Statistical Models for Co-occurrence Data

Abstract

Modeling and predicting co-occurrences of events is a fundamental problem of unsupervised learning. In this contribution we develop a statistical framework for analyzing co-occurrence data in a general setting where elementary observations are joint occurrences of pairs of abstract objects from two #nite sets. The main challenge for statistical models in this context is to overcome the inherent data sparseness and to estimate the probabilities for pairs whichwere rarely observed or even unobserved in a given sample set. Moreover, it is often of considerable interest to extract grouping structure or to #nd a hierarchical data organization.Anovel family of mixturemodels is proposed which explain the observed data bya #nite number of shared aspects or clusters. This provides a common framework for statistical inference and structure discovery and also includes several recently proposed models as special cases. Adopting the maximum likelihood principle, EM algorithms are derived t...