State-Space Abstractions for Probabilistic Inference: A Systematic Review

Abstract

Tasks such as social network analysis, human behavior recognition, or modeling biochemical reactions, can be solved elegantly by using the probabilistic inference framework. However, standard probabilistic inference algorithms work at a propositional level, and thus cannot capture the symmetries and redundancies that are present in these tasks.Algorithms that exploit those symmetries have been devised in different research fields, for example by the lifted inference-, multiple object tracking-, and modeling and simulationcommunities. The common idea, that we call state space abstraction, is to perform inference over compact representations of sets of symmetric states. Although they are concerned with a similar topic, the relationship between these approaches has not been investigated systematically.This survey provides the following contributions. We perform a systematic literature review to outline the state of the art in probabilistic inference methods exploiting symmetries. From an initial set of more than 4,000 papers, we identify 116 relevant papers. Furthermore, we provide new high-level categories that classify the approaches, based on common properties of the approaches. The research areas underlying each of the categories are introduced concisely. Researchers from different fields that are confronted with a state space explosion problem in a probabilistic system can use this classification to identify possible solutions. Finally, based on this conceptualization, we identify potentials for future research, as some relevant application domains are not addressed by current approaches.

Abstracting probabilistic models: Relations, constraints and beyond

“…Along these lines, a recent thrust in PRMs is the question of how to make inference more efficient by exploiting the relational vocabulary, referred to as "lifted reasoning" [71,64]. This is justifiably sometimes referred to as a type of "abstraction" [46]. There seem to be two implications for our work.…”

Abstracting Probabilistic Models: A Logical Perspective

“…Along these lines, a recent thrust in PRMs is the question of how to make inference more efficient by exploiting the relational vocabulary, referred to as "lifted reasoning" [61,54]. This is justifiably sometimes referred to as a type of "abstraction" [38]. There seem to be two implications for our work.…”

Goal Agnostic Learning and Planning without Reward Functions

“…𝑄(𝛼 𝑇 ) is directly correlated to the impact 𝛼 𝑇 has on performance, resolving the metric problem brought up in [16]. Because 𝛼 + 𝑇 is not strictly positive definite, 𝛼 𝑇 which improve performance are possible, albeit difficult to design.…”