Inference Trees: Adaptive Inference with Exploration
This addresses the challenge of adaptive sampling in Bayesian inference for researchers and practitioners, offering a novel method to alleviate pathologies in existing techniques.
The paper tackles the problem of adaptive inference by introducing inference trees, a method that balances exploration and exploitation to identify high posterior mass regions while maintaining uncertainty estimates. The result is a consistent approach that, when combined with sequential Monte Carlo, captures long-range dependencies and yields improvements beyond existing adaptive methods.
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.