Relational Logistic Regression

Logistic regression is a commonly used representation for aggregators in Bayesian belief networks when a child has multiple parents. In this paper we consider extending logistic regression to relational models, where we want to model varying populations and interactions among parents. 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, whereas the traditional logistic regression cannot. Then we examine representing interactions among the 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 among parents and arbitrary polynomial decision thresholds. Finally, we show how other well-known aggregators can be represented using this relational logistic regression.