Aggregation and Population Growth: The Relational Logistic Regression and Markov Logic Cases

This paper considers how relational probabilistic models adapt to population size. First we show that what are arbitrary choices for nonrelational domains become a commitment to how a relational model adapts to population change. We show how this manifests in a directed model where the conditional probabilities are represented using the logistic function, and show why it needs to be extended to a relational logistic function. Second we prove that directed aggregation models cannot be represented by Markov Logic without clauses that involve multiple individuals. Third we show how these models change as a function of population size.