Scaling the weight parameters in Markov logic networks and relational logistic regression models
This work addresses parameter scaling issues in statistical relational AI, offering insights for model selection and application in areas like random sampling, but it is incremental as it builds on existing formalisms.
The paper investigates the effect of scaling weight parameters with domain size in statistical relational AI models, showing that relational logistic regression allows transparent asymptotic control and providing an algorithm for asymptotic probabilities, while Markov logic networks do not exhibit this property.
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.