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Title: | A New Reliable & Parsimonious Learning Strategy Comprising Two Layers of Gaussian Processes, to Address Inhomogeneous Empirical Correlation Structures |
Authors: | Roy, G Chakrabarty, D |
Keywords: | nested Gaussian processes;covariance kernel parametrisation;non-parametric non-stationary kernel;Markov chain Monte Carlo;probabilistic machine learning |
Issue Date: | 18-Apr-2024 |
Publisher: | Cornell University |
Citation: | Roy, G. and Chakrabarty, D. (2024) 'A New Reliable & Parsimonious Learning Strategy Comprising Two Layers of Gaussian Processes, to Address Inhomogeneous Empirical Correlation Structures', arXiv:2404.12478v1 [stat.ML], pp. 1 - 28. doi: 10.48550/arXiv.2404.12478. |
Abstract: | We present a new strategy for learning the functional relation between a pair of variables, while addressing inhomogeneities in the correlation structure of the available data, by modelling the sought function as a sample function of a non-stationary Gaussian Process (GP), that nests within itself multiple other GPs, each of which we prove can be stationary, thereby establishing sufficiency of two GP layers. In fact, a non-stationary kernel is envisaged, with each hyperparameter set as dependent on the sample function drawn from the outer non-stationary GP, such that a new sample function is drawn at every pair of input values at which the kernel is computed. However, such a model cannot be implemented, and we substitute this by recalling that the average effect of drawing different sample functions from a given GP is equivalent to that of drawing a sample function from each of a set of GPs that are rendered different, as updated during the equilibrium stage of the undertaken inference (via MCMC). The kernel is fully non-parametric, and it suffices to learn one hyperparameter per layer of GP, for each dimension of the input variable. We illustrate this new learning strategy on a real dataset. |
Description: | MSC classes: Probability theory and stochastic processes : 60-XX, Stochastic Processes : 60Gxx, Gaussian Processes : 60G15, Generalised stochastic processes : 60G20 This is a preprint version of the article. It has not been certified by peer review. |
URI: | https://bura.brunel.ac.uk/handle/2438/29823 |
DOI: | https://doi.org/10.48550/arXiv.2404.12478 |
Other Identifiers: | ORCiD: Dalia Chakrabarty https://orcid.org/0000-0003-1246-4235 |
Appears in Collections: | Dept of Mathematics Research Papers |
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File | Description | Size | Format | |
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Preprint.pdf | Copyright © 2024 The Author(s). This work is licensed under a Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/). | 3.53 MB | Adobe PDF | View/Open |
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