相关论文: Optimal transport couplings of Gibbs samplers on p…

We present a new notion of probabilistic duality for random variables involving mixture distributions. Using this notion, we show how to implement a highly-parallelizable Gibbs sampler for weakly coupled discrete pairwise graphical models…

Machine learning systems operate under the assumption that training and test data are sampled from a fixed probability distribution. However, this assumptions is rarely verified in practice, as the conditions upon which data was acquired…

We study Bayesian estimation of mixture models and argue in favor of fitting the marginal posterior distribution over component assignments directly, rather than Gibbs sampling from the joint posterior on components and parameters as is…

Bayesian regression remains a simple but effective tool based on Bayesian inference techniques. For large-scale applications, with complicated posterior distributions, Markov Chain Monte Carlo methods are applied. To improve the well-known…

We propose a methodology to parallelize Hamiltonian Monte Carlo estimators. Our approach constructs a pair of Hamiltonian Monte Carlo chains that are coupled in such a way that they meet exactly after some random number of iterations. These…

Recent advances on overfitting Bayesian mixture models provide a solid and straightforward approach for inferring the underlying number of clusters and model parameters in heterogeneous datasets. The applicability of such a framework in…

Markov chain Monte Carlo (MCMC) methods provide consistent of integrals as the number of iterations goes to infinity. MCMC estimators are generally biased after any fixed number of iterations. We propose to remove this bias by using…

Performing numerical integration when the integrand itself cannot be evaluated point-wise is a challenging task that arises in statistical analysis, notably in Bayesian inference for models with intractable likelihood functions. Markov…

This paper proposes solutions to three issues pertaining to the estimation of finite mixture models with an unknown number of components: the non-identifiability induced by overfitting the number of components, the mixing limitations of…

We present a novel method for reducing the computational complexity of rigorously estimating the partition functions (normalizing constants) of Gibbs (Boltzmann) distributions, which arise ubiquitously in probabilistic graphical models. A…

Markov jump processes and continuous time Bayesian networks are important classes of continuous time dynamical systems. In this paper, we tackle the problem of inferring unobserved paths in these models by introducing a fast auxiliary…

In statistical analysis, Monte Carlo (MC) stands as a classical numerical integration method. When encountering challenging sample problem, Markov chain Monte Carlo (MCMC) is a commonly employed method. However, the MCMC estimator is biased…

This paper derives two new optimization-driven Monte Carlo algorithms inspired from variable splitting and data augmentation. In particular, the formulation of one of the proposed approaches is closely related to the alternating direction…

Sampling from lattice Gaussian distribution has emerged as an important problem in coding, decoding and cryptography. In this paper, the classic Gibbs algorithm from Markov chain Monte Carlo (MCMC) methods is demonstrated to be…

Conformal prediction is a distribution-free uncertainty quantification method that has gained popularity in the machine learning community due to its finite-sample guarantees and ease of use. Its most common variant, dubbed split conformal…

Perfect sampling is a technique that uses coupling arguments to provide a sample from the stationary distribution of a Markov chain in a finite time without ever computing the distribution. This technique is very efficient if all the events…

We consider local Markov chain Monte-Carlo algorithms for sampling from the weighted distribution of independent sets with activity $\l$, where the weight of an independent set $I$ is $\l^{|I|}$. A recent result has established that Gibbs…

Finite mixtures are a flexible modeling tool for irregularly shaped densities and samples from heterogeneous populations. When modeling with mixtures using an exchangeable prior on the component features, the component labels are arbitrary…

We show that Markov couplings can be used to improve the accuracy of Markov chain Monte Carlo calculations in some situations where the steady-state probability distribution is not explicitly known. The technique generalizes the notion of…

Hybrid Gibbs samplers represent a prominent class of approximated Gibbs algorithms that utilize Markov chains to approximate conditional distributions, with the Metropolis-within-Gibbs algorithm standing out as a well-known example. Despite…