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Gaussian processes are widely employed as versatile modelling and predictive tools in spatial statistics, functional data analysis, computer modelling and diverse applications of machine learning. They have been widely studied over…
Functional data analysis, which models data as realizations of random functions over a continuum, has emerged as a useful tool for time series data. Often, the goal is to infer the dynamic connections (or time-varying conditional…
Multi-task Gaussian process (MTGP) is a well-known non-parametric Bayesian model for learning correlated tasks effectively by transferring knowledge across tasks. But current MTGPs are usually limited to the multi-task scenario defined in…
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…
In many real-world applications we are interested in approximating costly functions that are analytically unknown, e.g. complex computer codes. An emulator provides a fast approximation of such functions relying on a limited number of…
Background: Continuous traits evolution of a group of taxa that are correlated through a phylogenetic tree is commonly modelled using parametric stochastic differential equations to represent deterministic change of trait through time,…
We introduce priors and algorithms to perform Bayesian inference in Gaussian models defined by acyclic directed mixed graphs. Such a class of graphs, composed of directed and bi-directed edges, is a representation of conditional…
Varying coefficient models (VCMs) are widely used for estimating nonlinear regression functions for functional data. Their Bayesian variants using Gaussian process priors on the functional coefficients, however, have received limited…
We consider the problem of variable selection in varying-coefficient functional linear models, where multiple predictors are functions and a response is a scalar and depends on an exogenous variable. The varying-coefficient functional…
A multivariate distribution can be described by a triangular transport map from the target distribution to a simple reference distribution. We propose Bayesian nonparametric inference on the transport map by modeling its components using…
Gaussian processes are popular and flexible models for spatial, temporal, and functional data, but they are computationally infeasible for large datasets. We discuss Gaussian-process approximations that use basis functions at multiple…
Gaussian process regression is widely applied in computational science and engineering for surrogate modeling owning to its kernel-based and probabilistic nature. In this work, we propose a Bayesian approach that integrates the variability…
Uncertainty control and scalability to large datasets are the two main issues for the deployment of Gaussian process (GP) models within the autonomous machine learning-based prediction pipelines in material science and chemistry. One way to…
Multi-output regression models must exploit dependencies between outputs to maximise predictive performance. The application of Gaussian processes (GPs) to this setting typically yields models that are computationally demanding and have…
As Deep Learning continues to yield successful applications in Computer Vision, the ability to quantify all forms of uncertainty is a paramount requirement for its safe and reliable deployment in the real-world. In this work, we leverage…
Scientific and engineering problems often require the use of artificial intelligence to aid understanding and the search for promising designs. While Gaussian processes (GP) stand out as easy-to-use and interpretable learners, they have…
The design of an experiment can be always be considered at least implicitly Bayesian, with prior knowledge used informally to aid decisions such as the variables to be studied and the choice of a plausible relationship between the…
Spatial models are used in a variety research areas, such as environmental sciences, epidemiology, or physics. A common phenomenon in many spatial regression models is spatial confounding. This phenomenon takes place when spatially indexed…
An obstacle to artificial general intelligence is set by continual learning of multiple tasks of different nature. Recently, various heuristic tricks, both from machine learning and from neuroscience angles, were proposed, but they lack a…
Some scenarios require the computation of a predictive distribution of a new value evaluated on an objective function conditioned on previous observations. We are interested on using a model that makes valid assumptions on the objective…