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1

Reasoning methods in general and stuctured Bayesian networks

Kłopotek M. A.

Studia Informatica : systems and information technology

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2003

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Vol. 1(1)

5--25

EN

Bayesian networks have many practical applications due to their capability to represent joint probability distribution in many variables in a compact way. Though there exist many algorithms for learning Bayesian networks from data, they are not satisfactory because the learned networks usually are not suitable for reasoning. So far only a restricted class of very simple Bayesian networks: trees and poly-trees are directly applicable in reasoning. This paper defines and explores a new class of networks: the Structured Bayesian Networks. Two methods of reasoning are outlined for this type of networks. Possible methods of learning from data are indicated. Similarity to hiearachical networks is pointed at.

2

On the Distance Hypothesis in Tree-like Bayesian Networks

Kłopotek M.

Prace Instytutu Podstaw Informatyki Polskiej Akademii Nauk

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2003

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Nr 952

1-14

EN

Bayesian networks have many practical applications due to their capability to represent joint probability distribution in many variables in a compact way. Though there exist many algorithms for learning Bayesian networks from data, they are not satisfactory because the learned networks usually are not suitable for reasoning. So far only for tree-like and poly-tree Bayesian networks and also for so-called Structured Bayesian networks a satisfactory reasoning algorithms applicable directly for Bayesian networks have been invented. This radically increases the need for efficient learning algorithms for these classes of Bayesian networks. In fact, algorithms learning tree-like Bayesian networks have been created allowing for learning in case of large numbers of variables. The fastest algorithm, however, relies on the assumption of special node similarity measure properties. This paper defines and explores a definition of such a similarity measure. It is also demonstrated that this measure facilitates development of algorithms for learning Structured Bayesian Networks from data.

PL

Sieci bayesowskie mają wiele praktycznych zastosowań związanych z ich zdolnością do zwartej reprezentacji rozkładów prawdopodobieństwa w wielu zmiennych. Choć znanych jest wiele algorytmów uczących sieci bayesowskie z danych, nie są one satysfakcjonujące, ponieważ wynikowe struktury sieci na ogół nie nadają się do celów wnioskowania eksperckiego, z wyjątkiem sieci drzewiastych, polidrzewiastych oraz strukturalnych. Szybkie metody uczenia dla sieci drzewiastych opierają się na postulacie specjalnej postaci funkcji podobieństaw między zmiennymi. Niniejszy artykół pokazuje, że w istocie istnieje postulowana miara podobieństwa. Demonstruje również implikacje wynikające dla uczenia sieci strukturalnych z danych.

3

Reasoning and Learning in Extended Structured Bayesian Networks

Kłopotek M. A.

Fundamenta Informaticae

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2003

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Vol. 58, nr 2

105--137

EN

Bayesian networks have many practical applications due to their capability to represent joint probability distribution over many variables in a compact way. Though there exist many algorithms for learning Bayesian networks from data, they are not satisfactory because the learned networks usually are not suitable directly for reasoning as they need to be transformed to some other form (tree, polytree, hypertree) statically or dynamically, and this transformation is not trivial [25]. So far only a restricted class of very simple Bayesian networks: trees and poly-trees are directly applicable in reasoning. This paper defines and explores a new class of networks: the Structured Bayesian Networks. Two methods of reasoning are outlined for this type of networks. Possible methods of learning from data are indicated. Similarity to hierarchical networks is pointed at.