IBIA: An Incremental Build-Infer-Approximate Framework for Approximate Inference of Partition Function

Published: 28 Sept 2023, Last Modified: 28 Sept 2023Accepted by TMLREveryoneRevisionsBibTeX
Abstract: Exact computation of the partition function is known to be intractable, necessitating approximate inference techniques. Existing methods for approximate inference are slow to converge for many benchmarks. The control of accuracy-complexity trade-off is also non-trivial in many of these methods. We propose a novel incremental build-infer-approximate (IBIA) framework for approximate inference that addresses these issues. In this framework, the probabilistic graphical model is converted into a sequence of clique tree forests (SCTF) with bounded clique sizes. We show that the SCTF can be used to efficiently compute the partition function. We propose two new algorithms which are used to construct the SCTF and prove the correctness of both. The first is an algorithm for incremental construction of CTFs that is guaranteed to give a valid CTF with bounded clique sizes and the second is an approximation algorithm that takes a calibrated CTF as input and yields a valid and calibrated CTF with reduced clique sizes as the output. We have evaluated our method using several benchmark sets from recent UAI competitions and our results show good accuracies with competitive runtimes.
License: Creative Commons Attribution 4.0 International (CC BY 4.0)
Submission Length: Long submission (more than 12 pages of main content)
Changes Since Last Submission: Changes made to the camera ready version. 1. Reworded the statement of Proposition 9. Instead of saying "the normalization constant $Z_k$ is an estimate of the PR of factors added to $CTF_1$ to $CTF_k$", the statement now just gives an equation for $Z_k$. This equation is essentially Equation 10 in the previous version of the paper for an arbitrary $k$. 2. Removed the phrase "estimate of the PR" from the statement of Theorem 2. We have explained why it is an estimate in the main text. 3. Elaborated the proofs of Proposition 9 and Theorem 2 to make them more clear.
Video: https://www.youtube.com/watch?v=143xjwN-MSw
Assigned Action Editor: ~Kuldeep_S._Meel2
Submission Number: 1052