invcov.shrink {corpcor}R Documentation

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 Schaefer 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 Schaefer 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

The trick that allows the fast computation of the inverses of the shrinkage covariance and correlation matrices is the Woodbury matrix identity - see, e.g., http://en.wikipedia.org/wiki/Woodbury_matrix_identity. The key insight from this identity is that for inverting the covariance/correlation shrinkage estimator obtained from a n x p matrix you only need to invert a matrix of the size of the rank of the data matrix (which in "small n, large p" setting may mean substantial savings in computions).

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 Schaefer (http://www.stat.math.ethz.ch/~schaefer/) and Korbinian Strimmer (http://www.statistik.lmu.de/~strimmer/).

References

Schaefer, J., and Strimmer, K. (2005). A shrinkage approach to large-scale covariance estimation and implications for functional genomics. Statist. Appl. Genet. Mol. Biol.4:32. (http://www.bepress.com/sagmb/vol4/iss1/art32/)

See Also

cov.shrink, pcor.shrink, cor2pcor

Examples

## Not run: 

# load corpcor library
library("corpcor")

# generate data matrix
p <- 2000
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)

## End(Not run)

[Package corpcor version 1.4.1 Index]