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Inter-domain Gaussian processes (GPs) allow for high flexibility and low computational cost when performing approximate inference in GP models. They are particularly suitable for modeling data exhibiting global structure but are limited to…

Deep Gaussian processes have recently been proposed as natural objects to fit, similarly to deep neural networks, possibly complex features present in modern data samples, such as compositional structures. Adopting a Bayesian nonparametric…

Modern scientific problems are often multi-disciplinary and require integration of computer models from different disciplines, each with distinct functional complexities, programming environments, and computation times. Linked Gaussian…

We present a multi-fidelity method for uncertainty quantification of parameter estimates in complex systems, leveraging generative models trained to sample the target conditional distribution. In the Bayesian inference setting, traditional…

Gaussian processes offer an attractive framework for predictive modeling from longitudinal data, i.e., irregularly sampled, sparse observations from a set of individuals over time. However, such methods have two key shortcomings: (i) They…

Recent advances in Deep Gaussian Processes (DGPs) show the potential to have more expressive representation than that of traditional Gaussian Processes (GPs). However, there exists a pathology of deep Gaussian processes that their learning…

We present a multi-task learning formulation for Deep Gaussian processes (DGPs), through non-linear mixtures of latent processes. The latent space is composed of private processes that capture within-task information and shared processes…

Solving nonlinear partial differential equations (PDEs) using kernel methods offers a compelling alternative to traditional numerical solvers. However, the performance of these methods strongly depends on the choice of kernel. In this work,…

A multi-layer deep Gaussian process (DGP) model is a hierarchical composition of GP models with a greater expressive power. Exact DGP inference is intractable, which has motivated the recent development of deterministic and stochastic…

Although Gaussian processes (GPs) with deep kernels have been successfully used for meta-learning in regression tasks, its uncertainty estimation performance can be poor. We propose a meta-learning method for calibrating deep kernel GPs for…

Deep Gaussian Processes (DGPs) are hierarchical generalizations of Gaussian Processes that combine well calibrated uncertainty estimates with the high flexibility of multilayer models. One of the biggest challenges with these models is that…

Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…

Multi-fidelity modelling arises in many situations in computational science and engineering world. It enables accurate inference even when only a small set of accurate data is available. Those data often come from a high-fidelity model,…

Gaussian processes (GPs) provide flexible distributions over functions, with inductive biases controlled by a kernel. However, in many applications Gaussian processes can struggle with even moderate input dimensionality. Learning a low…

We introduce a novel stochastic variational inference method for Gaussian process ($\mathcal{GP}$) regression, by deriving a posterior over a learnable set of coresets: i.e., over pseudo-input/output, weighted pairs. Unlike former free-form…

Multi-output Gaussian processes (MOGPs) have been introduced to deal with multiple tasks by exploiting the correlations between different outputs. Generally, MOGPs models assume a flat correlation structure between the outputs. However,…

The Gaussian process (GP) is a widely used probabilistic machine learning method with implicit uncertainty characterization for stochastic function approximation, stochastic modeling, and analyzing real-world measurements of nonlinear…

Deep kernel processes are a recently introduced class of deep Bayesian models that have the flexibility of neural networks, but work entirely with Gram matrices. They operate by alternately sampling a Gram matrix from a distribution over…

Gaussian Processes (GPs) are a class of kernel methods that have shown to be very useful in geoscience applications. They are widely used because they are simple, flexible and provide very accurate estimates for nonlinear problems,…

This paper is concerned with a state-space approach to deep Gaussian process (DGP) regression. We construct the DGP by hierarchically putting transformed Gaussian process (GP) priors on the length scales and magnitudes of the next level of…