This paper addresses a data integration problem: given several mutually consistent datasetseach of which measures a subset of the variables of interest, how can one construct a probabilisticmodel that fits the data and gives reasonable answers to questions which are under-determined bythe data? Here we show how to obtain a Bayesian network model which represents the uniqueprobability function that agrees with the probability distributions measured by the datasets and oth-erwise has maximum entropy. We provide a general algorithm, OBN-cDS, which offers substantialefficiency savings over the standard brute-force approach to determining the maximum entropyprobability function. Furthermore, we develop modifications to the general algorithm which en-able further efficiency savings but which are only applicable in particular situations. We show thatthere are circumstances in which one can obtain the model (i) directly from the data; (ii) by solvingalgebraic problems; and (iii) by solving relatively simple independent optimisation problems.

Objective Bayesian Nets for Integrating Consistent Datasets / J. Landes, J. Williamson. - In: THE JOURNAL OF ARTIFICIAL INTELLIGENCE RESEARCH. - ISSN 1076-9757. - 74:(2022), pp. 393-458. [10.1613/jair.1.13363]

Objective Bayesian Nets for Integrating Consistent Datasets

J. Landes;
2022

Abstract

This paper addresses a data integration problem: given several mutually consistent datasetseach of which measures a subset of the variables of interest, how can one construct a probabilisticmodel that fits the data and gives reasonable answers to questions which are under-determined bythe data? Here we show how to obtain a Bayesian network model which represents the uniqueprobability function that agrees with the probability distributions measured by the datasets and oth-erwise has maximum entropy. We provide a general algorithm, OBN-cDS, which offers substantialefficiency savings over the standard brute-force approach to determining the maximum entropyprobability function. Furthermore, we develop modifications to the general algorithm which en-able further efficiency savings but which are only applicable in particular situations. We show thatthere are circumstances in which one can obtain the model (i) directly from the data; (ii) by solvingalgebraic problems; and (iii) by solving relatively simple independent optimisation problems.
Settore M-FIL/02 - Logica e Filosofia della Scienza
Settore INF/01 - Informatica
Settore MAT/01 - Logica Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/937846
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