factor_mle: Regularized maximum likelihood factor analysis with...

In dcgerard/succotashr: Surrogate and Confounder Correction Occuring Together with Adaptive Shrinkage

Description

factor_mle implements regularized maximum likelihood estimation on a data matrix where the mean is low rank (with the rank known) and the columns are heteroscedastic but independent.

Usage

factor_mle(Y, k, itermax = 100, tol = 10^-6, print_diff = FALSE,
  sig_reg = 0.01)

Arguments

Y	A matrix. This is an n by p matrix, where the the columns are heteroscedastic.
k	A numeric. The rank of the mean matrix.
itermax	An integer. The maximum number of block-coordinate ascent iterations to perform when calculating the MLE.
tol	A numeric. When the difference from one of the ratio of two successive log-likelihoods is less than tol, the algorithm will stop.
print_diff	A logical. Should we print to the screen the updates?
sig_reg	The regularization parameter. Never set to 0.

Details

This function calculates the regularized MLE under a normal model with a low-rank mean, a diagonal column covariance matrix, and an identity row covariance matrix. The regularization is on the covariance matrix.

The unregularized version of this factor analysis can be found in Sun et al (2012). However, the likelihood is unbounded and there are many "MLE's" that have that unbounded likelihood. This apparently was unnoticed in Sun et al (2012). sig_reg should never be set to 0.

Value

A The low rank mean estimate.

sig_diag A vector of the variance estimates of the columns.

dcgerard/succotashr documentation built on May 15, 2019, 1:25 a.m.