### Abstract

In previous work approximate solutions have been used for
expectation and variance of the {\em information component (IC)}. This
report presents an analytical approach to calculate exact expressions
for the expectation and variance of the information component (IC).
The IC is used in a Bayesian neural network
[ref TRITA-NA-P9325]
as a weight between neurons representing discrete events.
The IC relates the information
possessed about one state of one variable with one state of
another variable, and is used for calculation of a posterior
probability distribution conditioned on a set of given input events.
It is used as a measure of disproportionality in data mining

Explanation of data mining methods
.

The mutual information between two variables, as defined in
information theory [ref Shannon 1948, A Mathematical
Theory of Communication],
can in its discrete form be
regarded as a weighted sum of ICs. The expectation of the IC provides a
measure of the strength of an association between two states and its
variance a measure of the uncertainty, which is essential for low counter
values.

Timo Koski

Roland Orre
Last modified: Mon Feb 17 03:38:06 CET 2003