In MGallow/ADMMsigma: Penalized Precision Matrix Estimation via ADMM

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

Overview

ADMMsigma is an R package that estimates a penalized precision matrix via the alternating direction method of multipliers (ADMM) algorithm. It currently supports a general elastic-net penalty that allows for both ridge and lasso-type penalties as special cases.

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

ADMMsigma() computes the estimated precision matrix (ridge, lasso, and elastic-net type regularization optional)
RIDGEsigma() computes the estimated ridge penalized precision matrix via closed-form solution
plot.ADMMsigma() produces a heat map or line graph for cross validation errors
plot.RIDGEsigma() produces a heat map or line graph for cross validation errors

See package website or manual.

Installation

# The easiest way to install is from CRAN
install.packages("ADMMsigma")

# You can also install the development version from GitHub:
# install.packages("devtools")
devtools::install_github("MGallow/ADMMsigma")

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(ADMMsigma)
set.seed(1234)

# generate data from a sparse oracle precision matrix
# we will try to estimate this matrix from the data

# first compute the oracle covariance matrix
S = matrix(0.7, nrow = 5, ncol = 5)
for (i in 1:5){
  for (j in 1:5){
    S[i, j] = S[i, j]^abs(i - j)
  }
}

# print oracle precision matrix
# because its sparse, some shrinkage might be useful
(Omega = round(qr.solve(S), 3))

# generate 100 x 5 data matrix with rows drawn from iid N_p(0, S)
set.seed(123)
Z = matrix(rnorm(100*5), nrow = 100, ncol = 5)
out = eigen(S, symmetric = TRUE)
S.sqrt = out$vectors %*% diag(out$values^0.5) %*% t(out$vectors)
X = Z %*% S.sqrt


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

# now use ADMMsigma to provide estimates
# elastic-net type penalty (set tolerance to 1e-8)
ADMMsigma(X, tol.abs = 1e-8, tol.rel = 1e-8)

# lasso penalty (default tolerance)
ADMMsigma(X, alpha = 1)

# elastic-net penalty (alpha = 0.5)
ADMMsigma(X, alpha = 0.5)

# ridge penalty
ADMMsigma(X, alpha = 0)

# ridge penalty (using closed-form solution)
RIDGEsigma(X, lam = 10^seq(-8, 8, 0.01))

# produce CV heat map for ADMMsigma
ADMM = ADMMsigma(X, lam = 10^seq(-5, 5, 0.1), alpha = seq(0, 1, 0.1))
plot(ADMM, type = "heatmap")

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

# produce CV heat map for RIDGEsigma
RIDGE = RIDGEsigma(X, lam = 10^seq(-8, 8, 0.01))
plot(RIDGE, type = "heatmap")

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