# Sparse regression with paired covariates

The R package palasso implements the paired lasso.

## Installation

Installing the current release from CRAN:

install.packages("palasso")

Installing the latest development version from GitHub:

#install.packages("devtools")
library(devtools)
install_github("rauschenberger/palasso")

## Initialisation

We use glmnet for the standard lasso, and palasso for the paired lasso.

library(glmnet)
library(palasso)

Attaching some data to reproduce the examples:

attach(toydata)

Data are available for $$n=30$$ samples and $$p=50$$ covariate pairs. The object y contains the response (numeric vector of length $$n$$). The object X contains the covariates (list of two numeric matrices, both with $$n$$ rows and $$p$$ columns).

## Standard lasso

The standard lasso is a good choice for exploiting either the first or the second covariate group:

object <- glmnet(y=y,x=X[[1]])
object <- glmnet(y=y,x=X[[2]])

## Paired lasso

But the paired lasso might be a better choice for exploiting both covariates groups at once:

object <- palasso(y=y,X=X)

In contrast to the standard lasso, the paired lasso accounts for the structure between the covariate groups.

Given a limited number of non-zero coefficients, we expect the paired lasso to outperform the standard lasso:

object <- palasso(y=y,X=X,max=10)

## Methods

Standard methods are available for the paired lasso:

weights(object)
fitted(object)
residuals(object)
predict(object,newdata=X)

## Reference

A Rauschenberger, I Ciocanea-Teodorescu, RX Menezes, MA Jonker, and MA van de Wiel (2020). “Sparse classification with paired covariates”. Advances in Data Analysis and Classification. 14:571-588. doi: 10.1007/s11634-019-00375-6