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Gibbs sampling methods are standard tools to perform posterior inference for mixture models. These have been broadly classified into two categories: marginal and conditional methods. While conditional samplers are more widely applicable…
We present doubly stochastic gradient MCMC, a simple and generic method for (approximate) Bayesian inference of deep generative models (DGMs) in a collapsed continuous parameter space. At each MCMC sampling step, the algorithm randomly…
Efficient sampling from a classical Gibbs distribution is an important computational problem with applications ranging from statistical physics over Monte Carlo and optimization algorithms to machine learning. We introduce a family of…
There has been substantial interest in developing Markov chain Monte Carlo algorithms based on piecewise-deterministic Markov processes. However existing algorithms can only be used if the target distribution of interest is differentiable…
We give a algorithm for exact sampling from the Bingham distribution $p(x)\propto \exp(x^\top A x)$ on the sphere $\mathcal S^{d-1}$ with expected runtime of $\operatorname{poly}(d, \lambda_{\max}(A)-\lambda_{\min}(A))$. The algorithm is…
The inadequate mixing of conventional Markov Chain Monte Carlo (MCMC) methods for multi-modal distributions presents a significant challenge in practical applications such as Bayesian inference and molecular dynamics. Addressing this, we…
We study the problem of learning mixtures of $k$ Gaussians in $d$ dimensions. We make no separation assumptions on the underlying mixture components: we only require that the covariance matrices have bounded condition number and that the…
We consider the task of MCMC sampling from a distribution defined on a discrete space. Building on recent insights provided in [Zan19], we devise a class of efficient continuous-time, non-reversible algorithms which make active use of the…
As a special example of piecewise deterministic Markov process, bouncy particle sampler is a rejection-free, irreversible Markov chain Monte Carlo algorithm and can draw samples from target distribution efficiently. We generalize bouncy…
Determinantal Point Processes (DPPs) were introduced by Macchi as a model for repulsive (fermionic) particle distributions. But their recent popularization is largely due to their usefulness for encouraging diversity in the final stage of a…
We present the simplicial sampler, a class of parallel MCMC methods that generate and choose from multiple proposals at each iteration. The algorithm's multiproposal randomly rotates a simplex connected to the current Markov chain state in…
We study quadrature rules for functions from an RKHS, using nodes sampled from a determinantal point process (DPP). DPPs are parametrized by a kernel, and we use a truncated and saturated version of the RKHS kernel. This link between the…
Determinantal Point Process (DPPs) are statistical models for repulsive point patterns. Both sampling and inference are tractable for DPPs, a rare feature among models with negative dependence that explains their popularity in machine…
In this paper, we propose a novel class of Piecewise Deterministic Markov Processes (PDMPs) that are designed to sample from probability distributions $\pi$ supported on a convex set $\mathcal{M}$. This class of PDMPs adapts the concept of…
Markov Chain Monte Carlo (MCMC) techniques have long been studied in computational geometry subjects whereabouts the problems to be studied are complex geometric objects which by their nature require optimized techniques to be deployed or…
In this paper we introduce a new sampling algorithm which has the potential to be adopted as a universal replacement to the Metropolis--Hastings algorithm. It is related to the slice sampler, and motivated by an algorithm which is…
We present a determinantal point process (DPP) inspired alternative to non-maximum suppression (NMS) which has become an integral step in all state-of-the-art object detection frameworks. DPPs have been shown to encourage diversity in…
In this article, we derive a novel non-reversible, continuous-time Markov chain Monte Carlo (MCMC) sampler, called Coordinate Sampler, based on a piecewise deterministic Markov process (PDMP), which can be seen as a variant of the Zigzag…
Learning to sample from complex unnormalized distributions is a fundamental challenge in computational physics and machine learning. While score-based and variational methods have achieved success in continuous domains, extending them to…
We propose discrete determinantal point processes (DPPs) for priors on the model parameter in Bayesian variable selection. By our variable selection method, collinear predictors are less likely to be selected simultaneously because of the…