Related papers: Gaussian Processes with Sample Paths in Reproducin…

Gaussian processes are important models in the field of probabilistic numerics. We present a procedure for optimizing Mat\'ern kernel temporal Gaussian processes with respect to the kernel covariance function's hyperparameters. It is based…

We consider multi-dimensional Gaussian processes and give a new condition on the covariance, simple and sharp, for the existence of stochastic area(s). Gaussian rough paths are constructed with a variety of weak and strong approximation…

We propose an estimator for the mean of random variables in separable real Banach spaces using the empirical characteristic function. Assuming that the covariance operator of the random variable is bounded in a precise sense, we show that…

Gaussian process regression is a well-established Bayesian machine learning method. We propose a new approach to Gaussian process regression using quantum kernels based on parameterized quantum circuits. By employing a hardware-efficient…

In the article we study properties of the random integral operator in $L_2(\mathbb{R})$ whose kernel is obtained as a convolution of Gaussian density with a stationary point process.

In high-energy physics it is a recurring challenge to efficiently and precisely (enough) calculate the global significance of, e.g., a potential new resonance. We propose a new method that models the significance in the search region as a…

The method of regularization with the Gaussian reproducing kernel is popular in the machine learning literature and successful in many practical applications. In this paper we consider the periodic version of the Gaussian kernel…

Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…

Whilst deep neural networks have shown great empirical success, there is still much work to be done to understand their theoretical properties. In this paper, we study the relationship between random, wide, fully connected, feedforward…

Bayesian model updating based on Gaussian Process (GP) models has received attention in recent years, which incorporates kernel-based GPs to provide enhanced fidelity response predictions. Although most kernel functions provide high fitting…

Statistical physics approaches can be used to derive accurate predictions for the performance of inference methods learning from potentially noisy data, as quantified by the learning curve defined as the average error versus number of…

In the context of kernel optimization, we prove a result that yields new factorizations and realizations. Our initial context is that of general positive operator-valued kernels. We further present implications for Hilbert space-valued…

Gaussian processes regression models are an appealing machine learning method as they learn expressive non-linear models from exemplar data with minimal parameter tuning and estimate both the mean and covariance of unseen points. However,…

Motivated by questions in quantum theory, we study Hilbert space valued Gaussian processes, and operator-valued kernels, i.e., kernels taking values in B(H) (= all bounded linear operators in a fixed Hilbert space H). We begin with a…

We construct and analyze conformally invariant random fields on 4-dimensional Riemannian manifolds $(M,g)$. These centered Gaussian fields $h$, called \emph{co-biharmonic Gaussian fields}, are characterized by their covariance kernels $k$…

We obtain a representation theorem for Banach space valued Gaussian random variables as integrals against a white noise. As a corollary we obtain necessary and sufficient conditions for the existence of a white noise representation for a…

Given a positive operator-valued measure $\nu$ acting on the Borel sets of a locally compact Hausdorff space $X$, with outcomes in the algebra $\mathcal B(\mathcal H)$ of all bounded operators on a (possibly infinite-dimensional) Hilbert…

We prove a Wegner estimate for discrete Schr\"odinger operators with a potential given by a Gaussian random process. The only assumption is that the covariance function decays exponentially, no monotonicity assumption is required. This…

Gaussian processes are machine learning models capable of learning unknown functions in a way that represents uncertainty, thereby facilitating construction of optimal decision-making systems. Motivated by a desire to deploy Gaussian…

Variable selection for Gaussian process models is often done using automatic relevance determination, which uses the inverse length-scale parameter of each input variable as a proxy for variable relevance. This implicitly determined…