Related papers: Uncertainty Quantification and Experimental Design…

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…

Model Predictive Control (MPC) of an unknown system that is modelled by Gaussian Process (GP) techniques is studied in this paper. Using GP, the variances computed during the modelling and inference processes allow us to take model…

The proliferation of capable and efficient machine learning (ML) models marks one of the strongest methodological shifts in signal processing (SP) in its nearly 100-year history. ML models support the development of SP systems that…

Exact Gaussian Process (GP) regression has O(N^3) runtime for data size N, making it intractable for large N. Many algorithms for improving GP scaling approximate the covariance with lower rank matrices. Other work has exploited structure…

Standard Gaussian Process (GP) regression, a powerful machine learning tool, is computationally expensive when it is applied to large datasets, and potentially inaccurate when data points are sparsely distributed in a high-dimensional…

Gaussian Processes (GPs) are Bayesian models that provide uncertainty estimates associated to the predictions made. They are also very flexible due to their non-parametric nature. Nevertheless, GPs suffer from poor scalability as the number…

By enabling constraint-aware online model adaptation, model predictive control using Gaussian process (GP) regression has exhibited impressive performance in real-world applications and received considerable attention in the learning-based…

Functional covariates arise in many scientific and engineering applications when model inputs take the form of time-dependent or spatially distributed profiles, such as varying boundary conditions or changing material behaviours. In…

Gaussian Process (GP) models are a powerful tool in probabilistic machine learning with a solid theoretical foundation. Thanks to current advances, modeling complex data with GPs is becoming increasingly feasible, which makes them an…

Bayesian Optimization is an iterative method, tailored to optimizing expensive black box objective functions. Surrogate models like Gaussian Processes, which are the gold standard in Bayesian Optimization, can be inefficient for inputs with…

Posterior sampling by Monte Carlo methods provides a more comprehensive solution approach to inverse problems than computing point estimates such as the maximum posterior using optimization methods, at the expense of usually requiring many…

Computational models of complex physical systems often rely on simplifying assumptions which inevitably introduce model error, with consequent predictive errors. Given data on model observables, the estimation of parameterized model-error…

Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…

Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…

Deep Gaussian processes (DGPs) upgrade ordinary GPs through functional composition, in which intermediate GP layers warp the original inputs, providing flexibility to model non-stationary dynamics. Two DGP regimes have emerged in recent…

Gaussian process (GP) models that combine both categorical and continuous input variables have found use in analysis of longitudinal data and computer experiments. However, standard inference for these models has the typical cubic scaling,…

Gaussian Process state-space models capture complex temporal dependencies in a principled manner by placing a Gaussian Process prior on the transition function. These models have a natural interpretation as discretized stochastic…

Gaussian Process (GP) models provide a flexible framework for prediction and uncertainty quantification. For most covariance functions, however, exact GP prediction with $n$ points scales as $\mathcal{O}(n^3)$, making it prohibitively…

Geoscientists often solve inverse problems to estimate values of parameters of interest given relevant data sets. Bayesian inference solves these problems by combining probability distributions that describe uncertainties in both…

Deep Gaussian process models typically employ discrete hierarchies, but recent advancements in differential Gaussian processes (DiffGPs) have extended these models to infinite depths. However, existing DiffGP approaches often overlook the…