{"paper":{"title":"Learning Sparse Additive Models with Interactions in High Dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","stat.ML"],"primary_cat":"cs.LG","authors_text":"Anastasios Kyrillidis, Andreas Krause, Bernd G\\\"artner, Hemant Tyagi","submitted_at":"2016-04-18T17:09:48Z","abstract_excerpt":"A function $f: \\mathbb{R}^d \\rightarrow \\mathbb{R}$ is referred to as a Sparse Additive Model (SPAM), if it is of the form $f(\\mathbf{x}) = \\sum_{l \\in \\mathcal{S}}\\phi_{l}(x_l)$, where $\\mathcal{S} \\subset [d]$, $|\\mathcal{S}| \\ll d$. Assuming $\\phi_l$'s and $\\mathcal{S}$ to be unknown, the problem of estimating $f$ from its samples has been studied extensively. In this work, we consider a generalized SPAM, allowing for second order interaction terms. For some $\\mathcal{S}_1 \\subset [d], \\mathcal{S}_2 \\subset {[d] \\choose 2}$, the function $f$ is assumed to be of the form: $$f(\\mathbf{x}) = \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.05307","kind":"arxiv","version":1},"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"}