idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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3,101 | How to simulate data that satisfy specific constraints such as having specific mean and standard deviation? | In general, to make your sample mean and variance exactly equal to a pre-specified value, you can appropriately shift and scale the variable. Specifically, if $X_1, X_2, ..., X_n$ is a sample, then the new variables
$$ Z_i = \sqrt{c_{1}} \left( \frac{X_i-\overline{X}}{s_{X}} \right) + c_{2} $$
where $\overline{X} = \... | How to simulate data that satisfy specific constraints such as having specific mean and standard dev | In general, to make your sample mean and variance exactly equal to a pre-specified value, you can appropriately shift and scale the variable. Specifically, if $X_1, X_2, ..., X_n$ is a sample, then th | How to simulate data that satisfy specific constraints such as having specific mean and standard deviation?
In general, to make your sample mean and variance exactly equal to a pre-specified value, you can appropriately shift and scale the variable. Specifically, if $X_1, X_2, ..., X_n$ is a sample, then the new variab... | How to simulate data that satisfy specific constraints such as having specific mean and standard dev
In general, to make your sample mean and variance exactly equal to a pre-specified value, you can appropriately shift and scale the variable. Specifically, if $X_1, X_2, ..., X_n$ is a sample, then th |
3,102 | How to simulate data that satisfy specific constraints such as having specific mean and standard deviation? | Regarding your request for papers, there is:
Chatterjee, S. & Firat, A. (2007). Generating data with identical statistics but dissimilar graphics: A follow up to the Anscombe dataset. The American Statistician, 61, 3, pp. 248-254.
This isn't quite what you're looking for, but might serve as grist for the mill. ... | How to simulate data that satisfy specific constraints such as having specific mean and standard dev | Regarding your request for papers, there is:
Chatterjee, S. & Firat, A. (2007). Generating data with identical statistics but dissimilar graphics: A follow up to the Anscombe dataset. The American | How to simulate data that satisfy specific constraints such as having specific mean and standard deviation?
Regarding your request for papers, there is:
Chatterjee, S. & Firat, A. (2007). Generating data with identical statistics but dissimilar graphics: A follow up to the Anscombe dataset. The American Statisticia... | How to simulate data that satisfy specific constraints such as having specific mean and standard dev
Regarding your request for papers, there is:
Chatterjee, S. & Firat, A. (2007). Generating data with identical statistics but dissimilar graphics: A follow up to the Anscombe dataset. The American |
3,103 | How to simulate data that satisfy specific constraints such as having specific mean and standard deviation? | Are there any programs in R that do this?
The Runuran R package contains many methods for generating random variates. It uses C libraries from the UNU.RAN (Universal Non-Uniform RAndom Number generator) project. My own knowledge of the field of random variate generation is limited, but the Runuran vignette provides a ... | How to simulate data that satisfy specific constraints such as having specific mean and standard dev | Are there any programs in R that do this?
The Runuran R package contains many methods for generating random variates. It uses C libraries from the UNU.RAN (Universal Non-Uniform RAndom Number generat | How to simulate data that satisfy specific constraints such as having specific mean and standard deviation?
Are there any programs in R that do this?
The Runuran R package contains many methods for generating random variates. It uses C libraries from the UNU.RAN (Universal Non-Uniform RAndom Number generator) project.... | How to simulate data that satisfy specific constraints such as having specific mean and standard dev
Are there any programs in R that do this?
The Runuran R package contains many methods for generating random variates. It uses C libraries from the UNU.RAN (Universal Non-Uniform RAndom Number generat |
3,104 | How to simulate data that satisfy specific constraints such as having specific mean and standard deviation? | The general technique is the 'Rejection Method', where you just reject results that don't meet your constraints. Unless you have some sort of guidance (like MCMC), then you could be generating a lot of cases (depending on your scenario) which are rejected!
Where you're looking for something like a mean and standard de... | How to simulate data that satisfy specific constraints such as having specific mean and standard dev | The general technique is the 'Rejection Method', where you just reject results that don't meet your constraints. Unless you have some sort of guidance (like MCMC), then you could be generating a lot | How to simulate data that satisfy specific constraints such as having specific mean and standard deviation?
The general technique is the 'Rejection Method', where you just reject results that don't meet your constraints. Unless you have some sort of guidance (like MCMC), then you could be generating a lot of cases (de... | How to simulate data that satisfy specific constraints such as having specific mean and standard dev
The general technique is the 'Rejection Method', where you just reject results that don't meet your constraints. Unless you have some sort of guidance (like MCMC), then you could be generating a lot |
3,105 | How to simulate data that satisfy specific constraints such as having specific mean and standard deviation? | It seems that there is an R package meeting your requirement published just yesterday!
simstudy By Keith Goldfeld
Simulates data sets in order to explore modeling techniques or better understand data generating processes. The user specifies a set of relationships between covariates, and generates data based on these s... | How to simulate data that satisfy specific constraints such as having specific mean and standard dev | It seems that there is an R package meeting your requirement published just yesterday!
simstudy By Keith Goldfeld
Simulates data sets in order to explore modeling techniques or better understand data | How to simulate data that satisfy specific constraints such as having specific mean and standard deviation?
It seems that there is an R package meeting your requirement published just yesterday!
simstudy By Keith Goldfeld
Simulates data sets in order to explore modeling techniques or better understand data generating ... | How to simulate data that satisfy specific constraints such as having specific mean and standard dev
It seems that there is an R package meeting your requirement published just yesterday!
simstudy By Keith Goldfeld
Simulates data sets in order to explore modeling techniques or better understand data |
3,106 | How to simulate data that satisfy specific constraints such as having specific mean and standard deviation? | This is an answer coming so late it is presumably meaningless, but there is always an MCMC solution to the question. Namely, to project the joint density of the sample$$\prod_{i=1}^n f(x_i)$$on the manifold defined by the constraints, for instance
$$\sum_{i=1}^n x_i=\mu_0\qquad\sum_{i=1}^n x_i^2=\sigma_0^2$$
The only i... | How to simulate data that satisfy specific constraints such as having specific mean and standard dev | This is an answer coming so late it is presumably meaningless, but there is always an MCMC solution to the question. Namely, to project the joint density of the sample$$\prod_{i=1}^n f(x_i)$$on the ma | How to simulate data that satisfy specific constraints such as having specific mean and standard deviation?
This is an answer coming so late it is presumably meaningless, but there is always an MCMC solution to the question. Namely, to project the joint density of the sample$$\prod_{i=1}^n f(x_i)$$on the manifold defin... | How to simulate data that satisfy specific constraints such as having specific mean and standard dev
This is an answer coming so late it is presumably meaningless, but there is always an MCMC solution to the question. Namely, to project the joint density of the sample$$\prod_{i=1}^n f(x_i)$$on the ma |
3,107 | How to simulate data that satisfy specific constraints such as having specific mean and standard deviation? | This answer considers another approach to the case where you want to force the variates to lie in a specified range and additionally dictate the mean and/or variance.
Restrict our attention to the unit interval $[0,1]$. Let's use a weighted mean for generality, so fix some weights $w_k\in[0,1]$ with $\sum_{k=1}^Nw_k=1$... | How to simulate data that satisfy specific constraints such as having specific mean and standard dev | This answer considers another approach to the case where you want to force the variates to lie in a specified range and additionally dictate the mean and/or variance.
Restrict our attention to the uni | How to simulate data that satisfy specific constraints such as having specific mean and standard deviation?
This answer considers another approach to the case where you want to force the variates to lie in a specified range and additionally dictate the mean and/or variance.
Restrict our attention to the unit interval $... | How to simulate data that satisfy specific constraints such as having specific mean and standard dev
This answer considers another approach to the case where you want to force the variates to lie in a specified range and additionally dictate the mean and/or variance.
Restrict our attention to the uni |
3,108 | How to simulate data that satisfy specific constraints such as having specific mean and standard deviation? | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
In my answer here, I listed three R packages for doing... | How to simulate data that satisfy specific constraints such as having specific mean and standard dev | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
| How to simulate data that satisfy specific constraints such as having specific mean and standard deviation?
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
... | How to simulate data that satisfy specific constraints such as having specific mean and standard dev
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
|
3,109 | Clustering with a distance matrix | There are a number of options.
k-medoids clustering
First, you could try partitioning around medoids (pam) instead of using k-means clustering. This one is more robust, and could give better results. Van der Laan reworked the algorithm. If you're going to implement it yourself, his article is worth a read.
There is a s... | Clustering with a distance matrix | There are a number of options.
k-medoids clustering
First, you could try partitioning around medoids (pam) instead of using k-means clustering. This one is more robust, and could give better results. | Clustering with a distance matrix
There are a number of options.
k-medoids clustering
First, you could try partitioning around medoids (pam) instead of using k-means clustering. This one is more robust, and could give better results. Van der Laan reworked the algorithm. If you're going to implement it yourself, his art... | Clustering with a distance matrix
There are a number of options.
k-medoids clustering
First, you could try partitioning around medoids (pam) instead of using k-means clustering. This one is more robust, and could give better results. |
3,110 | Clustering with a distance matrix | One way to highlight clusters on your distance matrix is by way of Multidimensional scaling. When projecting individuals (here what you call your nodes) in an 2D-space, it provides a comparable solution to PCA. This is unsupervised, so you won't be able to specify a priori the number of clusters, but I think it may hel... | Clustering with a distance matrix | One way to highlight clusters on your distance matrix is by way of Multidimensional scaling. When projecting individuals (here what you call your nodes) in an 2D-space, it provides a comparable soluti | Clustering with a distance matrix
One way to highlight clusters on your distance matrix is by way of Multidimensional scaling. When projecting individuals (here what you call your nodes) in an 2D-space, it provides a comparable solution to PCA. This is unsupervised, so you won't be able to specify a priori the number o... | Clustering with a distance matrix
One way to highlight clusters on your distance matrix is by way of Multidimensional scaling. When projecting individuals (here what you call your nodes) in an 2D-space, it provides a comparable soluti |
3,111 | Clustering with a distance matrix | Spectral Clustering [1] requires an affinity matrix, clustering being defined by the $K$ first eigenfunctions of the decomposition of
$$\textbf{L} = \textbf{D}^{-1/2} \textbf{A} \textbf{D}^{-1/2}$$
With $\textbf{A}$ being the affinity matrix of the data and $\textbf{D}$ being the diagonal matrix defined as (edit: sor... | Clustering with a distance matrix | Spectral Clustering [1] requires an affinity matrix, clustering being defined by the $K$ first eigenfunctions of the decomposition of
$$\textbf{L} = \textbf{D}^{-1/2} \textbf{A} \textbf{D}^{-1/2}$$
| Clustering with a distance matrix
Spectral Clustering [1] requires an affinity matrix, clustering being defined by the $K$ first eigenfunctions of the decomposition of
$$\textbf{L} = \textbf{D}^{-1/2} \textbf{A} \textbf{D}^{-1/2}$$
With $\textbf{A}$ being the affinity matrix of the data and $\textbf{D}$ being the dia... | Clustering with a distance matrix
Spectral Clustering [1] requires an affinity matrix, clustering being defined by the $K$ first eigenfunctions of the decomposition of
$$\textbf{L} = \textbf{D}^{-1/2} \textbf{A} \textbf{D}^{-1/2}$$
|
3,112 | Clustering with a distance matrix | What you're doing is trying to cluster together nodes of a graph, or network, that are close to each other.
There is a entire field of research dedicated to this problem which is sometimes called community detection in networks.
Looking at your problem from this point of view can probably clarify things.
You will find ... | Clustering with a distance matrix | What you're doing is trying to cluster together nodes of a graph, or network, that are close to each other.
There is a entire field of research dedicated to this problem which is sometimes called comm | Clustering with a distance matrix
What you're doing is trying to cluster together nodes of a graph, or network, that are close to each other.
There is a entire field of research dedicated to this problem which is sometimes called community detection in networks.
Looking at your problem from this point of view can proba... | Clustering with a distance matrix
What you're doing is trying to cluster together nodes of a graph, or network, that are close to each other.
There is a entire field of research dedicated to this problem which is sometimes called comm |
3,113 | Clustering with a distance matrix | Well, It is possible to perform K-means clustering on a given similarity matrix, at first you need to center the matrix and then take the eigenvalues of the matrix. The final and the most important step is multiplying the first two set of eigenvectors to the square root of diagonals of the eigenvalues to get the vector... | Clustering with a distance matrix | Well, It is possible to perform K-means clustering on a given similarity matrix, at first you need to center the matrix and then take the eigenvalues of the matrix. The final and the most important st | Clustering with a distance matrix
Well, It is possible to perform K-means clustering on a given similarity matrix, at first you need to center the matrix and then take the eigenvalues of the matrix. The final and the most important step is multiplying the first two set of eigenvectors to the square root of diagonals of... | Clustering with a distance matrix
Well, It is possible to perform K-means clustering on a given similarity matrix, at first you need to center the matrix and then take the eigenvalues of the matrix. The final and the most important st |
3,114 | Clustering with a distance matrix | Before you try running the clustering on the matrix you can try doing one of the factor analysis techniques, and keep just the most important variables to compute the distance matrix.
Another thing you can do is to try use fuzzy-methods which tend to work better (at least in my experience) in this kind of cases, try fi... | Clustering with a distance matrix | Before you try running the clustering on the matrix you can try doing one of the factor analysis techniques, and keep just the most important variables to compute the distance matrix.
Another thing yo | Clustering with a distance matrix
Before you try running the clustering on the matrix you can try doing one of the factor analysis techniques, and keep just the most important variables to compute the distance matrix.
Another thing you can do is to try use fuzzy-methods which tend to work better (at least in my experie... | Clustering with a distance matrix
Before you try running the clustering on the matrix you can try doing one of the factor analysis techniques, and keep just the most important variables to compute the distance matrix.
Another thing yo |
3,115 | Clustering with a distance matrix | Co-clustering is one of the answers I think. But Im not expert here. Co-clustring isn't newborn method, so you can find some algos in R, wiki shows that concepts in good way. Another method that isnt menthioned is graph partitioning (but I see that graph wouldnt be sparse,graph partitioning would be useful if your matr... | Clustering with a distance matrix | Co-clustering is one of the answers I think. But Im not expert here. Co-clustring isn't newborn method, so you can find some algos in R, wiki shows that concepts in good way. Another method that isnt | Clustering with a distance matrix
Co-clustering is one of the answers I think. But Im not expert here. Co-clustring isn't newborn method, so you can find some algos in R, wiki shows that concepts in good way. Another method that isnt menthioned is graph partitioning (but I see that graph wouldnt be sparse,graph partiti... | Clustering with a distance matrix
Co-clustering is one of the answers I think. But Im not expert here. Co-clustring isn't newborn method, so you can find some algos in R, wiki shows that concepts in good way. Another method that isnt |
3,116 | Clustering with a distance matrix | You can also use the Kruskal algorithm for finding minimum spanning trees, but ending as soon as you get the three clusters. I tried this way and it produces the clusters you mentioned: {ABCD}, {EFGH} and {IJKL}. | Clustering with a distance matrix | You can also use the Kruskal algorithm for finding minimum spanning trees, but ending as soon as you get the three clusters. I tried this way and it produces the clusters you mentioned: {ABCD}, {EFGH} | Clustering with a distance matrix
You can also use the Kruskal algorithm for finding minimum spanning trees, but ending as soon as you get the three clusters. I tried this way and it produces the clusters you mentioned: {ABCD}, {EFGH} and {IJKL}. | Clustering with a distance matrix
You can also use the Kruskal algorithm for finding minimum spanning trees, but ending as soon as you get the three clusters. I tried this way and it produces the clusters you mentioned: {ABCD}, {EFGH} |
3,117 | Why bother with the dual problem when fitting SVM? | Based on the lecture notes referenced in @user765195's answer (thanks!), the most apparent reasons seem to be:
Solving the primal problem, we obtain the optimal $w$, but know nothing about the $\alpha_i$. In order to classify a query point $x$ we need to explicitly compute the scalar product $w^Tx$, which may be expens... | Why bother with the dual problem when fitting SVM? | Based on the lecture notes referenced in @user765195's answer (thanks!), the most apparent reasons seem to be:
Solving the primal problem, we obtain the optimal $w$, but know nothing about the $\alpha | Why bother with the dual problem when fitting SVM?
Based on the lecture notes referenced in @user765195's answer (thanks!), the most apparent reasons seem to be:
Solving the primal problem, we obtain the optimal $w$, but know nothing about the $\alpha_i$. In order to classify a query point $x$ we need to explicitly com... | Why bother with the dual problem when fitting SVM?
Based on the lecture notes referenced in @user765195's answer (thanks!), the most apparent reasons seem to be:
Solving the primal problem, we obtain the optimal $w$, but know nothing about the $\alpha |
3,118 | Why bother with the dual problem when fitting SVM? | Read the second paragraph in page 13 and the discussion proceeding it in these notes:
Tengyu Ma and Andrew Ng. Part V: Kernel Methods. CS229 Lecture Notes. 2020 October 7. | Why bother with the dual problem when fitting SVM? | Read the second paragraph in page 13 and the discussion proceeding it in these notes:
Tengyu Ma and Andrew Ng. Part V: Kernel Methods. CS229 Lecture Notes. 2020 October 7. | Why bother with the dual problem when fitting SVM?
Read the second paragraph in page 13 and the discussion proceeding it in these notes:
Tengyu Ma and Andrew Ng. Part V: Kernel Methods. CS229 Lecture Notes. 2020 October 7. | Why bother with the dual problem when fitting SVM?
Read the second paragraph in page 13 and the discussion proceeding it in these notes:
Tengyu Ma and Andrew Ng. Part V: Kernel Methods. CS229 Lecture Notes. 2020 October 7. |
3,119 | Why bother with the dual problem when fitting SVM? | Here's one reason why the dual formulation is attractive from a numerical optimization point of view. You can find the details in the following paper:
Hsieh, C.-J., Chang, K.-W., Lin, C.-J., Keerthi, S. S., and Sundararajan, S., “A Dual coordinate descent method forlarge-scale linear SVM”, Proceedings of the 25th Inte... | Why bother with the dual problem when fitting SVM? | Here's one reason why the dual formulation is attractive from a numerical optimization point of view. You can find the details in the following paper:
Hsieh, C.-J., Chang, K.-W., Lin, C.-J., Keerthi, | Why bother with the dual problem when fitting SVM?
Here's one reason why the dual formulation is attractive from a numerical optimization point of view. You can find the details in the following paper:
Hsieh, C.-J., Chang, K.-W., Lin, C.-J., Keerthi, S. S., and Sundararajan, S., “A Dual coordinate descent method forla... | Why bother with the dual problem when fitting SVM?
Here's one reason why the dual formulation is attractive from a numerical optimization point of view. You can find the details in the following paper:
Hsieh, C.-J., Chang, K.-W., Lin, C.-J., Keerthi, |
3,120 | Why bother with the dual problem when fitting SVM? | In my opinion, the prediction time argument (that predictions from the dual solution are faster than from the primal solution) is nonsense.
A comparison makes only sense if you use a linear kernel in the first place, because otherwise you cannot make predictions with the primal (or at least it is not clear to me how th... | Why bother with the dual problem when fitting SVM? | In my opinion, the prediction time argument (that predictions from the dual solution are faster than from the primal solution) is nonsense.
A comparison makes only sense if you use a linear kernel in | Why bother with the dual problem when fitting SVM?
In my opinion, the prediction time argument (that predictions from the dual solution are faster than from the primal solution) is nonsense.
A comparison makes only sense if you use a linear kernel in the first place, because otherwise you cannot make predictions with t... | Why bother with the dual problem when fitting SVM?
In my opinion, the prediction time argument (that predictions from the dual solution are faster than from the primal solution) is nonsense.
A comparison makes only sense if you use a linear kernel in |
3,121 | Intuitive explanation of Fisher Information and Cramer-Rao bound | Here I explain why the asymptotic variance of the maximum likelihood estimator is the Cramer-Rao lower bound. Hopefully this will provide some insight as to the relevance of the Fisher information.
Statistical inference proceeds with the use of a likelihood function $\mathcal{L}(\theta)$ which you construct from the d... | Intuitive explanation of Fisher Information and Cramer-Rao bound | Here I explain why the asymptotic variance of the maximum likelihood estimator is the Cramer-Rao lower bound. Hopefully this will provide some insight as to the relevance of the Fisher information.
S | Intuitive explanation of Fisher Information and Cramer-Rao bound
Here I explain why the asymptotic variance of the maximum likelihood estimator is the Cramer-Rao lower bound. Hopefully this will provide some insight as to the relevance of the Fisher information.
Statistical inference proceeds with the use of a likelih... | Intuitive explanation of Fisher Information and Cramer-Rao bound
Here I explain why the asymptotic variance of the maximum likelihood estimator is the Cramer-Rao lower bound. Hopefully this will provide some insight as to the relevance of the Fisher information.
S |
3,122 | Intuitive explanation of Fisher Information and Cramer-Rao bound | One way that I understand the fisher information is by the following definition:
$$I(\theta)=\int_{\cal{X}} \frac{\partial^{2}f(x|\theta)}{\partial \theta^{2}}dx-\int_{\cal{X}} f(x|\theta)\frac{\partial^{2}}{\partial \theta^{2}}\log[f(x|\theta)]dx$$
The Fisher Information can be written this way whenever the density $f... | Intuitive explanation of Fisher Information and Cramer-Rao bound | One way that I understand the fisher information is by the following definition:
$$I(\theta)=\int_{\cal{X}} \frac{\partial^{2}f(x|\theta)}{\partial \theta^{2}}dx-\int_{\cal{X}} f(x|\theta)\frac{\parti | Intuitive explanation of Fisher Information and Cramer-Rao bound
One way that I understand the fisher information is by the following definition:
$$I(\theta)=\int_{\cal{X}} \frac{\partial^{2}f(x|\theta)}{\partial \theta^{2}}dx-\int_{\cal{X}} f(x|\theta)\frac{\partial^{2}}{\partial \theta^{2}}\log[f(x|\theta)]dx$$
The F... | Intuitive explanation of Fisher Information and Cramer-Rao bound
One way that I understand the fisher information is by the following definition:
$$I(\theta)=\int_{\cal{X}} \frac{\partial^{2}f(x|\theta)}{\partial \theta^{2}}dx-\int_{\cal{X}} f(x|\theta)\frac{\parti |
3,123 | Intuitive explanation of Fisher Information and Cramer-Rao bound | Although the explanations provided above are very interesting and I've enjoyed going through them, I feel that the nature of the Cramer-Rao Lower Bound was best explained to me from a geometric perspective. This intuition is a summary of the concept of concentration ellipses from Chapter 6 of Scharf's book on Statistic... | Intuitive explanation of Fisher Information and Cramer-Rao bound | Although the explanations provided above are very interesting and I've enjoyed going through them, I feel that the nature of the Cramer-Rao Lower Bound was best explained to me from a geometric perspe | Intuitive explanation of Fisher Information and Cramer-Rao bound
Although the explanations provided above are very interesting and I've enjoyed going through them, I feel that the nature of the Cramer-Rao Lower Bound was best explained to me from a geometric perspective. This intuition is a summary of the concept of co... | Intuitive explanation of Fisher Information and Cramer-Rao bound
Although the explanations provided above are very interesting and I've enjoyed going through them, I feel that the nature of the Cramer-Rao Lower Bound was best explained to me from a geometric perspe |
3,124 | Intuitive explanation of Fisher Information and Cramer-Rao bound | This is the most intuitive article that I have seen so far:
The Cramér-Rao Lower Bound on Variance: Adam and Eve’s “Uncertainty Principle” by
Michael R. Powers, Journal of Risk Finance, Vol. 7, No. 3, 2006
The bound is explained by an analogy of Adam and Eve in the Garden of Eden tossing a coin to see who gets to eat ... | Intuitive explanation of Fisher Information and Cramer-Rao bound | This is the most intuitive article that I have seen so far:
The Cramér-Rao Lower Bound on Variance: Adam and Eve’s “Uncertainty Principle” by
Michael R. Powers, Journal of Risk Finance, Vol. 7, No. 3 | Intuitive explanation of Fisher Information and Cramer-Rao bound
This is the most intuitive article that I have seen so far:
The Cramér-Rao Lower Bound on Variance: Adam and Eve’s “Uncertainty Principle” by
Michael R. Powers, Journal of Risk Finance, Vol. 7, No. 3, 2006
The bound is explained by an analogy of Adam and... | Intuitive explanation of Fisher Information and Cramer-Rao bound
This is the most intuitive article that I have seen so far:
The Cramér-Rao Lower Bound on Variance: Adam and Eve’s “Uncertainty Principle” by
Michael R. Powers, Journal of Risk Finance, Vol. 7, No. 3 |
3,125 | Is this the solution to the p-value problem? | I've been advocating for my own new approach to statistical decision making called RADD: Roll A Damn Die. It also addresses all the key points.
1) RADD can indicate how compatible the data are with a specified statistical model.
If you roll a higher number, clearly the evidence is more in favor of your model! An ext... | Is this the solution to the p-value problem? | I've been advocating for my own new approach to statistical decision making called RADD: Roll A Damn Die. It also addresses all the key points.
1) RADD can indicate how compatible the data are with a | Is this the solution to the p-value problem?
I've been advocating for my own new approach to statistical decision making called RADD: Roll A Damn Die. It also addresses all the key points.
1) RADD can indicate how compatible the data are with a specified statistical model.
If you roll a higher number, clearly the evi... | Is this the solution to the p-value problem?
I've been advocating for my own new approach to statistical decision making called RADD: Roll A Damn Die. It also addresses all the key points.
1) RADD can indicate how compatible the data are with a |
3,126 | Is this the solution to the p-value problem? | I must say from my experience that in business reality STOP is the default decision making criteria, preferred to $p$-values and other frequentist, or Bayesian methods. From business perspective STOP provides simple and definitive answers what makes it more reliable than uncertain "probabilistic" methods. Moreover, in ... | Is this the solution to the p-value problem? | I must say from my experience that in business reality STOP is the default decision making criteria, preferred to $p$-values and other frequentist, or Bayesian methods. From business perspective STOP | Is this the solution to the p-value problem?
I must say from my experience that in business reality STOP is the default decision making criteria, preferred to $p$-values and other frequentist, or Bayesian methods. From business perspective STOP provides simple and definitive answers what makes it more reliable than unc... | Is this the solution to the p-value problem?
I must say from my experience that in business reality STOP is the default decision making criteria, preferred to $p$-values and other frequentist, or Bayesian methods. From business perspective STOP |
3,127 | Is this the solution to the p-value problem? | This fine adjunct to the p-value debate, interesting but also somewhat stale in my opinion, reminds me of a unique paper published some years ago in the Christmas issue of the British Medical Journal (BMJ), which every Christmas publishes real yet funny research articles.
In particular, this work by Isaacs and Fitzgera... | Is this the solution to the p-value problem? | This fine adjunct to the p-value debate, interesting but also somewhat stale in my opinion, reminds me of a unique paper published some years ago in the Christmas issue of the British Medical Journal | Is this the solution to the p-value problem?
This fine adjunct to the p-value debate, interesting but also somewhat stale in my opinion, reminds me of a unique paper published some years ago in the Christmas issue of the British Medical Journal (BMJ), which every Christmas publishes real yet funny research articles.
In... | Is this the solution to the p-value problem?
This fine adjunct to the p-value debate, interesting but also somewhat stale in my opinion, reminds me of a unique paper published some years ago in the Christmas issue of the British Medical Journal |
3,128 | What are some valuable Statistical Analysis open source projects? | The R-project
http://www.r-project.org/
R is valuable and significant because it was the first widely-accepted Open-Source alternative to big-box packages. It's mature, well supported, and a standard within many scientific communities.
Some reasons why it is useful and valuable
There are some nice tutorials here. | What are some valuable Statistical Analysis open source projects? | The R-project
http://www.r-project.org/
R is valuable and significant because it was the first widely-accepted Open-Source alternative to big-box packages. It's mature, well supported, and a standard | What are some valuable Statistical Analysis open source projects?
The R-project
http://www.r-project.org/
R is valuable and significant because it was the first widely-accepted Open-Source alternative to big-box packages. It's mature, well supported, and a standard within many scientific communities.
Some reasons why... | What are some valuable Statistical Analysis open source projects?
The R-project
http://www.r-project.org/
R is valuable and significant because it was the first widely-accepted Open-Source alternative to big-box packages. It's mature, well supported, and a standard |
3,129 | What are some valuable Statistical Analysis open source projects? | For doing a variety of MCMC tasks in Python, there's PyMC, which I've gotten quite a bit of use out of. I haven't run across anything that I can do in BUGS that I can't do in PyMC, and the way you specify models and bring in data seems to be a lot more intuitive to me. | What are some valuable Statistical Analysis open source projects? | For doing a variety of MCMC tasks in Python, there's PyMC, which I've gotten quite a bit of use out of. I haven't run across anything that I can do in BUGS that I can't do in PyMC, and the way you sp | What are some valuable Statistical Analysis open source projects?
For doing a variety of MCMC tasks in Python, there's PyMC, which I've gotten quite a bit of use out of. I haven't run across anything that I can do in BUGS that I can't do in PyMC, and the way you specify models and bring in data seems to be a lot more ... | What are some valuable Statistical Analysis open source projects?
For doing a variety of MCMC tasks in Python, there's PyMC, which I've gotten quite a bit of use out of. I haven't run across anything that I can do in BUGS that I can't do in PyMC, and the way you sp |
3,130 | What are some valuable Statistical Analysis open source projects? | This may get downvoted to oblivion, but I happily used the Matlab clone Octave for many years. There are fairly good libraries in octave forge for generation of random variables from different distributions, statistical tests, etc, though clearly it is dwarfed by R. One possible advantage over R is that Matlab/octave i... | What are some valuable Statistical Analysis open source projects? | This may get downvoted to oblivion, but I happily used the Matlab clone Octave for many years. There are fairly good libraries in octave forge for generation of random variables from different distrib | What are some valuable Statistical Analysis open source projects?
This may get downvoted to oblivion, but I happily used the Matlab clone Octave for many years. There are fairly good libraries in octave forge for generation of random variables from different distributions, statistical tests, etc, though clearly it is d... | What are some valuable Statistical Analysis open source projects?
This may get downvoted to oblivion, but I happily used the Matlab clone Octave for many years. There are fairly good libraries in octave forge for generation of random variables from different distrib |
3,131 | What are some valuable Statistical Analysis open source projects? | Two projects spring to mind:
Bugs - taking (some of) the pain out of Bayesian statistics. It allows the user to focus more on the model and a bit less on MCMC.
Bioconductor - perhaps the most popular statistical tool in Bioinformatics. I know it's a R repository, but there are a large number of people who want to lear... | What are some valuable Statistical Analysis open source projects? | Two projects spring to mind:
Bugs - taking (some of) the pain out of Bayesian statistics. It allows the user to focus more on the model and a bit less on MCMC.
Bioconductor - perhaps the most popular | What are some valuable Statistical Analysis open source projects?
Two projects spring to mind:
Bugs - taking (some of) the pain out of Bayesian statistics. It allows the user to focus more on the model and a bit less on MCMC.
Bioconductor - perhaps the most popular statistical tool in Bioinformatics. I know it's a R r... | What are some valuable Statistical Analysis open source projects?
Two projects spring to mind:
Bugs - taking (some of) the pain out of Bayesian statistics. It allows the user to focus more on the model and a bit less on MCMC.
Bioconductor - perhaps the most popular |
3,132 | What are some valuable Statistical Analysis open source projects? | Incanter is a Clojure-based, R-like platform (environment + libraries) for statistical computing and graphics. | What are some valuable Statistical Analysis open source projects? | Incanter is a Clojure-based, R-like platform (environment + libraries) for statistical computing and graphics. | What are some valuable Statistical Analysis open source projects?
Incanter is a Clojure-based, R-like platform (environment + libraries) for statistical computing and graphics. | What are some valuable Statistical Analysis open source projects?
Incanter is a Clojure-based, R-like platform (environment + libraries) for statistical computing and graphics. |
3,133 | What are some valuable Statistical Analysis open source projects? | Weka for data mining - contains many classification and clustering algorithms in Java. | What are some valuable Statistical Analysis open source projects? | Weka for data mining - contains many classification and clustering algorithms in Java. | What are some valuable Statistical Analysis open source projects?
Weka for data mining - contains many classification and clustering algorithms in Java. | What are some valuable Statistical Analysis open source projects?
Weka for data mining - contains many classification and clustering algorithms in Java. |
3,134 | What are some valuable Statistical Analysis open source projects? | ggobi "is an open source visualization program for exploring high-dimensional data."
Mat Kelcey has a good 5 minute intro to ggobi. | What are some valuable Statistical Analysis open source projects? | ggobi "is an open source visualization program for exploring high-dimensional data."
Mat Kelcey has a good 5 minute intro to ggobi. | What are some valuable Statistical Analysis open source projects?
ggobi "is an open source visualization program for exploring high-dimensional data."
Mat Kelcey has a good 5 minute intro to ggobi. | What are some valuable Statistical Analysis open source projects?
ggobi "is an open source visualization program for exploring high-dimensional data."
Mat Kelcey has a good 5 minute intro to ggobi. |
3,135 | What are some valuable Statistical Analysis open source projects? | There are also those projects initiated by the FSF or redistributed under GNU General Public License, like:
PSPP, which aims to be a free alternative to SPSS
GRETL, mostly dedicated to regression and econometrics
There is even applications that were released just as a companion software for a textbook, like JMulTi, b... | What are some valuable Statistical Analysis open source projects? | There are also those projects initiated by the FSF or redistributed under GNU General Public License, like:
PSPP, which aims to be a free alternative to SPSS
GRETL, mostly dedicated to regression and | What are some valuable Statistical Analysis open source projects?
There are also those projects initiated by the FSF or redistributed under GNU General Public License, like:
PSPP, which aims to be a free alternative to SPSS
GRETL, mostly dedicated to regression and econometrics
There is even applications that were re... | What are some valuable Statistical Analysis open source projects?
There are also those projects initiated by the FSF or redistributed under GNU General Public License, like:
PSPP, which aims to be a free alternative to SPSS
GRETL, mostly dedicated to regression and |
3,136 | What are some valuable Statistical Analysis open source projects? | RapidMiner for data and text mining | What are some valuable Statistical Analysis open source projects? | RapidMiner for data and text mining | What are some valuable Statistical Analysis open source projects?
RapidMiner for data and text mining | What are some valuable Statistical Analysis open source projects?
RapidMiner for data and text mining |
3,137 | What are some valuable Statistical Analysis open source projects? | First of all let me tell you that in my opinion the best tool of all by far is R, which has tons of libraries and utilities I am not going to enumerate here.
Let me expand the discussion about weka
There is a library for R, which is called RWeka, which you can easily install in R, and use many of the functionalities fr... | What are some valuable Statistical Analysis open source projects? | First of all let me tell you that in my opinion the best tool of all by far is R, which has tons of libraries and utilities I am not going to enumerate here.
Let me expand the discussion about weka
Th | What are some valuable Statistical Analysis open source projects?
First of all let me tell you that in my opinion the best tool of all by far is R, which has tons of libraries and utilities I am not going to enumerate here.
Let me expand the discussion about weka
There is a library for R, which is called RWeka, which y... | What are some valuable Statistical Analysis open source projects?
First of all let me tell you that in my opinion the best tool of all by far is R, which has tons of libraries and utilities I am not going to enumerate here.
Let me expand the discussion about weka
Th |
3,138 | What are some valuable Statistical Analysis open source projects? | Colin Gillespie mentioned BUGS, but a better option for Gibbs Sampling, etc, is JAGS.
If all you want to do is ARIMA, you can't beat X12-ARIMA, which is a gold-standard in the field and open source. It doesn't do real graphs (I use R to do that), but the diagnostics are a lesson on their own.
Venturing a bit farther af... | What are some valuable Statistical Analysis open source projects? | Colin Gillespie mentioned BUGS, but a better option for Gibbs Sampling, etc, is JAGS.
If all you want to do is ARIMA, you can't beat X12-ARIMA, which is a gold-standard in the field and open source. I | What are some valuable Statistical Analysis open source projects?
Colin Gillespie mentioned BUGS, but a better option for Gibbs Sampling, etc, is JAGS.
If all you want to do is ARIMA, you can't beat X12-ARIMA, which is a gold-standard in the field and open source. It doesn't do real graphs (I use R to do that), but the... | What are some valuable Statistical Analysis open source projects?
Colin Gillespie mentioned BUGS, but a better option for Gibbs Sampling, etc, is JAGS.
If all you want to do is ARIMA, you can't beat X12-ARIMA, which is a gold-standard in the field and open source. I |
3,139 | What are some valuable Statistical Analysis open source projects? | I really enjoy working with RooFit for easy proper fitting of signal and background distributions and TMVA for quick principal component analyses and modelling of multivariate problems with some standard tools (like genetic algorithms and neural networks, also does BDTs). They are both part of the ROOT C++ libraries wh... | What are some valuable Statistical Analysis open source projects? | I really enjoy working with RooFit for easy proper fitting of signal and background distributions and TMVA for quick principal component analyses and modelling of multivariate problems with some stand | What are some valuable Statistical Analysis open source projects?
I really enjoy working with RooFit for easy proper fitting of signal and background distributions and TMVA for quick principal component analyses and modelling of multivariate problems with some standard tools (like genetic algorithms and neural networks... | What are some valuable Statistical Analysis open source projects?
I really enjoy working with RooFit for easy proper fitting of signal and background distributions and TMVA for quick principal component analyses and modelling of multivariate problems with some stand |
3,140 | What are some valuable Statistical Analysis open source projects? | GSL for those of you who wish to program in C / C++ is a valuable resource as it provides several routines for random generators, linear algebra etc. While GSL is primarily available for Linux there are also ports for Windows (See: this and this). | What are some valuable Statistical Analysis open source projects? | GSL for those of you who wish to program in C / C++ is a valuable resource as it provides several routines for random generators, linear algebra etc. While GSL is primarily available for Linux there a | What are some valuable Statistical Analysis open source projects?
GSL for those of you who wish to program in C / C++ is a valuable resource as it provides several routines for random generators, linear algebra etc. While GSL is primarily available for Linux there are also ports for Windows (See: this and this). | What are some valuable Statistical Analysis open source projects?
GSL for those of you who wish to program in C / C++ is a valuable resource as it provides several routines for random generators, linear algebra etc. While GSL is primarily available for Linux there a |
3,141 | What are some valuable Statistical Analysis open source projects? | Few more on top of already mentioned:
KNIME together with R, Python and Weka integration extensions for data mining
Mondrian for quick EDA
And from spatial perspective:
GeoDa for spatial EDA and clustering of areal data
SaTScan for clustering of point data | What are some valuable Statistical Analysis open source projects? | Few more on top of already mentioned:
KNIME together with R, Python and Weka integration extensions for data mining
Mondrian for quick EDA
And from spatial perspective:
GeoDa for spatial EDA and cl | What are some valuable Statistical Analysis open source projects?
Few more on top of already mentioned:
KNIME together with R, Python and Weka integration extensions for data mining
Mondrian for quick EDA
And from spatial perspective:
GeoDa for spatial EDA and clustering of areal data
SaTScan for clustering of point... | What are some valuable Statistical Analysis open source projects?
Few more on top of already mentioned:
KNIME together with R, Python and Weka integration extensions for data mining
Mondrian for quick EDA
And from spatial perspective:
GeoDa for spatial EDA and cl |
3,142 | What are some valuable Statistical Analysis open source projects? | I second that Jay. Why is R valuable? Here's a short list of reasons. http://www.inside-r.org/why-use-r. Also check out ggplot2 - a very nice graphics package for R. Some nice tutorials here. | What are some valuable Statistical Analysis open source projects? | I second that Jay. Why is R valuable? Here's a short list of reasons. http://www.inside-r.org/why-use-r. Also check out ggplot2 - a very nice graphics package for R. Some nice tutorials here. | What are some valuable Statistical Analysis open source projects?
I second that Jay. Why is R valuable? Here's a short list of reasons. http://www.inside-r.org/why-use-r. Also check out ggplot2 - a very nice graphics package for R. Some nice tutorials here. | What are some valuable Statistical Analysis open source projects?
I second that Jay. Why is R valuable? Here's a short list of reasons. http://www.inside-r.org/why-use-r. Also check out ggplot2 - a very nice graphics package for R. Some nice tutorials here. |
3,143 | What are some valuable Statistical Analysis open source projects? | This falls on the outer limits of 'statistical analysis', but Eureqa is a very user friendly program for data-mining nonlinear relationships in data via genetic programming. Eureqa is not as general purpose, but it does what it does fairly well, and the GUI is quite intuitive. It can also take advantage of the availabl... | What are some valuable Statistical Analysis open source projects? | This falls on the outer limits of 'statistical analysis', but Eureqa is a very user friendly program for data-mining nonlinear relationships in data via genetic programming. Eureqa is not as general p | What are some valuable Statistical Analysis open source projects?
This falls on the outer limits of 'statistical analysis', but Eureqa is a very user friendly program for data-mining nonlinear relationships in data via genetic programming. Eureqa is not as general purpose, but it does what it does fairly well, and the ... | What are some valuable Statistical Analysis open source projects?
This falls on the outer limits of 'statistical analysis', but Eureqa is a very user friendly program for data-mining nonlinear relationships in data via genetic programming. Eureqa is not as general p |
3,144 | What are some valuable Statistical Analysis open source projects? | Symbolic mathematics software can be a good support for statistics, too. Here are a few GPL ones I use from time to time:
sympy is python-based and very small, but can still do a lot: derivatives, integrals, symbolic sums, combinatorics, series expansions, tensor manipulations, etc. There is an R package to call it ... | What are some valuable Statistical Analysis open source projects? | Symbolic mathematics software can be a good support for statistics, too. Here are a few GPL ones I use from time to time:
sympy is python-based and very small, but can still do a lot: derivatives, | What are some valuable Statistical Analysis open source projects?
Symbolic mathematics software can be a good support for statistics, too. Here are a few GPL ones I use from time to time:
sympy is python-based and very small, but can still do a lot: derivatives, integrals, symbolic sums, combinatorics, series expans... | What are some valuable Statistical Analysis open source projects?
Symbolic mathematics software can be a good support for statistics, too. Here are a few GPL ones I use from time to time:
sympy is python-based and very small, but can still do a lot: derivatives, |
3,145 | What are some valuable Statistical Analysis open source projects? | Meta.Numerics is a .NET library with good support for statistical analysis.
Unlike R (an S clone) and Octave (a Matlab clone), it does not have a "front end". It is more like GSL, in that it is a library that you link to when you are writing your own application that needs to do statistical analysis. C# and Visual Basi... | What are some valuable Statistical Analysis open source projects? | Meta.Numerics is a .NET library with good support for statistical analysis.
Unlike R (an S clone) and Octave (a Matlab clone), it does not have a "front end". It is more like GSL, in that it is a libr | What are some valuable Statistical Analysis open source projects?
Meta.Numerics is a .NET library with good support for statistical analysis.
Unlike R (an S clone) and Octave (a Matlab clone), it does not have a "front end". It is more like GSL, in that it is a library that you link to when you are writing your own app... | What are some valuable Statistical Analysis open source projects?
Meta.Numerics is a .NET library with good support for statistical analysis.
Unlike R (an S clone) and Octave (a Matlab clone), it does not have a "front end". It is more like GSL, in that it is a libr |
3,146 | What are some valuable Statistical Analysis open source projects? | clusterPy for analytical
regionalization or geospatial
clustering
PySal for spatial data analysis. | What are some valuable Statistical Analysis open source projects? | clusterPy for analytical
regionalization or geospatial
clustering
PySal for spatial data analysis. | What are some valuable Statistical Analysis open source projects?
clusterPy for analytical
regionalization or geospatial
clustering
PySal for spatial data analysis. | What are some valuable Statistical Analysis open source projects?
clusterPy for analytical
regionalization or geospatial
clustering
PySal for spatial data analysis. |
3,147 | Removing duplicated rows data frame in R [closed] | unique() indeed answers your question, but another related and interesting function to achieve the same end is duplicated().
It gives you the possibility to look up which rows are duplicated.
a <- c(rep("A", 3), rep("B", 3), rep("C",2))
b <- c(1,1,2,4,1,1,2,2)
df <-data.frame(a,b)
duplicated(df)
[1] FALSE TRUE FALSE ... | Removing duplicated rows data frame in R [closed] | unique() indeed answers your question, but another related and interesting function to achieve the same end is duplicated().
It gives you the possibility to look up which rows are duplicated.
a <- c(r | Removing duplicated rows data frame in R [closed]
unique() indeed answers your question, but another related and interesting function to achieve the same end is duplicated().
It gives you the possibility to look up which rows are duplicated.
a <- c(rep("A", 3), rep("B", 3), rep("C",2))
b <- c(1,1,2,4,1,1,2,2)
df <-data... | Removing duplicated rows data frame in R [closed]
unique() indeed answers your question, but another related and interesting function to achieve the same end is duplicated().
It gives you the possibility to look up which rows are duplicated.
a <- c(r |
3,148 | Removing duplicated rows data frame in R [closed] | You are looking for unique().
a <- c(rep("A", 3), rep("B", 3), rep("C",2))
b <- c(1,1,2,4,1,1,2,2)
df <-data.frame(a,b)
unique(df)
> unique(df)
a b
1 A 1
3 A 2
4 B 4
5 B 1
7 C 2 | Removing duplicated rows data frame in R [closed] | You are looking for unique().
a <- c(rep("A", 3), rep("B", 3), rep("C",2))
b <- c(1,1,2,4,1,1,2,2)
df <-data.frame(a,b)
unique(df)
> unique(df)
a b
1 A 1
3 A 2
4 B 4
5 B 1
7 C 2 | Removing duplicated rows data frame in R [closed]
You are looking for unique().
a <- c(rep("A", 3), rep("B", 3), rep("C",2))
b <- c(1,1,2,4,1,1,2,2)
df <-data.frame(a,b)
unique(df)
> unique(df)
a b
1 A 1
3 A 2
4 B 4
5 B 1
7 C 2 | Removing duplicated rows data frame in R [closed]
You are looking for unique().
a <- c(rep("A", 3), rep("B", 3), rep("C",2))
b <- c(1,1,2,4,1,1,2,2)
df <-data.frame(a,b)
unique(df)
> unique(df)
a b
1 A 1
3 A 2
4 B 4
5 B 1
7 C 2 |
3,149 | Why does ridge estimate become better than OLS by adding a constant to the diagonal? | In an unpenalized regression, you can often get a ridge* in parameter space, where many different values along the ridge all do as well or nearly as well on the least squares criterion.
* (at least, it's a ridge in the likelihood function -- they're actually valleys$ in the RSS criterion, but I'll continue to call it... | Why does ridge estimate become better than OLS by adding a constant to the diagonal? | In an unpenalized regression, you can often get a ridge* in parameter space, where many different values along the ridge all do as well or nearly as well on the least squares criterion.
* (at least, | Why does ridge estimate become better than OLS by adding a constant to the diagonal?
In an unpenalized regression, you can often get a ridge* in parameter space, where many different values along the ridge all do as well or nearly as well on the least squares criterion.
* (at least, it's a ridge in the likelihood fun... | Why does ridge estimate become better than OLS by adding a constant to the diagonal?
In an unpenalized regression, you can often get a ridge* in parameter space, where many different values along the ridge all do as well or nearly as well on the least squares criterion.
* (at least, |
3,150 | Why does ridge estimate become better than OLS by adding a constant to the diagonal? | +1 on Glen_b's illustration and the stats comments on the Ridge estimator. I would just like to add a purely mathematical (linear algebra) pov on Ridge regression which answers OPs questions 1) and 2).
First note that $X'X$ is a $p \times p$ symmetric positive semidefinite matrix - $n$ times the sample covariance mat... | Why does ridge estimate become better than OLS by adding a constant to the diagonal? | +1 on Glen_b's illustration and the stats comments on the Ridge estimator. I would just like to add a purely mathematical (linear algebra) pov on Ridge regression which answers OPs questions 1) and 2 | Why does ridge estimate become better than OLS by adding a constant to the diagonal?
+1 on Glen_b's illustration and the stats comments on the Ridge estimator. I would just like to add a purely mathematical (linear algebra) pov on Ridge regression which answers OPs questions 1) and 2).
First note that $X'X$ is a $p \t... | Why does ridge estimate become better than OLS by adding a constant to the diagonal?
+1 on Glen_b's illustration and the stats comments on the Ridge estimator. I would just like to add a purely mathematical (linear algebra) pov on Ridge regression which answers OPs questions 1) and 2 |
3,151 | Why does ridge estimate become better than OLS by adding a constant to the diagonal? | @Glen_b's demonstration is wonderful. I would just add that aside from the exact cause of the problem and description about how quadratic penalized regression works, there is the bottom line that penalization has the net effect of shrinking the coefficients other than the intercept towards zero. This provides a direc... | Why does ridge estimate become better than OLS by adding a constant to the diagonal? | @Glen_b's demonstration is wonderful. I would just add that aside from the exact cause of the problem and description about how quadratic penalized regression works, there is the bottom line that pen | Why does ridge estimate become better than OLS by adding a constant to the diagonal?
@Glen_b's demonstration is wonderful. I would just add that aside from the exact cause of the problem and description about how quadratic penalized regression works, there is the bottom line that penalization has the net effect of shr... | Why does ridge estimate become better than OLS by adding a constant to the diagonal?
@Glen_b's demonstration is wonderful. I would just add that aside from the exact cause of the problem and description about how quadratic penalized regression works, there is the bottom line that pen |
3,152 | What is a "saturated" model? | A saturated model is one in which there are as many estimated parameters as data points. By definition, this will lead to a perfect fit, but will be of little use statistically, as you have no data left to estimate variance.
For example, if you have 6 data points and fit a 5th-order polynomial to the data, you would ha... | What is a "saturated" model? | A saturated model is one in which there are as many estimated parameters as data points. By definition, this will lead to a perfect fit, but will be of little use statistically, as you have no data le | What is a "saturated" model?
A saturated model is one in which there are as many estimated parameters as data points. By definition, this will lead to a perfect fit, but will be of little use statistically, as you have no data left to estimate variance.
For example, if you have 6 data points and fit a 5th-order polynom... | What is a "saturated" model?
A saturated model is one in which there are as many estimated parameters as data points. By definition, this will lead to a perfect fit, but will be of little use statistically, as you have no data le |
3,153 | What is a "saturated" model? | A saturated model is a model that is overparameterized to the point that it is basically just interpolating the data. In some settings, such as image compression and reconstruction, this isn't necessarily a bad thing, but if you're trying to build a predictive model it's very problematic.
In short, saturated models le... | What is a "saturated" model? | A saturated model is a model that is overparameterized to the point that it is basically just interpolating the data. In some settings, such as image compression and reconstruction, this isn't necess | What is a "saturated" model?
A saturated model is a model that is overparameterized to the point that it is basically just interpolating the data. In some settings, such as image compression and reconstruction, this isn't necessarily a bad thing, but if you're trying to build a predictive model it's very problematic.
... | What is a "saturated" model?
A saturated model is a model that is overparameterized to the point that it is basically just interpolating the data. In some settings, such as image compression and reconstruction, this isn't necess |
3,154 | What is a "saturated" model? | As everybody else said before, it means that you have as much parameters have you have data points. So, no goodness of fit testing. But this does not mean that "by definition", the model can perfectly fit any data point. I can tell you by personal experience of working with some saturated models that could not predict ... | What is a "saturated" model? | As everybody else said before, it means that you have as much parameters have you have data points. So, no goodness of fit testing. But this does not mean that "by definition", the model can perfectly | What is a "saturated" model?
As everybody else said before, it means that you have as much parameters have you have data points. So, no goodness of fit testing. But this does not mean that "by definition", the model can perfectly fit any data point. I can tell you by personal experience of working with some saturated m... | What is a "saturated" model?
As everybody else said before, it means that you have as much parameters have you have data points. So, no goodness of fit testing. But this does not mean that "by definition", the model can perfectly |
3,155 | What is a "saturated" model? | A model is saturated if and only if it has as many parameters as it has data points (observations). Or put otherwise, in non-saturated models the degrees of freedom are bigger than zero.
This basically means that this model is useless, because it does not describe the data more parsimoniously than the raw data does (an... | What is a "saturated" model? | A model is saturated if and only if it has as many parameters as it has data points (observations). Or put otherwise, in non-saturated models the degrees of freedom are bigger than zero.
This basicall | What is a "saturated" model?
A model is saturated if and only if it has as many parameters as it has data points (observations). Or put otherwise, in non-saturated models the degrees of freedom are bigger than zero.
This basically means that this model is useless, because it does not describe the data more parsimonious... | What is a "saturated" model?
A model is saturated if and only if it has as many parameters as it has data points (observations). Or put otherwise, in non-saturated models the degrees of freedom are bigger than zero.
This basicall |
3,156 | What is a "saturated" model? | In regression, a common use of the term "saturated model" is as follows. A saturated model has as many independent variables as there are unique levels (combinations) of the covariates. Of course this is only possible with categorical covariates. So if you have two dummy variables X1 and X2, a regression is saturated i... | What is a "saturated" model? | In regression, a common use of the term "saturated model" is as follows. A saturated model has as many independent variables as there are unique levels (combinations) of the covariates. Of course this | What is a "saturated" model?
In regression, a common use of the term "saturated model" is as follows. A saturated model has as many independent variables as there are unique levels (combinations) of the covariates. Of course this is only possible with categorical covariates. So if you have two dummy variables X1 and X2... | What is a "saturated" model?
In regression, a common use of the term "saturated model" is as follows. A saturated model has as many independent variables as there are unique levels (combinations) of the covariates. Of course this |
3,157 | What is a "saturated" model? | It is also useful if you need to calculate AIC for a quasi-likelihood model. The estimate of dispersion should come from the saturated model. You would divide the LL you are fitting by the estimated dispersion from the saturated model in the AIC calculation. | What is a "saturated" model? | It is also useful if you need to calculate AIC for a quasi-likelihood model. The estimate of dispersion should come from the saturated model. You would divide the LL you are fitting by the estimated | What is a "saturated" model?
It is also useful if you need to calculate AIC for a quasi-likelihood model. The estimate of dispersion should come from the saturated model. You would divide the LL you are fitting by the estimated dispersion from the saturated model in the AIC calculation. | What is a "saturated" model?
It is also useful if you need to calculate AIC for a quasi-likelihood model. The estimate of dispersion should come from the saturated model. You would divide the LL you are fitting by the estimated |
3,158 | What is a "saturated" model? | In the context of SEM (or path analysis), a saturated model or a just-identified model is a model in which the number of free parameters exactly equals the number of variances and unique covariances. For example the following model is a saturated model because there are 3*4/2 data points (variances and unique covarianc... | What is a "saturated" model? | In the context of SEM (or path analysis), a saturated model or a just-identified model is a model in which the number of free parameters exactly equals the number of variances and unique covariances. | What is a "saturated" model?
In the context of SEM (or path analysis), a saturated model or a just-identified model is a model in which the number of free parameters exactly equals the number of variances and unique covariances. For example the following model is a saturated model because there are 3*4/2 data points (v... | What is a "saturated" model?
In the context of SEM (or path analysis), a saturated model or a just-identified model is a model in which the number of free parameters exactly equals the number of variances and unique covariances. |
3,159 | Look and you shall find (a correlation) | This is an excellent question, worthy of someone who is a clear statistical thinker, because it recognizes a subtle but important aspect of multiple testing.
There are standard methods to adjust the p-values of multiple correlation coefficients (or, equivalently, to broaden their confidence intervals), such as the Bonf... | Look and you shall find (a correlation) | This is an excellent question, worthy of someone who is a clear statistical thinker, because it recognizes a subtle but important aspect of multiple testing.
There are standard methods to adjust the p | Look and you shall find (a correlation)
This is an excellent question, worthy of someone who is a clear statistical thinker, because it recognizes a subtle but important aspect of multiple testing.
There are standard methods to adjust the p-values of multiple correlation coefficients (or, equivalently, to broaden their... | Look and you shall find (a correlation)
This is an excellent question, worthy of someone who is a clear statistical thinker, because it recognizes a subtle but important aspect of multiple testing.
There are standard methods to adjust the p |
3,160 | Look and you shall find (a correlation) | From your follow up response to Peter Flom's question, it sounds like you might be better served by techniques that look at higher level structure in your correlation matrix.
Techniques like factor analysis, PCA, multidimensional scaling, and cluster analysis of variables can be used to group your variables into sets o... | Look and you shall find (a correlation) | From your follow up response to Peter Flom's question, it sounds like you might be better served by techniques that look at higher level structure in your correlation matrix.
Techniques like factor an | Look and you shall find (a correlation)
From your follow up response to Peter Flom's question, it sounds like you might be better served by techniques that look at higher level structure in your correlation matrix.
Techniques like factor analysis, PCA, multidimensional scaling, and cluster analysis of variables can be ... | Look and you shall find (a correlation)
From your follow up response to Peter Flom's question, it sounds like you might be better served by techniques that look at higher level structure in your correlation matrix.
Techniques like factor an |
3,161 | Look and you shall find (a correlation) | Perhaps you could do a preliminary analysis on a random subset of the data to form hypotheses, and then test those few hypotheses of interest using the rest of the data. That way you would not have to correct for nearly as many multiple tests. (I think...)
Of course, if you use such a procedure you will be reducing the... | Look and you shall find (a correlation) | Perhaps you could do a preliminary analysis on a random subset of the data to form hypotheses, and then test those few hypotheses of interest using the rest of the data. That way you would not have to | Look and you shall find (a correlation)
Perhaps you could do a preliminary analysis on a random subset of the data to form hypotheses, and then test those few hypotheses of interest using the rest of the data. That way you would not have to correct for nearly as many multiple tests. (I think...)
Of course, if you use s... | Look and you shall find (a correlation)
Perhaps you could do a preliminary analysis on a random subset of the data to form hypotheses, and then test those few hypotheses of interest using the rest of the data. That way you would not have to |
3,162 | Look and you shall find (a correlation) | This is an example of multiple comparisons. There's a large literature on this.
If you have, say, 100 variables, then you will have 100*99/2 =4950 correlations.
If the data are just noise, then you would expect 1 in 20 of these to be significant at p = .05. That's 247.5
Before going farther, though, it would be good... | Look and you shall find (a correlation) | This is an example of multiple comparisons. There's a large literature on this.
If you have, say, 100 variables, then you will have 100*99/2 =4950 correlations.
If the data are just noise, then you | Look and you shall find (a correlation)
This is an example of multiple comparisons. There's a large literature on this.
If you have, say, 100 variables, then you will have 100*99/2 =4950 correlations.
If the data are just noise, then you would expect 1 in 20 of these to be significant at p = .05. That's 247.5
Before... | Look and you shall find (a correlation)
This is an example of multiple comparisons. There's a large literature on this.
If you have, say, 100 variables, then you will have 100*99/2 =4950 correlations.
If the data are just noise, then you |
3,163 | What problem do shrinkage methods solve? | I suspect you want a deeper answer, and I'll have to let someone else provide that, but I can give you some thoughts on ridge regression from a loose, conceptual perspective.
OLS regression yields parameter estimates that are unbiased (i.e., if such samples are gathered and parameters are estimated indefinitely, the ... | What problem do shrinkage methods solve? | I suspect you want a deeper answer, and I'll have to let someone else provide that, but I can give you some thoughts on ridge regression from a loose, conceptual perspective.
OLS regression yields p | What problem do shrinkage methods solve?
I suspect you want a deeper answer, and I'll have to let someone else provide that, but I can give you some thoughts on ridge regression from a loose, conceptual perspective.
OLS regression yields parameter estimates that are unbiased (i.e., if such samples are gathered and pa... | What problem do shrinkage methods solve?
I suspect you want a deeper answer, and I'll have to let someone else provide that, but I can give you some thoughts on ridge regression from a loose, conceptual perspective.
OLS regression yields p |
3,164 | What problem do shrinkage methods solve? | The error of an estimator is a combination of (squared) bias and variance components. However in practice we want to fit a model to a particular finite sample of data and we want to minimise the total error of the estimator evaluated on the particular sample of data we actually have, rather than a zero error on avera... | What problem do shrinkage methods solve? | The error of an estimator is a combination of (squared) bias and variance components. However in practice we want to fit a model to a particular finite sample of data and we want to minimise the tot | What problem do shrinkage methods solve?
The error of an estimator is a combination of (squared) bias and variance components. However in practice we want to fit a model to a particular finite sample of data and we want to minimise the total error of the estimator evaluated on the particular sample of data we actuall... | What problem do shrinkage methods solve?
The error of an estimator is a combination of (squared) bias and variance components. However in practice we want to fit a model to a particular finite sample of data and we want to minimise the tot |
3,165 | What problem do shrinkage methods solve? | I guess that there are a few answers that may be applicable:
Ridge regression can provide identification when the matrix of predictors is not full column rank.
Lasso and LAR can be used when the number of predictors is greater than the number of observations (another variant of the non-singular issue).
Lasso and LAR a... | What problem do shrinkage methods solve? | I guess that there are a few answers that may be applicable:
Ridge regression can provide identification when the matrix of predictors is not full column rank.
Lasso and LAR can be used when the numb | What problem do shrinkage methods solve?
I guess that there are a few answers that may be applicable:
Ridge regression can provide identification when the matrix of predictors is not full column rank.
Lasso and LAR can be used when the number of predictors is greater than the number of observations (another variant of... | What problem do shrinkage methods solve?
I guess that there are a few answers that may be applicable:
Ridge regression can provide identification when the matrix of predictors is not full column rank.
Lasso and LAR can be used when the numb |
3,166 | What problem do shrinkage methods solve? | Here's a basic applied example from Biostatistics
Let's assume that I am studying possible relationships between the presence of ovarian cancer and a set of genes.
My dependent variable is a binary (coded as a zero or a 1)
My independent variables codes data from a proteomic database.
As is common in many genetics stud... | What problem do shrinkage methods solve? | Here's a basic applied example from Biostatistics
Let's assume that I am studying possible relationships between the presence of ovarian cancer and a set of genes.
My dependent variable is a binary (c | What problem do shrinkage methods solve?
Here's a basic applied example from Biostatistics
Let's assume that I am studying possible relationships between the presence of ovarian cancer and a set of genes.
My dependent variable is a binary (coded as a zero or a 1)
My independent variables codes data from a proteomic dat... | What problem do shrinkage methods solve?
Here's a basic applied example from Biostatistics
Let's assume that I am studying possible relationships between the presence of ovarian cancer and a set of genes.
My dependent variable is a binary (c |
3,167 | What problem do shrinkage methods solve? | Another problem which linear regression shrinkage methods can address is obtaining a low variance (possibly unbiased) estimate of an average treatment effect (ATE) in high-dimensional case-control studies on observational data.
Specifically, in cases where 1) there are a large number of variables (making it difficult t... | What problem do shrinkage methods solve? | Another problem which linear regression shrinkage methods can address is obtaining a low variance (possibly unbiased) estimate of an average treatment effect (ATE) in high-dimensional case-control stu | What problem do shrinkage methods solve?
Another problem which linear regression shrinkage methods can address is obtaining a low variance (possibly unbiased) estimate of an average treatment effect (ATE) in high-dimensional case-control studies on observational data.
Specifically, in cases where 1) there are a large n... | What problem do shrinkage methods solve?
Another problem which linear regression shrinkage methods can address is obtaining a low variance (possibly unbiased) estimate of an average treatment effect (ATE) in high-dimensional case-control stu |
3,168 | Is PCA followed by a rotation (such as varimax) still PCA? | This question is largely about definitions of PCA/FA, so opinions might differ. My opinion is that PCA+varimax should not be called either PCA or FA, bur rather explicitly referred to e.g. as "varimax-rotated PCA".
I should add that this is quite a confusing topic. In this answer I want to explain what a rotation actua... | Is PCA followed by a rotation (such as varimax) still PCA? | This question is largely about definitions of PCA/FA, so opinions might differ. My opinion is that PCA+varimax should not be called either PCA or FA, bur rather explicitly referred to e.g. as "varimax | Is PCA followed by a rotation (such as varimax) still PCA?
This question is largely about definitions of PCA/FA, so opinions might differ. My opinion is that PCA+varimax should not be called either PCA or FA, bur rather explicitly referred to e.g. as "varimax-rotated PCA".
I should add that this is quite a confusing to... | Is PCA followed by a rotation (such as varimax) still PCA?
This question is largely about definitions of PCA/FA, so opinions might differ. My opinion is that PCA+varimax should not be called either PCA or FA, bur rather explicitly referred to e.g. as "varimax |
3,169 | Is PCA followed by a rotation (such as varimax) still PCA? | Principal Components Analysis (PCA) and Common Factor Analysis (CFA) are distinct methods. Often, they produce similar results and PCA is used as the default extraction method in the SPSS Factor Analysis routines. This undoubtedly results in a lot of confusion about the distinction between the two.
The bottom line is... | Is PCA followed by a rotation (such as varimax) still PCA? | Principal Components Analysis (PCA) and Common Factor Analysis (CFA) are distinct methods. Often, they produce similar results and PCA is used as the default extraction method in the SPSS Factor Anal | Is PCA followed by a rotation (such as varimax) still PCA?
Principal Components Analysis (PCA) and Common Factor Analysis (CFA) are distinct methods. Often, they produce similar results and PCA is used as the default extraction method in the SPSS Factor Analysis routines. This undoubtedly results in a lot of confusio... | Is PCA followed by a rotation (such as varimax) still PCA?
Principal Components Analysis (PCA) and Common Factor Analysis (CFA) are distinct methods. Often, they produce similar results and PCA is used as the default extraction method in the SPSS Factor Anal |
3,170 | Is PCA followed by a rotation (such as varimax) still PCA? | This answer is to present, in a path chart form, things about which @amoeba reasoned in his deep (but slightly complicated) answer on this thread (I'm a kind of agree with it by 95%) and how they appear to me.
PCA in its proper, minimal form is the specific orthogonal rotation of correlated data to its uncorrelated for... | Is PCA followed by a rotation (such as varimax) still PCA? | This answer is to present, in a path chart form, things about which @amoeba reasoned in his deep (but slightly complicated) answer on this thread (I'm a kind of agree with it by 95%) and how they appe | Is PCA followed by a rotation (such as varimax) still PCA?
This answer is to present, in a path chart form, things about which @amoeba reasoned in his deep (but slightly complicated) answer on this thread (I'm a kind of agree with it by 95%) and how they appear to me.
PCA in its proper, minimal form is the specific ort... | Is PCA followed by a rotation (such as varimax) still PCA?
This answer is to present, in a path chart form, things about which @amoeba reasoned in his deep (but slightly complicated) answer on this thread (I'm a kind of agree with it by 95%) and how they appe |
3,171 | Is PCA followed by a rotation (such as varimax) still PCA? | In psych::principal() you can do different types of rotations/transformations to your extracted Principal Component(s) or ''PCs'' using the rotate= argument, like:
"none", "varimax" (Default), "quatimax", "promax", "oblimin", "simplimax", and "cluster". You have to empirically decide which one should make sense in your... | Is PCA followed by a rotation (such as varimax) still PCA? | In psych::principal() you can do different types of rotations/transformations to your extracted Principal Component(s) or ''PCs'' using the rotate= argument, like:
"none", "varimax" (Default), "quatim | Is PCA followed by a rotation (such as varimax) still PCA?
In psych::principal() you can do different types of rotations/transformations to your extracted Principal Component(s) or ''PCs'' using the rotate= argument, like:
"none", "varimax" (Default), "quatimax", "promax", "oblimin", "simplimax", and "cluster". You hav... | Is PCA followed by a rotation (such as varimax) still PCA?
In psych::principal() you can do different types of rotations/transformations to your extracted Principal Component(s) or ''PCs'' using the rotate= argument, like:
"none", "varimax" (Default), "quatim |
3,172 | Is PCA followed by a rotation (such as varimax) still PCA? | My understanding is that the distinction between PCA and Factor analysis primarily is in whether there is an error term. Thus PCA can, and will, faithfully represent the data whereas factor analysis is less faithful to the data it is trained on but attempts to represent underlying trends or communality in the data. Un... | Is PCA followed by a rotation (such as varimax) still PCA? | My understanding is that the distinction between PCA and Factor analysis primarily is in whether there is an error term. Thus PCA can, and will, faithfully represent the data whereas factor analysis i | Is PCA followed by a rotation (such as varimax) still PCA?
My understanding is that the distinction between PCA and Factor analysis primarily is in whether there is an error term. Thus PCA can, and will, faithfully represent the data whereas factor analysis is less faithful to the data it is trained on but attempts to ... | Is PCA followed by a rotation (such as varimax) still PCA?
My understanding is that the distinction between PCA and Factor analysis primarily is in whether there is an error term. Thus PCA can, and will, faithfully represent the data whereas factor analysis i |
3,173 | Is PCA followed by a rotation (such as varimax) still PCA? | Thanks to the chaos in definitions of both they are effectively a synonyms. Don't believe words and look deep into the docks to find the equations. | Is PCA followed by a rotation (such as varimax) still PCA? | Thanks to the chaos in definitions of both they are effectively a synonyms. Don't believe words and look deep into the docks to find the equations. | Is PCA followed by a rotation (such as varimax) still PCA?
Thanks to the chaos in definitions of both they are effectively a synonyms. Don't believe words and look deep into the docks to find the equations. | Is PCA followed by a rotation (such as varimax) still PCA?
Thanks to the chaos in definitions of both they are effectively a synonyms. Don't believe words and look deep into the docks to find the equations. |
3,174 | Is PCA followed by a rotation (such as varimax) still PCA? | Although this question has already an accepted answer I'd like to add something to the point of the question.
"PCA" -if I recall correctly - means "principal components analysis"; so as long as you're analyzing the principal components, may it be without rotation or with rotation, we are still in the ana... | Is PCA followed by a rotation (such as varimax) still PCA? | Although this question has already an accepted answer I'd like to add something to the point of the question.
"PCA" -if I recall correctly - means "principal components analysis"; so as | Is PCA followed by a rotation (such as varimax) still PCA?
Although this question has already an accepted answer I'd like to add something to the point of the question.
"PCA" -if I recall correctly - means "principal components analysis"; so as long as you're analyzing the principal components, may it be... | Is PCA followed by a rotation (such as varimax) still PCA?
Although this question has already an accepted answer I'd like to add something to the point of the question.
"PCA" -if I recall correctly - means "principal components analysis"; so as |
3,175 | Is PCA followed by a rotation (such as varimax) still PCA? | I found this to be the most helpful: Abdi & Williams, 2010, Principal component analysis.
ROTATION
After the number of components has been determined,
and in order to facilitate the interpretation, the
analysis often involves a rotation of the components
that were retained [see, e.g., Ref 40 and 67, for
more details].... | Is PCA followed by a rotation (such as varimax) still PCA? | I found this to be the most helpful: Abdi & Williams, 2010, Principal component analysis.
ROTATION
After the number of components has been determined,
and in order to facilitate the interpretation, t | Is PCA followed by a rotation (such as varimax) still PCA?
I found this to be the most helpful: Abdi & Williams, 2010, Principal component analysis.
ROTATION
After the number of components has been determined,
and in order to facilitate the interpretation, the
analysis often involves a rotation of the components
that ... | Is PCA followed by a rotation (such as varimax) still PCA?
I found this to be the most helpful: Abdi & Williams, 2010, Principal component analysis.
ROTATION
After the number of components has been determined,
and in order to facilitate the interpretation, t |
3,176 | How to interpret type I, type II, and type III ANOVA and MANOVA? | What you are calling type II SS, I would call type III SS. Lets imagine that there are just two factors A and B (and we'll throw in the A*B interaction later to distinguish type II SS). Further, lets imagine that there are different $n$s in the four cells (e.g., $n_{11}$=11, $n_{12}$=9, $n_{21}$=9, and $n_{22}$=11). ... | How to interpret type I, type II, and type III ANOVA and MANOVA? | What you are calling type II SS, I would call type III SS. Lets imagine that there are just two factors A and B (and we'll throw in the A*B interaction later to distinguish type II SS). Further, let | How to interpret type I, type II, and type III ANOVA and MANOVA?
What you are calling type II SS, I would call type III SS. Lets imagine that there are just two factors A and B (and we'll throw in the A*B interaction later to distinguish type II SS). Further, lets imagine that there are different $n$s in the four cel... | How to interpret type I, type II, and type III ANOVA and MANOVA?
What you are calling type II SS, I would call type III SS. Lets imagine that there are just two factors A and B (and we'll throw in the A*B interaction later to distinguish type II SS). Further, let |
3,177 | How to interpret type I, type II, and type III ANOVA and MANOVA? | For illustration I assume a two dimensional ANOVA model specified by y ~ A * B
Type I ANOVA
Line term in ANOVA table
Hypothesis from model
Hypothesis to model
A
y~ A
y~ 1
B
y~ A+B
y~ A
A:B
y~ A*B
y~ A+B
The from-model of every line is the to-model of the line below. The to-model is the from-model withou... | How to interpret type I, type II, and type III ANOVA and MANOVA? | For illustration I assume a two dimensional ANOVA model specified by y ~ A * B
Type I ANOVA
Line term in ANOVA table
Hypothesis from model
Hypothesis to model
A
y~ A
y~ 1
B
y~ A+B
y~ A
A:B | How to interpret type I, type II, and type III ANOVA and MANOVA?
For illustration I assume a two dimensional ANOVA model specified by y ~ A * B
Type I ANOVA
Line term in ANOVA table
Hypothesis from model
Hypothesis to model
A
y~ A
y~ 1
B
y~ A+B
y~ A
A:B
y~ A*B
y~ A+B
The from-model of every line is the ... | How to interpret type I, type II, and type III ANOVA and MANOVA?
For illustration I assume a two dimensional ANOVA model specified by y ~ A * B
Type I ANOVA
Line term in ANOVA table
Hypothesis from model
Hypothesis to model
A
y~ A
y~ 1
B
y~ A+B
y~ A
A:B |
3,178 | Linear model with log-transformed response vs. generalized linear model with log link | Although it may appear that the mean of the log-transformed variables is preferable (since this is how log-normal is typically parameterised), from a practical point of view, the log of the mean is typically much more useful.
This is particularly true when your model is not exactly correct, and to quote George Box: "Al... | Linear model with log-transformed response vs. generalized linear model with log link | Although it may appear that the mean of the log-transformed variables is preferable (since this is how log-normal is typically parameterised), from a practical point of view, the log of the mean is ty | Linear model with log-transformed response vs. generalized linear model with log link
Although it may appear that the mean of the log-transformed variables is preferable (since this is how log-normal is typically parameterised), from a practical point of view, the log of the mean is typically much more useful.
This is ... | Linear model with log-transformed response vs. generalized linear model with log link
Although it may appear that the mean of the log-transformed variables is preferable (since this is how log-normal is typically parameterised), from a practical point of view, the log of the mean is ty |
3,179 | Linear model with log-transformed response vs. generalized linear model with log link | Here are my two cents from an advanced data analysis course I took while studying biostatistics (although I don't have any references other than my professor's notes):
It boils down to whether or not you need to address linearity and heteroscedasticity (unequal variances) in your data, or just linearity.
She notes that... | Linear model with log-transformed response vs. generalized linear model with log link | Here are my two cents from an advanced data analysis course I took while studying biostatistics (although I don't have any references other than my professor's notes):
It boils down to whether or not | Linear model with log-transformed response vs. generalized linear model with log link
Here are my two cents from an advanced data analysis course I took while studying biostatistics (although I don't have any references other than my professor's notes):
It boils down to whether or not you need to address linearity and ... | Linear model with log-transformed response vs. generalized linear model with log link
Here are my two cents from an advanced data analysis course I took while studying biostatistics (although I don't have any references other than my professor's notes):
It boils down to whether or not |
3,180 | Linear model with log-transformed response vs. generalized linear model with log link | In the following I try to give some additional details to @Meg's answer with some mathematical notation.
The fixed part is the same for both, transformation and GLM. However, the transformation also affects the random part, while this is not the case for the link in the GLM.
Transformation
When we speak of a gaussian l... | Linear model with log-transformed response vs. generalized linear model with log link | In the following I try to give some additional details to @Meg's answer with some mathematical notation.
The fixed part is the same for both, transformation and GLM. However, the transformation also a | Linear model with log-transformed response vs. generalized linear model with log link
In the following I try to give some additional details to @Meg's answer with some mathematical notation.
The fixed part is the same for both, transformation and GLM. However, the transformation also affects the random part, while this... | Linear model with log-transformed response vs. generalized linear model with log link
In the following I try to give some additional details to @Meg's answer with some mathematical notation.
The fixed part is the same for both, transformation and GLM. However, the transformation also a |
3,181 | Linear model with log-transformed response vs. generalized linear model with log link | Corvus pretty much answered the question. I can add:
Transformation introduces 'bias' such that the mean on the transformed scale is not consistent with that on the original scale (see the first formula in the answer from Corvus).
The log-transform can be useful when effects are nonlinear and multiplicative (Pek et al... | Linear model with log-transformed response vs. generalized linear model with log link | Corvus pretty much answered the question. I can add:
Transformation introduces 'bias' such that the mean on the transformed scale is not consistent with that on the original scale (see the first form | Linear model with log-transformed response vs. generalized linear model with log link
Corvus pretty much answered the question. I can add:
Transformation introduces 'bias' such that the mean on the transformed scale is not consistent with that on the original scale (see the first formula in the answer from Corvus).
Th... | Linear model with log-transformed response vs. generalized linear model with log link
Corvus pretty much answered the question. I can add:
Transformation introduces 'bias' such that the mean on the transformed scale is not consistent with that on the original scale (see the first form |
3,182 | What is the relationship between independent component analysis and factor analysis? | FA, PCA, and ICA, are all 'related', in as much as all three of them seek basis vectors that the data is projected against, such that you maximize insert-criteria-here. Think of the basis vectors as just encapsulating linear combinations.
For example, lets say your data matrix $\mathbf Z$ was a $2$ x $N$ matrix, that ... | What is the relationship between independent component analysis and factor analysis? | FA, PCA, and ICA, are all 'related', in as much as all three of them seek basis vectors that the data is projected against, such that you maximize insert-criteria-here. Think of the basis vectors as j | What is the relationship between independent component analysis and factor analysis?
FA, PCA, and ICA, are all 'related', in as much as all three of them seek basis vectors that the data is projected against, such that you maximize insert-criteria-here. Think of the basis vectors as just encapsulating linear combinatio... | What is the relationship between independent component analysis and factor analysis?
FA, PCA, and ICA, are all 'related', in as much as all three of them seek basis vectors that the data is projected against, such that you maximize insert-criteria-here. Think of the basis vectors as j |
3,183 | What is the relationship between independent component analysis and factor analysis? | Not quite. Factor analysis operates with the second moments, and really hopes that the data are Gaussian so that the likelihood ratios and stuff like that is not affected by non-normality. ICA, on the other hand, is motivated by the idea that when you add things up, you get something normal, due to CLT, and really hope... | What is the relationship between independent component analysis and factor analysis? | Not quite. Factor analysis operates with the second moments, and really hopes that the data are Gaussian so that the likelihood ratios and stuff like that is not affected by non-normality. ICA, on the | What is the relationship between independent component analysis and factor analysis?
Not quite. Factor analysis operates with the second moments, and really hopes that the data are Gaussian so that the likelihood ratios and stuff like that is not affected by non-normality. ICA, on the other hand, is motivated by the id... | What is the relationship between independent component analysis and factor analysis?
Not quite. Factor analysis operates with the second moments, and really hopes that the data are Gaussian so that the likelihood ratios and stuff like that is not affected by non-normality. ICA, on the |
3,184 | Difference between "kernel" and "filter" in CNN | In the context of convolutional neural networks, kernel = filter = feature detector.
Here is a great illustration from Stanford's deep learning tutorial (also nicely explained by Denny Britz).
The filter is the yellow sliding window, and its value is:
\begin{bmatrix}
1 & 0 & 1 \\
0 & 1 & 0 \\
... | Difference between "kernel" and "filter" in CNN | In the context of convolutional neural networks, kernel = filter = feature detector.
Here is a great illustration from Stanford's deep learning tutorial (also nicely explained by Denny Britz).
The | Difference between "kernel" and "filter" in CNN
In the context of convolutional neural networks, kernel = filter = feature detector.
Here is a great illustration from Stanford's deep learning tutorial (also nicely explained by Denny Britz).
The filter is the yellow sliding window, and its value is:
\begin{bmatrix}
... | Difference between "kernel" and "filter" in CNN
In the context of convolutional neural networks, kernel = filter = feature detector.
Here is a great illustration from Stanford's deep learning tutorial (also nicely explained by Denny Britz).
The |
3,185 | Difference between "kernel" and "filter" in CNN | How about we use the term "kernel" for a 2D array of weights, and the term "filter" for the 3D structure of multiple kernels stacked together? The dimension of a filter is $k \times k \times C$ (assuming square kernels). Each one of the $C$ kernels that compose a filter will be convolved with one of the $C$ channels of... | Difference between "kernel" and "filter" in CNN | How about we use the term "kernel" for a 2D array of weights, and the term "filter" for the 3D structure of multiple kernels stacked together? The dimension of a filter is $k \times k \times C$ (assum | Difference between "kernel" and "filter" in CNN
How about we use the term "kernel" for a 2D array of weights, and the term "filter" for the 3D structure of multiple kernels stacked together? The dimension of a filter is $k \times k \times C$ (assuming square kernels). Each one of the $C$ kernels that compose a filter w... | Difference between "kernel" and "filter" in CNN
How about we use the term "kernel" for a 2D array of weights, and the term "filter" for the 3D structure of multiple kernels stacked together? The dimension of a filter is $k \times k \times C$ (assum |
3,186 | Difference between "kernel" and "filter" in CNN | Filter consists of kernels. This means, in 2D convolutional neural network, filter is 3D. Check this gif from CS231n Convolutional Neural Networks for Visual Recognition:
Those three 3x3 kernels in second column of this gif form a filter. So as in the third column. The number of filters always equal to the number of f... | Difference between "kernel" and "filter" in CNN | Filter consists of kernels. This means, in 2D convolutional neural network, filter is 3D. Check this gif from CS231n Convolutional Neural Networks for Visual Recognition:
Those three 3x3 kernels in s | Difference between "kernel" and "filter" in CNN
Filter consists of kernels. This means, in 2D convolutional neural network, filter is 3D. Check this gif from CS231n Convolutional Neural Networks for Visual Recognition:
Those three 3x3 kernels in second column of this gif form a filter. So as in the third column. The n... | Difference between "kernel" and "filter" in CNN
Filter consists of kernels. This means, in 2D convolutional neural network, filter is 3D. Check this gif from CS231n Convolutional Neural Networks for Visual Recognition:
Those three 3x3 kernels in s |
3,187 | Difference between "kernel" and "filter" in CNN | A feature map is the same as a filter or "kernel" in this particular context.
The weights of the filter determine what specific features are detected.
So for example, Franck has provided a great visual. Notice that his filter/feature-detector has x1 along the diagonal elements and x0 along all the other elements. Thi... | Difference between "kernel" and "filter" in CNN | A feature map is the same as a filter or "kernel" in this particular context.
The weights of the filter determine what specific features are detected.
So for example, Franck has provided a great visua | Difference between "kernel" and "filter" in CNN
A feature map is the same as a filter or "kernel" in this particular context.
The weights of the filter determine what specific features are detected.
So for example, Franck has provided a great visual. Notice that his filter/feature-detector has x1 along the diagonal el... | Difference between "kernel" and "filter" in CNN
A feature map is the same as a filter or "kernel" in this particular context.
The weights of the filter determine what specific features are detected.
So for example, Franck has provided a great visua |
3,188 | Difference between "kernel" and "filter" in CNN | The existing answers are excellent and comprehensively answer the question. Just want to add that filters in Convolutional networks are shared across the entire image (i.e., the input is convolved with the filter, as visualized in Franck's answer). The receptive field of a particular neuron are all input units that aff... | Difference between "kernel" and "filter" in CNN | The existing answers are excellent and comprehensively answer the question. Just want to add that filters in Convolutional networks are shared across the entire image (i.e., the input is convolved wit | Difference between "kernel" and "filter" in CNN
The existing answers are excellent and comprehensively answer the question. Just want to add that filters in Convolutional networks are shared across the entire image (i.e., the input is convolved with the filter, as visualized in Franck's answer). The receptive field of ... | Difference between "kernel" and "filter" in CNN
The existing answers are excellent and comprehensively answer the question. Just want to add that filters in Convolutional networks are shared across the entire image (i.e., the input is convolved wit |
3,189 | Difference between "kernel" and "filter" in CNN | To be straightforward:
A filter is a collection of kernels, although we use filter and kernel interchangeably.
Example:
Let's say you want to apply P 3x3xN filter to a K x K x N input with stride =1 and pad = 0. So each of the 3 x 3 matrix in 3 x 3 x N filter is a kernel. And your output will be K-2 x K-2 x P . | Difference between "kernel" and "filter" in CNN | To be straightforward:
A filter is a collection of kernels, although we use filter and kernel interchangeably.
Example:
Let's say you want to apply P 3x3xN filter to a K x K x N input with stride =1 a | Difference between "kernel" and "filter" in CNN
To be straightforward:
A filter is a collection of kernels, although we use filter and kernel interchangeably.
Example:
Let's say you want to apply P 3x3xN filter to a K x K x N input with stride =1 and pad = 0. So each of the 3 x 3 matrix in 3 x 3 x N filter is a kernel.... | Difference between "kernel" and "filter" in CNN
To be straightforward:
A filter is a collection of kernels, although we use filter and kernel interchangeably.
Example:
Let's say you want to apply P 3x3xN filter to a K x K x N input with stride =1 a |
3,190 | Is ridge regression useless in high dimensions ($n \ll p$)? How can OLS fail to overfit? | A natural regularization happens because of the presence of many small components in the theoretical PCA of $x$. These small components are implicitly used to fit the noise using small coefficients. When using minimum norm OLS, you fit the noise with many small independent components and this has a regularizing effect ... | Is ridge regression useless in high dimensions ($n \ll p$)? How can OLS fail to overfit? | A natural regularization happens because of the presence of many small components in the theoretical PCA of $x$. These small components are implicitly used to fit the noise using small coefficients. W | Is ridge regression useless in high dimensions ($n \ll p$)? How can OLS fail to overfit?
A natural regularization happens because of the presence of many small components in the theoretical PCA of $x$. These small components are implicitly used to fit the noise using small coefficients. When using minimum norm OLS, you... | Is ridge regression useless in high dimensions ($n \ll p$)? How can OLS fail to overfit?
A natural regularization happens because of the presence of many small components in the theoretical PCA of $x$. These small components are implicitly used to fit the noise using small coefficients. W |
3,191 | Is ridge regression useless in high dimensions ($n \ll p$)? How can OLS fail to overfit? | Thanks everybody for the great ongoing discussion. The crux of the matter seems to be that minimum-norm OLS is effectively performing shrinkage that is similar to the ridge regression. This seems to occur whenever $p\gg n$. Ironically, adding pure noise predictors can even be used as a very weird form or regularization... | Is ridge regression useless in high dimensions ($n \ll p$)? How can OLS fail to overfit? | Thanks everybody for the great ongoing discussion. The crux of the matter seems to be that minimum-norm OLS is effectively performing shrinkage that is similar to the ridge regression. This seems to o | Is ridge regression useless in high dimensions ($n \ll p$)? How can OLS fail to overfit?
Thanks everybody for the great ongoing discussion. The crux of the matter seems to be that minimum-norm OLS is effectively performing shrinkage that is similar to the ridge regression. This seems to occur whenever $p\gg n$. Ironica... | Is ridge regression useless in high dimensions ($n \ll p$)? How can OLS fail to overfit?
Thanks everybody for the great ongoing discussion. The crux of the matter seems to be that minimum-norm OLS is effectively performing shrinkage that is similar to the ridge regression. This seems to o |
3,192 | Is ridge regression useless in high dimensions ($n \ll p$)? How can OLS fail to overfit? | Here is an artificial situation where this occurs. Suppose each predictor variable is a copy of the target variable with a large amount of gaussian noise applied. The best possible model is an average of all predictor variables.
library(glmnet)
set.seed(1846)
noise <- 10
N <- 80
num.vars <- 100
target <- runif(N,-1,1)
... | Is ridge regression useless in high dimensions ($n \ll p$)? How can OLS fail to overfit? | Here is an artificial situation where this occurs. Suppose each predictor variable is a copy of the target variable with a large amount of gaussian noise applied. The best possible model is an average | Is ridge regression useless in high dimensions ($n \ll p$)? How can OLS fail to overfit?
Here is an artificial situation where this occurs. Suppose each predictor variable is a copy of the target variable with a large amount of gaussian noise applied. The best possible model is an average of all predictor variables.
li... | Is ridge regression useless in high dimensions ($n \ll p$)? How can OLS fail to overfit?
Here is an artificial situation where this occurs. Suppose each predictor variable is a copy of the target variable with a large amount of gaussian noise applied. The best possible model is an average |
3,193 | Is ridge regression useless in high dimensions ($n \ll p$)? How can OLS fail to overfit? | So I decided to run nested cross-validation using the specialized mlr package in R to see what's actually coming from the modelling approach.
Code (it takes a few minutes to run on an ordinary notebook)
library(mlr)
daf = read.csv("https://pastebin.com/raw/p1cCCYBR", sep = " ", header = FALSE)
tsk = list(
tsk1110 = ... | Is ridge regression useless in high dimensions ($n \ll p$)? How can OLS fail to overfit? | So I decided to run nested cross-validation using the specialized mlr package in R to see what's actually coming from the modelling approach.
Code (it takes a few minutes to run on an ordinary noteboo | Is ridge regression useless in high dimensions ($n \ll p$)? How can OLS fail to overfit?
So I decided to run nested cross-validation using the specialized mlr package in R to see what's actually coming from the modelling approach.
Code (it takes a few minutes to run on an ordinary notebook)
library(mlr)
daf = read.csv(... | Is ridge regression useless in high dimensions ($n \ll p$)? How can OLS fail to overfit?
So I decided to run nested cross-validation using the specialized mlr package in R to see what's actually coming from the modelling approach.
Code (it takes a few minutes to run on an ordinary noteboo |
3,194 | Is ridge regression useless in high dimensions ($n \ll p$)? How can OLS fail to overfit? | How can (minimal norm) OLS fail to overfit?
In short:
Experimental parameters that correlate with the (unknown) parameters in the true model will be more likely to be estimated with high values in a minimal norm OLS fitting procedure. That is because they will fit the 'model+noise' whereas the other parameters will on... | Is ridge regression useless in high dimensions ($n \ll p$)? How can OLS fail to overfit? | How can (minimal norm) OLS fail to overfit?
In short:
Experimental parameters that correlate with the (unknown) parameters in the true model will be more likely to be estimated with high values in a | Is ridge regression useless in high dimensions ($n \ll p$)? How can OLS fail to overfit?
How can (minimal norm) OLS fail to overfit?
In short:
Experimental parameters that correlate with the (unknown) parameters in the true model will be more likely to be estimated with high values in a minimal norm OLS fitting proced... | Is ridge regression useless in high dimensions ($n \ll p$)? How can OLS fail to overfit?
How can (minimal norm) OLS fail to overfit?
In short:
Experimental parameters that correlate with the (unknown) parameters in the true model will be more likely to be estimated with high values in a |
3,195 | Is ridge regression useless in high dimensions ($n \ll p$)? How can OLS fail to overfit? | If you're familiar with linear operators then you may like my answer as most direct path to understanding the phenomenon: why doesn't least norm regression fail outright? The reason is that your problem ($n\ll p$) is the ill posed inverse problem and pseudo-inverse is one of the ways of solving it. Regularization is an... | Is ridge regression useless in high dimensions ($n \ll p$)? How can OLS fail to overfit? | If you're familiar with linear operators then you may like my answer as most direct path to understanding the phenomenon: why doesn't least norm regression fail outright? The reason is that your probl | Is ridge regression useless in high dimensions ($n \ll p$)? How can OLS fail to overfit?
If you're familiar with linear operators then you may like my answer as most direct path to understanding the phenomenon: why doesn't least norm regression fail outright? The reason is that your problem ($n\ll p$) is the ill posed ... | Is ridge regression useless in high dimensions ($n \ll p$)? How can OLS fail to overfit?
If you're familiar with linear operators then you may like my answer as most direct path to understanding the phenomenon: why doesn't least norm regression fail outright? The reason is that your probl |
3,196 | Why is logistic regression a linear classifier? | Logistic regression is linear in the sense that the predictions can be written as
$$ \hat{p} = \frac{1}{1 + e^{-\hat{\mu}}}, \text{ where } \hat{\mu} = \hat{\theta} \cdot x. $$
Thus, the prediction can be written in terms of $\hat{\mu}$, which is a linear function of $x$. (More precisely, the predicted log-odds is a li... | Why is logistic regression a linear classifier? | Logistic regression is linear in the sense that the predictions can be written as
$$ \hat{p} = \frac{1}{1 + e^{-\hat{\mu}}}, \text{ where } \hat{\mu} = \hat{\theta} \cdot x. $$
Thus, the prediction ca | Why is logistic regression a linear classifier?
Logistic regression is linear in the sense that the predictions can be written as
$$ \hat{p} = \frac{1}{1 + e^{-\hat{\mu}}}, \text{ where } \hat{\mu} = \hat{\theta} \cdot x. $$
Thus, the prediction can be written in terms of $\hat{\mu}$, which is a linear function of $x$.... | Why is logistic regression a linear classifier?
Logistic regression is linear in the sense that the predictions can be written as
$$ \hat{p} = \frac{1}{1 + e^{-\hat{\mu}}}, \text{ where } \hat{\mu} = \hat{\theta} \cdot x. $$
Thus, the prediction ca |
3,197 | Why is logistic regression a linear classifier? | As Stefan Wagner notes, the decision boundary for a logistic classifier is linear. (The classifier needs the inputs to be linearly separable.) I wanted to expand on the math for this in case it's not obvious.
The decision boundary is the set of x such that
$${1 \over {1 + e^{-{\theta \cdot x}}}} = 0.5$$
A little bi... | Why is logistic regression a linear classifier? | As Stefan Wagner notes, the decision boundary for a logistic classifier is linear. (The classifier needs the inputs to be linearly separable.) I wanted to expand on the math for this in case it's no | Why is logistic regression a linear classifier?
As Stefan Wagner notes, the decision boundary for a logistic classifier is linear. (The classifier needs the inputs to be linearly separable.) I wanted to expand on the math for this in case it's not obvious.
The decision boundary is the set of x such that
$${1 \over ... | Why is logistic regression a linear classifier?
As Stefan Wagner notes, the decision boundary for a logistic classifier is linear. (The classifier needs the inputs to be linearly separable.) I wanted to expand on the math for this in case it's no |
3,198 | Why is logistic regression a linear classifier? | It we have two classes, $C_{0}$ and $C_{1}$, then we can express the conditional probability as,
$$
P(C_{0}|x) = \frac{P(x|C_{0})P(C_{0})}{P(x)}
$$
applying the Bayes' theorem,
$$
P(C_{0}|x) = \frac{P(x|C_{0})P(C_{0})}{P(x|C_{0})P(C_{0})+P(x|C_{1})P(C_{1})}
= \frac{1}{1+ \exp\left(-\log\frac{P(x|C_{0})}{P(x|C_{1})}-\lo... | Why is logistic regression a linear classifier? | It we have two classes, $C_{0}$ and $C_{1}$, then we can express the conditional probability as,
$$
P(C_{0}|x) = \frac{P(x|C_{0})P(C_{0})}{P(x)}
$$
applying the Bayes' theorem,
$$
P(C_{0}|x) = \frac{P | Why is logistic regression a linear classifier?
It we have two classes, $C_{0}$ and $C_{1}$, then we can express the conditional probability as,
$$
P(C_{0}|x) = \frac{P(x|C_{0})P(C_{0})}{P(x)}
$$
applying the Bayes' theorem,
$$
P(C_{0}|x) = \frac{P(x|C_{0})P(C_{0})}{P(x|C_{0})P(C_{0})+P(x|C_{1})P(C_{1})}
= \frac{1}{1+ ... | Why is logistic regression a linear classifier?
It we have two classes, $C_{0}$ and $C_{1}$, then we can express the conditional probability as,
$$
P(C_{0}|x) = \frac{P(x|C_{0})P(C_{0})}{P(x)}
$$
applying the Bayes' theorem,
$$
P(C_{0}|x) = \frac{P |
3,199 | Why is the validation accuracy fluctuating? | If I understand the definition of accuracy correctly, accuracy (% of data points classified correctly) is less cumulative than let's say MSE (mean squared error). That's why you see that your loss is rapidly increasing, while accuracy is fluctuating.
Intuitively, this basically means, that some portion of examples is ... | Why is the validation accuracy fluctuating? | If I understand the definition of accuracy correctly, accuracy (% of data points classified correctly) is less cumulative than let's say MSE (mean squared error). That's why you see that your loss is | Why is the validation accuracy fluctuating?
If I understand the definition of accuracy correctly, accuracy (% of data points classified correctly) is less cumulative than let's say MSE (mean squared error). That's why you see that your loss is rapidly increasing, while accuracy is fluctuating.
Intuitively, this basica... | Why is the validation accuracy fluctuating?
If I understand the definition of accuracy correctly, accuracy (% of data points classified correctly) is less cumulative than let's say MSE (mean squared error). That's why you see that your loss is |
3,200 | Why is the validation accuracy fluctuating? | This question is old but posting this as it hasn't been pointed out yet:
Possibility 1: You're applying some sort of preprocessing (zero meaning, normalizing, etc.) to either your training set or validation set, but not the other.
Possibility 2: If you built some layers that perform differently during training and infe... | Why is the validation accuracy fluctuating? | This question is old but posting this as it hasn't been pointed out yet:
Possibility 1: You're applying some sort of preprocessing (zero meaning, normalizing, etc.) to either your training set or vali | Why is the validation accuracy fluctuating?
This question is old but posting this as it hasn't been pointed out yet:
Possibility 1: You're applying some sort of preprocessing (zero meaning, normalizing, etc.) to either your training set or validation set, but not the other.
Possibility 2: If you built some layers that ... | Why is the validation accuracy fluctuating?
This question is old but posting this as it hasn't been pointed out yet:
Possibility 1: You're applying some sort of preprocessing (zero meaning, normalizing, etc.) to either your training set or vali |
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