{"paper":{"title":"Optimal linear estimation under unknown nonlinear transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"stat.ML","authors_text":"Constantine Caramanis, Han Liu, Xinyang Yi, Zhaoran Wang","submitted_at":"2015-05-13T06:50:37Z","abstract_excerpt":"Linear regression studies the problem of estimating a model parameter $\\beta^* \\in \\mathbb{R}^p$, from $n$ observations $\\{(y_i,\\mathbf{x}_i)\\}_{i=1}^n$ from linear model $y_i = \\langle \\mathbf{x}_i,\\beta^* \\rangle + \\epsilon_i$. We consider a significant generalization in which the relationship between $\\langle \\mathbf{x}_i,\\beta^* \\rangle$ and $y_i$ is noisy, quantized to a single bit, potentially nonlinear, noninvertible, as well as unknown. This model is known as the single-index model in statistics, and, among other things, it represents a significant generalization of one-bit compressed "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03257","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"}