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Conventional frequentist learning, as assumed by existing federated learning protocols, is limited in its ability to quantify uncertainty, incorporate prior knowledge, guide active learning, and enable continual learning. Bayesian learning…

We introduce a new scalable approximation for Gaussian processes with provable guarantees which hold simultaneously over its entire parameter space. Our approximation is obtained from an improved sample complexity analysis for sparse…

This study addresses the problem of discrete signal reconstruction from the perspective of sparse Bayesian learning (SBL). Generally, it is intractable to perform the Bayesian inference with the ideal discretization prior under the SBL…

Bayesian optimization through Gaussian process regression is an effective method of optimizing an unknown function for which every measurement is expensive. It approximates the objective function and then recommends a new measurement point…

This work introduces a new method designed for Bayesian deep learning called scalable Bayesian Monte Carlo (SBMC). The method is comprised of a model and an algorithm. The model interpolates between a point estimator and the posterior. The…

Quantifying the complexity and irregularity of time series data is a primary pursuit across various data-scientific disciplines. Sample entropy (SampEn) is a widely adopted metric for this purpose, but its reliability is sensitive to the…

Bayesian nonparametric (BNP) models provide elegant methods for discovering underlying latent features within a data set, but inference in such models can be slow. We exploit the fact that completely random measures, which commonly used…

Sparse signal reconstruction algorithms have attracted research attention due to their wide applications in various fields. In this paper, we present a simple Bayesian approach that utilizes the sparsity constraint and a priori statistical…

Implicit samplers are algorithms for producing independent, weighted samples from multi-variate probability distributions. These are often applied in Bayesian data assimilation algorithms. We use Laplace asymptotic expansions to analyze two…

Functional mixed models are widely useful for regression analysis with dependent functional data, including longitudinal functional data with scalar predictors. However, existing algorithms for Bayesian inference with these models only…

Sparse Bayesian learning (SBL) can be implemented with low complexity based on the approximate message passing (AMP) algorithm. However, it is vulnerable to `difficult' measurement matrices as AMP can easily diverge. Damped AMP has been…

We design and analyse variations of the classical Thompson sampling (TS) procedure for Bayesian optimisation (BO) in settings where function evaluations are expensive, but can be performed in parallel. Our theoretical analysis shows that a…

The rising interest in Bayesian deep learning (BDL) has led to a plethora of methods for estimating the posterior distribution. However, efficient computation of inferences, such as predictions, has been largely overlooked with Monte Carlo…

In this paper, we discuss a class of distributed detection algorithms which can be viewed as implementations of Bayes' law in distributed settings. Some of the algorithms are proposed in the literature most recently, and others are first…

In this paper we consider the problem of joint segmentation of hyperspectral images in the Bayesian framework. The proposed approach is based on a Hidden Markov Modeling (HMM) of the images with common segmentation, or equivalently with…

The problem of Bayesian filtering and smoothing in nonlinear models with additive noise is an active area of research. Classical Taylor series as well as more recent sigma-point based methods are two well-known strategies to deal with these…

An efficient numerical algorithm is presented for massively parallel simulations of dispersion-managed wavelength-division-multiplexed optical fiber systems. The algorithm is based on a weak nonlinearity approximation and independent…

Bayesian hierarchical Poisson models are an essential tool for analyzing count data. However, designing efficient algorithms to sample from the posterior distribution of the target parameters remains a challenging task for this class of…

This paper concerns pseudo labelling in segmentation. Our contribution is fourfold. Firstly, we present a new formulation of pseudo-labelling as an Expectation-Maximization (EM) algorithm for clear statistical interpretation. Secondly, we…

Data assimilation is a core component of numerical weather prediction systems. The large quantity of data processed during assimilation requires the computation to be distributed across increasingly many compute nodes, yet existing…