Bayesian analysis of GUHA hypotheses

Authors:
Robert Piché;Marko Järvenpää;Esko Turunen;Milan Šimůnek
Affiliations:
Tampere University of Technology, Tampere, Finland;Tampere University of Technology, Tampere, Finland;Center for Machine Perception, Department of Cybernetics, Faculty of Electrical Engineering, Czech Technical University, Prague, Czech Republic;University of Economics Prague, Prague, Czech Republic
Venue:
Journal of Intelligent Information Systems
Year:
2014

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Abstract

The LISp-Miner system for data mining and knowledge discovery uses the GUHA method to comb through a large data base and finds 2 脳 2 contingency tables that satisfy a certain condition given by generalised quantifiers and thereby suggest the existence of possible relations between attributes. In this paper, we show how a more detailed interpretation of the data in the tables that were found by GUHA can be obtained using Bayesian statistical methods. Using a multinomial sampling model and Dirichlet prior, we derive posterior distributions for parameters that correspond to GUHA generalised quantifiers. Examples are presented illustrating the new Bayesian post-processing tools implemented in LISp-Miner. A statistical model for the analysis of contingency tables for data from two subpopulations is also presented.