{"paper":{"title":"Fast tree inference with weighted fusion penalties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.CO","authors_text":"Guillem Rigaill, Julien Chiquet, Pierre Gutierrez","submitted_at":"2014-07-22T15:57:04Z","abstract_excerpt":"Given a data set with many features observed in a large number of conditions, it is desirable to fuse and aggregate conditions which are similar to ease the interpretation and extract the main characteristics of the data. This paper presents a multidimensional fusion penalty framework to address this question when the number of conditions is large. If the fusion penalty is encoded by an $\\ell_q$-norm, we prove for uniform weights that the path of solutions is a tree which is suitable for interpretability. For the $\\ell_1$ and $\\ell_\\infty$-norms, the path is piecewise linear and we derive a ho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5915","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}