Towards Completely Lifted Search-based Probabilistic Inference

TL;DR

This paper investigates the fundamental limits of lifted probabilistic inference, providing conditions under which inference can be performed efficiently without grounding, and introduces new polynomial-time algorithms for specific cases.

Contribution

It characterizes when grounding is polynomial and presents lifted inference methods that are polynomial in population size, improving efficiency over traditional grounding methods.

Findings

Grounding is polynomial in certain cases, enabling efficient inference.

Lifted inference can be polynomial in the logarithm of population size under specific conditions.

For some cases, lifted inference is polynomial while grounding is exponential.

Abstract

The promise of lifted probabilistic inference is to carry out probabilistic inference in a relational probabilistic model without needing to reason about each individual separately (grounding out the representation) by treating the undistinguished individuals as a block. Current exact methods still need to ground out in some cases, typically because the representation of the intermediate results is not closed under the lifted operations. We set out to answer the question as to whether there is some fundamental reason why lifted algorithms would need to ground out undifferentiated individuals. We have two main results: (1) We completely characterize the cases where grounding is polynomial in a population size, and show how we can do lifted inference in time polynomial in the logarithm of the population size for these cases. (2) For the case of no-argument and single-argument parametrized random variables where the grounding is not polynomial in a population size, we present lifted inference which is polynomial in the population size whereas grounding is exponential. Neither of these cases requires reasoning separately about the individuals that are not explicitly mentioned.