Related papers: Orthogonally Decoupled Variational Gaussian Proces…
We introduce a new scalable approximation for Gaussian processes with provable guarantees which hold simultaneously over its entire parameter space. Our approximation is obtained from an improved sample complexity analysis for sparse…
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 processes (GPs) have been proven to be powerful tools in various areas of machine learning. However, there are very few applications of GPs in the scenario of multi-view learning. In this paper, we present a new GP model for…
Gaussian processes (GPs) are commonplace in spatial statistics. Although many non-stationary models have been developed, there is arguably a lack of flexibility compared to equipping each location with its own parameters. However, the…
This paper presents a Gaussian process (GP) model for estimating piecewise continuous regression functions. In scientific and engineering applications of regression analysis, the underlying regression functions are piecewise continuous in…
We propose a new method for simplification of Gaussian process (GP) models by projecting the information contained in the full encompassing model and selecting a reduced number of variables based on their predictive relevance. Our results…
This paper presents an approach for constrained Gaussian Process (GP) regression where we assume that a set of linear transformations of the process are bounded. It is motivated by machine learning applications for high-consequence…
We introduce a framework and early results for massively scalable Gaussian processes (MSGP), significantly extending the KISS-GP approach of Wilson and Nickisch (2015). The MSGP framework enables the use of Gaussian processes (GPs) on…
Data in many applications follows systems of Ordinary Differential Equations (ODEs). This paper presents a novel algorithmic and symbolic construction for covariance functions of Gaussian Processes (GPs) with realizations strictly following…
Gaussian processes (GPs) are distributions over functions, which provide a Bayesian nonparametric approach to regression and classification. In spite of their success, GPs have limited use in some applications, for example, in some cases a…
Gaussian Processes (GPs) provide a general and analytically tractable way of modeling complex time-varying, nonparametric functions. The Automatic Bayesian Covariance Discovery (ABCD) system constructs natural-language description of…
We address the problem of continual learning in multi-task Gaussian process (GP) models for handling sequential input-output observations. Our approach extends the existing prior-posterior recursion of online Bayesian inference, i.e.\ past…
With the development of new remote sensing technology, large or even massive spatial datasets covering the globe become available. Statistical analysis of such data is challenging. This article proposes a semiparametric approach to model…
Maximizing high-dimensional, non-convex functions through noisy observations is a notoriously hard problem, but one that arises in many applications. In this paper, we tackle this challenge by modeling the unknown function as a sample from…
The accurate prediction of time-changing variances is an important task in the modeling of financial data. Standard econometric models are often limited as they assume rigid functional relationships for the variances. Moreover, function…
Gaussian Process (GP) regression models typically assume that residuals are Gaussian and have the same variance for all observations. However, applications with input-dependent noise (heteroscedastic residuals) frequently arise in practice,…
Differential equations are important mechanistic models that are integral to many scientific and engineering applications. With the abundance of available data there has been a growing interest in data-driven physics-informed models.…
Gaussian processes provide a compact representation for modeling and estimating an unknown function, that can be updated as new measurements of the function are obtained. This paper extends this powerful framework to the case where the…
Two complementary approaches have been extensively used in signal and image processing leading to novel results, the sparse representation methodology and the variational strategy. Recently, a new sparsity based model has been proposed, the…
Exact Gaussian Process (GP) regression has O(N^3) runtime for data size N, making it intractable for large N. Many algorithms for improving GP scaling approximate the covariance with lower rank matrices. Other work has exploited structure…