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#### Complex Probabilistic Modeling with Recursive Relational Bayesian Networks

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##### Zitation

Jaeger, M. (2001). Complex Probabilistic Modeling with Recursive Relational Bayesian
Networks.* Annals of Mathematics and Artificial Intelligence,* *32*,
179-220.

Zitierlink: http://hdl.handle.net/11858/00-001M-0000-000F-31F6-2

##### Zusammenfassung

A number of representation systems have been proposed that
extend the purely propositional Bayesian network paradigm
with representation tools for some types of first-order
probabilistic dependencies. Examples of such systems are
dynamic Bayesian networks and systems for knowledge based
model construction. We can identify the representation of
probabilistic relational
models as a common well-defined semantic
core of such systems.
Recursive relational Bayesian networks (RRBNs) are a
framework for the representation of probabilistic relational models.
A main design goal for RRBNs
is to achieve greatest possible expressiveness
with as few elementary syntactic constructs as possible. The advantage
of such an approach is that a system based on a small number
of elementary constructs will be much more amenable to a thorough
mathematical investigation of its semantic and algorithmic
properties than a system based on a larger number of high-level
constructs. In this paper we show that with RRBNs
we have achieved our goal, by showing, first,
how to solve within that framework a number of non-trivial
representation problems. In the second part of the paper
we show how to construct from a RRBN and a specific query,
a standard Bayesian network in which the answer to the query
can be computed with standard inference algorithms. Here the
simplicity of the underlying representation framework
greatly facilitates the development of simple algorithms
and correctness proofs. As a result we obtain a construction
algorithm that even for RRBNs that represent models for complex first-order
and statistical dependencies generates standard Bayesian networks
of size polynomial in the size of the domain given in a specific
application instance.