# A Distance-based Framework for Gaussian Processes over Probability Distributions

arXiv: https://arxiv.org/abs/1809.09193 · HTML: https://mlsanity.com/paper/1809.09193/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Sep 2018.

## Built on by (most cited first, 1 of 1)

- [Gaussian Process regression over discrete probability measures: on the non-stationarity relation between Euclidean and Wasserstein Squared Exponential Kernels](https://mlsanity.com/paper/2212.01310/) (2022)

## Abstract (arXiv)

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.