Second-order asymptotically optimal statistical classification

Zhou, Lin; Tan, Vincent Y. F.; Motani, Mehul

doi:10.1093/imaiai/iay023

Cited by 8 publications

(15 citation statements)

References 24 publications

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“…First, a resolution of Conjecture 5 would be desirable as it would allow us to parallel the main results in [2] for arbitrary and finite α ∈ R + . Second, we can consider deriving second-order asymptotic results in the spirit of Zhou, Tan, and Motani [16]. This would shed further insights into the finite-length behavior of the proposed tests.…”

Section: Discussionmentioning

confidence: 99%

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Distributed Detection with Empirically Observed Statistics

Zhou

Tan

2019

2019 IEEE Information Theory Workshop (ITW)

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Consider a distributed detection problem in which the underlying distributions of the observations are unknown; instead of these distributions, noisy versions of empirically observed statistics are available to the fusion center. These empirically observed statistics, together with source (test) sequences, are transmitted through different channels to the fusion center. The fusion center decides which distribution the source sequence is sampled from based on these data. For the binary case, we derive the optimal type-II error exponent given that the type-I error decays exponentially fast. The type-II error exponent is maximized over the proportions of channels for both source and training sequences. We conclude that as the ratio of the lengths of training to test sequences α tends to infinity, using only one channel is optimal. By calculating the derived exponents numerically, we conjecture that the same is true when α is finite under certain conditions. We relate our results to the classical distributed detection problem studied by Tsitsiklis, in which the underlying distributions are known. Finally, our results are extended to the case of m-ary distributed detection with a rejection option.

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Section: Discussionmentioning

confidence: 99%

“…To state our results succinctly, we begin by stating some somewhat non-standard definitions. Given any pair of distributions (Q,Q) ∈ P([L]) 2 and any α ∈ R + , the generalized Jensen-Shannon divergence [16,Eqn. (3)] is defined as…”

Section: B Definitionsmentioning

confidence: 99%

Distributed Detection with Empirically Observed Statistics

Zhou

Tan

2019

2019 IEEE Information Theory Workshop (ITW)

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“…Hypothesis testing includes approaches such as the Bayesian test [1,2] and the Neyman-Pearson test [3][4][5]. In this paper, we take the latter approach to formulate the best asymptotic error exponent (the exponential part of an error probability).…”

Section: Introduction 1backgroundmentioning

confidence: 99%

Analysis on Optimal Error Exponents of Binary Classification for Source with Multiple Subclasses

Kuramata

Yagi

2022

Entropy

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We consider a binary classification problem for a test sequence to determine from which source the sequence is generated. The system classifies the test sequence based on empirically observed (training) sequences obtained from unknown sources P1 and P2. We analyze the asymptotic fundamental limits of statistical classification for sources with multiple subclasses. We investigate the first- and second-order maximum error exponents under the constraint that the type-I error probability for all pairs of distributions decays exponentially fast and the type-II error probability is upper bounded by a small constant. In this paper, we first give a classifier which achieves the asymptotically maximum error exponent in the class of deterministic classifiers for sources with multiple subclasses, and then provide a characterization of the first-order error exponent. We next provide a characterization of the second-order error exponent in the case where only P2 has multiple subclasses but P1 does not. We generalize our results to classification in the case that P1 and P2 are a stationary and memoryless source and a mixed memoryless source with general mixture, respectively.

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“…In this paper, we will propose a new Chernoff type bound such that its ratio with Bayes error probability is upper and lower bounded by constants. Although a comparable "second-order" asymptotics for asymmetric hypothesis testing was investigated in [Li+14;ZTM18], there is no direct application to the symmetric case. Indeed, a non-asymptotic bound in the symmetric case requires extra effort.…”

Section: Introductionmentioning

confidence: 99%

Rate optimal Chernoff bound and application to community detection in the stochastic block models

Li¹

2020

Electron. J. Statist.

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Chernoff coefficient is an upper bound of Bayes error probability in classification problem. In this paper, we will develop sharp Chernoff type bound on Bayes error probability. The new bound is not only an upper bound but also a lower bound of Bayes error probability up to a constant in a non-asymptotic setting. Moreover, we will apply this result to community detection in stochastic block model. As a clustering problem, the optimal error rate of community detection can be characterized by our Chernoff type bound. This can be formalized by deriving a minimax error rate over certain class of parameter space, then achieving such error rate by a feasible algorithm employ multiple steps of EM type updates.

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Second-order asymptotically optimal statistical classification

Cited by 8 publications

References 24 publications

Distributed Detection with Empirically Observed Statistics

Distributed Detection with Empirically Observed Statistics

Analysis on Optimal Error Exponents of Binary Classification for Source with Multiple Subclasses

Rate optimal Chernoff bound and application to community detection in the stochastic block models

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