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The choice of the kernel characterizes one\u2019s assumption on how the unknown function autocovaries. It is a core aspect of a GP design, since the posterior distribution can significantly vary for different kernels. The spectral mixture (SM) kernel is derived by modelling a spectral density - the Fourier transform of a kernel - with a linear mixture of Gaussian components. As such, the SM kernel cannot model dependencies between components. In this paper we use cross convolution to model dependencies between components and derive a new kernel called Generalized Convolution Spectral Mixture (GCSM). Experimental analysis of GCSM on synthetic and real-life datasets indicates the benefit of modeling dependencies between components for reducing uncertainty and for improving performance in extrapolation tasks.<\/jats:p>","DOI":"10.1007\/978-3-030-46147-8_34","type":"book-chapter","created":{"date-parts":[[2020,5,1]],"date-time":"2020-05-01T02:03:39Z","timestamp":1588298619000},"page":"565-581","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Incorporating Dependencies in Spectral Kernels for Gaussian Processes"],"prefix":"10.1007","author":[{"given":"Kai","family":"Chen","sequence":"first","affiliation":[]},{"given":"Twan","family":"van Laarhoven","sequence":"additional","affiliation":[]},{"given":"Jinsong","family":"Chen","sequence":"additional","affiliation":[]},{"given":"Elena","family":"Marchiori","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,4,30]]},"reference":[{"key":"34_CR1","volume-title":"Theory and Application of Digital Signal Processing","author":"B Gold","year":"1975","unstructured":"Gold, B.: Theory and Application of Digital Signal Processing. 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