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Leveraging the wealth of unlabeled data produced in recent years provides great potential for improving supervised models. When the cost of acquiring labels is high, probabilistic active learning methods can be used to greedily select the…

Advances in sensing technology have made it possible to collect large volumes of high-dimensional time-series data. In fields like genetics and neuroscience, key questions concern whether directed relationships between variables can be…

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…

This paper introduces a new sparse spatio-temporal structured Gaussian process regression framework for online and offline Bayesian inference. This is the first framework that gives a time-evolving representation of the interdependencies…

Sequential learning with Gaussian processes (GPs) is challenging when access to past data is limited, for example, in continual and active learning. In such cases, errors can accumulate over time due to inaccuracies in the posterior,…

We introduce a variational Bayesian neural network where the parameters are governed via a probability distribution on random matrices. Specifically, we employ a matrix variate Gaussian \cite{gupta1999matrix} parameter posterior…

We propose Bayesian methods for Gaussian graphical models that lead to sparse and adaptively shrunk estimators of the precision (inverse covariance) matrix. Our methods are based on lasso-type regularization priors leading to parsimonious…

Gaussian processes (GPs) are typically criticised for their unfavourable scaling in both computational and memory requirements. For large datasets, sparse GPs reduce these demands by conditioning on a small set of inducing variables…

Nonparametric Bayesian models are used routinely as flexible and powerful models of complex data. Many times, a statistician may have additional informative beliefs about data distribution of interest, e.g., its mean or subset components,…

Variational autoencoders often assume isotropic Gaussian priors and mean-field posteriors, hence do not exploit structure in scenarios where we may expect similarity or consistency across latent variables. Gaussian process variational…

Smoothed model checking based on Gaussian process classification provides a powerful approach for statistical model checking of parametric continuous time Markov chain models. The method constructs a model for the functional dependence of…

We consider chance constrained optimization where it is sought to optimize a function while complying with constraints, both of which are affected by uncertainties. The high computational cost of realistic simulations strongly limits the…

Kernel methods on discrete domains have shown great promise for many challenging data types, for instance, biological sequence data and molecular structure data. Scalable kernel methods like Support Vector Machines may offer good predictive…

Gaussian processes retain the linear model either as a special case, or in the limit. We show how this relationship can be exploited when the data are at least partially linear. However from the perspective of the Bayesian posterior, the…

Gaussian mixture models are a popular tool for model-based clustering, and mixtures of factor analyzers are Gaussian mixture models having parsimonious factor covariance structure for mixture components. There are several recent extensions…

In this paper we propose the first non-parametric Bayesian model using Gaussian Processes to make inference on Poisson Point Processes without resorting to gridding the domain or to introducing latent thinning points. Unlike competing…

Gaussian process state-space models (GPSSMs) provide a principled and flexible approach to modeling the dynamics of a latent state, which is observed at discrete-time points via a likelihood model. However, inference in GPSSMs is…

Generalising well in supervised learning tasks relies on correctly extrapolating the training data to a large region of the input space. One way to achieve this is to constrain the predictions to be invariant to transformations on the input…

As Gaussian processes are used to answer increasingly complex questions, analytic solutions become scarcer and scarcer. Monte Carlo methods act as a convenient bridge for connecting intractable mathematical expressions with actionable…

Recent machine learning advances have proposed black-box estimation of unknown continuous-time system dynamics directly from data. However, earlier works are based on approximative ODE solutions or point estimates. We propose a novel…