invcov.shrink {corpcor}

Fast Computation of the Inverse of the Covariance and Correlation Matrix

Description

The functions invcov.shrink and invcor.shrink implement an algorithm to efficiently compute the inverses of shrinkage estimates of covariance (cov.shrink) and correlation (cor.shrink).

Usage

invcov.shrink(x, lambda, lambda.var, w, verbose=TRUE)
invcor.shrink(x, lambda, w, verbose=TRUE)

Arguments

x

a data matrix

lambda

the correlation shrinkage intensity (range 0-1). If lambda is not specified (the default) it is estimated using an analytic formula from Sch\"afer and Strimmer (2005) - see cor.shrink. For lambda=0 the empirical correlations are recovered.

lambda.var

the variance shrinkage intensity (range 0-1). If lambda.var is not specified (the default) it is estimated using an analytic formula from Sch\"afer and Strimmer (2005) - see var.shrink. For lambda.var=0 the empirical variances are recovered.

w

optional: weights for each data point - if not specified uniform weights are assumed (w = rep(1/n, n) with n = nrow(x)).

verbose

output status while computing (default: TRUE)

Details

Both invcov.shrink and invcor.shrink rely on powcor.shrink. This allows to compute the inverses in a very efficient fashion (much more efficient than directly inverting the matrices - see the example).

Value

invcov.shrink returns the inverse of the output from cov.shrink.

invcor.shrink returns the inverse of the output from cor.shrink.

Author(s)

Juliane Sch\"afer and Korbinian Strimmer (https://strimmerlab.github.io).

References

Sch\"afer, J., and K. Strimmer. 2005. A shrinkage approach to large-scale covariance estimation and implications for functional genomics. Statist. Appl. Genet. Mol. Biol. 4:32. <DOI:10.2202/1544-6115.1175>

See Also

powcor.shrink, cov.shrink, pcor.shrink, cor2pcor

Examples

# load corpcor library
library("corpcor")

# generate data matrix
p = 500
n = 10
X = matrix(rnorm(n*p), nrow = n, ncol = p)

lambda = 0.23  # some arbitrary lambda

# slow
system.time(
  (W1 =  solve(cov.shrink(X, lambda)))
)

# very fast
system.time(
  (W2 = invcov.shrink(X, lambda))
)

# no difference
sum((W1-W2)^2)