A competitive Neyman-Pearson approach to universal hypothesis testing with applications

Levitan, E.; Merhav, Neri

doi:10.1109/tit.2002.800478

Cited by 35 publications

(31 citation statements)

References 22 publications

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“…Indeed, the hypothesis test used is a simple Neyman-Pearson test for p, q minimizing the RHS of (1). This result was previously known in the non-adaptive case, where it is sometimes referred to as composite hypothesis testing [37].…”

Section: Asymmetric Hypothesis Testingmentioning

confidence: 56%

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Adversarial Hypothesis Testing and a Quantum Stein’s Lemma for Restricted Measurements

Brandão

Harrow

Lee

et al. 2020

IEEE Trans. Inform. Theory

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Recall the classical hypothesis testing setting with two sets of probability distributions P and Q. One receives either n i.i.d. samples from a distribution p ∈ P or from a distribution q ∈ Q and wants to decide from which set the points were sampled. It is known that the optimal exponential rate at which errors decrease can be achieved by a simple maximum-likelihood ratio test which does not depend on p or q, but only on the sets P and Q.We consider an adaptive generalization of this model where the choice of p ∈ P and q ∈ Q can change in each sample in some way that depends arbitrarily on the previous samples. In other words, in the k th round, an adversary, having observed all the previous samples in rounds 1, . . . , k − 1, chooses p k ∈ P and q k ∈ Q, with the goal of confusing the hypothesis test. We prove that even in this case, the optimal exponential error rate can be achieved by a simple maximum-likelihood test that depends only on P and Q.We then show that the adversarial model has applications in hypothesis testing for quantum states using restricted measurements. For example, it can be used to study the problem of distinguishing entangled states from the set of all separable states using only measurements that can be implemented with local operations and classical communication (LOCC). The basic idea is that in our setup, the deleterious effects of entanglement can be simulated by an adaptive classical adversary.We prove a quantum Stein's Lemma in this setting: In many circumstances, the optimal hypothesis testing rate is equal to an appropriate notion of quantum relative entropy between two states. In particular, our arguments yield an alternate proof of Li and Winter's recent strengthening of strong subadditivity for von Neumann entropy.

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Section: Asymmetric Hypothesis Testingmentioning

confidence: 56%

“…We can, in fact, relate D ALL , D, E using D ALL (· S) (57) ≥ E(·, S) (38) = D(· S) (37) ≥ D ALL (· S) (39)…”

Section: E(ρ σ) = D(ρ σ)mentioning

confidence: 99%

Adversarial Hypothesis Testing and a Quantum Stein’s Lemma for Restricted Measurements

Brandão

Harrow

Lee

et al. 2020

IEEE Trans. Inform. Theory

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“…A generalization of the classical hypothesis testing problem is studied in [11], where a Bayesian decision maker is designed to enhance its information about the correct hypothesis. Information theory has also been applied to study nonparametric hypothesis testing problems with the primary focus being on the Neyman-Pearson formulation [6], [7]. An informationtheoretic approach to the problem of a nonparametric hypothesis test with a Bayesian formulation is presented in [12].…”

Section: B Related Workmentioning

confidence: 99%

“…and data compression needs to be carried out in a decentralized manner. Additionally, information theory has also been applied to solve nonparametric hypothesis testing problems under the Neyman-Pearson framework [6], [7].…”

mentioning

confidence: 99%

Nonparametric Composite Hypothesis Testing in an Asymptotic Regime

Wang

Bucci

et al. 2018

IEEE J. Sel. Top. Signal Process.

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We investigate the nonparametric, composite hypothesis testing problem for arbitrary unknown distributions in the asymptotic regime where both the sample size and the number of hypotheses grow exponentially large. Such asymptotic analysis is important in many practical problems, where the number of variations that can exist within a family of distributions can be countably infinite. We introduce the notion of discrimination capacity, which captures the largest exponential growth rate of the number of hypotheses relative to the sample size so that there exists a test with asymptotically vanishing probability of error. Our approach is based on various distributional distance metrics in order to incorporate the generative model of the data. We provide analyses of the error exponent using the maximum mean discrepancy (MMD) and Kolmogorov-Smirnov (KS) distance and characterize the corresponding discrimination rates, i.e., lower bounds on the discrimination capacity, for these tests. Finally, an upper bound on the discrimination capacity based on Fano's inequality is developed. Numerical results are presented to validate the theoretical results.

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“…An optimal fixed sample size universal test for finite alphabets is derived in [14]. Error exponents for these tests are studied in [23]. In [33] mismatched divergence is used to study this problem.…”

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confidence: 99%

Nonparametric distributed sequential detection via universal source coding

Sreedharan

Sharma

2013

2013 Information Theory and Applications Workshop (ITA)

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Abstract-We consider nonparametric or universal sequential hypothesis testing when the distribution under the null hypothesis is fully known but the alternate hypothesis corresponds to some other unknown distribution. These algorithms are primarily motivated from spectrum sensing in Cognitive Radios and intruder detection in wireless sensor networks. We use easily implementable universal lossless source codes to propose simple algorithms for such a setup. The algorithms are first proposed for discrete alphabet. Their performance and asymptotic properties are studied theoretically. Later these are extended to continuous alphabets. Their performance with two well known universal source codes, Lempel-Ziv code and KT-estimator with Arithmetic Encoder are compared. These algorithms are also compared with the tests using various other nonparametric estimators. Finally a decentralized version utilizing spatial diversity is also proposed and analysed.

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A competitive Neyman-Pearson approach to universal hypothesis testing with applications

Cited by 35 publications

References 22 publications

Adversarial Hypothesis Testing and a Quantum Stein’s Lemma for Restricted Measurements

Adversarial Hypothesis Testing and a Quantum Stein’s Lemma for Restricted Measurements

Nonparametric Composite Hypothesis Testing in an Asymptotic Regime

Nonparametric distributed sequential detection via universal source coding

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