From 3c181c2c781f3fafdb1db9b72edd855dd0fe2d50 Mon Sep 17 00:00:00 2001
From: Pierre-Edouard Portier <p6e7p7@freeshell.org>
Date: Tue, 30 Nov 2021 18:44:47 +0100
Subject: [PATCH] =?UTF-8?q?Introduction=20de=20la=20standardisation=20des?=
 =?UTF-8?q?=20variables=20explicatives=20dans=20l'inf=C3=A9rence=20des=20p?=
 =?UTF-8?q?aram=C3=A8tres=20de=20la=20r=C3=A9gression=20Ridge=20par=20cons?=
 =?UTF-8?q?truction=20explicite=20de=20la=20matrice=20de=20Gram.=20La=20ve?=
 =?UTF-8?q?rsion=20de=20l'inf=C3=A9rence=20qui=20utilise=20le=20SVD=20donn?=
 =?UTF-8?q?e=20bien=20les=20m=C3=AAmes=20param=C3=A8tres=20pour=20une=20m?=
 =?UTF-8?q?=C3=AAme=20valeur=20de=20l'hyperparam=C3=A8tre=20de=20r=C3=A9gu?=
 =?UTF-8?q?larisation.?=
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---
 15_loocv.R | 10 ++++++++--
 1 file changed, 8 insertions(+), 2 deletions(-)

diff --git a/15_loocv.R b/15_loocv.R
index 03b6635..f77884d 100644
--- a/15_loocv.R
+++ b/15_loocv.R
@@ -4,10 +4,16 @@
 # un polynôme de degré fixé et avec l'ajout d'un facteur de régularisation en
 # norme L2 dont l'importance est contrôlée par l'hyperparamètre alpha.
 ridge.gram <- function(alpha, data, degre) {
-  A <- outer(c(data$X), 0:degre, "^")
+  A <- scale(outer(c(data$X), 1:degre, "^"))
+  Y <- data$Y
+  Ym <- mean(Y)
+  Y <- Y - Ym
   gram <- t(A) %*% A
   diag(gram) <- diag(gram) + alpha
-  solve(gram, as.vector(t(A) %*% data$Y))
+  coef <- solve(gram, as.vector(t(A) %*% Y))
+  coef <- coef / attr(A,"scaled:scale")
+  inter <- Ym - coef %*% attr(A,"scaled:center")
+  coef <- c(inter, coef)
 }
 
 ridge.svd <- function(alpha, data, degre) {