Inference Trees: Adaptive Inference with Exploration

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.

References in corpus (4)

• Analysis of Thompson Sampling for the multi-armed bandit problem
• Layered Adaptive Importance Sampling
• Lookahead Strategies for Sequential Monte Carlo
• Neural Adaptive Sequential Monte Carlo

Cited by in corpus (5)

• A RAD approach to deep mixture models
• Divide, Conquer, and Combine: a New Inference Strategy for Probabilistic Programs with Stochastic Support
• Trust-Region Variational Inference with Gaussian Mixture Models
• On Exploration, Exploitation and Learning in Adaptive Importance Sampling
• Approximate Inference in Discrete Distributions with Monte Carlo Tree Search and Value Functions