From 94e0bd32b1581f8dee7894df3c09622890698534 Mon Sep 17 00:00:00 2001 From: mhjensen Date: Fri, 7 Sep 2018 05:45:51 +0200 Subject: [PATCH] update on html slides for regression --- .../Regression/html/._Regression-bs051.html | 14 +++++++------- .../Regression/html/Regression-reveal.html | 14 +++++++------- .../Regression/html/Regression-solarized.html | 14 +++++++------- doc/pub/Regression/html/Regression.html | 14 +++++++------- doc/pub/Regression/ipynb/Regression.ipynb | 14 +++++++------- .../ipynb/ipynb-Regression-src.tar.gz | Bin 211 -> 210 bytes .../pdf/Regression-beamer-handouts2x3.pdf | Bin 411066 -> 410824 bytes doc/pub/Regression/pdf/Regression-beamer.pdf | Bin 366730 -> 366730 bytes doc/pub/Regression/pdf/Regression-minted.pdf | Bin 405967 -> 405910 bytes doc/src/Regression/Regression.do.txt | 14 +++++++------- 10 files changed, 42 insertions(+), 42 deletions(-) diff --git a/doc/pub/Regression/html/._Regression-bs051.html b/doc/pub/Regression/html/._Regression-bs051.html index 7542dbe4a..26b39e68a 100644 --- a/doc/pub/Regression/html/._Regression-bs051.html +++ b/doc/pub/Regression/html/._Regression-bs051.html @@ -262,11 +262,11 @@ MathJax.Hub.Config({

How to set up the cross-validation for Ridge and/or Lasso

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+ $$ \begin{align*} @@ -277,11 +277,11 @@ $$ $$ -
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+ $$ \begin{align*} @@ -290,9 +290,9 @@ $$ $$ -
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diff --git a/doc/pub/Regression/html/Regression-reveal.html b/doc/pub/Regression/html/Regression-reveal.html index 63a356a89..df03e6c5f 100644 --- a/doc/pub/Regression/html/Regression-reveal.html +++ b/doc/pub/Regression/html/Regression-reveal.html @@ -1904,11 +1904,11 @@ cross-validation (LOOCV).

How to set up the cross-validation for Ridge and/or Lasso

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    +

    • Define a range of interest for the penalty parameter.
    • Divide the data set into training and test set comprising samples \( \{1, \ldots, n\} \setminus i \) and \( \{ i \} \), respectively.
    • Fit the linear regression model by means of ridge estimation for each \( \lambda \) in the grid using the training set, and the corresponding estimate of the error variance \( \hat{\sigma}_{-i}^2(\lambda) \), as
    • -
+

 
$$ \begin{align*} @@ -1920,11 +1920,11 @@ $$

 
-

    +

    • Evaluate the prediction performance of these models on the test set by \( \log\{L[y_i, \hat{X}_{i, \ast}; \hat{\beta}_{-i}(\lambda), \hat{\sigma}_{-i}^2(\lambda)]\} \). Or, by the prediction error \( |y_i - \hat{X}_{i, \ast} \hat{\beta}_{-i}(\lambda)| \), the relative error, the error squared or the R2 score function.
    • -

    • Repeat steps 1) to 3) such that each sample plays the role of the test set once.
    • +

    • Repeat the first three steps such that each sample plays the role of the test set once.
    • Average the prediction performances of the test sets at each grid point of the penalty bias/parameter by computing the cross-validated log-likelihood. It is an estimate of the prediction performance of the model corresponding to this value of the penalty parameter on novel data. It is defined as
    • -
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$$ \begin{align*} @@ -1934,9 +1934,9 @@ $$

 
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    • The value of the penalty parameter that maximizes the cross-validated log-likelihood is the value of choice. Or we can use the MSE or the R2 score functions.
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diff --git a/doc/pub/Regression/html/Regression-solarized.html b/doc/pub/Regression/html/Regression-solarized.html index 88feb089c..575b33a94 100644 --- a/doc/pub/Regression/html/Regression-solarized.html +++ b/doc/pub/Regression/html/Regression-solarized.html @@ -1863,11 +1863,11 @@ cross-validation (LOOCV).

How to set up the cross-validation for Ridge and/or Lasso

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+ $$ \begin{align*} @@ -1878,11 +1878,11 @@ $$ $$ -
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+ $$ \begin{align*} @@ -1891,9 +1891,9 @@ $$ $$ -
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diff --git a/doc/pub/Regression/html/Regression.html b/doc/pub/Regression/html/Regression.html index a53c0e587..a6ee19e22 100644 --- a/doc/pub/Regression/html/Regression.html +++ b/doc/pub/Regression/html/Regression.html @@ -1868,11 +1868,11 @@ cross-validation (LOOCV).

How to set up the cross-validation for Ridge and/or Lasso

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+ $$ \begin{align*} @@ -1883,11 +1883,11 @@ $$ $$ -
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+ $$ \begin{align*} @@ -1896,9 +1896,9 @@ $$ $$ -
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diff --git a/doc/pub/Regression/ipynb/Regression.ipynb b/doc/pub/Regression/ipynb/Regression.ipynb index 09033bf6f..f86beff59 100644 --- a/doc/pub/Regression/ipynb/Regression.ipynb +++ b/doc/pub/Regression/ipynb/Regression.ipynb @@ -2267,11 +2267,11 @@ "\n", "## How to set up the cross-validation for Ridge and/or Lasso\n", "\n", - "1. Define a range of interest for the penalty parameter.\n", + "* Define a range of interest for the penalty parameter.\n", "\n", - "2. Divide the data set into training and test set comprising samples $\\{1, \\ldots, n\\} \\setminus i$ and $\\{ i \\}$, respectively.\n", + "* Divide the data set into training and test set comprising samples $\\{1, \\ldots, n\\} \\setminus i$ and $\\{ i \\}$, respectively.\n", "\n", - "3. Fit the linear regression model by means of ridge estimation for each $\\lambda$ in the grid using the training set, and the corresponding estimate of the error variance $\\hat{\\sigma}_{-i}^2(\\lambda)$, as" + "* Fit the linear regression model by means of ridge estimation for each $\\lambda$ in the grid using the training set, and the corresponding estimate of the error variance $\\hat{\\sigma}_{-i}^2(\\lambda)$, as" ] }, { @@ -2291,11 +2291,11 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "1. Evaluate the prediction performance of these models on the test set by $\\log\\{L[y_i, \\hat{X}_{i, \\ast}; \\hat{\\beta}_{-i}(\\lambda), \\hat{\\sigma}_{-i}^2(\\lambda)]\\}$. Or, by the prediction error $|y_i - \\hat{X}_{i, \\ast} \\hat{\\beta}_{-i}(\\lambda)|$, the relative error, the error squared or the R2 score function.\n", + "* Evaluate the prediction performance of these models on the test set by $\\log\\{L[y_i, \\hat{X}_{i, \\ast}; \\hat{\\beta}_{-i}(\\lambda), \\hat{\\sigma}_{-i}^2(\\lambda)]\\}$. Or, by the prediction error $|y_i - \\hat{X}_{i, \\ast} \\hat{\\beta}_{-i}(\\lambda)|$, the relative error, the error squared or the R2 score function.\n", "\n", - "2. Repeat steps 1) to 3) such that each sample plays the role of the test set once.\n", + "* Repeat the first three steps such that each sample plays the role of the test set once.\n", "\n", - "3. Average the prediction performances of the test sets at each grid point of the penalty bias/parameter by computing the *cross-validated log-likelihood*. It is an estimate of the prediction performance of the model corresponding to this value of the penalty parameter on novel data. It is defined as" + "* Average the prediction performances of the test sets at each grid point of the penalty bias/parameter by computing the *cross-validated log-likelihood*. It is an estimate of the prediction performance of the model corresponding to this value of the penalty parameter on novel data. It is defined as" ] }, { @@ -2313,7 +2313,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "1. The value of the penalty parameter that maximizes the cross-validated log-likelihood is the value of choice. Or we can use the MSE or the R2 score functions.\n", + "* The value of the penalty parameter that maximizes the cross-validated log-likelihood is the value of choice. Or we can use the MSE or the R2 score functions.\n", "\n", "## Predicted Residual Error Sum of Squares\n", "Another approach in the LOOCV scheme is to the use the so-called Predicted Residual Error Sum of Squares (PRESS). \n", diff --git a/doc/pub/Regression/ipynb/ipynb-Regression-src.tar.gz b/doc/pub/Regression/ipynb/ipynb-Regression-src.tar.gz index c0e43e8017395b8a747bd43e4e15c180a6fcb7ef..0e95f5af2e78df29a7855f94bdf152a582fa3064 100644 GIT binary patch literal 210 zcmV;@04@I?iwFQx^pRTt1MSbvY63A7hGExU#kqnZlbPzepo=aFBHln`q7#3TF^S;Z zea8{nRlAc?`aYYFLq5Ve>*ed>eOcsNo;;0GYF5{B&-v_SOr;<5sMMvDRaMv3T$fsl z8i$Ff=dJYRnzD(*D(%7gWc|0jp|;!o@XzBE`OH6J)4C*Yt3J2Eix1guLpaLX?xRh~ z1z)(X_giU#P4{Ps_HuR6it)Xerg3@bnA5b2VIR#o71Q572mk;800000000000091p M4@u{R-vB580OmJqm;e9( literal 211 zcmb2|=3tQiJTaPq`R)0$Sxkl^ZHd?8j_zzyOkT8(dsjiAz(+PE;kiF1-%x2P{@%y+ zcGX=^&D!~Ak1NVQoOAV0?l-&jr?&FMxoMgjy1lcU+atfy?flP$a#w@0b9?4pbIT6= zYY@g9xIX&jX;tyrzd~>A<-XaPUtOEK`|rc~&ow{ItUt2rYoyrebz2NQI*#Th*_=4_ 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-1539,11 +1539,11 @@ cross-validation (LOOCV). !split ===== How to set up the cross-validation for Ridge and/or Lasso ===== -o Define a range of interest for the penalty parameter. +* Define a range of interest for the penalty parameter. -o Divide the data set into training and test set comprising samples $\{1, \ldots, n\} \setminus i$ and $\{ i \}$, respectively. +* Divide the data set into training and test set comprising samples $\{1, \ldots, n\} \setminus i$ and $\{ i \}$, respectively. -o Fit the linear regression model by means of ridge estimation for each $\lambda$ in the grid using the training set, and the corresponding estimate of the error variance $\hat{\sigma}_{-i}^2(\lambda)$, as +* Fit the linear regression model by means of ridge estimation for each $\lambda$ in the grid using the training set, and the corresponding estimate of the error variance $\hat{\sigma}_{-i}^2(\lambda)$, as !bt \begin{align*} \hat{\beta}_{-i}(\lambda) & = ( \hat{X}_{-i, \ast}^{\top} @@ -1552,18 +1552,18 @@ o Fit the linear regression model by means of ridge estimation for each $\lambd \end{align*} !et -o Evaluate the prediction performance of these models on the test set by $\log\{L[y_i, \hat{X}_{i, \ast}; \hat{\beta}_{-i}(\lambda), \hat{\sigma}_{-i}^2(\lambda)]\}$. Or, by the prediction error $|y_i - \hat{X}_{i, \ast} \hat{\beta}_{-i}(\lambda)|$, the relative error, the error squared or the R2 score function. +* Evaluate the prediction performance of these models on the test set by $\log\{L[y_i, \hat{X}_{i, \ast}; \hat{\beta}_{-i}(\lambda), \hat{\sigma}_{-i}^2(\lambda)]\}$. Or, by the prediction error $|y_i - \hat{X}_{i, \ast} \hat{\beta}_{-i}(\lambda)|$, the relative error, the error squared or the R2 score function. -o Repeat steps 1) to 3) such that each sample plays the role of the test set once. +* Repeat the first three steps such that each sample plays the role of the test set once. -o Average the prediction performances of the test sets at each grid point of the penalty bias/parameter by computing the *cross-validated log-likelihood*. It is an estimate of the prediction performance of the model corresponding to this value of the penalty parameter on novel data. It is defined as +* Average the prediction performances of the test sets at each grid point of the penalty bias/parameter by computing the *cross-validated log-likelihood*. It is an estimate of the prediction performance of the model corresponding to this value of the penalty parameter on novel data. It is defined as !bt \begin{align*} \frac{1}{n} \sum_{i = 1}^n \log\{L[y_i, \mathbf{X}_{i, \ast}; \hat{\beta}_{-i}(\lambda), \hat{\sigma}_{-i}^2(\lambda)]\}. \end{align*} !et -o The value of the penalty parameter that maximizes the cross-validated log-likelihood is the value of choice. Or we can use the MSE or the R2 score functions. +* The value of the penalty parameter that maximizes the cross-validated log-likelihood is the value of choice. Or we can use the MSE or the R2 score functions. !split ===== Predicted Residual Error Sum of Squares =====