Biclassified blockmodels as mixtures of standardized contingency tables with beta-distributed entries

Abstract

The blockmodel defined here is built of standardized random contingency table models, where the entries are independent beta-distributed with parameters depending on their row and column labels. Sufficient statistics are specified, and based on them, a convergent algorithm is introduced to find the MLE of the parameters. The model is extended to the multiclass scenario, where for fixed number of biclusters, the parameters of the beta-distributed entries also depend on their row and column cluster memberships. To find the clusters and estimate the parameters, an EM iteration for mixtures of exponential-family distributions is used. The algorithm is applicable to microarrays, and a genetic example is presented.