Inference Trees: Adaptive Inference with Exploration

TL;DR

Inference trees (ITs) are a novel adaptive inference method inspired by Monte Carlo tree search, which dynamically partitions the parameter space to improve sampling efficiency, uncertainty estimation, and long-range dependency capture.

Contribution

We propose inference trees, a new adaptive sampling framework that learns hierarchical partitions online, enhancing existing inference methods like sequential Monte Carlo.

Findings

ITs improve sampling efficiency and accuracy.

ITs effectively identify high posterior regions.

ITs enhance sequential Monte Carlo performance.

Abstract

We introduce inference trees (ITs), a new class of inference methods that build on ideas from Monte Carlo tree search to perform adaptive sampling in a manner that balances exploration with exploitation, ensures consistency, and alleviates pathologies in existing adaptive methods. ITs adaptively sample from hierarchical partitions of the parameter space, while simultaneously learning these partitions in an online manner. This enables ITs to not only identify regions of high posterior mass, but also maintain uncertainty estimates to track regions where significant posterior mass may have been missed. ITs can be based on any inference method that provides a consistent estimate of the marginal likelihood. They are particularly effective when combined with sequential Monte Carlo, where they capture long-range dependencies and yield improvements beyond proposal adaptation alone.