Relational logistic regression

Aggregation is a technique for representing conditional probability distributions as an analytic function of parents. Logistic regression is a commonly used representation for aggregators in Bayesian belief networks when a child has multiple parents. In this thesis, we consider extending logistic regression to directed relational models, where there are objects and relations among them, and we want to model varying populations and interactions among parents. 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. We compare our relational logistic regression to Markov logic networks and represent their analogies and differences. Finally, we show how other well-known aggregators can be represented using relational logistic regression.