On non-graphical description of models of conditional
independence structure. Paper presented at
HSSS Workshop on Stochastic Systems for Individual Behaviours,
January 22-23, 2001, Louvain la Neuve, Belgium.
Several graphical structural models, including some models with latent
variables can be viewed as models of conditional independence structure.
However, usual graphical methods do not allow one to describe all possible
stochastic conditional independence structures. Therefore an attempt
to develop a general method of mathematical description of conditional
independence structures by means of certain integer-valued functions,
called structural imsets, was made. The main part of the paper
is an outline of this approach. The presented results concern
the mathematical basis of this method. After exposition of theoretical
background some open questions are discussed: the problem of internal
computer representation of models, inferential problems and
interpretation question. The paper is concluded by a cursory
reflection on what are suitable learning strategies and relevant data
generating procedures for models of conditional independence
- AMS classification 68T30
- conditional independence structure
- structural imset
- marginally continuous measures
postscript version (493kB) is available.