Type: Package
Title: Sparse Principal Component Regression
Version: 2.1.1
Date: 2022-10-15
Author: Shuichi Kawano
Maintainer: Shuichi Kawano <skawano@math.kyushu-u.ac.jp>
Description: The sparse principal component regression is computed. The regularization parameters are optimized by cross-validation.
License: GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
URL: https://doi.org/10.1016/j.csda.2015.03.016, https://doi.org/10.1016/j.csda.2018.03.008, https://sites.google.com/site/shuichikawanoen/software
Repository: CRAN
NeedsCompilation: yes
Packaged: 2022-10-15 09:08:48 UTC; shuichi
Date/Publication: 2022-10-16 07:30:06 UTC

Cross-validation for spcr

Description

This function performs cross-validation for spcr. cv.spcr enables us to determine two regularization parameters \lambda_\beta and \lambda_\gamma objectively.

Usage

cv.spcr(x, y, k, w=0.1, xi=0.01, nfolds=5, adaptive=FALSE, 
	center=TRUE, scale=FALSE, lambda.B.length=10, lambda.gamma.length=10,
	lambda.B=NULL, lambda.gamma=NULL)

Arguments

x

A data matrix.

y

A response vector.

k

The number of principal components.

w

Weight parameter with 0\le w \le 1. The default is 0.1.

xi

The elastic net mixing parameter with 0\le \alpha \le 1. The default is 0.01.

nfolds

The number of folds. The default is 5.

adaptive

If "TRUE", the adaptive SPCR is used.

center

If "TRUE", the data matrix is centered.

scale

If "TRUE", the data matrix is scaled.

lambda.B.length

The number of candidates for the parameter \lambda_\beta. The default is 10.

lambda.gamma.length

The number of candidates for the parameter \lambda_\gamma. The default is 10.

lambda.B

Optional user-supplied candidates for the parameter \lambda_\beta. The default is NULL.

lambda.gamma

Optional user-supplied candidates for the parameter \lambda_\gamma. The default is NULL.

Value

lambda.gamma.seq

The values of lambda.gamma in the fit.

lambda.B.seq

The values of lambda.B in the fit.

CV.mat

Matrix of the mean values of cross-validation. The row shows a sequence of lambda.gamma. The column shows a sequence of lambda.B.

lambda.gamma.cv

The value of lambda.gamma selected by cross-validation.

lambda.B.cv

The value of lambda.B selected by cross-validation.

cvm

The minimum of the mean cross-validated error.

Author(s)

Shuichi Kawano
skawano@ai.lab.uec.ac.jp

References

Kawano, S., Fujisawa, H., Takada, T. and Shiroishi, T. (2015). Sparse principal component regression with adaptive loading. Compuational Statistics & Data Analysis, 89, 192–203.

See Also

spcr

Examples

#data
n <- 50
np <- 5
set.seed(1)
nu0 <- c(-1, 1)
x <- matrix( rnorm(np*n), n, np )
e <- rnorm(n)
y <- nu0[1]*x[ ,1] + nu0[2]*x[ ,2] + e

#fit
cv.spcr.fit <- cv.spcr(x=x, y=y, k=2)
cv.spcr.fit

#fit (adaptive SPCR)
cv.adaspcr.fit <- cv.spcr(x=x, y=y, k=2, adaptive=TRUE)
cv.adaspcr.fit

Cross-validation for spcr-glm

Description

This function performs cross-validation for SPCR-glm. cv.spcrglm enables us to determine two regularization parameters \lambda_\beta and \lambda_\gamma objectively.

Usage

cv.spcrglm(x, y, k, family=c("binomial","poisson","multinomial"), 
	w=0.1, xi=0.01, nfolds=5, adaptive=FALSE, q=1, center=TRUE, 
	scale=FALSE, lambda.B.length=10, lambda.gamma.length=10,
	lambda.B=NULL, lambda.gamma=NULL)

Arguments

x

A data matrix.

y

A response vector.

k

The number of principal components.

family

Response type.

w

Weight parameter with w \ge 0. The default is 0.1.

xi

The elastic net mixing parameter with 0\le \alpha \le 1. The default is 0.01.

nfolds

The number of folds. The default is 5.

adaptive

If "TRUE", the adaptive SPCR-glm (aSPCR-glm) is used.

q

The tuning parameter that controls weights in aSPCR-glm. The default is 1.

center

If "TRUE", the data matrix is centered.

scale

If "TRUE", the data matrix is scaled.

lambda.B.length

The number of candidates for the parameter \lambda_\beta. The default is 10.

lambda.gamma.length

The number of candidates for the parameter \lambda_\gamma. The default is 10.

lambda.B

Optional user-supplied candidates for the parameter \lambda_\beta. The default is NULL.

lambda.gamma

Optional user-supplied candidates for the parameter \lambda_\gamma. The default is NULL.

Value

lambda.gamma.seq

The values of lambda.gamma in the fit.

lambda.B.seq

The values of lambda.B in the fit.

CV.mat

Matrix of the mean values of cross-validation. The row shows a sequence of lambda.gamma. The column shows a sequence of lambda.B.

lambda.gamma.cv

The value of lambda.gamma selected by cross-validation.

lambda.B.cv

The value of lambda.B selected by cross-validation.

cvm

The minimum of the mean cross-validated error.

Author(s)

Shuichi Kawano
skawano@ai.lab.uec.ac.jp

References

Kawano, S., Fujisawa, H., Takada, T. and Shiroishi, T. (2018). Sparse principal component regression for generalized linear models. Compuational Statistics & Data Analysis, 124, 180–196.

See Also

spcrglm

Examples

# binomial
n <- 100
np <- 3
nu0 <- c(-1, 1)
set.seed(4)
x <- matrix( rnorm(np*n), n, np )
y <- rbinom(n,1,1-1/(1+exp(  (nu0[1]*x[ ,1] + nu0[2]*x[ ,2]  ))))
cv.spcrglm.fit <- cv.spcrglm(x=x, y=y, k=1, family="binomial")
cv.spcrglm.fit

# Poisson
set.seed(5)
y <- rpois(n, 1)
cv.spcrglm.fit <- cv.spcrglm(x=x, y=y, k=1, family="poisson")
cv.spcrglm.fit

# multinomial
set.seed(4)
y <- sample(1:4, n, replace=TRUE)
cv.spcrglm.fit <- cv.spcrglm(x=x, y=y, k=1, family="multinomial")
cv.spcrglm.fit

Fit a sparse principal component regression (SPCR)

Description

This function computes a principal component regression model via sparse regularization.

Usage

spcr(x, y, k, lambda.B, lambda.gamma, w=0.1, xi=0.01, 
	adaptive=FALSE, center=TRUE, scale=FALSE)

Arguments

x

A data matrix.

y

A response vector.

k

The number of principal components.

lambda.B

The regularization parameter for the parameter B.

lambda.gamma

The regularization parameter for the coefficient vector \gamma.

w

Weight parameter with 0\le w \le 1. The default is 0.1.

xi

The elastic net mixing parameter with 0\le \alpha \le 1. The default is 0.01.

adaptive

If "TRUE", the adaptive SPCR is used.

center

If "TRUE", the data matrix is centered.

scale

If "TRUE", the data matrix is scaled.

Value

loadings.B

the loading matrix B

gamma

the coefficient

gamma0

intercept

loadings.A

the loading matrix A

Author(s)

Shuichi Kawano
skawano@ai.lab.uec.ac.jp

References

Kawano, S., Fujisawa, H., Takada, T. and Shiroishi, T. (2015). Sparse principal component regression with adaptive loading. Compuational Statistics & Data Analysis, 89, 192–203.

See Also

cv.spcr

Examples

#data
n <- 100
np <- 5
set.seed(4)
nu0 <- c(-1, 1)
x <- matrix( rnorm(np*n), n, np )
e <- rnorm(n)
y <- nu0[1]*x[ ,1] + nu0[2]*x[ ,2] + e

#fit
spcr.fit <- spcr(x=x, y=y, k=2, lambda.B=6, lambda.gamma=2)
spcr.fit

#fit (adaptive SPCR)
adaspcr.fit <- spcr(x=x, y=y, k=2, lambda.B=6, lambda.gamma=2, adaptive=TRUE)
adaspcr.fit

Fit a sparse principal component regression for generalized linear models (SPCR-glm)

Description

This function computes a principal component regression for generalized linear models via sparse regularization.

Usage

spcrglm(x, y, k, family=c("binomial","poisson","multinomial"), lambda.B, 
	lambda.gamma, w=0.1, xi=0.01, adaptive=FALSE, q=1, center=TRUE, scale=FALSE)

Arguments

x

A data matrix.

y

A response data.

k

The number of principal components.

family

Response type.

lambda.B

The regularization parameter for the parameter B.

lambda.gamma

The regularization parameter for the coefficient vector \gamma.

w

Weight parameter with w \ge 0. The default is 0.1.

xi

The elastic net mixing parameter with 0\le \alpha \le 1. The default is 0.01.

adaptive

If "TRUE", the adaptive SPCR-glm (aSPCR-glm) is used.

q

The tuning parameter that controls weights in aSPCR-glm. The default is 1.

center

If "TRUE", the data matrix is centered.

scale

If "TRUE", the data matrix is scaled.

Value

loadings.B

the loading matrix B

gamma

the coefficient

gamma0

intercept

loadings.A

the loading matrix A

Author(s)

Shuichi Kawano
skawano@ai.lab.uec.ac.jp

References

Kawano, S., Fujisawa, H., Takada, T. and Shiroishi, T. (2018). Sparse principal component regression for generalized linear models. Compuational Statistics & Data Analysis, 124, 180–196.

See Also

cv.spcrglm

Examples

# binomial
n <- 100
np <- 5
nu0 <- c(-1, 1)
set.seed(4)
x <- matrix( rnorm(np*n), n, np )
y <- rbinom(n,1,1-1/(1+exp(  (nu0[1]*x[ ,1] + nu0[2]*x[ ,2]  ))))
spcrglm.fit <- spcrglm(x=x, y=y, k=2, family="binomial", lambda.B=2, lambda.gamma=1)
spcrglm.fit

# Poisson
set.seed(4)
y <- rpois(n, exp(  (nu0[1]*x[ ,1] + nu0[2]*x[ ,2] ) ))
spcrglm.fit <- spcrglm(x=x, y=y, k=2, family="poisson", lambda.B=2, lambda.gamma=1)
spcrglm.fit

# multinomial
set.seed(4)
y <- sample(1:4, n, replace=TRUE)
spcrglm.fit <- spcrglm(x=x, y=y, k=2, family="multinomial", lambda.B=2, lambda.gamma=2)
spcrglm.fit