In MGallow/SCPME: Shrinking Characteristics of Precision Matrix Estimators

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 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(SCPME)
library(microbenchmark)

#  generate data from tri-diagonal (sparse) matrix
data = data_gen(p = 100, n = 1000, r = 5)

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

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

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# benchmark shrink - default tolerance
microbenchmark(shrink(S = sample, crit.cv = "loglik", lam = 0.1, 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 shrink - tolerance 1e-8
microbenchmark(shrink(S = sample, crit.cv = "loglik", lam = 0.1, tol.abs = 1e-8, tol.rel = 1e-8, trace = "none"))

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Default convergence tolerance with cross validation for lam:

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# benchmark shrink CV - default parameter grid
microbenchmark(shrink(X = data$X, Y = data$Y, trace = "none"), times = 5)

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Parallel (cores = 2) cross validation:

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# benchmark shrink parallel CV
microbenchmark(shrink(X = data$X, Y = data$Y, cores = 2, trace = "none"), times = 5)

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Cross validation with $B = \hat{\Sigma}_{xy}$:

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# benchmark shrink penalizing beta
lam_max = max(abs(crossprod(data$X, data$Y)))
microbenchmark(shrink(X = data$X, Y = data$Y, B = cov(data$X, data$Y), lam.max = lam_max, lam.min.ratio = 1e-4, trace = "none"), times = 5)

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Cross validation with $B = \left[\hat{\Sigma}{xy}, I{p} \right]$:

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# benchmark shrink penalizing beta and omega
microbenchmark(shrink(X = data$X, Y = data$Y, B = cbind(cov(data$X, data$Y), diag(ncol(data$X))), lam.max = 10, lam.min.ratio = 1e-4, trace = "none"), times = 5)