The random numbers driving Markov chain Monte Carlo (MCMC) simulation are usually modeled as independent U(0, 1) random variables. Tribble [24] reports substantial improvements when those random numbers are replaced by carefully balanced inputs from completely uniformly distributed sequences. The previous theoretical justification for using anything other than IID U(0, 1) points shows consisten...

Recent advances in stochastic gradient techniques have made it possible to estimate posterior distributions from large datasets via Markov Chain Monte Carlo (MCMC). However, when the target posterior is multimodal, mixing performance is often poor. This results in inadequate exploration of the posterior distribution. A framework is proposed to improve the sampling efficiency of stochastic gradi...

Markov processes, both classical and higher order, are often used to model dynamic processes, such as stock prices, molecular dynamics, and Monte Carlo methods. Previous works have shown that an autoencoder can be formulated as a specific type of Markov chain. Here, we propose a generative neural network known as a transition encoder, or transcoder, which learns such continuous-state dynamic pr...

Strongly Rayleigh distributions are natural generalizations of product and determinantal probability distributions and satisfy the strongest form of negative dependence properties. We show that the “natural” Monte Carlo Markov Chain (MCMC) algorithm mixes rapidly in the support of a homogeneous strongly Rayleigh distribution. As a byproduct, our proof implies Markov chains can be used to effici...

We connect known results about diffusion limits of Markov chain Monte Carlo (MCMC) algorithms to the Computer Science notion of algorithm complexity. Our main result states that any diffusion limit of a Markov process implies a corresponding complexity bound (in an appropriate metric). We then combine this result with previously-known MCMC diffusion limit results to prove that under appropriate...

Restricted Boltzmann machines (RBMs) are probabilistic graphical models that can be interpreted as stochastic neural networks. The increase in computational power and the development of faster learning algorithms have made them applicable to relevant machine learning problems. They attracted much attention recently after being proposed as building blocks of multi-layer learning systems called d...

In this report, we propose an original approach to solve Fredholm equations of the second kind. We interpret the standard von Neumann expansion of the solution as an expectation with respect to a probability distribution de…ned on an union of subspaces of variable dimension. Based on this representation, it is possible to use trans-dimensional Markov Chain Monte Carlo (MCMC) methods such as Rev...

This paper develops a systematic Markov Chain Monte Carlo (MCMC) framework based upon E cient Importance Sampling (EIS) which can be used for the analysis of a wide range of econometric models involving integrals without an analytical solution. EIS is a simple, generic and yet accurate Monte-Carlo integration procedure based on sampling densities which are chosen to be global approximations to ...

The random numbers driving Markov chain Monte Carlo (MCMC) simulation are usually modeled as independent U(0, 1) random variables. Tribble [24] reports substantial improvements when those random numbers are replaced by carefully balanced inputs from completely uniformly distributed sequences. The previous theoretical justification for using anything other than IID U(0, 1) points shows consisten...