Partition Function Estimation: A Quantitative Study

Abstract

Probabilistic graphical models have emerged as a powerful modeling tool for several real-world scenarios where one needs to reason under uncertainty. A graphical model's partition function is a central quantity of interest, and its computation is key to several probabilistic reasoning tasks. Given the #P-hardness of computing the partition function, several techniques have been proposed over the years with varying guarantees on the quality of estimates and their runtime behavior. This paper seeks to present a survey of 18 techniques and a rigorous empirical study of their behavior across an extensive set of benchmarks. Our empirical study draws up a surprising observation: exact techniques are as efficient as the approximate ones, and therefore, we conclude with an optimistic view of opportunities for the design of approximate techniques with enhanced scalability. Motivated by the observation of an order of magnitude difference between the Virtual Best Solver and the best performing tool, we envision an exciting line of research focused on the development of portfolio solvers.

IBIA: Bayesian Inference via Incremental Build-Infer-Approximate operations on Clique Trees

“…Also, they give an estimate of all the queries of interest. These results agree with the results for PR reported in a recent evaluation of various approximate methods (Agrawal, Pote, & Meel, 2021). As a consistency check, we used both these methods for comparison.…”

“…Both libDAI and Merlin are robust and have been used for comparison with other methods (Agrawal et al, 2021;Lin et al, 2020).…”

Automatically Finding the Right Probabilities in Bayesian Networks

“…To evaluate our PMC-based tool for performing probabilistic inference on BNs, we took the state-of-the-art BN inference tool Ace as baseline. Ace 9 is developed by Darwiche's group that is the state-of-the-art for probabilistic inference on Bayesian networks; see the recent study (Agrawal, Pote, & Meel, 2021). It takes a BN as input and compiles it into an arithmetic circuit (AC).…”

Tractable Boolean and Arithmetic Circuits

“…The Boolean formula is then compiled into a tractable Boolean circuit (deterministic, decomposable and smooth), from which a tractable arithmetic circuit known as an AC is finally extracted. This approach is implemented by the ACE system, 8 which was recently evaluated in [1] and shown to exhibit state-of-the-art performance; see also [52].…”

“…These properties of tractable circuits made them very suitable for integration with modern pipelines for machine learning and neuro-symbolic AI; see, for example, [51,112,111,70,22,72,92,54,59,53] where tractable circuits have been recently employed in and/or integrated with neural networks, deep reinforcement learning, Bayesian network classifiers and (deep) probabilistic logic programs. 1 Even the traditional offline/online divide that originally motivated knowledge compilation for reasoning is now being exploited in modern settings as it is aligned with the training/inference divide that governs modern AI systems; see, e.g., [51]. As such, a recent trend has emerged in which tools and techniques that were initially envisioned for reasoning tasks are now being employed to facilitate learning and its integration with knowledge and reasoning.…”