corpcor (version 1.4.0)

invcov.shrink: 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.shri

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

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)

Value

• invcov.shrink returns the inverse of the output from cov.shrink. invcor.shrink returns the inverse of the output from cor.shrink.

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).

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

# 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)