log_likelihood: Calculate the log likelihood for StPCA with given parameters

In JimSkinner/spca: Structured PCA

Description

Calculate the log likelihood for StPCA with given parameters

Usage

log_likelihood(X, W, mu, sigSq)

Arguments

X

Data

Value

log likelihood (numeric)

Examples

d = 50
k = 5
n = 15

set.seed(1)
X  = matrix(rnorm(n*d), nrow=n, ncol=d)
mu = colMeans(X)
Xc = sweep(X, 2, mu, '-')
covar.svd = svd(Xc/sqrt(n), nu=0, nv=k)
covar.eigval = covar.svd$d^2
sigSq = sum(covar.eigval[-(1:k)])/(d-k)
W     = covar.svd$v %*% diag(sqrt(covar.eigval[1:k] - sigSq), ncol=k, nrow=k)

R     = svd(matrix(rnorm(k*k), ncol=k, nrow=k))$u # Random orthonormal matrix

# The likelihood is invariant to multiplying  by an orthonormal matrix.
l1 = log_likelihood(X, W, mu, sigSq)
l2 = log_likelihood(X, W%*%R, mu, sigSq)
stopifnot(all.equal(l1, l2))

JimSkinner/spca documentation built on May 7, 2019, 10:52 a.m.