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The Hidden Markov Model (HMM) is a widely-used statistical model for handling sequential data. However, the presence of missing observations in real-world datasets often complicates the application of the model. The EM algorithm and Gibbs…
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…
The particle Gibbs sampler is a Markov chain Monte Carlo (MCMC) algorithm to sample from the full posterior distribution of a state-space model. It does so by executing Gibbs sampling steps on an extended target distribution defined on the…
Models of physics beyond the Standard Model often contain a large number of parameters. These form a high-dimensional space that is computationally intractable to fully explore. Experimental constraints project onto a subspace of viable…
In some applied scenarios, the availability of complete data is restricted, often due to privacy concerns; only aggregated, robust and inefficient statistics derived from the data are made accessible. These robust statistics are not…
While gradient-based discrete samplers are effective in sampling from complex distributions, they are susceptible to getting trapped in local minima, particularly in high-dimensional, multimodal discrete distributions, owing to the…
Various Markov chain Monte Carlo (MCMC) methods are studied to improve upon random walk Metropolis sampling, for simulation from complex distributions. Examples include Metropolis-adjusted Langevin algorithms, Hamiltonian Monte Carlo, and…
We consider Ising mixed $p$-spin glasses at high-temperature and without external field, and study the problem of sampling from the Gibbs distribution $\mu$ in polynomial time. We develop a new sampling algorithm with complexity of the same…
We propose a multi-hop diffusion strategy for a sensor network to perform distributed least mean-squares (LMS) estimation under local and network-wide energy constraints. At each iteration of the strategy, each node can combine intermediate…
An Automated Sliced Gibbs framework is proposed for fully automated Markov chain Monte Carlo sampling from arbitrary finite dimensional probability kernels. The method targets unnormalized, non-smooth, heavy tailed, and highly multimodal…
Gibbs sampling on factor graphs is a widely used inference technique, which often produces good empirical results. Theoretical guarantees for its performance are weak: even for tree structured graphs, the mixing time of Gibbs may be…
We consider convex optimization with non-smooth objective function and log-concave sampling with non-smooth potential (negative log density). In particular, we study two specific settings where the convex objective/potential function is…
We address the problem of sampling double-ended diffusive paths. The ensemble of paths is expressed using a symmetric version of the Onsager-Machlup formula, which only requires evaluation of the force field and which, upon direct time…
Bayesian methods of sampling from a posterior distribution are becoming increasingly popular due to their ability to precisely display the uncertainty of a model fit. Classical methods based on iterative random sampling and posterior…
Stochastic differential equations (SDEs) or diffusions are continuous-valued continuous-time stochastic processes widely used in the applied and mathematical sciences. Simulating paths from these processes is usually an intractable problem,…
Local samplers are algorithms that generate random samples based on local queries to high-dimensional distributions, ensuring the samples follow the correct induced distributions while maintaining time complexity that scales locally with…
Sampling from the full posterior distribution of high-dimensional non-linear, non-Gaussian latent dynamical models presents significant computational challenges. While Particle Gibbs (also known as conditional sequential Monte Carlo) is…
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…
The challenges posed by high-dimensional data and use of the simplex constraint are two major concerns in the empirical application of the synthetic control method (SCM) in econometric studies. To address both issues simultaneously, we…
We develop a new sampling strategy that uses the hit-and-run algorithm within level sets of the target density. Our method can be applied to any quasi-concave density, which covers a broad class of models. Our sampler performs well in…