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We first describe a generic approach that covers any penalty matrix \u003ci\u003eD\u003c/i\u003e and any (full column rank) matrix \u003ci\u003eX\u003c/i\u003e of predictor variables. We then describe fast implementations for the special cases of trend filtering problems, fused lasso problems, and sparse fused lasso problems, both with \u003ci\u003eX\u003c/i\u003e = \u003ci\u003eI\u003c/i\u003e and a general matrix \u003ci\u003eX\u003c/i\u003e. These specialized implementations offer a considerable improvement over the generic implementation, both in terms of numerical stability and efficiency of the solution path computation. These algorithms are all available for use in the genlasso R package, which can be found in the CRAN repository.","descriptionType":"Abstract"}],"geoLocations":[],"fundingReferences":[],"xml":"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","url":"https://tandf.figshare.com/articles/dataset/Efficient_Implementations_of_the_Generalized_Lasso_Dual_Path_Algorithm/1327717","contentUrl":null,"metadataVersion":2,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"mds","isActive":true,"state":"findable","reason":null,"viewCount":0,"viewsOverTime":[],"downloadCount":0,"downloadsOverTime":[],"referenceCount":0,"citationCount":0,"citationsOverTime":[],"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2015-03-06T20:22:47.000Z","registered":"2015-03-06T20:22:48.000Z","published":"2015","updated":"2020-09-04T18:42:24.000Z"},"relationships":{"client":{"data":{"id":"figshare.ars","type":"clients"}},"provider":{"data":{"id":"otjm","type":"providers"}},"media":{"data":{"id":"10.6084/m9.figshare.1327717","type":"media"}},"references":{"data":[]},"citations":{"data":[]},"parts":{"data":[]},"partOf":{"data":[]},"versions":{"data":[]},"versionOf":{"data":[]}}}}