相关论文: Gaussian Processes indexed on the symmetric group:…

The second-order, small-scale dependence structure of a stochastic process defined in the space-time domain is key to prediction (or kriging). While great efforts have been dedicated to developing models for cases in which the spatial…

We present an operator learning framework for solving non-perturbative functional renormalization group equations, which are integro-differential equations defined on functionals. Our proposed approach uses Gaussian process operator…

Gaussian processes models are widely adopted for nonparameteric/semi-parametric modeling. Identifiability issues occur when the mean model contains polynomials with unknown coefficients. Though resulting prediction is unaffected, this leads…

Gaussian processes have become a promising tool for various safety-critical settings, since the posterior variance can be used to directly estimate the model error and quantify risk. However, state-of-the-art techniques for safety-critical…

Optimization problems with uncertain black-box constraints, modeled by warped Gaussian processes, have recently been considered in the Bayesian optimization setting. This work introduces a new class of constraints in which the same…

The expected supremum of a Gaussian process indexed by the image of an index set under a function class is bounded in terms of separate properties of the index set and the function class. The bound is relevant to the estimation of nonlinear…

This paper presents a kriging method for spatial prediction of temporal intensity functions, for situations where a temporal point process is observed at different spatial locations. Assuming that several replications of the processes are…

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…

Safety-critical technical systems operating in unknown environments require the ability to quickly adapt their behavior, which can be achieved in control by inferring a model online from the data stream generated during operation. Gaussian…

As Gaussian processes are used to answer increasingly complex questions, analytic solutions become scarcer and scarcer. Monte Carlo methods act as a convenient bridge for connecting intractable mathematical expressions with actionable…

In this work, we consider the problem of steering the first two moments of the uncertain state of an unknown discrete-time stochastic nonlinear system to a given terminal distribution in finite time. Toward that goal, first, a…

The Log-Gaussian Cox Process is a commonly used model for the analysis of spatial point patterns. Fitting this model is difficult because of its doubly-stochastic property, i.e., it is an hierarchical combination of a Poisson process at the…

The Gaussian process (GP) is a Bayesian nonparametric paradigm that is widely adopted for uncertainty quantification (UQ) in a number of safety-critical applications, including robotics, healthcare, as well as surveillance. The consistency…

Falsification is the basis for testing existing hypotheses, and a great danger is posed when results incorrectly reject our prior notions (false positives). Though nonparametric and nonlinear exploratory methods of uncovering coupling…

We propose a new definition of the Gaussian multiplicative chaos (GMC) and an approach based on the relation of subcritical GMC to randomized shifts of a Gaussian measure. Using this relation we prove general uniqueness and convergence…

Gaussian processes are ubiquitous in machine learning, statistics, and applied mathematics. They provide a flexible modelling framework for approximating functions, whilst simultaneously quantifying uncertainty. However, this is only true…

This paper presents a new variable selection approach integrated with Gaussian process (GP) regression. We consider a sparse projection of input variables and a general stationary covariance model that depends on the Euclidean distance…

Propagating input uncertainty through non-linear Gaussian process (GP) mappings is intractable. This hinders the task of training GPs using uncertain and partially observed inputs. In this paper we refer to this task as "semi-described…

Gaussian process (GP) models form a core part of probabilistic machine learning. Considerable research effort has been made into attacking three issues with GP models: how to compute efficiently when the number of data is large; how to…

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…