Black-box density function estimation using recursive partitioning
This provides a black-box solution for Bayesian computation that could benefit researchers in fields like physics who need density estimation without manual tuning.
The authors tackled the problem of Bayesian inference without requiring gradients or problem-specific tuning by developing a recursive partitioning method that approximates entire density functions with asymptotic exactness. Their algorithm achieved competitive performance compared to state-of-the-art methods on synthetic and real-world problems, including gravitational-wave physics applications.
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.