bibkey: “gaostoev2020support” authors: “Zheng Gao; Stilian Stoev” year: 2020 title: “Fundamental limits of exact support recovery in high dimensions” doi: “10.3150/20-BEJ1197” url: “https://arxiv.org/abs/1811.05124v4” claim: “Exact support recovery in additive sparse-signal models is related to maxima and minima; the paper gives first-order recovery boundaries under broad dependence conditions and independent-coordinate likelihood-ranking Bayes results.” strata_touched: [] license: “citation-only” triage: “anchor”

Fundamental limits of exact support recovery in high dimensions

The inspected primary manuscript is arXiv:1811.05124v4, 15 April 2019, 42 pages. The published work appeared in Bernoulli in 2020 with the DOI above. The source models observations as a sparse additive signal plus noise; its sparsity parameter and amplitude parameter must not be identified with this repository’s parameters merely because their letters coincide.

Theorem 2.1, printed p. 7, gives an upper recovery boundary for asymptotically generalized Gaussian marginal tails. It allows arbitrary dependence in the upper bound. Theorem 4.1, p. 19, proves probability-one failure below the boundary for thresholding procedures when maxima and minima are uniformly relatively stable. Its class includes thresholds depending on the observations. This is a statement about exact set recovery, not a conclusion inferred from divergence of expected Hamming loss.

Theorem 3.1, pp. 13–14, characterizes uniform relative stability for Gaussian triangular arrays through uniform decreasing dependence. The discussion on p. 14 distinguishes this first-order property from a Gumbel distributional limit and displays the familiar Gaussian logarithmic correction. It explicitly explains why finer distributional convergence requires stronger information than relative stability. Therefore first-order thresholds alone do not supply a critical-window risk curve.

Section 5 supplies Bayes lower-bound arguments beyond thresholding. In particular, Proposition 5.1 and Theorem 5.1, p. 23, concern independent coordinates with log-concave densities. Lemma 5.3, pp. 23–24, discusses likelihood-ratio ranking for independent coordinates with a common signal density. The present parity analysis uses its own complete-data likelihood, fixed-cardinality posterior and explicit randomization at discrete ties. No independence or continuous-score assumption is transferred to a Markov trajectory from these source statements.

The extreme-value viewpoint and likelihood-ranking principles are literature-attested. The source does not directly instantiate the parity model’s observation-dependent compound-Poisson row laws, compensated background, common-law fixed-row comparison, or full-data minimax reduction. The second-order parity recovery curve in PARITY_HIDDEN_ARROW requires those additional arguments. This attribution is not a claim that a worldwide search has established originality of the general method or of every possible equivalent formulation.