README.md
In echi/mSIM: Multivariate Response Single Index Model

mSIM

This package implements the Multivariate Single index Model(mSIM) proposed by Feng et al. It can be formulated as following:

(\mathbf{y}{i}=\left{f{1}\left(\mathbf{x}{i}^{\top} \mathbf{B}{1}\right), \cdots, f_{q}\left(\mathbf{x}{i}^{\top} \mathbf{B}{\cdot q}\right)\right}^{\top}+\boldsymbol{\epsilon}_{i})

The mSIM algorithm can both tackle potential nonlinearity in multivariate response regression and challenges with high dimensional data. For more details, please read Feng’s paper Sparse Single Index Models for Multivariate Responses.

The package provides simulation data generation, mSIM model fitting, Bayesian Information Criteria evaluation and prediction to solve Multivariate Single Index Model problems.

The current working version can be installed from Github:

library(devtools)
install_github("ecchi/mSIM")

We use a small dataset within our package to illustrate our package.

library(mSIM)
## basic example code

## fitting the mSIM model
X_train = scale(X_train)
Y_train = scale(Y_train)
result = get_B_ADMM(Y = Y_train, X = X_train, lambda=0.03877, rank=3)

## Predict index covariate matrix
test_result = model_pred(Y = Y_train, X = X_train, B = result$B.sparse, Y.true = Y_test, X.pred = X_test)

if you want to run multiple (lambda, rank) pair and use Bayesian Information criteria to evaluate them, the following code is an example.

## Evaluating by using Bayesian Information criteria
# set up tuning parameter
range = c(0.25, 0.75)
rank = c(3, 10)
tuning = list() # all combination of tuning parameters
len.tuning = 0
for(i in rank){
  for(j in range){
    len.tuning = len.tuning + 1
    tuning[[len.tuning]] = c(j, i)
  }
} 

# mSIM model.
temp = list()
for(i in 1:length(tuning)){
    temp[[i]] = get_B_ADMM(Y=Y_train, X=X_train, lambda=tuning[[i]][1],
rank=tuning[[i]][2], alpha=1, control1=list(max.iter=5e1, tol=1e-3), select.method='linear', plot=F)
}
# B for each tuning parameter.
B = list()
for(i in 1:length(tuning)){
    B[[i]] = temp[[i]]$B.sparse
}

BIC.msim = NULL
# BIC for each tuning parameter.
for(i in 1:length(tuning)){
    BIC.msim = rbind(BIC.msim, B_BIC(Y=Y_train, X=X_train, B=B[[i]], tuning=tuning[[i]], linear=F))
}