Abstract
We propose non-stationary spectral kernels for Gaussian process regression. We propose to model the spectral density of a non-stationary kernel function as a mixture of input-dependent Gaussian process frequency density surfaces. We solve the generalised Fourier transform with such a model, and present a family of non-stationary and non-monotonic kernels that can learn input-dependent and potentially long-range, non-monotonic covariances between inputs. We derive efficient inference using model whitening and marginalized posterior, and show with case studies that these kernels are necessary when modelling even rather simple time series, image or geospatial data with non-stationary characteristics.
Original language | English |
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Title of host publication | Advances in Neural Information Processing Systems 30 |
Subtitle of host publication | Proceedings of NIPS2017 |
Publisher | Curran Associates, Inc. |
Pages | 4645-4654 |
Publication status | Published - 2017 |
MoE publication type | A4 Article in a conference publication |
Event | NIPS Symposium on Interpretable Machine Learning - Long Beach, Los Angeles, United States Duration: 4 Dec 2017 → 9 Dec 2017 Conference number: 31 |
Publication series
Name | Advances in Neural Information Processing Systems |
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Publisher | Curran Associates |
Volume | 30 |
ISSN (Print) | 1049-5258 |
Conference
Conference | NIPS Symposium on Interpretable Machine Learning |
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Country | United States |
City | Los Angeles |
Period | 04/12/2017 → 09/12/2017 |