
Constrained Monte Carlo Markov Chains on Graphs
This paper presents a novel theoretical Monte Carlo Markov chain procedu...
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Normalizing Constant Estimation with Gaussianized Bridge Sampling
Normalizing constant (also called partition function, Bayesian evidence,...
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A Markov Jump Process for More Efficient Hamiltonian Monte Carlo
In most sampling algorithms, including Hamiltonian Monte Carlo, transiti...
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Iterative Markov Chain Monte Carlo Computation of Reference Priors and Minimax Risk
We present an iterative Markov chainMonte Carlo algorithm for computingr...
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Efficient sampling of conditioned Markov jump processes
We consider the task of generating draws from a Markov jump process (MJP...
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On Markov chain Monte Carlo for sparse and filamentary distributions
A novel strategy that combines a given collection of reversible Markov k...
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Bayesian analysis of Turkish Income and Living Conditions data, using clustered longitudinal ordinal modelling with Bridge distributed randomeffects
This paper is motivated by the panel surveys, called Statistics on Incom...
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Schrödinger Bridge Samplers
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 socalled 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 regressionbased 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.
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