{"paper":{"title":"Online covariance estimation for stochastic gradient descent under Markovian sampling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.OC","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Abhishek Roy, Krishnakumar Balasubramanian","submitted_at":"2023-08-03T00:21:30Z","abstract_excerpt":"We investigate the online overlapping batch-means covariance estimator for Stochastic Gradient Descent (SGD) under Markovian sampling. Convergence rates of order $O\\big(\\sqrt{d}\\,n^{-1/8}(\\log n)^{1/4}\\big)$ and $O\\big(\\sqrt{d}\\,n^{-1/8}\\big)$ are established under state-dependent and state-independent Markovian sampling, respectively, where $d$ is the dimensionality and $n$ denotes observations or SGD iterations. These rates match the best-known convergence rate for independent and identically distributed (i.i.d) data. Our analysis overcomes significant challenges that arise due to Markovian "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.01481","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2308.01481/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}