Optimal Rate-Exponent Region for a Class of Hypothesis Testing Against Conditional Independence Problems

Zaidi, Abdellatif; Aguerri, Iñaki Estella

doi:10.1109/itw44776.2019.8989303

Cited by 11 publications

(7 citation statements)

References 22 publications

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“…is said achievable if for all blocklengths n there exist functions φ 1,n , φ 2,n , ψ 1,n and ψ 2,n as in (3), (5), (6), and (9) so that the following limits hold:…”

Section: Formal Problem Statementmentioning

confidence: 99%

“…In the general case, binning is necessary, and the optimal exponent is yet to be found. Notable exceptions where exponents achieved with binning are shown to be optimal can be found in [4], [6], [7], [17], [18], [24]- [26]. In [23] Zhao and Lai studied our setup in Figure 1 but where Detector 1 does not take any decision (i.e., Detector 1 does not produceĤ 1 ).…”

Section: Introductionmentioning

confidence: 99%

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Distributed Hypothesis Testing: Cooperation and Concurrent Detection

Escamilla

Wigger

Zaidi

2020

IEEE Trans. Inform. Theory

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A single-sensor two-detectors system is considered where the sensor communicates with both detectors and Detector 1 communicates with Detector 2, all over noise-free rate-limited links. The sensor and both detectors observe discrete memoryless source sequences whose joint probability mass function depends on a binary hypothesis. The goal at each detector is to guess the binary hypothesis in a way that, for increasing observation lengths, the probability of error under one of the hypotheses decays to zero with largest possible exponential decay, whereas the probability of error under the other hypothesis can decay to zero or to a small positive number arbitrarily slow. For the setting with positive communication rates from the sensor to the detectors and when both detectors are interested in maximizing the error exponent under the same hypothesis, we characterize the set of all possible exponents in a special case of testing against independence. In this case the cooperation link allows Detector 2 to increase its Type-II error exponent by an amount that is equal to the exponent attained at Detector 1. We also provide a general inner bound on the set of achievable error exponents that shows a tradeoff between the exponents at the two detectors in most cases. When the two detectors aim at maximizing the error exponent under different hypotheses and the distribution at the Sensor is different under the two hypotheses, then we show that such a tradeoff does not exist. We propose a general scheme that allows each detector to attain the same exponent as if it was the only detector in the system. For the setting with zerorate communication on both links, we exactly characterize the set of possible exponents and the gain brought up by cooperation, in function of the number of bits that are sent over the two links. Notice that, for this setting, tradeoffs between the exponents achieved at the two detectors arise only in few particular cases. In all other cases, each detector achieves the same performance as if it were the only detector in the system.

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“…is said achievable if for all blocklengths n there exist functions φ 1,n , φ 2,n , ψ 1,n and ψ 2,n as in (3), (5), (6), and (9) so that the following limits hold:…”

Section: Formal Problem Statementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Distributed Hypothesis Testing: Cooperation and Concurrent Detection

Escamilla

Wigger

Zaidi

2020

IEEE Trans. Inform. Theory

Self Cite

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“…In the general case, binning is necessary, which makes it hard to prove optimality of the achieved exponent. Notable exceptions are the results included in [4], [6], [18], [28], [29].…”

Section: Nmentioning

confidence: 99%

“…Definition 3 (Achievability with Fixed Communication Alphabets): For h1 ∈ {0, 1} and communication alphabet sizes W 1 , W 2 ≥ 0, an error-exponents pair (θ 1 , θ 2 ) is said achievable if for all blocklengths n there exist functions φ 1,n , φ 2,n , ψ 1,n and ψ 2,n as in (3), ( 5), (6), and (9) so that (19) and the limits in ( 15) and ( 16) hold.…”

Section: Formal Problem Statementmentioning

confidence: 99%

Distributed Hypothesis Testing: Cooperation and Concurrent Detection

Escamilla,

Wigger,

Zaidi

2019

Preprint

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A single-sensor two-detectors system is considered where the sensor communicates with both detectors and Detector 1 communicates with Detector 2, all over noise-free rate-limited links. The sensor and both detectors observe discrete memoryless source sequences whose joint probability mass function depends on a binary hypothesis. The goal at each detector is to guess the binary hypothesis in a way that, for increasing observation lengths, the probability of error under one of the hypotheses decays to zero with largest possible exponential decay, whereas the probability of error under the other hypothesis can decay to zero arbitrarily slow. For the setting with zero-rate communication on both links, we exactly characterize the set of possible exponents and the gain brought up by cooperation, in function of the number of bits that are sent over the two links. Notice that, for this setting, tradeoffs between the exponents achieved at the two detectors arise only in few particular cases. In all other cases, each detector achieves the same performance as if it were the only detector in the system. For the setting with positive communication rates from the sensor to the detectors, we characterize the set of all possible exponents in a special case of testing against independence. In this case the cooperation link allows Detector 2 to increase its Type-II error exponent by an amount that is equal to the exponent attained at Detector 1. We also provide a general inner bound on the set of achievable error exponents. For most cases it shows a tradeoff between the two exponents.

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“…In particular, [4] identified the largest type-II exponent that is achievable in a setup that they termed testing against conditional independence. An explicit expression for the vector Gaussian case was recently found in [5] (see Theorem 2 therein which actually provides the solution of a more general, distributed, setting). For all other cases a computable single-letter characterization of the largest achievable type-II error exponent remains open.…”

Section: Introductionmentioning

confidence: 99%

Some Results on the Vector Gaussian Hypothesis Testing Problem

Escamilla¹,

Zaidi²,

Wigger³

2020

Preprint

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This paper studies the problem of discriminating two multivariate Gaussian distributions in a distributed manner. Specifically, it characterizes in a special case the optimal type-II error exponent as a function of the available communication rate. As a side-result, the paper also presents the optimal type-II error exponent of a slight generalization of the hypothesis testing against conditional independence problem where the marginal distributions under the two hypotheses can be different.

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Optimal Rate-Exponent Region for a Class of Hypothesis Testing Against Conditional Independence Problems

Cited by 11 publications

References 22 publications

Distributed Hypothesis Testing: Cooperation and Concurrent Detection

Distributed Hypothesis Testing: Cooperation and Concurrent Detection

Distributed Hypothesis Testing: Cooperation and Concurrent Detection

Some Results on the Vector Gaussian Hypothesis Testing Problem

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