  In many applications (in particular information systems, such as pattern
recognition, machine learning, cheminformatics, bioinformatics to name but a
few) the assessment of uncertainty is essential - i.e., the estimation of the
underlying probability distribution function. More often than not, the form of
this function is unknown and it becomes necessary to non-parametrically
construct/estimate it from a given sample. One of the methods of choice to
non-parametrically estimate the unknown probability distribution function for a
given random variable (defined on binary space) has been the expansion of the
estimation function in Rademacher-Walsh Polynomial basis functions. In this
paper we demonstrate that the expansion of the probability distribution
function estimation in Rademacher-Walsh Polynomial basis functions is
equivalent to the expansion of the function estimation in a set of "Dirac
kernel" functions. The latter approach can ameliorate the computational
bottleneck and notational awkwardness often associated with the
Rademacher-Walsh Polynomial basis functions approach, in particular when the
binary input space is large.
