A. Perez, M. Studeny:
Comparison of two methods for approximation of probability
distributions with prescribed marginals.
Kybernetika 43 (2007),
n. 5, pp. 591-618.
Let P be a discrete multidimensional probability distribution
over a finite set of variables N which is only partially
specified by the requirement that it has prescribed given
marginals for A in S, where S is a class of
subsets of N whose union is N. The paper deals with the
problem of approximating P on the basis of those given
marginals. The divergence of an approximation P' from P
is measured by the relative entropy of P with respect
to P'. Two methods for approximating P are compared.
One of them uses formerly
introduced concept of dependence structure simplification.
The other one is based on an explicit expression,
which has to be normalized. We give examples showing that
neither of these two methods is universally better than the other.
If one of the considered approximations P' really has the
prescribed marginals then it appears to be the distribution P
with minimal possible multiinformation. A simple condition on the
class S implying the existence of an approximation P' with
prescribed marginals is recalled. If the condition holds then both
methods for approximating P give the same result.
- AMS classification 68T30
- marginal problem,
- relative entropy,
- explicit expression,
- dependence structure simplification,
- decomposable model,
pdf version of the published paper (462kB) is available.
The paper builds on the ideas developed in the paper:
- A. Perez:
of the dependence structure of random variables.
Kybernetika 13 (1979),