The p-convolution forest: a method for solving graphical models with additive probabilistic equations

TL;DR

The paper introduces the convolution forest, a novel method combining convolution trees, belief propagation, and p-convolution to efficiently solve complex networks with additive constraints, enhancing model prototyping and inference in various scientific applications.

Contribution

It presents the convolution forest approach, integrating multiple techniques for the first time, with an improved algorithm and implementation for practical, fast inference in models with additive relationships.

Findings

Successfully applied to NP-complete problems like subset sum and knapsack

Effective in genomic region identification with large HMMs

Accurate inference of molecular composition and elemental abundance

Abstract

Convolution trees, loopy belief propagation, and fast numerical p-convolution are combined for the first time to efficiently solve networks with several additive constraints between random variables. An implementation of this "convolution forest" approach is constructed from scratch, including an improved trimmed convolution tree algorithm and engineering details that permit fast inference in practice, and improve the ability of scientists to prototype models with additive relationships between discrete variables. The utility of this approach is demonstrated using several examples: these include illustrations on special cases of some classic NP-complete problems (subset sum and knapsack), identification of GC-rich genomic regions with a large hidden Markov model, inference of molecular composition from summary statistics of the intact molecule, and estimation of elemental abundance in the presence of overlapping isotope peaks.