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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…

Spike-and-slab and horseshoe regression are arguably the most popular Bayesian variable selection approaches for linear regression models. However, their performance can deteriorate if outliers and heteroskedasticity are present in the…

We develop a sequential low-complexity inference procedure for Dirichlet process mixtures of Gaussians for online clustering and parameter estimation when the number of clusters are unknown a-priori. We present an easily computable, closed…

Many popular Bayesian nonparametric priors can be characterized in terms of exchangeable species sampling sequences. However, in some applications, exchangeability may not be appropriate. We introduce a {novel and probabilistically coherent…

Model comparison and calibrated uncertainty quantification often require integrating over parameters, but scalable inference can be challenging for complex, multimodal targets. Nested Sampling is a robust alternative to standard MCMC, yet…

Passenger clustering based on trajectory records is essential for transportation operators. However, existing methods cannot easily cluster the passengers due to the hierarchical structure of the passenger trip information, including…

The use of Gaussian processes (GPs) is supported by efficient sampling algorithms, a rich methodological literature, and strong theoretical grounding. However, due to their prohibitive computation and storage demands, the use of exact GPs…

We establish some results for the rate of convergence in total variation of a Gibbs sampler to its equilibrium distribution. This sampler is motivated by a hierarchical Bayesian inference construction for a gamma random variable. Our…

Restricted Boltzmann Machines (RBMs) are one of the fundamental building blocks of deep learning. Approximate maximum likelihood training of RBMs typically necessitates sampling from these models. In many training scenarios, computationally…

Gibbs sampling is a Markov chain Monte Carlo method that is often used for learning and inference on graphical models. Minibatching, in which a small random subset of the graph is used at each iteration, can help make Gibbs sampling scale…

Next-generation sequencing technologies provide a revolutionary tool for generating gene expression data. Starting with a fixed RNA sample, they construct a library of millions of differentially abundant short sequence tags or "reads",…

Most machine learning and deep neural network algorithms rely on certain iterative algorithms to optimise their utility/cost functions, e.g. Stochastic Gradient Descent. In distributed learning, the networked nodes have to work…

Biochemical reaction networks are an amalgamation of reactions where each reaction represents the interaction of different species. Generally, these networks exhibit a multi-scale behavior caused by the high variability in reaction rates…

Learning the joint dependence of discrete variables is a fundamental problem in machine learning, with many applications including prediction, clustering and dimensionality reduction. More recently, the framework of copula modeling has…

In the realm of unsupervised learning, Bayesian nonparametric mixture models, exemplified by the Dirichlet Process Mixture Model (DPMM), provide a principled approach for adapting the complexity of the model to the data. Such models are…

Micro and survey datasets often contain private information about individuals, like their health status, income or political preferences. Previous studies have shown that, even after data anonymization, a malicious intruder could still be…

Bayesian change-point and segmentation models provide uncertainty-aware piecewise-constant representations of ordered data, but exact inference is often limited to narrow likelihood classes, single sequences, or index-uniform designs. We…

Discrete random structures are important tools in Bayesian nonparametrics and the resulting models have proven effective in density estimation, clustering, topic modeling and prediction, among others. In this paper, we consider nested…

The Dirichlet Process (DP) mixture model has become a popular choice for model-based clustering, largely because it allows the number of clusters to be inferred. The sequential updating and greedy search (SUGS) algorithm (Wang and Dunson,…

We develop the distance dependent Chinese restaurant process (CRP), a flexible class of distributions over partitions that allows for non-exchangeability. This class can be used to model many kinds of dependencies between data in infinite…