Two-Sample Testing can be as Hard as Structure Learning in Ising Models: Minimax Lower Bounds

Gangrade, Aditya; Nazer, Bobak; Saligrama, Venkatesh

doi:10.1109/icassp.2018.8462370

“…An extension of this question is to test whether the community structure of the full network is the same between the two observed SBMs rather than exclusively focusing on node i * . In this line of work, [16] has addressed the two community case.…”

Section: Auxiliary Definitions and Resultsmentioning

confidence: 99%

“…= P H1 {ϕ An = 0} (16) where c n = 2(1 + δ) log log(n). Since β satisfies condition (10) for A n for all sufficiently large n, it immediately follows that |E H1 (T n ( A n ))| diverges at a polynomial rate.…”

Section: A Sufficient Condition For Optimalitymentioning

confidence: 99%

Statistical limits of sparse mixture detection

Kotekal

¹

2022

Electron. J. Statist.

0

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We consider the problem of detecting a general sparse mixture and obtain an explicit characterization of the phase transition under some conditions, generalizing the univariate results of Cai and Wu. Additionally, we provide a sufficient condition for the adaptive optimality of a Higher Criticism type testing statistic formulated by Gao and Ma. In the course of establishing these results, we offer a unified perspective through the large deviations theory. The phase transition and adaptive optimality we establish are direct consequences of the large deviation principle of the normalized log-likelihood ratios between the null and the signal distributions.

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“…Solving the optimization problem yields β * (r) = β * IDJ (r). Turning our attention to the Higher Criticism statistic, observe that the general HC-type statistic (19) of Gao and Ma reduces to the original Higher Criticism statistic introduced by Donoho and Jin [13] HC…”

Section: Univariatementioning

confidence: 99%

“…An extension of this question is to test whether the community structure of the full network is the same between the two observed SBMs rather than exclusively focusing on node i * . In this line of work, [19] has addressed the two community case.…”

Section: Stochastic Block Modelmentioning

confidence: 99%

Statistical Limits of Sparse Mixture Detection

Kotekal¹

2021

Preprint

0

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We consider the problem of detecting a general sparse mixture and obtain an explicit characterization of the phase transition under some conditions, generalizing the univariate results of Cai and Wu. Additionally, we provide a sufficient condition for the adaptive optimality of a Higher Criticism type testing statistic formulated by Gao and Ma. In the course of establishing these results, we offer a unified perspective through the large deviations theory. The phase transition and adaptive optimality we establish are direct consequences of the large deviation principle of the normalized log-likelihood ratios between the null and the signal distributions.

show abstract