A Priori Approximation of Symmetries in Dynamic Probabilistic Relational Models

Abstract

Lifted inference approaches reduce computational work as inference is performed using representatives for sets of indistinguishable random variables, which allows for tractable inference w.r.t. domain sizes in dynamic probabilistic relational models. Unfortunately, maintaining a lifted representation is challenging in practically relevant application domains, as evidence often breaks symmetries making lifted techniques fall back on their ground counterparts. In existing approaches asymmetric evidence is counteracted by merging similar but distinguishable objects when moving forward in time. While undoing splits a posteriori is reasonable, we propose learning approximate model symmetries a priori to prevent unnecessary splits due to inaccuracy or one-time events. In particular, we propose a multivariate ordinal pattern symbolization approach followed by spectral clustering to determine sets of domain entities behaving approximately the same over time. By using object clusters, we avoid unnecessary splits by keeping entities together that tend to behave the same over time. Understanding symmetrical and asymmetrical entity behavior a priori allows for increasing accuracy in inference by means of inferred evidence for unobserved entities to better represent reality. Empirical results show that our approach reduces unnecessary splits, i.e., improves runtimes, while keeping accuracy in inference high.

Appendix