A* Sampling
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.
Cite
@article{arxiv.1411.0030,
title = {A* Sampling},
author = {Chris J. Maddison and Daniel Tarlow and Tom Minka},
journal= {arXiv preprint arXiv:1411.0030},
year = {2015}
}
Comments
V2: - reworded the last paragraph of Section 2 to clarify that the argmax is a sample from the normalized measure. - fixed notation in Algorithm 1. - fixed a typo in paragraph 2 of Section 5