Related papers: Probabilistic Richardson Extrapolation
For a class of finite elements approximations for linear stochastic parabolic PDEs it is proved that one can accelerate the rate of convergence by Richardson extrapolation. More precisely, by taking appropriate mixtures of finite elements…
We propose a multi-step Richardson-Romberg extrapolation method for the computation of expectations $E f(X_{_T})$ of a diffusion $(X_t)_{t\in [0,T]}$ when the weak time discretization error induced by the Euler scheme admits an expansion at…
Extrapolation is a well-known technique for solving convex optimization and variational inequalities and recently attracts some attention for non-convex optimization. Several recent works have empirically shown its success in some machine…
Gaussian process (GP) methods have been widely studied recently, especially for large-scale systems with big data and even more extreme cases when data is sparse. Key advantages of these methods consist in: 1) the ability to provide…
This article investigates the origin of numerical issues in maximum likelihood parameter estimation for Gaussian process (GP) interpolation and investigates simple but effective strategies for improving commonly used open-source software…
We introduce a class of unconditionally energy stable, high order accurate schemes for gradient flows in a very general setting. The new schemes are a high order analogue of the minimizing movements approach for generating a time discrete…
This work presents a new procedure for obtaining predictive distributions in the context of Gaussian process (GP) modeling, with a relaxation of the interpolation constraints outside ranges of interest: the mean of the predictive…
To enable closed form conditioning, a common assumption in Gaussian process (GP) regression is independent and identically distributed Gaussian observation noise. This strong and simplistic assumption is often violated in practice, which…
The Gaussian process (GP) regression can be severely biased when the data are contaminated by outliers. This paper presents a new robust GP regression algorithm that iteratively trims the most extreme data points. While the new algorithm…
We obtain an expansion of the implicit weak discretization error for the target of stochastic approximation algorithms introduced and studied in [Frikha2013]. This allows us to extend and develop the Richardson-Romberg extrapolation method…
Gaussian process (GP) models provide a powerful tool for prediction but are computationally prohibitive using large data sets. In such scenarios, one has to resort to approximate methods. We derive an approximation based on a composite…
We study numerical integration of smooth functions defined over the $s$-dimensional unit cube. A recent work by Dick et al. (2019) has introduced so-called extrapolated polynomial lattice rules, which achieve the almost optimal rate of…
The proximal gradient method is a generic technique introduced to tackle the non-smoothness in optimization problems, wherein the objective function is expressed as the sum of a differentiable convex part and a non-differentiable…
Chance constraints provide a principled framework to mitigate the risk of high-impact extreme events by modifying the controllable properties of a system. The low probability and rare occurrence of such events, however, impose severe…
Many iterative methods for solving optimization or feasibility problems have been invented, and often convergence of the iterates to some solution is proven. Under favourable conditions, one might have additional bounds on the distance of…
Vector extrapolation methods are widely used in large-scale simulation studies, and numerous extrapolation-based acceleration techniques have been developed to enhance the convergence of linear and nonlinear fixed-point iterative methods.…
This article advocates the use of conformal prediction (CP) methods for Gaussian process (GP) interpolation to enhance the calibration of prediction intervals. We begin by illustrating that using a GP model with parameters selected by…
In order to scale standard Gaussian process (GP) regression to large-scale datasets, aggregation models employ factorized training process and then combine predictions from distributed experts. The state-of-the-art aggregation models,…
The (conditional or unconditional) distribution of the continuous scan statistic in a one-dimensional Poisson process may be approximated by that of a discrete analogue via time discretization (to be referred to as the discrete…
We propose a novel sparse spectrum approximation of Gaussian process (GP) tailored for Bayesian optimization. Whilst the current sparse spectrum methods provide desired approximations for regression problems, it is observed that this…