# Introduction to BOSO

We present *BOSO*, an R package to perform feature selection in a linear regression problem. It implements a Bilevel Optimization Selector Operator.

## Installation

BOSO can be installed from CRAN repository:

`install.packages("BOSO")`

## Introduction

The package package has been prepared to work like ‘glmnet’ and ‘lasso’, presented in the *BestSubset* package.

```
library(BOSO)
## Load the data prepared for this test
data("sim.xy", package = "BOSO")
Xtr <- sim.xy[['high-5']]$x
Ytr <- sim.xy[['high-5']]$y
Xval <- sim.xy[['high-5']]$xval
Yval <- sim.xy[['high-5']]$yval
## Perform BOSO
time <- Sys.time()
obj <- BOSO(x = Xtr, y = Ytr,
xval = Xval, yval = Yval,
IC = 'eBIC',
nlambda=100,
intercept= 0,
standardize = 0,
Threads=4, timeLimit = 60, verbose = 3,
seed = 2021)
time <- as.numeric(Sys.time() - time)
```

`obj`

is a BOSO object, which have the following associated functions:

`coef(obj)`

returns the coefficients (betas) of the linear regression.

`predict(obj, xnew)`

returns the predicted outcome with a new X matrix.

```
betas <- coef(obj)
print(betas[betas!=0])
Ytr_predicted <- predict(obj, Xtr)
print(paste0("MSE for training set is ", round(mean((Ytr_predicted-Ytr)^2),5)))
Yval_predicted <- predict(obj, Xval)
print(paste0("MSE for validation set is ", round(mean((Yval_predicted-Yval)^2),5)))
```