In MGallow/ADMMsigma: Penalized Precision Matrix Estimation via ADMM

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

This is a short effort to give users an idea of how long the functions take to process. The benchmarks were performed using the default R install on Travis CI.

Note: the benchmarks -- particularly ADMMsigma -- run significantly faster on my personal machine (MacBook Pro Late 2016). In most cases, the processes take $\approx$ 25\% of the time.

We will be estimating a tri-diagonal precision matrix with dimension $p = 100$:

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library(ADMMsigma)
library(microbenchmark)

#  generate data from tri-diagonal (sparse) matrix
# compute covariance matrix (can confirm inverse is tri-diagonal)
S = matrix(0, nrow = 100, ncol = 100)

for (i in 1:100){
  for (j in 1:100){
    S[i, j] = 0.7^(abs(i - j))
  }
}

# generate 1000 x 100 matrix with rows drawn from iid N_p(0, S)
set.seed(123)
Z = matrix(rnorm(1000*100), nrow = 1000, ncol = 100)
out = eigen(S, symmetric = TRUE)
S.sqrt = out$vectors %*% diag(out$values^0.5) %*% t(out$vectors)
X = Z %*% S.sqrt

# calculate sample covariance matrix
Sample = (nrow(X) - 1)/nrow(X)*cov(X)

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• Default convergence tolerance with specified tuning parameters (no cross validation):

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# benchmark ADMMsigma - default tolerance
microbenchmark(ADMMsigma(S = Sample, lam = 0.1, alpha = 1, tol.abs = 1e-4, tol.rel = 1e-4, trace = "none"))

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• Stricter convergence tolerance with specified tuning parameters (no cross validation):

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# benchmark ADMMsigma - tolerance 1e-8
microbenchmark(ADMMsigma(S = Sample, lam = 0.1, alpha = 1, tol.abs = 1e-8, tol.rel = 1e-8, trace = "none"))

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• Default convergence tolerance with cross validation for both lam and alpha:

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# benchmark ADMMsigma CV - default parameter grid
microbenchmark(ADMMsigma(X, trace = "none"), times = 5)

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• Parallel (cores = 2) cross validation:

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# benchmark ADMMsigma parallel CV
microbenchmark(ADMMsigma(X, cores = 2, trace = "none"), times = 5)

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• Cross validation with log-likelihood convergence criteria:

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# benchmark ADMMsigma CV - likelihood convergence criteria
microbenchmark(ADMMsigma(X, crit = "loglik", trace = "none"), times = 5)

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• RIDGEsigma with fine parameter grid:

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# benchmark RIDGEsigma CV
microbenchmark(RIDGEsigma(X, lam = 10^seq(-8, 8, 0.01), trace = "none"), times = 5)

MGallow/ADMMsigma documentation built on May 15, 2019, 3:23 p.m.