{"id":153166,"date":"2007-11-01T00:00:00","date_gmt":"2007-11-01T00:00:00","guid":{"rendered":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/msr-research-item\/sparse-spectral-sampling-gaussian-processes\/"},"modified":"2018-10-16T21:02:15","modified_gmt":"2018-10-17T04:02:15","slug":"sparse-spectral-sampling-gaussian-processes","status":"publish","type":"msr-research-item","link":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/publication\/sparse-spectral-sampling-gaussian-processes\/","title":{"rendered":"Sparse Spectral Sampling Gaussian Processes"},"content":{"rendered":"<div class=\"asset-content\">\n<p>In this work we introduce Power Spectral Density Sampling (PSDS), a new method for building a reduced rank approximation to a stationary kernel matrix. We apply this method in the framework of Gaussian Processes (GP). The resulting model can be trained in an online fashion: As each training sample arrives, we can include it in the model using only O(r<sup>2<\/sup>) time and storage, where r is the selected number of spectral samples used in the approximation. For n training points, the overall cost is O(nr<sup>2<\/sup>) time and O(r<sup>2<\/sup>) storage. The resulting GP is properly defined and model hyper-parameters can be selected by evidence maximization. Though it is especially well-suited for low dimensional problems, it can reach and even outperform other (batch) state-of-the-art sparse GP methods on higher dimensional datasets if allowed to work in batch mode, learning the locations of the spectral samples. We check this possibility on some large datasets.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>In this work we introduce Power Spectral Density Sampling (PSDS), a new method for building a reduced rank approximation to a stationary kernel matrix. We apply this method in the framework of Gaussian Processes (GP). The resulting model can be trained in an online fashion: As each training sample arrives, we can include it in [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"MSR-TR-2007-152","msr_organization":"","msr_pages_string":"13","msr_page_range_start":"13","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"","msr_doi":"","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"","msr_other_contributors":"","msr_speaker":"","msr_award":"","msr_affiliation":"","msr_institution":"Microsoft 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