{"paper":{"title":"Hoeffding's lemma for Markov Chains and its applications to statistical learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Bai Jiang, Jianqing Fan, Qiang Sun","submitted_at":"2018-02-01T09:36:24Z","abstract_excerpt":"We extend Hoeffding's lemma to general-state-space and not necessarily reversible Markov chains. Let $\\{X_i\\}_{i \\ge 1}$ be a stationary Markov chain with invariant measure $\\pi$ and absolute spectral gap $1-\\lambda$, where $\\lambda$ is defined as the operator norm of the transition kernel acting on mean zero and square-integrable functions with respect to $\\pi$. Then, for any bounded functions $f_i: x \\mapsto [a_i,b_i]$, the sum of $f_i(X_i)$ is sub-Gaussian with variance proxy $\\frac{1+\\lambda}{1-\\lambda} \\cdot \\sum_i \\frac{(b_i-a_i)^2}{4}$. This result differs from the classical Hoeffding's"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.00211","kind":"arxiv","version":4},"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"}