Title: 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.