Related papers: Convergence Rates for Hierarchical Gibbs Samplers
Variational Bayesian inference and (collapsed) Gibbs sampling are the two important classes of inference algorithms for Bayesian networks. Both have their advantages and disadvantages: collapsed Gibbs sampling is unbiased but is also…
We study geometric ergodicity of the Gibbs sampler for linear latent non-Gaussian models (LLnGMs), a class of hierarchical models in which conditional Gaussian structure is preserved through generalized inverse Gaussian (GIG)…
The Gibbs entropy of a microcanonical network ensemble is the logarithm of the number of network configurations compatible with a set of hard constraints. This quantity characterizes the level of order and randomness encoded in features of…
We show that when the proportions of a countable set of species are organized as an exchangeable partition of the unit interval and we take a sample on it, then the Bayesian posterior entropy converges a.s. and in L^1 to the entropy of the…
We consider various versions of adaptive Gibbs and Metropolis within-Gibbs samplers, which update their selection probabilities (and perhaps also their proposal distributions) on the fly during a run, by learning as they go in an attempt to…
In the realm of statistical learning, the increasing volume of accessible data and increasing model complexity necessitate robust methodologies. This paper explores two branches of robust Bayesian methods in response to this trend. The…
Gradient information on the sampling distribution can be used to reduce the variance of Monte Carlo estimators via Stein's method. An important application is that of estimating an expectation of a test function along the sample path of a…
Quadratic variations of Gaussian processes play important role in both stochastic analysis and in applications such as estimation of model parameters, and for this reason the topic has been extensively studied in the literature. In this…
As soon as their extragalactic origins were established, the hope to make Gamma - Ray Bursts (GRBs) standardizeable candles to probe the very high - z universe has opened the search for scaling relations between redshift independent…
Gibbs sampling is the de facto Markov chain Monte Carlo method used for inference and learning on large scale graphical models. For complicated factor graphs with lots of factors, the performance of Gibbs sampling can be limited by the…
Due to their conjugate posteriors, Gaussian process priors are attractive for estimating the drift of stochastic differential equations with continuous time observations. However, their performance strongly depends on the choice of the…
We introduce a method to reconstruct an element of a Hilbert space in terms of an arbitrary finite collection of linearly independent reconstruction vectors, given a finite number of its samples with respect to any Riesz basis. As we…
In this paper, we study convergence properties of the gradient Expectation-Maximization algorithm \cite{lange1995gradient} for Gaussian Mixture Models for general number of clusters and mixing coefficients. We derive the convergence rate…
Variational inference is becoming more and more popular for approximating intractable posterior distributions in Bayesian statistics and machine learning. Meanwhile, a few recent works have provided theoretical justification and new…
Ground-based gravitational wave detectors are now routinely surveying the dark Universe, finding hundreds of collisions between compact objects such as black holes and neutron stars. However, terrestrial non-Gaussian noise artefacts,…
This Letter introduces a generalization of known duplication-divergence models for growing random graphs. This general duplication-divergence model includes a new coupled divergence asymmetry rate, which allows to obtain the structure of…
In this paper we describe how MAP inference can be used to sample efficiently from Gibbs distributions. Specifically, we provide means for drawing either approximate or unbiased samples from Gibbs' distributions by introducing low…
Monte Carlo methods are essential tools for Bayesian inference. Gibbs sampling is a well-known Markov chain Monte Carlo (MCMC) algorithm, extensively used in signal processing, machine learning, and statistics, employed to draw samples from…
We establish convergence theorems for Riemannian stochastic gradient descents in which the underlying probability spaces vary from iteration to iteration. As applications, we deduce convergence results for Riemannian stochastic gradient…
We revisit the problem of estimating the mean of a real-valued distribution, presenting a novel estimator with sub-Gaussian convergence: intuitively, "our estimator, on any distribution, is as accurate as the sample mean is for the Gaussian…