{"paper":{"title":"Max-Affine Regression: Provable, Tractable, and Near-Optimal Statistical Estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","cs.LG","math.IT","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Adityanand Guntuboyina, Ashwin Pananjady, Avishek Ghosh, Kannan Ramchandran","submitted_at":"2019-06-21T17:47:18Z","abstract_excerpt":"Max-affine regression refers to a model where the unknown regression function is modeled as a maximum of $k$ unknown affine functions for a fixed $k \\geq 1$. This generalizes linear regression and (real) phase retrieval, and is closely related to convex regression. Working within a non-asymptotic framework, we study this problem in the high-dimensional setting assuming that $k$ is a fixed constant, and focus on estimation of the unknown coefficients of the affine functions underlying the model. We analyze a natural alternating minimization (AM) algorithm for the non-convex least squares object"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.09255","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"}