Related papers: Noise Estimation in Gaussian Process Regression

In this work, we employ the Bayesian inference framework to solve the problem of estimating the solution and particularly, its derivatives, which satisfy a known differential equation, from the given noisy and scarce observations of the…

This note studies a method for the efficient estimation of a finite number of unknown parameters from linear equations, which are perturbed by Gaussian noise. In case the unknown parameters have only few nonzero entries, the proposed…

We consider the problem of estimating means of two Gaussians in a 2-Gaussian mixture, which is not balanced and is corrupted by noise of an arbitrary distribution. We present a robust algorithm to estimate the parameters, together with…

We consider a semiparametric generalized linear model and study estimation of both marginal and quantile effects in this model. We propose an approximate maximum likelihood estimator, and rigorously establish the consistency, the asymptotic…

We consider the problem of fitting a parametric model to time-series data that are afflicted by correlated noise. The noise is represented by a sum of two stationary Gaussian processes: one that is uncorrelated in time, and another that has…

Deep Gaussian processes (DGPs) can model complex marginal densities as well as complex mappings. Non-Gaussian marginals are essential for modelling real-world data, and can be generated from the DGP by incorporating uncorrelated variables…

We consider the problem of recovering the unknown noise variance in the linear regression model. To estimate the nuisance (a vector of regression coefficients) we use a family of spectral regularisers of the maximum likelihood estimator.…

The computational cost for inference and prediction of statistical models based on Gaussian processes with Mat\'ern covariance functions scales cubicly with the number of observations, limiting their applicability to large data sets. The…

We consider covariance parameter estimation for Gaussian processes with functional inputs. From an increasing-domain asymptotics perspective, we prove the asymptotic consistency and normality of the maximum likelihood estimator. We extend…

The lasso has been studied extensively as a tool for estimating the coefficient vector in the high-dimensional linear model; however, considerably less is known about estimating the error variance in this context. In this paper, we propose…

We consider estimation of a sparse parameter vector that determines the covariance matrix of a Gaussian random vector via a sparse expansion into known "basis matrices". Using the theory of reproducing kernel Hilbert spaces, we derive lower…

Large-scale Gaussian process inference has long faced practical challenges due to time and space complexity that is superlinear in dataset size. While sparse variational Gaussian process models are capable of learning from large-scale data,…

The main challenges that arise when adopting Gaussian Process priors in probabilistic modeling are how to carry out exact Bayesian inference and how to account for uncertainty on model parameters when making model-based predictions on…

Posterior computation for high-dimensional data with many parameters can be challenging. This article focuses on a new method for approximating posterior distributions of a low- to moderate-dimensional parameter in the presence of a…

In this paper, we introduce the notion of Gaussian processes indexed by probability density functions for extending the Mat\'ern family of covariance functions. We use some tools from information geometry to improve the efficiency and the…

The asymptotic variance of the maximum likelihood estimate is proved to decrease when the maximization is restricted to a subspace that contains the true parameter value. Maximum likelihood estimation allows a systematic fitting of…

This paper proposes novel noise-free Bayesian optimization strategies that rely on a random exploration step to enhance the accuracy of Gaussian process surrogate models. The new algorithms retain the ease of implementation of the classical…

Various approaches to stochastic processes exist, noting that key properties such as measurability and continuity are not trivially satisfied. We introduce a new theory for Gaussian processes using improper linear functionals. Using a…

Accurately estimating the statistical properties of noise is important in data analysis for space-based gravitational wave detectors. Noise in different time-delay interferometry channels correlates with each other. Many studies often…

Non-Gaussian impulsive noise (IN) with memory exists in many practical applications. When it is mixed with white Gaussian noise (WGN), the resultant mixed noise will be bursty. The performance of communication systems will degrade…