Schrödinger Bridge Samplers

12/31/2019
by   Espen Bernton, et al.
16

Consider a reference Markov process with initial distribution π_0 and transition kernels {M_t}_t∈[1:T], for some T∈N. Assume that you are given distribution π_T, which is not equal to the marginal distribution of the reference process at time T. In this scenario, Schrödinger addressed the problem of identifying the Markov process with initial distribution π_0 and terminal distribution equal to π_T which is the closest to the reference process in terms of Kullback–Leibler divergence. This special case of the so-called Schrödinger bridge problem can be solved using iterative proportional fitting, also known as the Sinkhorn algorithm. We leverage these ideas to develop novel Monte Carlo schemes, termed Schrödinger bridge samplers, to approximate a target distribution π on R^d and to estimate its normalizing constant. This is achieved by iteratively modifying the transition kernels of the reference Markov chain to obtain a process whose marginal distribution at time T becomes closer to π_T = π, via regression-based approximations of the corresponding iterative proportional fitting recursion. We report preliminary experiments and make connections with other problems arising in the optimal transport, optimal control and physics literatures.

READ FULL TEXT

page 8

page 38

research
06/28/2019

Constrained Monte Carlo Markov Chains on Graphs

This paper presents a novel theoretical Monte Carlo Markov chain procedu...
research
08/18/2021

Quantitative Uniform Stability of the Iterative Proportional Fitting Procedure

We establish the uniform in time stability, w.r.t. the marginals, of the...
research
08/16/2022

Score-Based Diffusion meets Annealed Importance Sampling

More than twenty years after its introduction, Annealed Importance Sampl...
research
04/03/2023

Diffusion Bridge Mixture Transports, Schrödinger Bridge Problems and Generative Modeling

The dynamic Schrödinger bridge problem seeks a stochastic process that d...
research
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...
research
12/06/2022

SURE-tuned Bridge Regression

Consider the ℓ_α regularized linear regression, also termed Bridge regre...
research
05/22/2023

Some power function distribution processes

It is known that all the proportional reversed hazard (PRH) processes ca...

Please sign up or login with your details

Forgot password? Click here to reset