoretical motivation for using log-likelihood vs likelihood | Additional point. Some of the commonly used probability distributions (including the normal distribution, the exponential distribution, the Laplace distribution, just to name a few) are log-concave. T | Theoretical motivation for using log-likelihood vs likelihood
Additional point. Some of the commonly used probability distributions (including the normal distribution, the exponential distribution, the Laplace distribution, just to name a few) are log-concave. This means that their logarithm is concave. This makes maxi... | Theoretical motivation for using log-likelihood vs likelihood
Additional point. Some of the commonly used probability distributions (including the normal distribution, the exponential distribution, the Laplace distribution, just to name a few) are log-concave. T |
8,941 | Theoretical motivation for using log-likelihood vs likelihood | TLDR: It is much easier to derive sums than products, because the derivative operator is linear with summation but with product u have to do the product rule. It is linear complexity versus some higher order polynomial complexity | Theoretical motivation for using log-likelihood vs likelihood | TLDR: It is much easier to derive sums than products, because the derivative operator is linear with summation but with product u have to do the product rule. It is linear complexity versus some highe | Theoretical motivation for using log-likelihood vs likelihood
TLDR: It is much easier to derive sums than products, because the derivative operator is linear with summation but with product u have to do the product rule. It is linear complexity versus some higher order polynomial complexity | Theoretical motivation for using log-likelihood vs likelihood
TLDR: It is much easier to derive sums than products, because the derivative operator is linear with summation but with product u have to do the product rule. It is linear complexity versus some highe |
8,942 | When to normalize data in regression? [duplicate] | Sometimes standardization helps for numerical issues (not so much these days with modern numerical linear algebra routines) or for interpretation, as mentioned in the other answer. Here is one "rule" that I will use for answering the answer myself: Is the regression method you are using invariant, in that the substant... | When to normalize data in regression? [duplicate] | Sometimes standardization helps for numerical issues (not so much these days with modern numerical linear algebra routines) or for interpretation, as mentioned in the other answer. Here is one "rule" | When to normalize data in regression? [duplicate]
Sometimes standardization helps for numerical issues (not so much these days with modern numerical linear algebra routines) or for interpretation, as mentioned in the other answer. Here is one "rule" that I will use for answering the answer myself: Is the regression me... | When to normalize data in regression? [duplicate]
Sometimes standardization helps for numerical issues (not so much these days with modern numerical linear algebra routines) or for interpretation, as mentioned in the other answer. Here is one "rule" |
8,943 | When to normalize data in regression? [duplicate] | It sometimes makes interpretation easier if you subtract the mean or some number within the range of the actual values as this can make the intercept more meaningful. For instance if you have people aged 65 and over subtract 65 and then the intercept is the predicted value for a 65-year old rather than a neonate. If yo... | When to normalize data in regression? [duplicate] | It sometimes makes interpretation easier if you subtract the mean or some number within the range of the actual values as this can make the intercept more meaningful. For instance if you have people a | When to normalize data in regression? [duplicate]
It sometimes makes interpretation easier if you subtract the mean or some number within the range of the actual values as this can make the intercept more meaningful. For instance if you have people aged 65 and over subtract 65 and then the intercept is the predicted va... | When to normalize data in regression? [duplicate]
It sometimes makes interpretation easier if you subtract the mean or some number within the range of the actual values as this can make the intercept more meaningful. For instance if you have people a |
8,944 | Recommendation for peer-reviewed open-source journal? | A rather lengthy list can be found at the Directory of Open Access Journals. Using the search term statistics yielded a list of 124 open-source journals (updated following the DOAJ's move to a new platform).
I have had good experiences and success in the past with the IMS and Bernoulli society co-sponsored open-source... | Recommendation for peer-reviewed open-source journal? | A rather lengthy list can be found at the Directory of Open Access Journals. Using the search term statistics yielded a list of 124 open-source journals (updated following the DOAJ's move to a new pla | Recommendation for peer-reviewed open-source journal?
A rather lengthy list can be found at the Directory of Open Access Journals. Using the search term statistics yielded a list of 124 open-source journals (updated following the DOAJ's move to a new platform).
I have had good experiences and success in the past with t... | Recommendation for peer-reviewed open-source journal?
A rather lengthy list can be found at the Directory of Open Access Journals. Using the search term statistics yielded a list of 124 open-source journals (updated following the DOAJ's move to a new pla |
8,945 | Recommendation for peer-reviewed open-source journal? | In case your method is somewhat implemented, Journal of Statistical Software is a pretty nice option -- they put emphasis on reproducibility and availability of methods and algorithms. | Recommendation for peer-reviewed open-source journal? | In case your method is somewhat implemented, Journal of Statistical Software is a pretty nice option -- they put emphasis on reproducibility and availability of methods and algorithms. | Recommendation for peer-reviewed open-source journal?
In case your method is somewhat implemented, Journal of Statistical Software is a pretty nice option -- they put emphasis on reproducibility and availability of methods and algorithms. | Recommendation for peer-reviewed open-source journal?
In case your method is somewhat implemented, Journal of Statistical Software is a pretty nice option -- they put emphasis on reproducibility and availability of methods and algorithms. |
8,946 | Recommendation for peer-reviewed open-source journal? | To add to what cardinal has said the journal Statistics in Biopharmaceutical Research is a purely online journal but you do have to subscribe. Like what cardinal says about Annals of Applied Statistics this journal does give selected issues or some individual articles out for free. It is published by Taylor and Franci... | Recommendation for peer-reviewed open-source journal? | To add to what cardinal has said the journal Statistics in Biopharmaceutical Research is a purely online journal but you do have to subscribe. Like what cardinal says about Annals of Applied Statistic | Recommendation for peer-reviewed open-source journal?
To add to what cardinal has said the journal Statistics in Biopharmaceutical Research is a purely online journal but you do have to subscribe. Like what cardinal says about Annals of Applied Statistics this journal does give selected issues or some individual articl... | Recommendation for peer-reviewed open-source journal?
To add to what cardinal has said the journal Statistics in Biopharmaceutical Research is a purely online journal but you do have to subscribe. Like what cardinal says about Annals of Applied Statistic |
8,947 | Proof of LOOCV formula | I'll show the result for any multiple linear regression, whether the regressors are polynomials of $X_t$ or not. In fact, it shows a little more than what you asked, because it shows that each LOOCV residual is identical to the corresponding leverage-weighted residual from the full regression, not just that you can obt... | Proof of LOOCV formula | I'll show the result for any multiple linear regression, whether the regressors are polynomials of $X_t$ or not. In fact, it shows a little more than what you asked, because it shows that each LOOCV r | Proof of LOOCV formula
I'll show the result for any multiple linear regression, whether the regressors are polynomials of $X_t$ or not. In fact, it shows a little more than what you asked, because it shows that each LOOCV residual is identical to the corresponding leverage-weighted residual from the full regression, no... | Proof of LOOCV formula
I'll show the result for any multiple linear regression, whether the regressors are polynomials of $X_t$ or not. In fact, it shows a little more than what you asked, because it shows that each LOOCV r |
8,948 | Getting p-values for "multinom" in R (nnet package) | You can use that custom function that I`ve created, for example you can just get true or false for Hipotesis test.
The TRUE ones should represent P-Value > 0,5.
zWald_test <- function(x){
zWald_modelo<- (summary(x)$coefficients /
summary(x)$standard.errors)
a <- t(apply(zWald_modelo... | Getting p-values for "multinom" in R (nnet package) | You can use that custom function that I`ve created, for example you can just get true or false for Hipotesis test.
The TRUE ones should represent P-Value > 0,5.
zWald_test <- function(x){
zWald_mode | Getting p-values for "multinom" in R (nnet package)
You can use that custom function that I`ve created, for example you can just get true or false for Hipotesis test.
The TRUE ones should represent P-Value > 0,5.
zWald_test <- function(x){
zWald_modelo<- (summary(x)$coefficients /
sum... | Getting p-values for "multinom" in R (nnet package)
You can use that custom function that I`ve created, for example you can just get true or false for Hipotesis test.
The TRUE ones should represent P-Value > 0,5.
zWald_test <- function(x){
zWald_mode |
8,949 | Getting p-values for "multinom" in R (nnet package) | What about using
z <- summary(test)$coefficients/summary(test)$standard.errors
# 2-tailed Wald z tests to test significance of coefficients
p <- (1 - pnorm(abs(z), 0, 1)) * 2
p
Basically, this would be based on the estimated coefficients relative to their standard error, and would use a z test to test against a signif... | Getting p-values for "multinom" in R (nnet package) | What about using
z <- summary(test)$coefficients/summary(test)$standard.errors
# 2-tailed Wald z tests to test significance of coefficients
p <- (1 - pnorm(abs(z), 0, 1)) * 2
p
Basically, this would | Getting p-values for "multinom" in R (nnet package)
What about using
z <- summary(test)$coefficients/summary(test)$standard.errors
# 2-tailed Wald z tests to test significance of coefficients
p <- (1 - pnorm(abs(z), 0, 1)) * 2
p
Basically, this would be based on the estimated coefficients relative to their standard er... | Getting p-values for "multinom" in R (nnet package)
What about using
z <- summary(test)$coefficients/summary(test)$standard.errors
# 2-tailed Wald z tests to test significance of coefficients
p <- (1 - pnorm(abs(z), 0, 1)) * 2
p
Basically, this would |
8,950 | Getting p-values for "multinom" in R (nnet package) | As already said by OP (by his quote of B Ripley), wald tests is not really good for multinomial models, we really should use likelihoodratio tests. Below I show an easy way of getting that via functions from the MASS package, using an example from the help page of nnet::multinom. The workhorse function used is MASS::dr... | Getting p-values for "multinom" in R (nnet package) | As already said by OP (by his quote of B Ripley), wald tests is not really good for multinomial models, we really should use likelihoodratio tests. Below I show an easy way of getting that via functio | Getting p-values for "multinom" in R (nnet package)
As already said by OP (by his quote of B Ripley), wald tests is not really good for multinomial models, we really should use likelihoodratio tests. Below I show an easy way of getting that via functions from the MASS package, using an example from the help page of nne... | Getting p-values for "multinom" in R (nnet package)
As already said by OP (by his quote of B Ripley), wald tests is not really good for multinomial models, we really should use likelihoodratio tests. Below I show an easy way of getting that via functio |
8,951 | Getting p-values for "multinom" in R (nnet package) | Also you could be interested in Likehood Ratio test p-values, as seen here:
http://thestatsgeek.com/2014/02/08/wald-vs-likelihood-ratio-test/
Wich you could extract like this (sorry, its a custom function :D)
likehoodmultinom_p <- function(model_lmm)
{
i <- 1
variables <-c("No funciona")
valores <- c("No funci... | Getting p-values for "multinom" in R (nnet package) | Also you could be interested in Likehood Ratio test p-values, as seen here:
http://thestatsgeek.com/2014/02/08/wald-vs-likelihood-ratio-test/
Wich you could extract like this (sorry, its a custom func | Getting p-values for "multinom" in R (nnet package)
Also you could be interested in Likehood Ratio test p-values, as seen here:
http://thestatsgeek.com/2014/02/08/wald-vs-likelihood-ratio-test/
Wich you could extract like this (sorry, its a custom function :D)
likehoodmultinom_p <- function(model_lmm)
{
i <- 1
v... | Getting p-values for "multinom" in R (nnet package)
Also you could be interested in Likehood Ratio test p-values, as seen here:
http://thestatsgeek.com/2014/02/08/wald-vs-likelihood-ratio-test/
Wich you could extract like this (sorry, its a custom func |
8,952 | Getting p-values for "multinom" in R (nnet package) | One way to think about the p-value is a likelihood test that your fit is better than some simpler fit with fewer terms (or possibly no terms, the constant fit). Below is some code.
# Multinomial fit
fit <- nnet::multinom(cyl ~ mpg + hp, data=datasets::mtcars)
# Multinomial fit with one or more terms dropped
base_fit ... | Getting p-values for "multinom" in R (nnet package) | One way to think about the p-value is a likelihood test that your fit is better than some simpler fit with fewer terms (or possibly no terms, the constant fit). Below is some code.
# Multinomial fit
| Getting p-values for "multinom" in R (nnet package)
One way to think about the p-value is a likelihood test that your fit is better than some simpler fit with fewer terms (or possibly no terms, the constant fit). Below is some code.
# Multinomial fit
fit <- nnet::multinom(cyl ~ mpg + hp, data=datasets::mtcars)
# Mult... | Getting p-values for "multinom" in R (nnet package)
One way to think about the p-value is a likelihood test that your fit is better than some simpler fit with fewer terms (or possibly no terms, the constant fit). Below is some code.
# Multinomial fit
|
8,953 | How to use early stopping properly for training deep neural network? | What would be a good validation frequency? Should I check my model on the validation data at the end of each epoch? (My batch size is 1)
There is no gold rule, computing the validation error after each epoch is quite common. Since your validation set much smaller than your training set, it will not slow down the train... | How to use early stopping properly for training deep neural network? | What would be a good validation frequency? Should I check my model on the validation data at the end of each epoch? (My batch size is 1)
There is no gold rule, computing the validation error after ea | How to use early stopping properly for training deep neural network?
What would be a good validation frequency? Should I check my model on the validation data at the end of each epoch? (My batch size is 1)
There is no gold rule, computing the validation error after each epoch is quite common. Since your validation set... | How to use early stopping properly for training deep neural network?
What would be a good validation frequency? Should I check my model on the validation data at the end of each epoch? (My batch size is 1)
There is no gold rule, computing the validation error after ea |
8,954 | How to use early stopping properly for training deep neural network? | To add to other excellent answers, you can also - not stop. I usually:
run NN for far more time I would have thought is sensible,
save the model weights every N epochs, and
when I see the training loss has stabilized, I just pick the model with lowest validation loss.
Of course that only makes sense when you don't pa... | How to use early stopping properly for training deep neural network? | To add to other excellent answers, you can also - not stop. I usually:
run NN for far more time I would have thought is sensible,
save the model weights every N epochs, and
when I see the training lo | How to use early stopping properly for training deep neural network?
To add to other excellent answers, you can also - not stop. I usually:
run NN for far more time I would have thought is sensible,
save the model weights every N epochs, and
when I see the training loss has stabilized, I just pick the model with lowes... | How to use early stopping properly for training deep neural network?
To add to other excellent answers, you can also - not stop. I usually:
run NN for far more time I would have thought is sensible,
save the model weights every N epochs, and
when I see the training lo |
8,955 | Sandwich estimator intuition | For OLS, you can imagine that you're using the estimated variance of the residuals (under the assumption of independence and homoscedasticity) as an estimate for the conditional variance of the $Y_i$s. In the sandwich based estimator, you're using the observed squared residuals as a plug-in estimate of the same varianc... | Sandwich estimator intuition | For OLS, you can imagine that you're using the estimated variance of the residuals (under the assumption of independence and homoscedasticity) as an estimate for the conditional variance of the $Y_i$s | Sandwich estimator intuition
For OLS, you can imagine that you're using the estimated variance of the residuals (under the assumption of independence and homoscedasticity) as an estimate for the conditional variance of the $Y_i$s. In the sandwich based estimator, you're using the observed squared residuals as a plug-in... | Sandwich estimator intuition
For OLS, you can imagine that you're using the estimated variance of the residuals (under the assumption of independence and homoscedasticity) as an estimate for the conditional variance of the $Y_i$s |
8,956 | Clustering variables based on correlations between them | Here's a simple example in R using the bfi dataset: bfi is a dataset of 25 personality test items organised around 5 factors.
library(psych)
data(bfi)
x <- bfi
A hiearchical cluster analysis using the euclidan distance between variables based on the absolute correlation between variables can be obtained like so:
plot... | Clustering variables based on correlations between them | Here's a simple example in R using the bfi dataset: bfi is a dataset of 25 personality test items organised around 5 factors.
library(psych)
data(bfi)
x <- bfi
A hiearchical cluster analysis using t | Clustering variables based on correlations between them
Here's a simple example in R using the bfi dataset: bfi is a dataset of 25 personality test items organised around 5 factors.
library(psych)
data(bfi)
x <- bfi
A hiearchical cluster analysis using the euclidan distance between variables based on the absolute cor... | Clustering variables based on correlations between them
Here's a simple example in R using the bfi dataset: bfi is a dataset of 25 personality test items organised around 5 factors.
library(psych)
data(bfi)
x <- bfi
A hiearchical cluster analysis using t |
8,957 | Clustering variables based on correlations between them | When Clustering Correlations it is important not to calculate the distance twice. When you take the correlation matrix you are in essence making a distance calculation. You will want to convert it to a true distance by taking 1 - the absolute value.
1-abs(cor(x))
When you go to convert this matrix to a distance obje... | Clustering variables based on correlations between them | When Clustering Correlations it is important not to calculate the distance twice. When you take the correlation matrix you are in essence making a distance calculation. You will want to convert it t | Clustering variables based on correlations between them
When Clustering Correlations it is important not to calculate the distance twice. When you take the correlation matrix you are in essence making a distance calculation. You will want to convert it to a true distance by taking 1 - the absolute value.
1-abs(cor(x)... | Clustering variables based on correlations between them
When Clustering Correlations it is important not to calculate the distance twice. When you take the correlation matrix you are in essence making a distance calculation. You will want to convert it t |
8,958 | What is the oracle property of an estimator? | An oracle knows the truth: it knows the true subset and is willing to act on it. The oracle property is that the asymptotic distribution of the estimator is the same as the asymptotic distribution of the MLE on only the true support. That is, the estimator adapts to knowing the true support without paying a price (in t... | What is the oracle property of an estimator? | An oracle knows the truth: it knows the true subset and is willing to act on it. The oracle property is that the asymptotic distribution of the estimator is the same as the asymptotic distribution of | What is the oracle property of an estimator?
An oracle knows the truth: it knows the true subset and is willing to act on it. The oracle property is that the asymptotic distribution of the estimator is the same as the asymptotic distribution of the MLE on only the true support. That is, the estimator adapts to knowing ... | What is the oracle property of an estimator?
An oracle knows the truth: it knows the true subset and is willing to act on it. The oracle property is that the asymptotic distribution of the estimator is the same as the asymptotic distribution of |
8,959 | What is the oracle property of an estimator? | The definition of Oracle property is related highly to the context. The very short but precise answer in linear regression (precisely high dimensional one) is this:
an oracle estimator must be consistent in parameter estimation and variable selection.
Notice that an estimator that is consistent in variable selection ... | What is the oracle property of an estimator? | The definition of Oracle property is related highly to the context. The very short but precise answer in linear regression (precisely high dimensional one) is this:
an oracle estimator must be consis | What is the oracle property of an estimator?
The definition of Oracle property is related highly to the context. The very short but precise answer in linear regression (precisely high dimensional one) is this:
an oracle estimator must be consistent in parameter estimation and variable selection.
Notice that an estima... | What is the oracle property of an estimator?
The definition of Oracle property is related highly to the context. The very short but precise answer in linear regression (precisely high dimensional one) is this:
an oracle estimator must be consis |
8,960 | Entropy-based refutation of Shalizi's Bayesian backward arrow of time paradox? | In short: 1:0 for Yudkowsky.
Cosma Shalizi considers a probability distribution subjected to some measurements. He updates the probabilities accordingly (here it is not important if it is the Bayensian inference or anything else).
No surprising at all, the entropy of the probability distribution decreases.
However, he... | Entropy-based refutation of Shalizi's Bayesian backward arrow of time paradox? | In short: 1:0 for Yudkowsky.
Cosma Shalizi considers a probability distribution subjected to some measurements. He updates the probabilities accordingly (here it is not important if it is the Bayensia | Entropy-based refutation of Shalizi's Bayesian backward arrow of time paradox?
In short: 1:0 for Yudkowsky.
Cosma Shalizi considers a probability distribution subjected to some measurements. He updates the probabilities accordingly (here it is not important if it is the Bayensian inference or anything else).
No surpri... | Entropy-based refutation of Shalizi's Bayesian backward arrow of time paradox?
In short: 1:0 for Yudkowsky.
Cosma Shalizi considers a probability distribution subjected to some measurements. He updates the probabilities accordingly (here it is not important if it is the Bayensia |
8,961 | Entropy-based refutation of Shalizi's Bayesian backward arrow of time paradox? | Shalizi's flaw is very basic and derives from assumption I, that the time evolution is invertible (reversible).
The time evolution of INDIVIDUAL states is reversible. The time evolution of a distribution over ALL OF PHASE SPACE is most certainly not reversible, unless the system is in equilibrium. The paper treats ti... | Entropy-based refutation of Shalizi's Bayesian backward arrow of time paradox? | Shalizi's flaw is very basic and derives from assumption I, that the time evolution is invertible (reversible).
The time evolution of INDIVIDUAL states is reversible. The time evolution of a distribu | Entropy-based refutation of Shalizi's Bayesian backward arrow of time paradox?
Shalizi's flaw is very basic and derives from assumption I, that the time evolution is invertible (reversible).
The time evolution of INDIVIDUAL states is reversible. The time evolution of a distribution over ALL OF PHASE SPACE is most cert... | Entropy-based refutation of Shalizi's Bayesian backward arrow of time paradox?
Shalizi's flaw is very basic and derives from assumption I, that the time evolution is invertible (reversible).
The time evolution of INDIVIDUAL states is reversible. The time evolution of a distribu |
8,962 | Entropy-based refutation of Shalizi's Bayesian backward arrow of time paradox? | The linked paper explicitly assumes that
The evolution operator T is invertible.
But if you use QM in the conventional way, then this assumption doesn't hold. Suppose you have a state X1 which can evolve into either X2 or X3 with equal probability. You would say that state X1 evolves into the weighted set [1/2 X2 + 1... | Entropy-based refutation of Shalizi's Bayesian backward arrow of time paradox? | The linked paper explicitly assumes that
The evolution operator T is invertible.
But if you use QM in the conventional way, then this assumption doesn't hold. Suppose you have a state X1 which can e | Entropy-based refutation of Shalizi's Bayesian backward arrow of time paradox?
The linked paper explicitly assumes that
The evolution operator T is invertible.
But if you use QM in the conventional way, then this assumption doesn't hold. Suppose you have a state X1 which can evolve into either X2 or X3 with equal pro... | Entropy-based refutation of Shalizi's Bayesian backward arrow of time paradox?
The linked paper explicitly assumes that
The evolution operator T is invertible.
But if you use QM in the conventional way, then this assumption doesn't hold. Suppose you have a state X1 which can e |
8,963 | Choosing among proper scoring rules | Why would someone use one of these rather than logarithmic scoring?
So ideally, we always distinguish fitting a model from making a decision. In Bayesian methodology, model scoring & selection should always be done using the marginal likelihood. You then use the model to make probabilistic predictions, and your loss f... | Choosing among proper scoring rules | Why would someone use one of these rather than logarithmic scoring?
So ideally, we always distinguish fitting a model from making a decision. In Bayesian methodology, model scoring & selection should | Choosing among proper scoring rules
Why would someone use one of these rather than logarithmic scoring?
So ideally, we always distinguish fitting a model from making a decision. In Bayesian methodology, model scoring & selection should always be done using the marginal likelihood. You then use the model to make probab... | Choosing among proper scoring rules
Why would someone use one of these rather than logarithmic scoring?
So ideally, we always distinguish fitting a model from making a decision. In Bayesian methodology, model scoring & selection should |
8,964 | Choosing among proper scoring rules | (as to my intuition)
the less the difference between predicted & actual - the more precise the forecast is. Just for the purpose of maximization of differencies - different scores are used - either log (log-loss) or difference between squares (Brier score). Everything is obvious in the mathematical formulation of the s... | Choosing among proper scoring rules | (as to my intuition)
the less the difference between predicted & actual - the more precise the forecast is. Just for the purpose of maximization of differencies - different scores are used - either lo | Choosing among proper scoring rules
(as to my intuition)
the less the difference between predicted & actual - the more precise the forecast is. Just for the purpose of maximization of differencies - different scores are used - either log (log-loss) or difference between squares (Brier score). Everything is obvious in t... | Choosing among proper scoring rules
(as to my intuition)
the less the difference between predicted & actual - the more precise the forecast is. Just for the purpose of maximization of differencies - different scores are used - either lo |
8,965 | Extending the birthday paradox to more than 2 people | This is a counting problem: there are $b^n$ possible assignments of $b$ birthdays to $n$ people. Of those, let $q(k; n, b)$ be the number of assignments for which no birthday is shared by more than $k$ people but at least one birthday actually is shared by $k$ people. The probability we seek can be found by summing t... | Extending the birthday paradox to more than 2 people | This is a counting problem: there are $b^n$ possible assignments of $b$ birthdays to $n$ people. Of those, let $q(k; n, b)$ be the number of assignments for which no birthday is shared by more than $ | Extending the birthday paradox to more than 2 people
This is a counting problem: there are $b^n$ possible assignments of $b$ birthdays to $n$ people. Of those, let $q(k; n, b)$ be the number of assignments for which no birthday is shared by more than $k$ people but at least one birthday actually is shared by $k$ peopl... | Extending the birthday paradox to more than 2 people
This is a counting problem: there are $b^n$ possible assignments of $b$ birthdays to $n$ people. Of those, let $q(k; n, b)$ be the number of assignments for which no birthday is shared by more than $ |
8,966 | Extending the birthday paradox to more than 2 people | It is always possible to solve this problem with a monte-carlo solution, although that's far from the most efficient. Here's a simple example of the 2 person problem in R (from a presentation I gave last year; I used this as an example of inefficient code), which could be easily adjusted to account for more than 2:
bi... | Extending the birthday paradox to more than 2 people | It is always possible to solve this problem with a monte-carlo solution, although that's far from the most efficient. Here's a simple example of the 2 person problem in R (from a presentation I gave | Extending the birthday paradox to more than 2 people
It is always possible to solve this problem with a monte-carlo solution, although that's far from the most efficient. Here's a simple example of the 2 person problem in R (from a presentation I gave last year; I used this as an example of inefficient code), which co... | Extending the birthday paradox to more than 2 people
It is always possible to solve this problem with a monte-carlo solution, although that's far from the most efficient. Here's a simple example of the 2 person problem in R (from a presentation I gave |
8,967 | Extending the birthday paradox to more than 2 people | This is an attempt at a general solution. There may be some mistakes so use with caution!
First some notation:
$P(x,n)$ be the probability that $x$ or more people share a birthday among $n$ people,
$P(y|n)$ be the probability that exactly $y$ people share a birthday among $n$ people.
Notes:
Abuse of notation as $P(.)$... | Extending the birthday paradox to more than 2 people | This is an attempt at a general solution. There may be some mistakes so use with caution!
First some notation:
$P(x,n)$ be the probability that $x$ or more people share a birthday among $n$ people,
$P | Extending the birthday paradox to more than 2 people
This is an attempt at a general solution. There may be some mistakes so use with caution!
First some notation:
$P(x,n)$ be the probability that $x$ or more people share a birthday among $n$ people,
$P(y|n)$ be the probability that exactly $y$ people share a birthday ... | Extending the birthday paradox to more than 2 people
This is an attempt at a general solution. There may be some mistakes so use with caution!
First some notation:
$P(x,n)$ be the probability that $x$ or more people share a birthday among $n$ people,
$P |
8,968 | Predicting with both continuous and categorical features | As far as I know, and I've researched this issue deeply in the past, there are no predictive modeling techniques (beside trees, XgBoost, etc.) that are designed to handle both types of input at the same time without simply transforming the type of the features.
Note that algorithms like Random Forest and XGBoost accept... | Predicting with both continuous and categorical features | As far as I know, and I've researched this issue deeply in the past, there are no predictive modeling techniques (beside trees, XgBoost, etc.) that are designed to handle both types of input at the sa | Predicting with both continuous and categorical features
As far as I know, and I've researched this issue deeply in the past, there are no predictive modeling techniques (beside trees, XgBoost, etc.) that are designed to handle both types of input at the same time without simply transforming the type of the features.
N... | Predicting with both continuous and categorical features
As far as I know, and I've researched this issue deeply in the past, there are no predictive modeling techniques (beside trees, XgBoost, etc.) that are designed to handle both types of input at the sa |
8,969 | Predicting with both continuous and categorical features | I know it's been a while since this question was posted, but if you're still looking at this problem (or similar ones) you may want to consider using generalized additive models (GAM's). I'm no expert, but these models allow you to combine different models to create a single prediction. The process used to find coeffic... | Predicting with both continuous and categorical features | I know it's been a while since this question was posted, but if you're still looking at this problem (or similar ones) you may want to consider using generalized additive models (GAM's). I'm no expert | Predicting with both continuous and categorical features
I know it's been a while since this question was posted, but if you're still looking at this problem (or similar ones) you may want to consider using generalized additive models (GAM's). I'm no expert, but these models allow you to combine different models to cre... | Predicting with both continuous and categorical features
I know it's been a while since this question was posted, but if you're still looking at this problem (or similar ones) you may want to consider using generalized additive models (GAM's). I'm no expert |
8,970 | Predicting with both continuous and categorical features | While discretization transforms continous data to discrete data it can hardly be said that dummy variables transform categorical data to continous data. Indeed, since algorithms can be run on computers there can hardly be a classificator algorithm which does NOT transform categorical data into dummy variables.
In the s... | Predicting with both continuous and categorical features | While discretization transforms continous data to discrete data it can hardly be said that dummy variables transform categorical data to continous data. Indeed, since algorithms can be run on computer | Predicting with both continuous and categorical features
While discretization transforms continous data to discrete data it can hardly be said that dummy variables transform categorical data to continous data. Indeed, since algorithms can be run on computers there can hardly be a classificator algorithm which does NOT ... | Predicting with both continuous and categorical features
While discretization transforms continous data to discrete data it can hardly be said that dummy variables transform categorical data to continous data. Indeed, since algorithms can be run on computer |
8,971 | Predicting with both continuous and categorical features | This is a deep philosophical question which is commonly addressed from the statistical as well as machine learning end. Some say, categorizing is better for discrete to categorical indicator, so that the packages can easily digest the model inputs. Others say, that binning can cause information loss, but however catego... | Predicting with both continuous and categorical features | This is a deep philosophical question which is commonly addressed from the statistical as well as machine learning end. Some say, categorizing is better for discrete to categorical indicator, so that | Predicting with both continuous and categorical features
This is a deep philosophical question which is commonly addressed from the statistical as well as machine learning end. Some say, categorizing is better for discrete to categorical indicator, so that the packages can easily digest the model inputs. Others say, th... | Predicting with both continuous and categorical features
This is a deep philosophical question which is commonly addressed from the statistical as well as machine learning end. Some say, categorizing is better for discrete to categorical indicator, so that |
8,972 | Is cross validation a proper substitute for validation set? | You have indeed correctly described the way to work with crossvalidation. In fact, you are 'lucky' to have a reasonable validation set at the end, because often, crossvalidation is used to optimize a model, but no "real" validation is done.
As @Simon Stelling said in his comment, crossvalidation will lead to lower esti... | Is cross validation a proper substitute for validation set? | You have indeed correctly described the way to work with crossvalidation. In fact, you are 'lucky' to have a reasonable validation set at the end, because often, crossvalidation is used to optimize a | Is cross validation a proper substitute for validation set?
You have indeed correctly described the way to work with crossvalidation. In fact, you are 'lucky' to have a reasonable validation set at the end, because often, crossvalidation is used to optimize a model, but no "real" validation is done.
As @Simon Stelling ... | Is cross validation a proper substitute for validation set?
You have indeed correctly described the way to work with crossvalidation. In fact, you are 'lucky' to have a reasonable validation set at the end, because often, crossvalidation is used to optimize a |
8,973 | Can a Multinomial(1/n, ..., 1/n) be characterized as a discretized Dirichlet(1, .., 1)? | Those the two distributions are different for every $n \geq 4$.
Notation
I'm going to rescale your simplex by a factor $n$, so that the lattice points have integer coordinates. This doesn't change anything, I just think it makes the notation a little less cumbersome.
Let $S$ be the $(n-1)$-simplex, given as the convex ... | Can a Multinomial(1/n, ..., 1/n) be characterized as a discretized Dirichlet(1, .., 1)? | Those the two distributions are different for every $n \geq 4$.
Notation
I'm going to rescale your simplex by a factor $n$, so that the lattice points have integer coordinates. This doesn't change any | Can a Multinomial(1/n, ..., 1/n) be characterized as a discretized Dirichlet(1, .., 1)?
Those the two distributions are different for every $n \geq 4$.
Notation
I'm going to rescale your simplex by a factor $n$, so that the lattice points have integer coordinates. This doesn't change anything, I just think it makes the... | Can a Multinomial(1/n, ..., 1/n) be characterized as a discretized Dirichlet(1, .., 1)?
Those the two distributions are different for every $n \geq 4$.
Notation
I'm going to rescale your simplex by a factor $n$, so that the lattice points have integer coordinates. This doesn't change any |
8,974 | Meaning of p-values in regression | The p-value for $a$ is the p-value in a test of the hypothesis "$\alpha = 0$" (usually a 2-sided $t$-test). The p-value for $b$ is the p-value in a test of the hypothesis "$\beta = 0$" (also usually a 2-sided $t$-test) and likewise for any other coefficients in the regression. The probability models for these tests a... | Meaning of p-values in regression | The p-value for $a$ is the p-value in a test of the hypothesis "$\alpha = 0$" (usually a 2-sided $t$-test). The p-value for $b$ is the p-value in a test of the hypothesis "$\beta = 0$" (also usually | Meaning of p-values in regression
The p-value for $a$ is the p-value in a test of the hypothesis "$\alpha = 0$" (usually a 2-sided $t$-test). The p-value for $b$ is the p-value in a test of the hypothesis "$\beta = 0$" (also usually a 2-sided $t$-test) and likewise for any other coefficients in the regression. The pr... | Meaning of p-values in regression
The p-value for $a$ is the p-value in a test of the hypothesis "$\alpha = 0$" (usually a 2-sided $t$-test). The p-value for $b$ is the p-value in a test of the hypothesis "$\beta = 0$" (also usually |
8,975 | Meaning of p-values in regression | wrt your first question: this depends on your software of choice. There are really two types of p-values that are used frequently in these scenarios, both typically based upon likelihood ratio tests (there are others but these are typically equivalent or at least differ little in their results).
It is important to real... | Meaning of p-values in regression | wrt your first question: this depends on your software of choice. There are really two types of p-values that are used frequently in these scenarios, both typically based upon likelihood ratio tests ( | Meaning of p-values in regression
wrt your first question: this depends on your software of choice. There are really two types of p-values that are used frequently in these scenarios, both typically based upon likelihood ratio tests (there are others but these are typically equivalent or at least differ little in their... | Meaning of p-values in regression
wrt your first question: this depends on your software of choice. There are really two types of p-values that are used frequently in these scenarios, both typically based upon likelihood ratio tests ( |
8,976 | Fitting an ARIMAX model with regularization or penalization (e.g. with the lasso, elastic net, or ridge regression) | This is not a solution but some reflections on the possibilities and difficulties that I know of.
Whenever it is possible to specify a time-series model as
$$Y_{t+1} = \mathbf{x}_t \beta + \epsilon_{t+1}$$
with $\mathbf{x}_t$ computable from covariates and time-lagged observations, it is also possible to compute the... | Fitting an ARIMAX model with regularization or penalization (e.g. with the lasso, elastic net, or ri | This is not a solution but some reflections on the possibilities and difficulties that I know of.
Whenever it is possible to specify a time-series model as
$$Y_{t+1} = \mathbf{x}_t \beta + \epsilon | Fitting an ARIMAX model with regularization or penalization (e.g. with the lasso, elastic net, or ridge regression)
This is not a solution but some reflections on the possibilities and difficulties that I know of.
Whenever it is possible to specify a time-series model as
$$Y_{t+1} = \mathbf{x}_t \beta + \epsilon_{t+... | Fitting an ARIMAX model with regularization or penalization (e.g. with the lasso, elastic net, or ri
This is not a solution but some reflections on the possibilities and difficulties that I know of.
Whenever it is possible to specify a time-series model as
$$Y_{t+1} = \mathbf{x}_t \beta + \epsilon |
8,977 | Fitting an ARIMAX model with regularization or penalization (e.g. with the lasso, elastic net, or ridge regression) | I was challenged by a client to solve this problem in an automatic i.e. turnkey way. I implemented an approach that for each pair ( i.e. y and a candidate x ) , prewhiten , compute cross-correlations of the pre-whitened series, identify the PDL ( OR ADL AUTOREGRESSIVE DISTRIBUTED LAG MODEL including any DEAD TIME ) whi... | Fitting an ARIMAX model with regularization or penalization (e.g. with the lasso, elastic net, or ri | I was challenged by a client to solve this problem in an automatic i.e. turnkey way. I implemented an approach that for each pair ( i.e. y and a candidate x ) , prewhiten , compute cross-correlations | Fitting an ARIMAX model with regularization or penalization (e.g. with the lasso, elastic net, or ridge regression)
I was challenged by a client to solve this problem in an automatic i.e. turnkey way. I implemented an approach that for each pair ( i.e. y and a candidate x ) , prewhiten , compute cross-correlations of t... | Fitting an ARIMAX model with regularization or penalization (e.g. with the lasso, elastic net, or ri
I was challenged by a client to solve this problem in an automatic i.e. turnkey way. I implemented an approach that for each pair ( i.e. y and a candidate x ) , prewhiten , compute cross-correlations |
8,978 | Beautifully written papers | I'll give it a shot...:
Benjamini, Yoav; Hochberg, Yosef (1995). "Controlling the false discovery rate: a practical and powerful approach to multiple testing". Journal of the Royal Statistical Society, Series B 57 (1): 289–300. MR 1325392.
Link to PDF: http://www.math.tau.ac.il/~ybenja/MyPapers/benjamini_hochberg1995.p... | Beautifully written papers | I'll give it a shot...:
Benjamini, Yoav; Hochberg, Yosef (1995). "Controlling the false discovery rate: a practical and powerful approach to multiple testing". Journal of the Royal Statistical Society | Beautifully written papers
I'll give it a shot...:
Benjamini, Yoav; Hochberg, Yosef (1995). "Controlling the false discovery rate: a practical and powerful approach to multiple testing". Journal of the Royal Statistical Society, Series B 57 (1): 289–300. MR 1325392.
Link to PDF: http://www.math.tau.ac.il/~ybenja/MyPape... | Beautifully written papers
I'll give it a shot...:
Benjamini, Yoav; Hochberg, Yosef (1995). "Controlling the false discovery rate: a practical and powerful approach to multiple testing". Journal of the Royal Statistical Society |
8,979 | Computing repeatability of effects from an lmer model | I think I can answer your questions at least concerning the unadjusted repeatability estimates, i.e., the classical intra-class correlations (ICCs). As for the "adjusted" repeatability estimates, I skimmed over the paper you linked and didn't really see where the formula that you apply can be found in the paper? Based ... | Computing repeatability of effects from an lmer model | I think I can answer your questions at least concerning the unadjusted repeatability estimates, i.e., the classical intra-class correlations (ICCs). As for the "adjusted" repeatability estimates, I sk | Computing repeatability of effects from an lmer model
I think I can answer your questions at least concerning the unadjusted repeatability estimates, i.e., the classical intra-class correlations (ICCs). As for the "adjusted" repeatability estimates, I skimmed over the paper you linked and didn't really see where the fo... | Computing repeatability of effects from an lmer model
I think I can answer your questions at least concerning the unadjusted repeatability estimates, i.e., the classical intra-class correlations (ICCs). As for the "adjusted" repeatability estimates, I sk |
8,980 | How to construct a multivariate Beta distribution? | It is natural to use a Gaussian copula for this construction. This amounts to transforming the marginal distributions of a $d$-dimensional Gaussian random variable into specified Beta marginals. The details are given below.
The question actually describes only $2d + d(d-1)/2$ parameters: two parameters $a_i, b_i$ for... | How to construct a multivariate Beta distribution? | It is natural to use a Gaussian copula for this construction. This amounts to transforming the marginal distributions of a $d$-dimensional Gaussian random variable into specified Beta marginals. The | How to construct a multivariate Beta distribution?
It is natural to use a Gaussian copula for this construction. This amounts to transforming the marginal distributions of a $d$-dimensional Gaussian random variable into specified Beta marginals. The details are given below.
The question actually describes only $2d + ... | How to construct a multivariate Beta distribution?
It is natural to use a Gaussian copula for this construction. This amounts to transforming the marginal distributions of a $d$-dimensional Gaussian random variable into specified Beta marginals. The |
8,981 | How to construct a multivariate Beta distribution? | Here is a paper that does it in arbitrary dimensions by extending the bivariate construction mentioned by other commenters:
Trippa, Lorenzo, Peter Müller, and Wesley Johnson. "The multivariate beta process and an extension of the Polya tree model." Biometrika 98.1 (2011): 17-34.
The paper has a lot of notation but the ... | How to construct a multivariate Beta distribution? | Here is a paper that does it in arbitrary dimensions by extending the bivariate construction mentioned by other commenters:
Trippa, Lorenzo, Peter Müller, and Wesley Johnson. "The multivariate beta pr | How to construct a multivariate Beta distribution?
Here is a paper that does it in arbitrary dimensions by extending the bivariate construction mentioned by other commenters:
Trippa, Lorenzo, Peter Müller, and Wesley Johnson. "The multivariate beta process and an extension of the Polya tree model." Biometrika 98.1 (201... | How to construct a multivariate Beta distribution?
Here is a paper that does it in arbitrary dimensions by extending the bivariate construction mentioned by other commenters:
Trippa, Lorenzo, Peter Müller, and Wesley Johnson. "The multivariate beta pr |
8,982 | What are the branches of statistics? | You could look into the keywords/tags of the Cross Validated website.
Branches as a network
One way to do this is to plot it as a network based on the relationships between the keywords (how often they coincide in the same post).
When you use this sql-script to get the data of the site from (data.stackexchange.com/sta... | What are the branches of statistics? | You could look into the keywords/tags of the Cross Validated website.
Branches as a network
One way to do this is to plot it as a network based on the relationships between the keywords (how often th | What are the branches of statistics?
You could look into the keywords/tags of the Cross Validated website.
Branches as a network
One way to do this is to plot it as a network based on the relationships between the keywords (how often they coincide in the same post).
When you use this sql-script to get the data of the ... | What are the branches of statistics?
You could look into the keywords/tags of the Cross Validated website.
Branches as a network
One way to do this is to plot it as a network based on the relationships between the keywords (how often th |
8,983 | What are the branches of statistics? | I find these classification systems extremely unhelpful and contradictory. For example:
neural networks is a form of supervised learning
Calculus is used in differential geometry
Probability theory can be formalized as a part of set theory
and so on. There are no unambiguous "branches" of mathematics, and nor should ... | What are the branches of statistics? | I find these classification systems extremely unhelpful and contradictory. For example:
neural networks is a form of supervised learning
Calculus is used in differential geometry
Probability theory c | What are the branches of statistics?
I find these classification systems extremely unhelpful and contradictory. For example:
neural networks is a form of supervised learning
Calculus is used in differential geometry
Probability theory can be formalized as a part of set theory
and so on. There are no unambiguous "bran... | What are the branches of statistics?
I find these classification systems extremely unhelpful and contradictory. For example:
neural networks is a form of supervised learning
Calculus is used in differential geometry
Probability theory c |
8,984 | What are the branches of statistics? | This is a minor counterpoint to Rob Hyndman's answer. It started off as a comment and then grew too complex for one. If this is too far from addressing the main question, I apologise and will delete it.
Biology has been depicting hierarchical relationships since long before Darwin's first doodle (see Nick Cox's comme... | What are the branches of statistics? | This is a minor counterpoint to Rob Hyndman's answer. It started off as a comment and then grew too complex for one. If this is too far from addressing the main question, I apologise and will delete i | What are the branches of statistics?
This is a minor counterpoint to Rob Hyndman's answer. It started off as a comment and then grew too complex for one. If this is too far from addressing the main question, I apologise and will delete it.
Biology has been depicting hierarchical relationships since long before Darwin... | What are the branches of statistics?
This is a minor counterpoint to Rob Hyndman's answer. It started off as a comment and then grew too complex for one. If this is too far from addressing the main question, I apologise and will delete i |
8,985 | What are the branches of statistics? | An easy way to go about answering your question is to look up the common classification tables. For instance, 2010 Mathematics Subject Classification is used by some publications to classify papers. These are relevant because that's how a lot of authors classify their own papers.
There are many examples of similar cla... | What are the branches of statistics? | An easy way to go about answering your question is to look up the common classification tables. For instance, 2010 Mathematics Subject Classification is used by some publications to classify papers. T | What are the branches of statistics?
An easy way to go about answering your question is to look up the common classification tables. For instance, 2010 Mathematics Subject Classification is used by some publications to classify papers. These are relevant because that's how a lot of authors classify their own papers.
T... | What are the branches of statistics?
An easy way to go about answering your question is to look up the common classification tables. For instance, 2010 Mathematics Subject Classification is used by some publications to classify papers. T |
8,986 | What are the branches of statistics? | One way to approach the problem is look at citation and co-authorship networks in statistics journals, such as the Annals of Statistics, Biometrika, JASA, and JRSS-B. This was done by:
Ji, P., & Jin, J. (2016). Coauthorship and citation networks for statisticians. The Annals of Applied Statistics, 10(4), 1779-1812.
T... | What are the branches of statistics? | One way to approach the problem is look at citation and co-authorship networks in statistics journals, such as the Annals of Statistics, Biometrika, JASA, and JRSS-B. This was done by:
Ji, P., & Jin, | What are the branches of statistics?
One way to approach the problem is look at citation and co-authorship networks in statistics journals, such as the Annals of Statistics, Biometrika, JASA, and JRSS-B. This was done by:
Ji, P., & Jin, J. (2016). Coauthorship and citation networks for statisticians. The Annals of App... | What are the branches of statistics?
One way to approach the problem is look at citation and co-authorship networks in statistics journals, such as the Annals of Statistics, Biometrika, JASA, and JRSS-B. This was done by:
Ji, P., & Jin, |
8,987 | What are the branches of statistics? | I see many amazing answers, and I don't know how an humble self made classification may be received, but I don't know any all-comprensive book of all statistics to show the summary of, and I do think that, as @mkt brillantly commented, a classification of a study field can be useful. So, here is my shot:
descriptive s... | What are the branches of statistics? | I see many amazing answers, and I don't know how an humble self made classification may be received, but I don't know any all-comprensive book of all statistics to show the summary of, and I do think | What are the branches of statistics?
I see many amazing answers, and I don't know how an humble self made classification may be received, but I don't know any all-comprensive book of all statistics to show the summary of, and I do think that, as @mkt brillantly commented, a classification of a study field can be useful... | What are the branches of statistics?
I see many amazing answers, and I don't know how an humble self made classification may be received, but I don't know any all-comprensive book of all statistics to show the summary of, and I do think |
8,988 | What are the branches of statistics? | One way to organize this information is to find a good book and look at the table of contents. This is a paradox because you specifically asked about statistics, whereas most introductory graduate level texts on the topic are for statistics and probability theory together. A book I am reading on regression now has the ... | What are the branches of statistics? | One way to organize this information is to find a good book and look at the table of contents. This is a paradox because you specifically asked about statistics, whereas most introductory graduate lev | What are the branches of statistics?
One way to organize this information is to find a good book and look at the table of contents. This is a paradox because you specifically asked about statistics, whereas most introductory graduate level texts on the topic are for statistics and probability theory together. A book I ... | What are the branches of statistics?
One way to organize this information is to find a good book and look at the table of contents. This is a paradox because you specifically asked about statistics, whereas most introductory graduate lev |
8,989 | What are the myths associated with linear regression, data transformations? | There are three myths that bother me.
Predictor variables need to be normal.
The pooled/marginal distribution of $Y$ has to be normal.
Predictor variables should not be correlated, and if they are, some should be removed.
I believe that the first two come from misunderstanding the standard assumption about normali... | What are the myths associated with linear regression, data transformations? | There are three myths that bother me.
Predictor variables need to be normal.
The pooled/marginal distribution of $Y$ has to be normal.
Predictor variables should not be correlated, and if they are, | What are the myths associated with linear regression, data transformations?
There are three myths that bother me.
Predictor variables need to be normal.
The pooled/marginal distribution of $Y$ has to be normal.
Predictor variables should not be correlated, and if they are, some should be removed.
I believe that th... | What are the myths associated with linear regression, data transformations?
There are three myths that bother me.
Predictor variables need to be normal.
The pooled/marginal distribution of $Y$ has to be normal.
Predictor variables should not be correlated, and if they are, |
8,990 | What are the myths associated with linear regression, data transformations? | Myth
A linear regression model can only model linear relationships between the outcome $y$ and the explanatory variables.
Fact
Despite the name, linear regression models can easily accomodate nonlinear relationships using polynomials, fractional polynomials, splines and other methods. The term "linear" in linear regres... | What are the myths associated with linear regression, data transformations? | Myth
A linear regression model can only model linear relationships between the outcome $y$ and the explanatory variables.
Fact
Despite the name, linear regression models can easily accomodate nonlinea | What are the myths associated with linear regression, data transformations?
Myth
A linear regression model can only model linear relationships between the outcome $y$ and the explanatory variables.
Fact
Despite the name, linear regression models can easily accomodate nonlinear relationships using polynomials, fractiona... | What are the myths associated with linear regression, data transformations?
Myth
A linear regression model can only model linear relationships between the outcome $y$ and the explanatory variables.
Fact
Despite the name, linear regression models can easily accomodate nonlinea |
8,991 | What are the myths associated with linear regression, data transformations? | @Dave's answers are excellent. Here are some more myths.
The original scale/transformation for Y is one you should use in the model.
The central limit theorem means you don't have to worry about any of this if N is moderately large.
Trying different transformations for Y does not distort standard errors, p-values, or... | What are the myths associated with linear regression, data transformations? | @Dave's answers are excellent. Here are some more myths.
The original scale/transformation for Y is one you should use in the model.
The central limit theorem means you don't have to worry about any | What are the myths associated with linear regression, data transformations?
@Dave's answers are excellent. Here are some more myths.
The original scale/transformation for Y is one you should use in the model.
The central limit theorem means you don't have to worry about any of this if N is moderately large.
Trying di... | What are the myths associated with linear regression, data transformations?
@Dave's answers are excellent. Here are some more myths.
The original scale/transformation for Y is one you should use in the model.
The central limit theorem means you don't have to worry about any |
8,992 | What are the myths associated with linear regression, data transformations? | Myth: Variables that are not "significant" should be removed from a multiple regression.
See When should one include a variable in a regression despite it not being statistically significant? for a discussion. Then search our site for "model identification," "regularization," "Lasso," etc. | What are the myths associated with linear regression, data transformations? | Myth: Variables that are not "significant" should be removed from a multiple regression.
See When should one include a variable in a regression despite it not being statistically significant? for a di | What are the myths associated with linear regression, data transformations?
Myth: Variables that are not "significant" should be removed from a multiple regression.
See When should one include a variable in a regression despite it not being statistically significant? for a discussion. Then search our site for "model i... | What are the myths associated with linear regression, data transformations?
Myth: Variables that are not "significant" should be removed from a multiple regression.
See When should one include a variable in a regression despite it not being statistically significant? for a di |
8,993 | What are the myths associated with linear regression, data transformations? | Myth: You should always standardize (or somehow "normalize") variables for the purpose of fitting regression models.
Usually not: software will either do this automatically (under the hood, as it were) or uses algorithms that accommodate huge ranges of values among the variables without losing numerical precision.
When... | What are the myths associated with linear regression, data transformations? | Myth: You should always standardize (or somehow "normalize") variables for the purpose of fitting regression models.
Usually not: software will either do this automatically (under the hood, as it were | What are the myths associated with linear regression, data transformations?
Myth: You should always standardize (or somehow "normalize") variables for the purpose of fitting regression models.
Usually not: software will either do this automatically (under the hood, as it were) or uses algorithms that accommodate huge r... | What are the myths associated with linear regression, data transformations?
Myth: You should always standardize (or somehow "normalize") variables for the purpose of fitting regression models.
Usually not: software will either do this automatically (under the hood, as it were |
8,994 | What are the myths associated with linear regression, data transformations? | Myths:
The normality of residuals (and possibly other assumptions of the model) should be tested with a formal hypothesis test, such as the Shapiro-Wilk test.
A small $p$-value of such tests indicates that the model is invalid.
Facts:
Formal test of normality (and of other assumptions such as homoskedasticity) do no... | What are the myths associated with linear regression, data transformations? | Myths:
The normality of residuals (and possibly other assumptions of the model) should be tested with a formal hypothesis test, such as the Shapiro-Wilk test.
A small $p$-value of such tests indicate | What are the myths associated with linear regression, data transformations?
Myths:
The normality of residuals (and possibly other assumptions of the model) should be tested with a formal hypothesis test, such as the Shapiro-Wilk test.
A small $p$-value of such tests indicates that the model is invalid.
Facts:
Formal... | What are the myths associated with linear regression, data transformations?
Myths:
The normality of residuals (and possibly other assumptions of the model) should be tested with a formal hypothesis test, such as the Shapiro-Wilk test.
A small $p$-value of such tests indicate |
8,995 | What are the myths associated with linear regression, data transformations? | Where do these ideas come from?
Poor texts (correction: very poor texts) after treating descriptive statistics often include some more or less mangled version of an idea that (1) you ideally need normally distributed variables to do anything inferential, or else (2) you need non-parametric tests. Then they may or may n... | What are the myths associated with linear regression, data transformations? | Where do these ideas come from?
Poor texts (correction: very poor texts) after treating descriptive statistics often include some more or less mangled version of an idea that (1) you ideally need norm | What are the myths associated with linear regression, data transformations?
Where do these ideas come from?
Poor texts (correction: very poor texts) after treating descriptive statistics often include some more or less mangled version of an idea that (1) you ideally need normally distributed variables to do anything in... | What are the myths associated with linear regression, data transformations?
Where do these ideas come from?
Poor texts (correction: very poor texts) after treating descriptive statistics often include some more or less mangled version of an idea that (1) you ideally need norm |
8,996 | What are the myths associated with linear regression, data transformations? | "Also, how did such myths come about?"
One common assumption in regression is homoscedasticity (and a myth is that this is also necessary). Transformations are used to bring the data closer to this assumption.
The violation of the assumption doesn't make the fitting method bad, least squares regression is the best unb... | What are the myths associated with linear regression, data transformations? | "Also, how did such myths come about?"
One common assumption in regression is homoscedasticity (and a myth is that this is also necessary). Transformations are used to bring the data closer to this a | What are the myths associated with linear regression, data transformations?
"Also, how did such myths come about?"
One common assumption in regression is homoscedasticity (and a myth is that this is also necessary). Transformations are used to bring the data closer to this assumption.
The violation of the assumption d... | What are the myths associated with linear regression, data transformations?
"Also, how did such myths come about?"
One common assumption in regression is homoscedasticity (and a myth is that this is also necessary). Transformations are used to bring the data closer to this a |
8,997 | What are the myths associated with linear regression, data transformations? | Myth: The error/deviation of the observations needs to be normally distributed.
No, it doesn't.
It is not just about the distribution of the errors of the observations, Instead what often matters is the distribution of the error of the estimates.
These estimates are computed as a weighted sum of the observations $$\hat... | What are the myths associated with linear regression, data transformations? | Myth: The error/deviation of the observations needs to be normally distributed.
No, it doesn't.
It is not just about the distribution of the errors of the observations, Instead what often matters is t | What are the myths associated with linear regression, data transformations?
Myth: The error/deviation of the observations needs to be normally distributed.
No, it doesn't.
It is not just about the distribution of the errors of the observations, Instead what often matters is the distribution of the error of the estimate... | What are the myths associated with linear regression, data transformations?
Myth: The error/deviation of the observations needs to be normally distributed.
No, it doesn't.
It is not just about the distribution of the errors of the observations, Instead what often matters is t |
8,998 | What are the myths associated with linear regression, data transformations? | Myth: If the histogram of the residuals is nicely bell-shaped, and if the normal q-q plot of the residuals is very close to a straight line (and the sample size is reasonably large so that sampling error is minor), then the normality assumption is reasonable. | What are the myths associated with linear regression, data transformations? | Myth: If the histogram of the residuals is nicely bell-shaped, and if the normal q-q plot of the residuals is very close to a straight line (and the sample size is reasonably large so that sampling er | What are the myths associated with linear regression, data transformations?
Myth: If the histogram of the residuals is nicely bell-shaped, and if the normal q-q plot of the residuals is very close to a straight line (and the sample size is reasonably large so that sampling error is minor), then the normality assumption... | What are the myths associated with linear regression, data transformations?
Myth: If the histogram of the residuals is nicely bell-shaped, and if the normal q-q plot of the residuals is very close to a straight line (and the sample size is reasonably large so that sampling er |
8,999 | For convex problems, does gradient in Stochastic Gradient Descent (SGD) always point at the global extreme value? | They say an image is worth more than a thousand words. In the following example (courtesy of MS Paint, a handy tool for amateur and professional statisticians both) you can see a convex function surface and a point where the direction of the steepest descent clearly differs from the direction towards the optimum.
On a... | For convex problems, does gradient in Stochastic Gradient Descent (SGD) always point at the global e | They say an image is worth more than a thousand words. In the following example (courtesy of MS Paint, a handy tool for amateur and professional statisticians both) you can see a convex function surfa | For convex problems, does gradient in Stochastic Gradient Descent (SGD) always point at the global extreme value?
They say an image is worth more than a thousand words. In the following example (courtesy of MS Paint, a handy tool for amateur and professional statisticians both) you can see a convex function surface and... | For convex problems, does gradient in Stochastic Gradient Descent (SGD) always point at the global e
They say an image is worth more than a thousand words. In the following example (courtesy of MS Paint, a handy tool for amateur and professional statisticians both) you can see a convex function surfa |
9,000 | For convex problems, does gradient in Stochastic Gradient Descent (SGD) always point at the global extreme value? | Gradient descent methods use the slope of the surface.
This will not necessarily (or even most likely not) point directly
towards the extreme point.
An intuitive view is to imagine a path of descent that is a curved path. See for instance the examples below.
As an analogy: Imagine I blindfold you and put you somewhere... | For convex problems, does gradient in Stochastic Gradient Descent (SGD) always point at the global e | Gradient descent methods use the slope of the surface.
This will not necessarily (or even most likely not) point directly
towards the extreme point.
An intuitive view is to imagine a path of descent | For convex problems, does gradient in Stochastic Gradient Descent (SGD) always point at the global extreme value?
Gradient descent methods use the slope of the surface.
This will not necessarily (or even most likely not) point directly
towards the extreme point.
An intuitive view is to imagine a path of descent that i... | For convex problems, does gradient in Stochastic Gradient Descent (SGD) always point at the global e
Gradient descent methods use the slope of the surface.
This will not necessarily (or even most likely not) point directly
towards the extreme point.
An intuitive view is to imagine a path of descent |
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