Related papers: Deep Gaussian Processes for Multi-fidelity Modelin…

Computer simulations are indispensable for analyzing complex systems, yet high-fidelity models often incur prohibitive computational costs. Multi-fidelity frameworks address this challenge by combining inexpensive low-fidelity simulations…

Gaussian graphical models are widely used to infer dependence structures. Bayesian methods are appealing to quantify uncertainty associated with structural learning, i.e., the plausibility of conditional independence statements given the…

Models of stochastic processes are widely used in almost all fields of science. Theory validation, parameter estimation, and prediction all require model calibration and statistical inference using data. However, data are almost always…

Methods for reasoning under uncertainty are a key building block of accurate and reliable machine learning systems. Bayesian methods provide a general framework to quantify uncertainty. However, because of model misspecification and the use…

A new type of nonstationary Gaussian process model is developed for approximating computationally expensive functions. The new model is a composite of two Gaussian processes, where the first one captures the smooth global trend and the…

This paper presents a new model called infinite mixtures of multivariate Gaussian processes, which can be used to learn vector-valued functions and applied to multitask learning. As an extension of the single multivariate Gaussian process,…

Outer loop tasks such as optimization, uncertainty quantification or inference can easily become intractable when the underlying high-fidelity model is computationally expensive. Similarly, data-driven architectures typically require large…

Deep Ensembles, as a type of Bayesian Neural Networks, can be used to estimate uncertainty on the prediction of multiple neural networks by collecting votes from each network and computing the difference in those predictions. In this paper,…

A Bayesian treatment of deep learning allows for the computation of uncertainties associated with the predictions of deep neural networks. We show how the concept of Errors-in-Variables can be used in Bayesian deep regression to also…

Gaussian process regression is widely used because of its ability to provide well-calibrated uncertainty estimates and handle small or sparse datasets. However, it struggles with high-dimensional data. One possible way to scale this…

Deep learning is a hierarchical inference method formed by subsequent multiple layers of learning able to more efficiently describe complex relationships. In this work, Deep Gaussian Mixture Models are introduced and discussed. A Deep…

We develop a novel multi-fidelity framework that goes far beyond the classical AR(1) Co-kriging scheme of Kennedy and O'Hagan (2000). Our method can handle general discontinuous cross-correlations among systems with different levels of…

We propose a new class of Bayesian neural networks (BNNs) that can be trained using noisy data of variable fidelity, and we apply them to learn function approximations as well as to solve inverse problems based on partial differential…

Deep Gaussian Processes (DGP) are hierarchical generalizations of Gaussian Processes (GP) that have proven to work effectively on a multiple supervised regression tasks. They combine the well calibrated uncertainty estimates of GPs with the…

In the presence of modeling errors, the mainstream Bayesian methods seldom give a realistic account of uncertainties as they commonly underestimate the inherent variability of parameters. This problem is not due to any misconception in the…

Complex-valued Gaussian processes are commonly used in Bayesian frequency-domain system identification as prior models for regression. If each realization of such a process were an $H_\infty$ function with probability one, then the same…

Hyper-differential sensitivity analysis with respect to model discrepancy was recently developed to enable uncertainty quantification for optimization problems. The approach consists of two primary steps: (i) Bayesian calibration of the…

We introduce a Bayesian framework for inference with a supervised version of the Gaussian process latent variable model. The framework overcomes the high correlations between latent variables and hyperparameters by using an unbiased pseudo…

When modelling time series, it is common to decompose observed variation into a "signal" process, the process of interest, and "noise", representing nuisance factors that obfuscate the signal. To separate signal from noise, assumptions must…

A large collection of time series poses significant challenges for classical and neural forecasting approaches. Classical time series models fail to fit data well and to scale to large problems, but succeed at providing uncertainty…