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Markov Chain Monte Carlo (MCMC) is a class of algorithms to sample complex and high-dimensional probability distributions. The Metropolis-Hastings (MH) algorithm, the workhorse of MCMC, provides a simple recipe to construct reversible…

Traditional Markov chain Monte Carlo (MCMC) sampling of hidden Markov models (HMMs) involves latent states underlying an imperfect observation process, and generates posterior samples for top-level parameters concurrently with nuisance…

Markov Chain Monte Carlo (MCMC) methods sample from unnormalized probability distributions and offer guarantees of exact sampling. However, in the continuous case, unfavorable geometry of the target distribution can greatly limit the…

Continuous-time random walks (CTRWs) on discrete state spaces, ranging from regular lattices to complex networks, are ubiquitous across physics, chemistry, and biology. Models with coarse-grained states, for example those employed in…

There is substantial empirical evidence about the success of dynamic implementations of Hamiltonian Monte Carlo (HMC), such as the No U-Turn Sampler (NUTS), in many challenging inference problems but theoretical results about their behavior…

We develop a probabilistic control algorithm, $\texttt{GTLProCo}$, for swarms of agents with heterogeneous dynamics and objectives, subject to high-level task specifications. The resulting algorithm not only achieves decentralized control…

The Monte Carlo within Metropolis (MCwM) algorithm, interpreted as a perturbed Metropolis-Hastings (MH) algorithm, provides an approach for approximate sampling when the target distribution is intractable. Assuming the unperturbed Markov…

Multiple kernel clustering (MKC) is committed to achieving optimal information fusion from a set of base kernels. Constructing precise and local kernel matrices is proved to be of vital significance in applications since the unreliable…

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…

This paper presents a novel approach to neural network pruning by integrating a graph-based observation space into an AutoML framework to address the limitations of existing methods. Traditional pruning approaches often depend on…

Posterior sampling is a task of central importance in Bayesian inference. For many applications in Bayesian meta-analysis and Bayesian transfer learning, the prior distribution is unknown and needs to be estimated from samples. In practice,…

Random sampling of graph partitions under constraints has become a popular tool for evaluating legislative redistricting plans. Analysts detect partisan gerrymandering by comparing a proposed redistricting plan with an ensemble of sampled…

Learning-based approaches have witnessed great successes in blind single image super-resolution (SISR) tasks, however, handcrafted kernel priors and learning based kernel priors are typically required. In this paper, we propose a…

We introduce weighted Markovian graphs, a random walk model that decouples the transition dynamics of a Markov chain from (random) edge weights representing the cost of traversing each edge. This decoupling allows us to study the…

Many sequence computations are easier to study as movement through internal states than as isolated local circuits. We introduce Markovian Circuit Tracing (MCT), a diagnostic pipeline for testing whether transformer activations contain…

This paper studies a non-random-walk Markov Chain Monte Carlo method, namely the Hamiltonian Monte Carlo (HMC) method in the context of Subset Simulation used for structural reliability analysis. The HMC method relies on a deterministic…

The shortest-path, commute time, and diffusion distances on undirected graphs have been widely employed in applications such as dimensionality reduction, link prediction, and trip planning. Increasingly, there is interest in using…

Recently, many Markov chain Monte Carlo methods have been developed with deterministic reversible transform proposals inspired by the Hamiltonian Monte Carlo method. The deterministic transform is relatively easy to reconcile with the local…

A new class of Markov chain Monte Carlo (MCMC) algorithms, based on simulating piecewise deterministic Markov processes (PDMPs), have recently shown great promise: they are non-reversible, can mix better than standard MCMC algorithms, and…

We tackle the problem of goal-directed graph construction: given a starting graph, a budget of modifications, and a global objective function, the aim is to find a set of edges whose addition to the graph achieves the maximum improvement in…