fista_LpS: low-rank plus sparse structure matrix estimation function...

In kevinbai92/LSvarEstimate: Low Rank Plus Sparse VAR Model Estimation

Description

low-rank plus sparse structure matrix estimation function solved by FISTA algorithm

Usage

fista_LpS(A, b, alpha = 0.25, lambda, mu, niter, backtracking = TRUE, x.true)

Arguments

A	design matrix
b	target vector
alpha	a positive constant the measuring the degree of separating sparse from low-rank, default value is 0.25
lambda	tuning parameter for sparse component
mu	tuning parameter for low-rank component
niter	the number of iterations for FISTA algorithm
backtracking	boolean argument, indicating whether use backtracking method or not
x.true	the true coefficient

Details

This function is the main estimation function. It provides the estimators for sparse and low rank components simultaneously and use the constraint space to separate sparse from low rank. The main theoretical results can be found in the papers: Basu Sumanta, Xianqi Li, George Michalidis (2019).

Value

A list consisting of:

sparse.comp	the estimated sparse component
lr.comp	the estimated low rank component
obj.val	the values of objective function
rel.err	the relative error, if we know the true transition matrix

References

Basu, Sumanta, Xianqi Li, and George Michailidis. "Low rank and structured modeling of high-dimensional vector autoregressions." IEEE Transactions on Signal Processing 67.5 (2019): 1207-1222.

Examples

A <- matrix(stats::rnorm(10000), nrow = 400, ncol = 25)
b <- matrix(stats::rnorm(10000), nrow = 400, ncol = 25)
lambda <- 0.1
mu <- 0.5
niter <- 1000
x.true <- diag(25)
fista_LpS(A, b, alpha = 0.25, lambda = lambda, mu = mu, niter = niter, TRUE, x.true = x.true)

kevinbai92/LSvarEstimate documentation built on May 8, 2020, 1:04 a.m.