# On Testing Whether an Embedded Bayesian Network Represents a Probability Model

Testing the validity of probabilistic models containing unmeasured (hidden) variables is shown to be a hard task. We show that the task of testing whether models are structurally incompatible with the data at hand, requires an exponential number of independence evaluations, each of the form: "X is conditionally independent of Y, given Z." In contrast, a linear number of such evaluations is required to test a standard Bayesian network (one per vertex). On the positive side, we show that if a network with hidden variables G has a tree skeleton, checking whether G represents a given probability model P requires the polynomial number of such independence evaluations. Moreover, we provide an algorithm that efficiently constructs a tree-structured Bayesian network (with hidden variables) that represents P if such a network exists, and further recognizes when such a network does not exist.

• 25 publications
• 2 publications
• 44 publications
01/16/2013

### Perfect Tree-Like Markovian Distributions

We show that if a strictly positive joint probability distribution for a...
10/22/2019

### Embedded Bayesian Network Classifiers

Low-dimensional probability models for local distribution functions in a...
07/20/2022

### Computing Tree Decompositions with Small Independence Number

The independence number of a tree decomposition is the maximum of the in...
01/10/2013

### A Bayesian Multiresolution Independence Test for Continuous Variables

In this paper we present a method ofcomputing the posterior probability ...
04/19/2022