{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/learning-the-kernel-matrix-via-predictive-low","title":"Learning the kernel matrix via predictive low-rank approximations","arxiv_id":"1601.04366","date":"2016-01-17","proceeding":null,"authors":["Martin Stražar","Tomaž Curk"],"abstract":"Efficient and accurate low-rank approximations of multiple data sources are\nessential in the era of big data. The scaling of kernel-based learning\nalgorithms to large datasets is limited by the O(n^2) computation and storage\ncomplexity of the full kernel matrix, which is required by most of the recent\nkernel learning algorithms.\n  We present the Mklaren algorithm to approximate multiple kernel matrices\nlearn a regression model, which is entirely based on geometrical concepts. The\nalgorithm does not require access to full kernel matrices yet it accounts for\nthe correlations between all kernels. It uses Incomplete Cholesky\ndecomposition, where pivot selection is based on least-angle regression in the\ncombined, low-dimensional feature space. The algorithm has linear complexity in\nthe number of data points and kernels. When explicit feature space induced by\nthe kernel can be constructed, a mapping from the dual to the primal Ridge\nregression weights is used for model interpretation.\n  The Mklaren algorithm was tested on eight standard regression datasets. It\noutperforms contemporary kernel matrix approximation approaches when learning\nwith multiple kernels. It identifies relevant kernels, achieving highest\nexplained variance than other multiple kernel learning methods for the same\nnumber of iterations. Test accuracy, equivalent to the one using full kernel\nmatrices, was achieved with at significantly lower approximation ranks. A\ndifference in run times of two orders of magnitude was observed when either the\nnumber of samples or kernels exceeds 3000.","url_abs":"http://arxiv.org/abs/1601.04366v2","url_pdf":"http://arxiv.org/pdf/1601.04366v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"learning-the-kernel-matrix-via-predictive-low","repo_url":"https://github.com/mstrazar/mklaren","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}