In MGallow/SCPME: Shrinking Characteristics of Precision Matrix Estimators

knitr::opts_chunk$set(echo = TRUE, tidy = TRUE)

Overview

SCPME is an implementation of the methods described in "Shrinking Characteristics of Precision Matrix Estimators" (link). It estimates a penalized precision matrix via a modified alternating direction method of multipliers (ADMM) algorithm.

A (possibly incomplete) list of functions contained in the package can be found below:

shrink() computes the estimated precision matrix
data_gen() data generation function (for convenience)
plot.shrink() produces a heat map or line graph for cross validation errors

See package website or manual.

Installation

# The easiest way to install is from GitHub:
# install.packages("devtools")
devtools::install_github("MGallow/shrink")

If there are any issues/bugs, please let me know: github. You can also contact me via my website. Pull requests are welcome!

Usage

library(SCPME)
set.seed(123)

# generate data from a sparse oracle precision matrix
# we can use the built-in `data_gen` function

# generate 100 x 5 X data matrix and 100 x 1 Y data matrix
data = data_gen(p = 5, n = 100, r = 1)

# the default regression coefficients are sparse
data$betas

# default oracle precision matrix is also sparse
round(qr.solve(data$SigmaX), 5)


# now suppose we are interested in estimating the precision

# print marginal sample precision matrix for X
# this is perhaps a bad estimate (not sparse)
sample = (nrow(data$X) - 1)/nrow(data$X)*cov(data$X)
round(qr.solve(sample), 5)

# now use SCPME to estimate preicison matrix (omega) assuming sparsity
# note that this is simply a lasso penalized preicision matrix
shrink(data$X, lam = 0.5, crit.cv = "loglik")

# what if we instead assumed sparsity in beta? (print estimated omega)
# recall that beta is a product of marginal precision of X and cov(X, Y)
lam_max = max(abs(t(data$X) %*% data$Y))
(shrink = shrink(data$X, data$Y, B = cov(data$X, data$Y), nlam = 20, lam.max = lam_max))

# print estimated beta
shrink$Z

# we could also assume sparsity in beta AND omega (print estimated omega)
(shrink2 = shrink(data$X, data$Y, B = cbind(cov(data$X, data$Y), diag(ncol(data$X))), nlam = 20, lam.max = 10, lam.min.ratio = 1e-4))

# print estimated beta
shrink2$Z[,1, drop = FALSE]

# produce CV heat map for shrink
plot(shrink, type = "heatmap")

# produce line graph for CV errors for shrink
plot(shrink, type = "line")