A* Sampling

TL;DR

This paper introduces A* sampling, a novel method that transforms the problem of sampling from continuous distributions into an optimization task over continuous space, utilizing the Gumbel process and A* search for efficiency.

Contribution

It presents a new construction of the Gumbel process and a practical A* sampling algorithm for continuous distributions, improving efficiency over existing methods.

Findings

A* sampling efficiently finds samples by maximizing the Gumbel process.

The method outperforms adaptive rejection sampling in bound and likelihood evaluations.

The approach is theoretically sound with proven correctness and convergence.

Abstract

The problem of drawing samples from a discrete distribution can be converted into a discrete optimization problem. In this work, we show how sampling from a continuous distribution can be converted into an optimization problem over continuous space. Central to the method is a stochastic process recently described in mathematical statistics that we call the Gumbel process. We present a new construction of the Gumbel process and A* sampling, a practical generic sampling algorithm that searches for the maximum of a Gumbel process using A* search. We analyze the correctness and convergence time of A* sampling and demonstrate empirically that it makes more efficient use of bound and likelihood evaluations than the most closely related adaptive rejection sampling-based algorithms.