Related papers: Posterior Inference for Sparse Hierarchical Non-st…

Bayesian max-margin models have shown superiority in various practical applications, such as text categorization, collaborative prediction, social network link prediction and crowdsourcing, and they conjoin the flexibility of Bayesian…

Bayesian hierarchical linear models provide a natural framework to analyze nested and clustered data. Classical estimation with Markov chain Monte Carlo produces well calibrated posterior distributions but becomes computationally expensive…

Gaussian Process (GP) models are a powerful and flexible tool for non-parametric regression and classification. Computation for GP models is intensive, since computing the posterior density, $\pi$, for covariance function parameters…

For large model spaces, the potential entrapment of Markov chain Monte Carlo (MCMC) based methods with spike-and-slab priors poses significant challenges in posterior computation in regression models. On the other hand, maximum a posteriori…

Posterior sampling by Monte Carlo methods provides a more comprehensive solution approach to inverse problems than computing point estimates such as the maximum posterior using optimization methods, at the expense of usually requiring many…

High-throughput characterization often requires estimating parameters and model dimension from experimental data of limited quantity and quality. Such data may result in an ill-posed inverse problem, where multiple sets of parameters and…

We present a novel approach for fully non-stationary Gaussian process regression (GPR), where all three key parameters -- noise variance, signal variance and lengthscale -- can be simultaneously input-dependent. We develop gradient-based…

Markov chain Monte Carlo (MCMC) algorithms have become powerful tools for Bayesian inference. However, they do not scale well to large-data problems. Divide-and-conquer strategies, which split the data into batches and, for each batch, run…

Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…

Stochastic gradient Markov Chain Monte Carlo (SGMCMC) is considered the gold standard for Bayesian inference in large-scale models, such as Bayesian neural networks. Since practitioners face speed versus accuracy tradeoffs in these models,…

Bayesian analysis often concerns an evaluation of models with different dimensionality as is necessary in, for example, model selection or mixture models. To facilitate this evaluation, transdimensional Markov chain Monte Carlo (MCMC)…

We examine an analytic variational inference scheme for the Gaussian Process State Space Model (GPSSM) - a probabilistic model for system identification and time-series modelling. Our approach performs variational inference over both the…

A fully Bayesian approach is proposed for ultrahigh-dimensional nonparametric additive models in which the number of additive components may be larger than the sample size, though ideally the true model is believed to include only a small…

A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems. The algorithm aims to mitigate some of the hurdles faced…

Decoding complex relationships among large numbers of variables with relatively few observations is one of the crucial issues in science. One approach to this problem is Gaussian graphical modeling, which describes conditional independence…

Variational inference techniques based on inducing variables provide an elegant framework for scalable posterior estimation in Gaussian process (GP) models. Besides enabling scalability, one of their main advantages over sparse…

Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the…

Scalable spatial GPs for massive datasets can be built via sparse Directed Acyclic Graphs (DAGs) where a small number of directed edges is sufficient to flexibly characterize spatial dependence. The DAG can be used to devise fast algorithms…

Deriving Bayesian inference for exponential random graph models (ERGMs) is a challenging "doubly intractable" problem as the normalizing constants of the likelihood and posterior density are both intractable. Markov chain Monte Carlo (MCMC)…

Hierarchical spatial models are very flexible and popular for a vast array of applications in areas such as ecology, social science, public health, and atmospheric science. It is common to carry out Bayesian inference for these models via…