Related papers: Gibbs Sampling using Anti-correlation Gaussian Dat…
We consider Markov chain Monte Carlo (MCMC) algorithms for Bayesian high-dimensional regression with continuous shrinkage priors. A common challenge with these algorithms is the choice of the number of iterations to perform. This is…
The emergence of big data has led to a growing interest in so-called convergence complexity analysis, which is the study of how the convergence rate of a Monte Carlo Markov chain (for an intractable Bayesian posterior distribution) scales…
Markov jump processes and continuous time Bayesian networks are important classes of continuous time dynamical systems. In this paper, we tackle the problem of inferring unobserved paths in these models by introducing a fast auxiliary…
Generative Bayesian Filtering (GBF) provides a powerful and flexible framework for performing posterior inference in complex nonlinear and non-Gaussian state-space models. Our approach extends Generative Bayesian Computation (GBC) to…
Additive-interactive regression has recently been shown to offer attractive minimax error rates over traditional nonparametric multivariate regression in a wide variety of settings, including cases where the predictor count is much larger…
Over the last decade, a large variety of clustering algorithms have been developed to detect coregulatory relationships among genes from microarray gene expression data. Model based clustering approaches have emerged as statistically well…
Gibbs sampling, as a model learning method, is known to produce the most accurate results available in a variety of domains, and is a de facto standard in these domains. Yet, it is also well known that Gibbs random walks usually have…
We consider the problem of inferring a latent function in a probabilistic model of data. When dependencies of the latent function are specified by a Gaussian process and the data likelihood is complex, efficient computation often involve…
Spike-and-slab priors are commonly used for Bayesian variable selection, due to their interpretability and favorable statistical properties. However, existing samplers for spike-and-slab posteriors incur prohibitive computational costs when…
While Bayesian inference provides a principled framework for reasoning under uncertainty, its widespread adoption is limited by the intractability of exact posterior computation, necessitating the use of approximate inference. However,…
This paper derives two new optimization-driven Monte Carlo algorithms inspired from variable splitting and data augmentation. In particular, the formulation of one of the proposed approaches is closely related to the alternating direction…
Recent crash frequency studies incorporate spatiotemporal correlations, but these studies have two key limitations: i) none of these studies accounts for temporal variation in model parameters; and ii) Gibbs sampler suffers from convergence…
We introduce a novel way to combine boosting with Gaussian process and mixed effects models. This allows for relaxing, first, the zero or linearity assumption for the prior mean function in Gaussian process and grouped random effects models…
We propose a novel approach to estimating the precision matrix of multivariate Gaussian data that relies on decomposing them into a low-rank and a diagonal component. Such decompositions are very popular for modeling large covariance…
The MC$^3$ (Madigan and York, 1995) and Gibbs (George and McCulloch, 1997) samplers are the most widely implemented algorithms for Bayesian Model Averaging (BMA) in linear regression models. These samplers draw a variable at random in each…
This paper proposes novel noise-free Bayesian optimization strategies that rely on a random exploration step to enhance the accuracy of Gaussian process surrogate models. The new algorithms retain the ease of implementation of the classical…
It is well known that the Lasso can be interpreted as a Bayesian posterior mode estimate with a Laplacian prior. Obtaining samples from the full posterior distribution, the Bayesian Lasso, confers major advantages in performance as compared…
We consider Bayesian inference for image deblurring with total variation (TV) prior. Since the posterior is analytically intractable, we resort to Markov chain Monte Carlo (MCMC) methods. However, since most MCMC methods significantly…
We show that a probabilistic version of the classical forward-stepwise variable inclusion procedure can serve as a general data-augmentation scheme for model space distributions in (generalized) linear models. This latent variable…
We introduce a new perfect sampling technique that can be applied to general Gibbs distributions and runs in linear time if the correlation decays faster than the neighborhood growth. In particular, in graphs with sub-exponential…