  We consider Markov logic networks and relational logistic regression as two
fundamental representation formalisms in statistical relational artificial
intelligence that use weighted formulas in their specification. However, Markov
logic networks are based on undirected graphs, while relational logistic
regression is based on directed acyclic graphs. We show that when scaling the
weight parameters with the domain size, the asymptotic behaviour of a
relational logistic regression model is transparently controlled by the
parameters, and we supply an algorithm to compute asymptotic probabilities. We
also show using two examples that this is not true for Markov logic networks.
We also discuss using several examples, mainly from the literature, how the
application context can help the user to decide when such scaling is
appropriate and when using the raw unscaled parameters might be preferable. We
highlight random sampling as a particularly promising area of application for
scaled models and expound possible avenues for further research.
