Related papers: Scale invariant process regression: Towards Bayesi…

Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…

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…

The Bayesian statistical framework provides a systematic approach to enhance the regularization model by incorporating prior information about the desired solution. For the Bayesian linear inverse problems with Gaussian noise and Gaussian…

Polynomial kernel regression is one of the standard and state-of-the-art learning strategies. However, as is well known, the choices of the degree of polynomial kernel and the regularization parameter are still open in the realm of model…

Inference in popular nonparametric Bayesian models typically relies on sampling or other approximations. This paper presents a general methodology for constructing novel tractable nonparametric Bayesian methods by applying the kernel trick…

Gaussian process regression is used throughout statistics and machine learning for prediction and uncertainty quantification. A Gaussian process is specified by its mean and covariance functions. Many covariance functions, including…

Scaling analysis, in which one infers scaling exponents and a scaling function in a scaling law from given data, is a powerful tool for determining universal properties of critical phenomena in many fields of science. However, there are…

We introduce a novel rule-based approach for handling regression problems. The new methodology carries elements from two frameworks: (i) it provides information about the uncertainty of the parameters of interest using Bayesian inference,…

This work is concerned with the convergence of Gaussian process regression. A particular focus is on hierarchical Gaussian process regression, where hyper-parameters appearing in the mean and covariance structure of the Gaussian process…

Existing Bayesian models, especially nonparametric Bayesian methods, rely on specially conceived priors to incorporate domain knowledge for discovering improved latent representations. While priors can affect posterior distributions through…

In the last years, the success of kernel-based regularisation techniques in solving impulse response modelling tasks has revived the interest on linear system identification. In this work, an alternative perspective on the same problem is…

We propose a vector-valued regression problem whose solution is equivalent to the reproducing kernel Hilbert space (RKHS) embedding of the Bayesian posterior distribution. This equivalence provides a new understanding of kernel Bayesian…

Gaussian process regression has proven very powerful in statistics, machine learning and inverse problems. A crucial aspect of the success of this methodology, in a wide range of applications to complex and real-world problems, is…

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…

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…

A method to perform unfolding with Gaussian processes (GPs) is presented. Using Bayesian regression, we define an estimator for the underlying truth distribution as the mode of the posterior. We show that in the case where the bin contents…

We show that regularizing Bayesian predictive regressions provides a framework for prior sensitivity analysis. We develop a procedure that jointly regularizes expectations and variance-covariance matrices using a pair of shrinkage priors.…

In this paper, we study random subsampling of Gaussian process regression, one of the simplest approximation baselines, from a theoretical perspective. Although subsampling discards a large part of training data, we show provable guarantees…

In this work, a method for obtaining pixel-wise error bounds in Bayesian regularization of inverse imaging problems is introduced. The proposed method employs estimates of the posterior variance together with techniques from conformal…

Bayesian learning is built on an assumption that the model space contains a true reflection of the data generating mechanism. This assumption is problematic, particularly in complex data environments. Here we present a Bayesian…