Linear transformation of binary random vectors and its application to approximating probability distributions

A nonsingular linear transformation of binary-valued random vectors
y = xA
which minimizes a mutual information criterion I(y) is considered. It is shown that a nonsingular A exists such that
I(y) = 0
if and only if
x
has a generalized binomial distribution. Computational algorithms for seeking an optimal
A
are developed, and dimensionality reduction is discussed briefly. This linear transformation is useful in improving the approximation of probability distributions. Numerical examples are presented.