@inproceedings{80c4171a7f094d8c8ffce2af964f4d19,
title = "Learning a Gaussian Process Model on the Riemannian Manifold of Non-decreasing Distribution Functions",
abstract = "In this work, we consider the problem of learning regression models from a finite set of functional objects. In particular, we introduce a novel framework to learn a Gaussian process model on the space of Strictly Non-decreasing Distribution Functions (SNDF). Gaussian processes (GPs) are commonly known to provide powerful tools for non-parametric regression and uncertainty estimation on vector spaces. On top of that, we define a Riemannian structure of the SNDF space and we learn a GP model indexed by SNDF. Such formulation enables to define an appropriate covariance function, extending the Mat{\'e}rn family of covariance functions. We also show how the full Gaussian process methodology, namely covariance parameter estimation and prediction, can be put into action on the SNDF space. The proposed method is tested using multiple simulations and validated on real-world data.",
keywords = "Functional data, Gaussian process, Riemannian manifold",
author = "Chafik Samir and Loubes, \{Jean Michel\} and Yao, \{Anne Fran{\c c}oise\} and Fran{\c c}ois Bachoc",
note = "Publisher Copyright: {\textcopyright} 2019, Springer Nature Switzerland AG.; 16th Pacific Rim International Conference on Artificial Intelligence, PRICAI 2019 ; Conference date: 26-08-2019 Through 30-08-2019",
year = "2019",
month = jan,
day = "1",
doi = "10.1007/978-3-030-29911-8\_9",
language = "English",
isbn = "9783030299101",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "107--120",
editor = "Nayak, \{Abhaya C.\} and Alok Sharma",
booktitle = "PRICAI 2019",
}