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The theory of two-sided matching has been extensively developed and applied to many real-life application domains. As the theory has been applied to increasingly diverse types of environments, researchers and practitioners have encountered…

The horseshoe prior is frequently employed in Bayesian analysis of high-dimensional models, and has been shown to achieve minimax optimal risk properties when the truth is sparse. While optimization-based algorithms for the extremely…

A Kernel Adaptive Metropolis-Hastings algorithm is introduced, for the purpose of sampling from a target distribution with strongly nonlinear support. The algorithm embeds the trajectory of the Markov chain into a reproducing kernel Hilbert…

Bayesian approaches have been successfully integrated into training deep neural networks. One popular family is stochastic gradient Markov chain Monte Carlo methods (SG-MCMC), which have gained increasing interest due to their scalability…

This paper develops a Bayesian computational platform at the interface between posterior sampling and optimization in models whose marginal likelihoods are difficult to evaluate. Inspired by adversarial optimization, namely Generative…

We develop a novel Markov chain Monte Carlo (MCMC) method that exploits a hierarchy of models of increasing complexity to efficiently generate samples from an unnormalized target distribution. Broadly, the method rewrites the Multilevel…

Bayesian inference provides a principled framework for learning from complex data and reasoning under uncertainty. It has been widely applied in machine learning tasks such as medical diagnosis, drug design, and policymaking. In these…

Probabilistic programming languages can simplify the development of machine learning techniques, but only if inference is sufficiently scalable. Unfortunately, Bayesian parameter estimation for highly coupled models such as regressions and…

We consider the problem of sampling from a posterior distribution arising in Bayesian inverse problems in science, engineering, and imaging. Our method belongs to the family of independence Metropolis-Hastings (IMH) sampling algorithms,…

A classical approach for approximating expectations of functions w.r.t. partially known distributions is to compute the average of function values along a trajectory of a Metropolis-Hastings (MH) Markov chain. A key part in the MH algorithm…

Bayesian inference in deep neural networks is challenging due to the high-dimensional, strongly multi-modal parameter posterior density landscape. Markov chain Monte Carlo approaches asymptotically recover the true posterior but are…

The general applicability and ease of use of the pseudo-marginal Metropolis--Hastings (PMMH) algorithm, and particle Metropolis--Hastings in particular, makes it a popular method for inference on discretely observed Markovian stochastic…

Markov chain Monte Carlo (MCMC) algorithms have become powerful tools for Bayesian inference. However, they do not scale well to large-data problems. Divide-and-conquer strategies, which split the data into batches and, for each batch, run…

In recent times empirical likelihood has been widely applied under Bayesian framework. Markov chain Monte Carlo (MCMC) methods are frequently employed to sample from the posterior distribution of the parameters of interest. However,…

Constantine et al. (2016) introduced a Metropolis-Hastings (MH) approach that target the active subspace of a posterior distribution: a linearly projected subspace that is informed by the likelihood. Schuster et al. (2017) refined this…

To avoid poor empirical performance in Metropolis-Hastings and other accept-reject-based algorithms practitioners often tune them by trial and error. Lower bounds on the convergence rate are developed in both total variation and Wasserstein…

Bayesian inference for models with intractable likelihoods, such as Markov random fields, poses a fundamental computational challenge due to the tradeoff between inferential accuracy and computational cost. Various MCMC methods have been…

In Bayesian inverse problems, the posterior distribution is used to quantify uncertainty about the reconstructed solution. In practice, Markov chain Monte Carlo algorithms often are used to draw samples from the posterior distribution.…

We investigate the properties of the Hybrid Monte-Carlo algorithm (HMC) in high dimensions. HMC develops a Markov chain reversible w.r.t. a given target distribution $\Pi$ by using separable Hamiltonian dynamics with potential $-\log\Pi$.…

Hamiltonian Monte Carlo (HMC) samples efficiently from high-dimensional posterior distributions with proposed parameter draws obtained by iterating on a discretized version of the Hamiltonian dynamics. The iterations make HMC…