Related papers: Ensuring Rapid Mixing and Low Bias for Asynchronou…

This chapter surveys the most standard Monte Carlo methods available for simulating from a posterior distribution associated with a mixture and conducts some experiments about the robustness of the Gibbs sampler in high dimensional Gaussian…

Inference in general Ising models is difficult, due to high treewidth making tree-based algorithms intractable. Moreover, when interactions are strong, Gibbs sampling may take exponential time to converge to the stationary distribution. We…

Sampling from Gibbs distributions and computing their log-partition function are fundamental tasks in statistics, machine learning, and statistical physics. While efficient algorithms are known for log-concave densities, the worst-case…

We consider the problem of approximate sampling from the finite volume Gibbs measure with a general pair interaction. We exhibit a parallel dynamics (Probabilistic Cellular Automaton) which efficiently implements the sampling. In this…

For large scale on-line inference problems the update strategy is critical for performance. We derive an adaptive scan Gibbs sampler that optimizes the update frequency by selecting an optimum mini-batch size. We demonstrate performance of…

In a series of recent works, Boyd, Diaconis, and their co-authors have introduced a semidefinite programming approach for computing the fastest mixing Markov chain on a graph of allowed transitions, given a target stationary distribution.…

Ising and Potts models are an important class of discrete probability distributions which originated from statistical physics and since then have found applications in several disciplines. Simulation from these models is a well known…

Variational Bayesian inference and (collapsed) Gibbs sampling are the two important classes of inference algorithms for Bayesian networks. Both have their advantages and disadvantages: collapsed Gibbs sampling is unbiased but is also…

A core problem in cognitive science and machine learning is to understand how humans derive semantic representations from perceptual objects, such as color from an apple, pleasantness from a musical chord, or seriousness from a face. Markov…

This simple note lays out a few observations which are well known in many ways but may not have been said in quite this way before. The basic idea is that when comparing two different Markov chains it is useful to couple them is such a way…

This paper addresses the mapping problem. Using a conjugate prior form, we derive the exact theoretical batch multi-object posterior density of the map given a set of measurements. The landmarks in the map are modeled as extended objects,…

We characterise the convergence of the Gibbs sampler which samples from the joint posterior distribution of parameters and missing data in hierarchical linear models with arbitrary symmetric error distributions. We show that the convergence…

Inference for Dirichlet process hierarchical models is typically performed using Markov chain Monte Carlo methods, which can be roughly categorised into marginal and conditional methods. The former integrate out analytically the…

A canonical approach to approximating the partition function of a Gibbs distribution via sampling is simulated annealing. This method has led to efficient reductions from counting to sampling, including: $\bullet$ classic non-adaptive…

Motivated by large-scale optimization problems arising in the context of machine learning, there have been several advances in the study of asynchronous parallel and distributed optimization methods during the past decade. Asynchronous…

The problem of efficiently sampling from a set of(undirected) graphs with a given degree sequence has many applications. One approach to this problem uses a simple Markov chain, which we call the switch chain, to perform the sampling. The…

High-dimensional data are routinely collected in many areas. We are particularly interested in Bayesian classification models in which one or more variables are imbalanced. Current Markov chain Monte Carlo algorithms for posterior…

The Hamiltonian Monte Carlo (HMC) algorithm is often lauded for its ability to effectively sample from high-dimensional distributions. In this paper we challenge the presumed domination of HMC for the Bayesian analysis of GLMs. By utilizing…

Single-chain Markov chain Monte Carlo simulates realizations from a Markov chain to estimate expectations with the empirical average. The single-chain simulation is generally of considerable length and restricts many advantages of modern…

Bayesian inference for undirected graphical models is mostly restricted to the class of decomposable graphs, as they enjoy a rich set of properties making them amenable to high-dimensional problems. While parameter inference is…