{"ID":2839704,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.15816","arxiv_id":"2511.15816","title":"Beyond Tsybakov: Model Margin Noise and $\\mathcal{H}$-Consistency Bounds","abstract":"We introduce a new low-noise condition for classification, the Model Margin Noise (MM noise) assumption, and derive enhanced $\\mathcal{H}$-consistency bounds under this condition. MM noise is weaker than Tsybakov noise condition: it is implied by Tsybakov noise condition but can hold even when Tsybakov fails, because it depends on the discrepancy between a given hypothesis and the Bayes-classifier rather than on the intrinsic distributional minimal margin (see Figure 1 for an illustration of an explicit example). This hypothesis-dependent assumption yields enhanced $\\mathcal{H}$-consistency bounds for both binary and multi-class classification. Our results extend the enhanced $\\mathcal{H}$-consistency bounds of Mao, Mohri, and Zhong (2025a) with the same favorable exponents but under a weaker assumption than the Tsybakov noise condition; they interpolate smoothly between linear and square-root regimes for intermediate noise levels. We also instantiate these bounds for common surrogate loss families and provide illustrative tables.","short_abstract":"We introduce a new low-noise condition for classification, the Model Margin Noise (MM noise) assumption, and derive enhanced $\\mathcal{H}$-consistency bounds under this condition. MM noise is weaker than Tsybakov noise condition: it is implied by Tsybakov noise condition but can hold even when Tsybakov fails, because i...","url_abs":"https://arxiv.org/abs/2511.15816","url_pdf":"https://arxiv.org/pdf/2511.15816v1","authors":"[\"Mehryar Mohri\",\"Yutao Zhong\"]","published":"2025-11-19T19:13:39Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"stat.ML\"]","methods":"[]","has_code":false}