{"paper":{"title":"Approximations of Lovasz extensions and their induced interaction index","license":"","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Jean-Luc Marichal, Pierre Mathonet","submitted_at":"2007-06-26T15:14:06Z","abstract_excerpt":"The Lovasz extension of a pseudo-Boolean function $f : \\{0,1\\}^n \\to R$ is defined on each simplex of the standard triangulation of $[0,1]^n$ as the unique affine function $\\hat f : [0,1]^n \\to R$ that interpolates $f$ at the $n+1$ vertices of the simplex. Its degree is that of the unique multilinear polynomial that expresses $f$. In this paper we investigate the least squares approximation problem of an arbitrary Lovasz extension $\\hat f$ by Lovasz extensions of (at most) a specified degree. We derive explicit expressions of these approximations. The corresponding approximation problem for ps"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.3856","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"}