Black-box density function estimation using recursive partitioning

TL;DR

This paper introduces a recursive partitioning method for density estimation that is gradient-free, tuning-free, and asymptotically exact, enabling efficient Bayesian inference and evidence estimation.

Contribution

It proposes a novel recursive partitioning approach for density estimation that does not rely on gradients or tuning, applicable to bounded domains and useful for Bayesian tasks.

Findings

Competitive performance on synthetic problems

Effective for gravitational-wave parameter inference

Provides accurate density approximations including normalization

Abstract

We present a novel approach to Bayesian inference and general Bayesian computation that is defined through a sequential decision loop. Our method defines a recursive partitioning of the sample space. It neither relies on gradients nor requires any problem-specific tuning, and is asymptotically exact for any density function with a bounded domain. The output is an approximation to the whole density function including the normalisation constant, via partitions organised in efficient data structures. Such approximations may be used for evidence estimation or fast posterior sampling, but also as building blocks to treat a larger class of estimation problems. The algorithm shows competitive performance to recent state-of-the-art methods on synthetic and real-world problems including parameter inference for gravitational-wave physics.