Related papers: Forgetting the starting distribution in finite int…

We demonstrate the use of a variational method to determine a quantitative lower bound on the rate of convergence of Markov Chain Monte Carlo (MCMC) algorithms as a function of the target density and proposal density. The bound relies on…

We introduce a Metropolis-Hastings Markov chain for Boltzmann distributions of classical spin systems. It relies on approximate tensor network contractions to propose correlated collective updates at each step of the evolution. We present…

Markov Chain Monte Carlo (MCMC) methods for sampling probability density functions (combined with abundant computational resources) have transformed the sciences, especially in performing probabilistic inferences, or fitting models to data.…

We study approximations of evolving probability measures by an interacting particle system. The particle system dynamics is a combination of independent Markov chain moves and importance sampling/resampling steps. Under global regularity…

Microscopic processes on surfaces such as adsorption, desorption, diffusion and reaction of interacting particles can be simulated using kinetic Monte Carlo (kMC) algorithms. Even though kMC methods are accurate, they are computationally…

Bayesian neural learning feature a rigorous approach to estimation and uncertainty quantification via the posterior distribution of weights that represent knowledge of the neural network. This not only provides point estimates of optimal…

Sampling from complex target distributions is a challenging task fundamental to Bayesian inference. Parallel tempering (PT) addresses this problem by constructing a Markov chain on the expanded state space of a sequence of distributions…

We present a new class of interacting Markov chain Monte Carlo algorithms for solving numerically discrete-time measure-valued equations. The associated stochastic processes belong to the class of self-interacting Markov chains. In contrast…

We introduce a new algorithm for approximate inference that combines reparametrization, Markov chain Monte Carlo and variational methods. We construct a very flexible implicit variational distribution synthesized by an arbitrary Markov…

Simulated tempering is a widely used strategy for sampling from multimodal distributions. In this paper, we consider simulated tempering combined with an arbitrary local Markov chain Monte Carlo sampler and present a new decomposition…

We introduce a new Markov chain Monte Carlo (MCMC) sampler called the Markov Interacting Importance Sampler (MIIS). The MIIS sampler uses conditional importance sampling (IS) approximations to jointly sample the current state of the Markov…

Adaptive Markov chain Monte Carlo (MCMC) algorithms, which automatically tune their parameters based on past samples, have proved extremely useful in practice. The self-tuning mechanism makes them `non-Markovian', which means that their…

Sequential Monte Carlo (SMC) is a methodology for sampling approximately from a sequence of probability distributions of increasing dimension and estimating their normalizing constants. We propose here an alternative methodology named…

Despite the enormous success of Hamiltonian Monte Carlo and related Markov Chain Monte Carlo (MCMC) methods, sampling often still represents the computational bottleneck in scientific applications. Availability of parallel resources can…

Markov chain Monte Carlo (MCMC) methods provide powerful framework for sampling unknown probability measures across a wide range of scientific applications. In some settings, the target distribution is supported on a lower-dimensional…

This paper analyzes the factorizability and geometry of transition matrices of multivariate Markov chains. Specifically, we demonstrate that the induced chains on factors of a product space can be regarded as information projections with…

Exponential random graphs are used extensively in the sociology literature. This model seeks to incorporate in random graphs the notion of reciprocity, that is, the larger than expected number of triangles and other small subgraphs.…

We compare convergence rates of Metropolis--Hastings chains to multi-modal target distributions when the proposal distributions can be of ``local'' and ``small world'' type. In particular, we show that by adding occasional long-range jumps…

Quasi-Monte Carlo (QMC) methods for estimating integrals are attractive since the resulting estimators typically converge at a faster rate than pseudo-random Monte Carlo. However, they can be difficult to set up on arbitrary posterior…

We consider the problem of inference in discrete probabilistic models, that is, distributions over subsets of a finite ground set. These encompass a range of well-known models in machine learning, such as determinantal point processes and…