Implicit Manifold Gaussian Process Regression
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Date
2024-07
Publication Type
Conference Paper
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yes
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Abstract
Gaussian process regression is widely used because of its ability to provide well-calibrated uncertainty estimates and handle small or sparse datasets. However, it struggles with high-dimensional data. One possible way to scale this technique to higher dimensions is to leverage the implicit low-dimensional manifold upon which the data actually lies, as postulated by the manifold hypothesis. Prior work ordinarily requires the manifold structure to be explicitly provided though, i.e. given by a mesh or be known to be one of the well-known manifolds like the sphere. In con trast, in this paper we propose a Gaussian process regression technique capable of inferring implicit structure directly from data (labeled and unlabeled) in a fully differentiable way. For the resulting model, we discuss its convergence to the Matérn Gaussian process on the assumed manifold. Our technique scales up to hundreds of thousands of data points, and improves the predictive performance and calibration of the standard Gaussian process regression in some high-dimensional settings.
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published
Book title
Advances in Neural Information Processing Systems 36
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Pages / Article No.
67701 - 67720
Publisher
Curran
Event
37th Annual Conference on Neural Information Processing Systems (NeurIPS 2023)
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Software
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Organisational unit
03908 - Krause, Andreas / Krause, Andreas
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Is new version of: https://openreview.net/forum?id=co4p15OMoc