tsmvr: Truly Spare MultiVariate Regression

In spcorum/tsmvr: Truly Sparse Multivariate Regression

Description

Calculates sparse solutions to the multivariate regression problem with correlated errors. Let X be the n-by-p predictor matrix, Y be the n-by-q response matrix, B be the p-by-q regression matrix, and Ω be the q-by-q precision matrix (inverse of the covariance matrix Σ). Let s1 be a sparsity parameter that only allows the top s1 values for B in aboslute value be nonzero, and lets s2 be defined similarly for Ω. Then this functions calculates the solution to

(B_hat,Ω_hat) = argmin_(B,Ω) (1/n*Tr[(Y-XB)^T*Ω*(Y-XB)] - log|Ω

|) such that ||B||_(1,1) ≤ s1 and ||Ω||_(1,1) ≤ s2. Here || * ||_(1,1) indicates the 1-1 "norm" that counts the number of nonzero matrix entries.

Usage

tsmvr(X, Y, s1 = NULL, s2 = NULL, s1_vec = NULL, s2_vec = NULL,
  method = c("single", "gs"), pars, quiet = FALSE, seed = NULL)

Arguments

X	n-by-p predictor matrix
Y	n-by-q response matrix
s1	sparsity for p-by-q regressor matrix B (positive integer or NULL)
s2	sparsity for q-by-q precision matrix Omega (positive integer or NULL)
s1_vec	s1 values for gridsearch (vector of integer valued numerics or NULL)
s2_vec	s2 values for gridsearch (vector of integer valued numerics or NULL)
method	method of solver ('single' is to solve a single problem, 'gs' is to perform gridsearch)
pars	list of algorithm parameters as constructed by the set_parameters function
quiet	whether not to print statuses to the screen (bool)
seed	set random seed (integer or NULL)

Value

A list containing the mean and sd of the error over the replicates as well as the means and standard deviations of the errors across each fold.

Note

See also set_parameters.

spcorum/tsmvr documentation built on Aug. 31, 2019, 8:58 p.m.