bibkey: “wolfer2020identity” authors: “Geoffrey Wolfer; Aryeh Kontorovich” year: 2020 title: “Minimax Testing of Identity to a Reference Ergodic Markov Chain” doi: null url: “https://proceedings.mlr.press/v108/wolfer20a.html” claim: “First visits to each state provide independent samples from its transition row; the identity tester separately controls failure to obtain the required number of visits.” strata_touched: [] license: “citation-only” triage: “anchor”

Minimax Testing of Identity to a Reference Ergodic Markov Chain

Proceedings of Machine Learning Research 108, 191–201 (AISTATS 2020). The publisher page confirms the title, authors, volume and pages. The inspected full author version is arXiv:1902.00080v3, corrected 24 September 2019, available as primary HTML.

Section 6.1.1, within the proof of Theorem 4.1, defines the mapping from an infinite trajectory to the successors of its first prescribed visits to a state. The authors credit Daskalakis et al. (2018) for this mapping. The resulting samples are independent with the specified transition-row law. Irreducibility makes the infinite-trajectory mapping almost surely well-defined. A finite trajectory can fail to contain enough visits. Section 6.1.2 compares the ideal infinite-sample event with the coverage failure event; it does not infer independence after conditioning on coverage.

First-visit sampling and its finite-horizon coupling are literature-attested. In the parity construction, the extra identities P^2 = Pi and zero outgoing parity mean under the actual reversed kernel supply a model-specific reduction to biased versus fair independent sign rows. The sharp sparse direction threshold and the quantitative comparison of full path and independent-pair experiments require separate repo-derived arguments. The cited identity-testing sample-complexity bound is not a direction-recovery theorem.