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Heloise Chevalier
projet SY19
Commits
5e18fb0b
Commit
5e18fb0b
authored
6 years ago
by
Heloise Chevalier
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ridge & lasso regression
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library
(
MASS
)
library
(
leaps
)
library
(
corrplot
)
library
(
glmnet
)
#chargement des donnes
reg.data
<-
read.table
(
"tp3_a18_reg_app.txt"
)
x.reg
<-
reg.data
[,
1
:
50
]
y.reg
<-
reg.data
[,
"y"
]
n
=
dim
(
reg.data
)[
1
]
reg.mask
=
sort
(
sample
(
x
=
1
:
n
,
size
=
trunc
(
n
*
2
/
3
)))
reg.appr
=
reg.data
[
reg.mask
,]
reg.test
=
reg.data
[
-
reg.mask
,]
x.appr
=
reg.appr
[,
1
:
50
]
y.appr
=
reg.appr
[,
"y"
]
x.test
=
reg.test
[,
1
:
50
]
y.test
=
reg.test
[,
"y"
]
#stocker modle dans le fichier RData
#pas stocker tous nos essais dans .Rdata (duh)
#fonctions : doivent retourner des prdictions partir du jeu de donnes en argument
#d'aprs Sylvain Rousseau : pour la rgression on a pas calculer d'erreurs de test
# on apprend sur toutes les donnes
# mais d'aprs le sujet il faut calculer l'esprance de l'erreur quadratique donc???
#il n'y aura pas la colonne y dans le data de test des profs
#infos sur donnes
summary
(
reg.data
)
cor
<-
cor
(
reg.data
)
corrplot
(
cor
)
#prdicteurs pas corrls entre eux ( part X19 corrl avec y maybe???)
#premire rgression test pour voir prdicteurs les plus significatifs
reg
<-
lm
(
y
~
.
,
data
=
reg.appr
)
summary
(
reg
)
confint
(
reg
)
plot
(
y.appr
,
reg
$
fitted.values
)
abline
(
0
,
1
)
#prdicteurs les plus significatifs:
# X1, X2, X3, -X10, X14, X19, -X24, X32, X34, X35, X37, X38, X39, -X40, X41, -X43
#esprance de l'erreur quadratique :
pred
<-
predict
(
reg
,
newdata
=
reg.test
)
plot
(
y.test
,
pred
)
abline
(
0
,
1
)
mean
((
y.test
-
pred
)
^
2
)
#2052.946
#infos sur les rsidus
rres
=
reg
$
residuals
rstd
=
rstandard
(
reg
)
rstu
=
rstudent
(
reg
)
plot
(
y.appr
,
rstd
)
plot
(
y.appr
,
rstu
)
shapiro.test
(
rres
)
## Q-Q plots
qqnorm
(
rres
,
asp
=
1
)
qqline
(
rres
,
dist
=
qnorm
)
qqnorm
(
rstd
,
asp
=
1
)
qqline
(
rstd
,
dist
=
qnorm
)
qqnorm
(
rstu
,
asp
=
1
)
qqline
(
rstu
,
dist
=
qnorm
)
#influence globale
plot
(
reg
,
which
=
4
,
cook.levels
=
c
(
0
,
0.1
))
plot
(
reg
,
which
=
5
,
cook.levels
=
c
(
0
,
0.1
))
#128 aberrant
#stepwise selection
reg.fit.exh
<-
regsubsets
(
y
~
.
,
data
=
reg.data
,
method
=
"exhaustive"
,
nvmax
=
15
,
really.big
=
T
)
x11
()
plot
(
reg.fit.exh
,
scale
=
"r2"
,
main
=
""
)
title
(
main
=
"best subset"
)
#forward
reg.fit.f
<-
regsubsets
(
y
~
.
,
data
=
reg.data
,
method
=
"forward"
,
nvmax
=
15
,
really.big
=
T
)
plot
(
reg.fit.f
,
scale
=
"r2"
,
main
=
""
)
title
(
main
=
"forward"
)
#backward
reg.fit.b
<-
regsubsets
(
y
~
.
,
data
=
reg.data
,
method
=
"backward"
,
nvmax
=
15
,
really.big
=
T
)
plot
(
reg.fit.b
,
scale
=
"r2"
,
main
=
""
)
title
(
main
=
"backward"
)
#AIC et BIC
reg.fit
<-
regsubsets
(
y
~
.
,
data
=
reg.data
,
method
=
"exhaustive"
,
nvmax
=
15
,
really.big
=
T
)
x11
()
plot
(
reg.fit
,
scale
=
"adjr2"
,
main
=
""
)
title
(
main
=
"AIC"
)
x11
()
plot
(
reg.fit
,
scale
=
"bic"
,
main
=
""
)
title
(
main
=
"BIC"
)
#pas de diffrence entre tous ces rsultats, on part sur un premier subset avec tous les prdicteurs au dessus de 0.9
reg.model
<-
lm
(
y
~
X1
+
X2
+
X3
+
X14
+
X19
+
X32
+
X34
+
X35
+
X37
+
X38
+
X39
+
X41
,
data
=
reg.appr
)
summary
(
reg.model
)
#X24, X46 et X49 pas trs significatif ici, ils dgagent
confint
(
reg.model
)
plot
(
y.appr
,
reg.model
$
fitted.values
)
abline
(
0
,
1
)
#esprance de l'erreur quadratique :
pred.model
<-
predict
(
reg.model
,
newdata
=
reg.test
)
plot
(
y.test
,
pred.model
)
abline
(
0
,
1
)
mean
((
y.test
-
pred.model
)
^
2
)
#1755.945 c mieux
#infos sur les rsidus
rres.model
=
reg.model
$
residuals
rstd.model
=
rstandard
(
reg.model
)
rstu.model
=
rstudent
(
reg.model
)
plot
(
y.appr
,
rstd.model
)
plot
(
y.appr
,
rstu.model
)
shapiro.test
(
rres.model
)
## Q-Q plots
qqnorm
(
rres.model
,
asp
=
1
)
qqline
(
rres.model
,
dist
=
qnorm
)
qqnorm
(
rstd.model
,
asp
=
1
)
qqline
(
rstd.model
,
dist
=
qnorm
)
qqnorm
(
rstu.model
,
asp
=
1
)
qqline
(
rstu.model
,
dist
=
qnorm
)
#influence globale
plot
(
reg.model
,
which
=
4
,
cook.levels
=
c
(
0
,
0.1
))
plot
(
reg.model
,
which
=
5
,
cook.levels
=
c
(
0
,
0.1
))
#aucun point aberrant on est contents (quelques point un peu limites : 114, 118, 140)
#transfo non linaires ?
# les plots des rsidus en fonction de chaque prdicteur ne rvlent aucune tendance qui suggrerait une transfo non linaire
plot
(
reg.appr
$
X1
,
rstd.model
)
plot
(
reg.appr
$
X2
,
rstd.model
)
plot
(
reg.appr
$
X3
,
rstd.model
)
plot
(
reg.appr
$
X14
,
rstd.model
)
plot
(
reg.appr
$
X17
,
rstd.model
)
plot
(
reg.appr
$
X19
,
rstd.model
)
#quadratique?
plot
(
reg.appr
$
X32
,
rstd.model
)
plot
(
reg.appr
$
X34
,
rstd.model
)
#quadratique?
plot
(
reg.appr
$
X35
,
rstd.model
)
plot
(
reg.appr
$
X37
,
rstd.model
)
plot
(
reg.appr
$
X38
,
rstd.model
)
plot
(
reg.appr
$
X39
,
rstd.model
)
plot
(
reg.data
$
X41
,
rstd.model
)
# voir
##ridge regression
x
<-
model.matrix
(
y
~
X1
+
X2
+
X3
+
X14
+
X19
+
X32
+
X34
+
X35
+
X37
+
X38
+
X39
+
X41
,
reg.data
)
xapp
<-
x
[
reg.mask
,]
xtst
<-
x
[
-
reg.mask
,]
cv.out
<-
cv.glmnet
(
xapp
,
y.appr
,
alpha
=
0
)
plot
(
cv.out
)
fit
<-
glmnet
(
xapp
,
y.appr
,
lambda
=
cv.out
$
lambda.min
,
alpha
=
0
)
#esperance de l'erreur quadratique :
pred.ridge
<-
predict
(
fit
,
s
=
cv.out
$
lambda.min
,
newx
=
xtst
)
plot
(
y.test
,
pred.ridge
)
abline
(
0
,
1
)
mean
((
y.test
-
pred.ridge
)
^
2
)
#1857.962 on a vu mieux
#lasso regression
cv.out.lasso
<-
cv.glmnet
(
xapp
,
y.appr
,
alpha
=
1
)
plot
(
cv.out.lasso
)
fit.lasso
<-
glmnet
(
xapp
,
y.appr
,
lambda
=
cv.out.lasso
$
lambda.min
,
alpha
=
1
)
pred.lasso
<-
predict
(
fit.lasso
,
s
=
cv.out.lasso
$
lambda.min
,
newx
=
xtst
)
plot
(
y.test
,
pred.lasso
)
abline
(
0
,
1
)
mean
((
y.test
-
pred.lasso
)
^
2
)
#1754.978
#meilleur resultat so far (pas de beaucoup par rapport au modle avec subset)
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