An approach to joint sequential detection and estimation with distributional uncertainties

Reinhard, Dominik; Fauß, Michael; Zoubir, Abdelhak M.

doi:10.1109/eusipco.2016.7760639

Cited by 9 publications

(5 citation statements)

References 13 publications

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“…In recent years, the trend of diversification in robust detection has continued, with new topics emerging, such as robust change detection [82]- [85], robust detection of adversarial attacks [86], [87], and robust Bayesian filtering [88]- [91]. Also, new combinations of existing problems have been investigated, such as robust distributed sequential detection [92], [93] and robust joint detection and estimation [94]. Some of these advanced topics will be picked up in later sections, after the necessary foundations have been introduced.…”

Section: B a Brief Historical Accountmentioning

confidence: 99%

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Minimax Robust Detection: Classic Results and Recent Advances

Fauß

Zoubir

Poor

2021

IEEE Trans. Signal Process.

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This paper provides an overview of results and concepts in minimax robust hypothesis testing for two and multiple hypotheses. It starts with an introduction to the subject, highlighting its connection to other areas of robust statistics and giving a brief recount of the most prominent developments. Subsequently, the minimax principle is introduced and its strengths and limitations are discussed. The first part of the paper focuses on the two-hypothesis case. After briefly reviewing the basics of statistical hypothesis testing, uncertainty sets are introduced as a generic way of modeling distributional uncertainty. The design of minimax detectors is then shown to reduce to the problem of determining a pair of least favorable distributions, and different criteria for their characterization are discussed. Explicit expressions are given for least favorable distributions under three types of uncertainty: ε-contamination, probability density bands, and f -divergence balls. Using examples, it is shown how the properties of these least favorable distributions translate to properties of the corresponding minimax detectors. The second part of the paper deals with the problem of robustly testing multiple hypotheses, starting with a discussion of why this is fundamentally different from the binary problem. Sequential detection is then introduced as a technique that enables the design of strictly minimax optimal tests in the multi-hypothesis case. Finally, the usefulness of robust detectors in practice is showcased using the example of ground penetrating radar. The paper concludes with an outlook on robust detection beyond the minimax principle and a brief summary of the presented material.

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Section: B a Brief Historical Accountmentioning

confidence: 99%

“…An interesting connection between Bayesian and minimax inference based on Wasserstein distance uncertainty sets has recently been shown in [224] and [225]. Some preliminary results on robust joint detection and estimation can be found in [94], [226].…”

Section: Beyond Minimax Robust Detectionmentioning

confidence: 99%

Minimax Robust Detection: Classic Results and Recent Advances

Fauß

Zoubir

Poor

2021

IEEE Trans. Signal Process.

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“…A drawback of these schemes is that, although the detection and estimation errors can be balanced by varying the weights of the cost function, there is no systematic way of choosing these coefficients such that a predefined performance in terms of error probabilities and estimation error, e.g., mean-squared-error (MSE), is achieved. In [14], we investigated the problem of sequential joint detection and estimation under model uncertainties. The problem of sequential joint signal detection and signal-to-noise ratio estimation was addressed in [15].…”

Section: Introductionmentioning

confidence: 99%

An Asymptotically Pointwise Optimal Procedure For Sequential Joint Detection And Estimation

Reinhard

Fauß

Zoubir

2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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We investigate the problem of jointly testing two hypotheses and estimating a random parameter based on sequentially observed data whose distribution belongs to the exponential family. The aim is to design a scheme which minimizes the expected number of used samples while limiting the detection and estimation errors to pre-set levels. This constrained problem is first converted to an unconstrained problem which is then reduced to an optimal stopping problem. To solve the optimal stopping problem, we propose an asymptotically pointwise optimal (APO) stopping rule, i.e., a stopping rule that is optimal when the tolerated detection and estimation errors tend to zero. The policy parameterizing coefficients are then chosen such that the constraints on the detection and estimation errors are fulfilled. The proposed theory is illustrated with a numerical example.

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“…In those works, the aim is to minimize the number of used samples under the constraint that a combined cost function, which incorporates detection and estimation errors, is kept below a certain level. We investigated the problem of joint detection and estimation under distributional uncertainties in [13]. In [14], we proposed a Bayesian framework in which the average number of samples is minimized under the constraints that the detection and estimation errors are kept below certain levels.…”

Section: Introductionmentioning

confidence: 99%

Distributed Joint Detection and Estimation: A Sequential Approach

Reinhard¹,

Fauß²,

Zoubir³

2020

Preprint

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We investigate the problem of jointly testing two hypotheses and estimating a random parameter based on data that is observed sequentially by sensors in a distributed network. In particular, we assume the data to be drawn from a Gaussian distribution, whose random mean is to be estimated. Forgoing the need for a fusion center, the processing is performed locally and the sensors interact with their neighbors following the consensus+innovations approach. We design the test at the individual sensors such that the performance measures, namely, error probabilities and mean-squared error, do not exceed predefined levels while the average sample number is minimized. After converting the constrained problem to an unconstrained problem and the subsequent reduction to an optimal stopping problem, we solve the latter utilizing dynamic programming. The solution is shown to be characterized by a set of non-linear Bellman equations, parametrized by cost coefficients, which are then determined by linear programming as to fulfill the performance specifications. A numerical example validates the proposed theory.

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An approach to joint sequential detection and estimation with distributional uncertainties

Cited by 9 publications

References 13 publications

Minimax Robust Detection: Classic Results and Recent Advances

Minimax Robust Detection: Classic Results and Recent Advances

An Asymptotically Pointwise Optimal Procedure For Sequential Joint Detection And Estimation

Distributed Joint Detection and Estimation: A Sequential Approach

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