Related papers: Optimal uncertainty bounds for multivariate kernel…
This work presents a nonparametric framework for dissipativity learning in reproducing kernel Hilbert spaces, which enables data-driven certification of stability and performance properties for unknown nonlinear systems without requiring an…
Consider the sequential optimization of a continuous, possibly non-convex, and expensive to evaluate objective function $f$. The problem can be cast as a Gaussian Process (GP) bandit where $f$ lives in a reproducing kernel Hilbert space…
The focus of this work is the convergence of non-stationary and deep Gaussian process regression. More precisely, we follow a Bayesian approach to regression or interpolation, where the prior placed on the unknown function $f$ is a…
We propose Kernel Predictive Control (KPC), a learning-based predictive control strategy that enjoys deterministic guarantees of safety. Noise-corrupted samples of the unknown system dynamics are used to learn several models through the…
Gaussian Process (GP) models are popular tools in uncertainty quantification (UQ) because they purport to furnish functional uncertainty estimates that can be used to represent model uncertainty. It is often difficult to state with…
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…
Black box optimization (BBO) focuses on optimizing unknown functions in high-dimensional spaces. In many applications, sampling the unknown function is expensive, imposing a tight sample budget. Ongoing work is making progress on reducing…
Modern datasets across many disciplines increasingly consist of time-evolving, potentially infinite-dimensional random objects, such as dynamic functional data, which are naturally modeled in Hilbert spaces. In these settings,…
In this paper, tight upper and lower bounds are derived on the weighted sum of minimum mean-squared errors for additive Gaussian noise channels. The bounds are obtained by constraining the input distribution to be close to a Gaussian…
We study noisy computation in randomly generated k-ary Boolean formulas. We establish bounds on the noise level above which the results of computation by random formulas are not reliable. This bound is saturated by formulas constructed from…
The application of Gaussian processes (GPs) to large data sets is limited due to heavy memory and computational requirements. A variety of methods has been proposed to enable scalability, one of which is to exploit structure in the kernel…
The high efficiency of a recently proposed method for computing with Gaussian processes relies on expanding a (translationally invariant) covariance kernel into complex exponentials, with frequencies lying on a Cartesian equispaced grid.…
Gaussian Process (GP) regression is a powerful nonparametric Bayesian framework, but its performance depends critically on the choice of covariance kernel. Selecting an appropriate kernel is therefore central to model quality, yet remains…
We address uncertainty quantification for Gaussian processes (GPs) under misspecified priors, with an eye towards Bayesian Optimization (BO). GPs are widely used in BO because they easily enable exploration based on posterior uncertainty…
We aim to optimize a black-box function $f:\mathcal{X} \mapsto \mathbb{R}$ under the assumption that $f$ is H\"older smooth and has bounded norm in the RKHS associated with a given kernel $K$. This problem is known to have an agnostic…
Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…
This paper studies convergence of empirical risks in reproducing kernel Hilbert spaces (RKHS). A conventional assumption in the existing research is that empirical training data do not contain any noise but this may not be satisfied in some…
Gaussian process (GP) regression is a Bayesian nonparametric method for regression and interpolation, offering a principled way of quantifying the uncertainties of predicted function values. For the quantified uncertainties to be…
We explore the use of non homogenous noise kernels in Gaussian process modelling to improve the potential energy curve models describing stochastic electronic structure data. We use the same noise kernels on energy curves describing…
We derive novel deterministic bounds on the approximation error of data-based bilinear surrogate models for unknown nonlinear systems. The surrogate models are constructed using kernel-based extended dynamic mode decomposition to…