Lifted Marginal MAP Inference

TL;DR

This paper introduces a novel lifted inference technique called SOM-R for marginal-MAP problems in relational models, reducing computational complexity by exploiting variable symmetries, leading to significant efficiency improvements.

Contribution

It defines the SOM and SOM-R equivalence classes, enabling domain reduction in lifted MMAP inference, which is a novel approach in this context.

Findings

Significant reductions in inference time and memory usage.

Effective domain reduction through SOM-R in benchmark domains.

Enhanced performance over existing lifted and ground inference methods.

Abstract

Lifted inference reduces the complexity of inference in relational probabilistic models by identifying groups of constants (or atoms) which behave symmetric to each other. A number of techniques have been proposed in the literature for lifting marginal as well MAP inference. We present the first application of lifting rules for marginal-MAP (MMAP), an important inference problem in models having latent (random) variables. Our main contribution is two fold: (1) we define a new equivalence class of (logical) variables, called Single Occurrence for MAX (SOM), and show that solution lies at extreme with respect to the SOM variables, i.e., predicate groundings differing only in the instantiation of the SOM variables take the same truth value (2) we define a sub-class {\em SOM-R} (SOM Reduce) and exploit properties of extreme assignments to show that MMAP inference can be performed by reducing the domain of SOM-R variables to a single constant.We refer to our lifting technique as the {\em SOM-R} rule for lifted MMAP. Combined with existing rules such as decomposer and binomial, this results in a powerful framework for lifted MMAP. Experiments on three benchmark domains show significant gains in both time and memory compared to ground inference as well as lifted approaches not using SOM-R.