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Gaussian Process Regression (GPR) is a popular regression method, which unlike most Machine Learning techniques, provides estimates of uncertainty for its predictions. These uncertainty estimates however, are based on the assumption that…
It has long been known that a single-layer fully-connected neural network with an i.i.d. prior over its parameters is equivalent to a Gaussian process (GP), in the limit of infinite network width. This correspondence enables exact Bayesian…
This paper introduces algorithms to select/design kernels in Gaussian process regression/kriging surrogate modeling techniques. We adopt the setting of kernel method solutions in ad hoc functional spaces, namely Reproducing Kernel Hilbert…
Additive Gaussian Processes (GPs) are popular approaches for nonparametric feature selection. The common training method for these models is Bayesian Back-fitting. However, the convergence rate of Back-fitting in training additive GPs is…
Random Feature (RF) models are used as efficient parametric approximations of kernel methods. We investigate, by means of random matrix theory, the connection between Gaussian RF models and Kernel Ridge Regression (KRR). For a Gaussian RF…
Many functions have approximately-known upper and/or lower bounds, potentially aiding the modeling of such functions. In this paper, we introduce Gaussian process models for functions where such bounds are (approximately) known. More…
In nonparametric regression, it is common for the inputs to fall in a restricted subset of Euclidean space. Typical kernel-based methods that do not take into account the intrinsic geometry of the domain across which observations are…
Gaussian process upper confidence bound (GP-UCB) is a theoretically promising approach for black-box optimization; however, the confidence parameter $\beta$ is considerably large in the theorem and chosen heuristically in practice. Then,…
Gaussian processes (GP) are a well studied Bayesian approach for the optimization of black-box functions. Despite their effectiveness in simple problems, GP-based algorithms hardly scale to high-dimensional functions, as their per-iteration…
Excellent variational approximations to Gaussian process posteriors have been developed which avoid the $\mathcal{O}\left(N^3\right)$ scaling with dataset size $N$. They reduce the computational cost to $\mathcal{O}\left(NM^2\right)$, with…
We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP) based method to approximate the joint distribution of the unknown parameters and the data. In particular, we…
In many contexts Gaussian Mixtures (GM) are used to approximate probability distributions, possibly time-varying. In some applications the number of GM components exponentially increases over time, and reduction procedures are required to…
We study the noise-free Gaussian Process (GP) bandits problem, in which the learner seeks to minimize regret through noise-free observations of the black-box objective function lying on the known reproducing kernel Hilbert space (RKHS).…
For a class of stochastic models with Gaussian and rough mean-reverting volatility that embeds the genuine rough Stein-Stein model, we study the weak approximation rate when using a Euler type scheme with integrated kernels. Our first…
The Gaussian process (GP) is a popular statistical technique for stochastic function approximation and uncertainty quantification from data. GPs have been adopted into the realm of machine learning in the last two decades because of their…
Gaussian Process (GP) regression is shown to be effective for learning unknown dynamics, enabling efficient and safety-aware control strategies across diverse applications. However, existing GP-based model predictive control (GP-MPC)…
Despite a large corpus of recent work on scaling up Gaussian processes, a stubborn trade-off between computational speed, prediction and uncertainty quantification accuracy, and customizability persists. This is because the vast majority of…
Various methods in statistical learning build on kernels considered in reproducing kernel Hilbert spaces. In applications, the kernel is often selected based on characteristics of the problem and the data. This kernel is then employed to…
Bayesian inference has many advantages for complex models, but standard Monte Carlo methods for summarizing the posterior can be computationally demanding, and it is attractive to consider optimization-based variational methods. Our work…
We study the use of Gaussian process emulators to approximate the parameter-to-observation map or the negative log-likelihood in Bayesian inverse problems. We prove error bounds on the Hellinger distance between the true posterior…