Relational Logistic Regression

ABSTRACT. Logistic regression is a commonly used representation for aggregators in Bayesian belief networks when a child has multiple parents. Variations of population, as well as a desire to model interactions between parents in relational models, introduce representational problems for using logistic regression in relational models. In this paper, we first examine the representational problems caused by population variation. We show how these problems arise even in simple cases with a single parametrized parent, and propose a linear relational logistic regression which we show can represent arbitrary linear (in population size) decision thresholds, where the traditional logistic regression cannot. Then we examine representing interactions between parents of a child node, and representing non-linear dependency on population size. We propose a multi-parent relational logistic regression which can represent interactions between parents and arbitrary polynomial decision thresholds. Finally, we show how other well-known aggregators can be represented using this relational logistic regression.