Parallel Tempering on Optimized Paths

02/15/2021
by   Saifuddin Syed, et al.
0

Parallel tempering (PT) is a class of Markov chain Monte Carlo algorithms that constructs a path of distributions annealing between a tractable reference and an intractable target, and then interchanges states along the path to improve mixing in the target. The performance of PT depends on how quickly a sample from the reference distribution makes its way to the target, which in turn depends on the particular path of annealing distributions. However, past work on PT has used only simple paths constructed from convex combinations of the reference and target log-densities. This paper begins by demonstrating that this path performs poorly in the setting where the reference and target are nearly mutually singular. To address this issue, we expand the framework of PT to general families of paths, formulate the choice of path as an optimization problem that admits tractable gradient estimates, and propose a flexible new family of spline interpolation paths for use in practice. Theoretical and empirical results both demonstrate that our proposed methodology breaks previously-established upper performance limits for traditional paths.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

07/01/2021

q-Paths: Generalizing the Geometric Annealing Path using Power Means

Many common machine learning methods involve the geometric annealing pat...
12/15/2021

The Apogee to Apogee Path Sampler

Amongst Markov chain Monte Carlo algorithms, Hamiltonian Monte Carlo (HM...
11/17/2019

State Space Emulation and Annealed Sequential Monte Carlo for High Dimensional Optimization

Many high dimensional optimization problems can be reformulated into a p...
12/05/2018

Rapid mixing of path integral Monte Carlo for 1D stoquastic Hamiltonians

Path integral quantum Monte Carlo (PIMC) is a method for estimating ther...
05/09/2019

Stein Point Markov Chain Monte Carlo

An important task in machine learning and statistics is the approximatio...
11/07/2014

Variational Tempering

Variational inference (VI) combined with data subsampling enables approx...
01/10/2013

Iterative Markov Chain Monte Carlo Computation of Reference Priors and Minimax Risk

We present an iterative Markov chainMonte Carlo algorithm for computingr...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.