Lost relatives of the Gumbel trick
Matej Balog,Nilesh Tripuraneni,Zoubin Ghahramani,Adrian Weller +3 more
- pp 371-379
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TLDR
The Gumbel trick as mentioned in this paper is a method to sample from a discrete probability distribution, or to estimate its normalizing partition function, which relies on repeatedly applying a random perturbation to the distribution in a particular way, each time solving for the most likely configuration.Abstract:
© 2017 International Machine Learning Society (IMLS). All rights reserved. The Gumbel trick is a method to sample from a discrete probability distribution, or to estimate its normalizing partition function. The method relies on repeatedly applying a random perturbation to the distribution in a particular way, each time solving for the most likely configuration. We derive an entire family of related methods, of which the Gumbel trick is one member, and show that the new methods have superior properties in several settings with minimal additional computational cost. In particular, for the Gumbel trick to yield computational benefits for discrete graphical models, Gumbel perturbations on all configurations are typically replaced with socalled low-rank perturbations. We show how a subfamily of our new methods adapts to this setting, proving new upper and lower bounds on the log partition function and deriving a family of sequential samplers for the Gibbs distribution. Finally, we balance the discussion by showing how the simpler analytical form of the Gumbel trick enables additional theoretical results.read more
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A* Sampling
TL;DR: A* sampling as mentioned in this paper is a generic sampling algorithm that searches for the maximum of a Gumbel process using A* search, which makes more efficient use of bound and likelihood evaluations than the most closely related adaptive rejection sampling based algorithms.