A Distance-based Framework for Gaussian Processes over Probability Distributions

2018/01/01 by Maxim Dolgov, Dolgov, Maxim, Uwe D. Hanebeck +1
Computer Science · Engineering · #Control Systems and Identification #FOS: Electrical engineering #Gaussian Processes and Bayesian Inference #Systems and Control (eess.SY) #Target Tracking and Data Fusion in Sensor Networks #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.1809.09193

openalex publication_date 2018/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Gaussian processes constitute a very powerful and well-understood method for non-parametric regression and classification. In the classical framework, the training data consists of deterministic vector-valued inputs and the corresponding (noisy) measurements whose joint distribution is assumed to be Gaussian. In many practical applications, however, the inputs are either noisy, i.e., each input is a vector-valued sample from an unknown probability distribution, or the probability distributions are the inputs. In this paper, we address Gaussian process regression with inputs given in form of probability distributions and propose a framework that is based on distances between such inputs. To this end, we review different admissible distance measures and provide a numerical example that demonstrates our framework.

Citations

• On Information and Sufficiency
• Divergence measures based on the Shannon entropy

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