Sequential joint detection and estimation

Yılmaz, Yasin; Moustakides, George V.; Wang, X

doi:10.4213/tvp4583

Cited by 4 publications

(11 citation statements)

References 15 publications

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“…Similarly, in the pure detection problem with an {G t }-adapted stopping time, we end up with a two-dimensional optimal stopping problem which is impossible to solve (analytically) since the thresholds for the running likelihood ratio depend on the sequence {H t }. Alternatively, in [9], [28]- [30], T is restricted to {F t }-adapted stopping times, which facilitates obtaining an optimal solution. In this paper, we are interested in {F t }-adapted stopping times as well.…”

Section: A Problem Formulationmentioning

confidence: 99%

“…2) The optimum scheme given by Theorem 1 is considerably more general and different than the one presented in [9]. Firstly, the estimator here is the optimum estimator under a weighted average of the probability distributions under {H i } since there are unknown parameter vectors under all hypotheses.…”

Section: Remarksmentioning

confidence: 99%

“…That is, the optimum estimator for the general problem introduced in (1)-(5) is coupled with the optimum detector. Whereas, no such coupling exists for the estimator in [9], which is the optimum estimator under H 1 as the unknown parameter appears only under H 1 (x = 0 under H 0 ). Secondly, the optimum detector in (19) is coupled with the estimator through the posterior estimation cost ∆ ji T under the combinations of the true and selected hypotheses.…”

Section: Remarksmentioning

confidence: 99%

“…Yilmaz solutions, or solve them together, as a composite hypothesis testing problem, using the generalized likelihood ratio test (GLRT) or its alternatives such as the Rao test, the Wald test, the Durbin test, and the Terrell test [6]. However, such approaches do not yield the overall optimum solution [8], [9]. In the former approach, for example, the likelihood ratio test is performed by averaging over the unknown parameters to solve the detection subproblem optimally; and then based on the detection decision, the Bayesian estimators are used to solve the estimation subproblem.…”

Section: Introductionmentioning

confidence: 99%

“…Although [13] discusses the case where observations are taken sequentially, it does not consider optimal stopping, limiting the scope of the work to the iterative computation of sufficient statistics. The only work that treats the joint detection and estimation problem in a "real" sequential manner is [9]. It provides the exact optimum triplet of stopping time, detector, and estimator for a linear scalar observation model with Gaussian noise, where there is an unknown parameter only under the alternative hypothesis.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Sequential Joint Detection and Estimation: Optimum Tests and Applications

Yılmaz

Wang

2016

IEEE Trans. Signal Process.

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We treat the statistical inference problems in which one needs to detect the correct signal model among multiple hypotheses and estimate a parameter simultaneously using as small number of samples as possible. Conventional methods treat the detection and estimation subproblems separately, ignoring the intrinsic coupling between them. However, a joint detection and estimation problem should be solved to maximize the overall performance. We address the sample size concern through a sequential and Bayesian setup. Specifically, we seek the optimum triplet of stopping time, detector, and estimator(s) that minimizes the number of samples subject to a constraint on the combined detection and estimation cost. A general framework for optimum sequential joint detection and estimation is developed. The resulting optimum detector and estimator(s) are strongly coupled with each other, proving that the separate treatment is strictly sub-optimum. The theoretical results derived for a quite general model are then applied to several problems with linear quadratic Gaussian (LQG) models, including dynamic spectrum access in cognitive radio, and state estimation in smart grid with topological uncertainty. Numerical results corroborate the superior overall detection and estimation performance of the proposed schemes over the conventional methods that handle the subproblems separately.

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Section: A Problem Formulationmentioning

confidence: 99%

Section: Remarksmentioning

confidence: 99%

Section: Remarksmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Sequential Joint Detection and Estimation: Optimum Tests and Applications

Yılmaz

Wang

2016

IEEE Trans. Signal Process.

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Multimodal factor analysis

Yılmaz

Hero

2015

2015 IEEE 25th International Workshop on Machine Learning for Signal Processing (MLSP)

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A multimodal system with Poisson, Gaussian, and multinomial observations is considered. A generative graphical model that combines multiple modalities through common factor loadings is proposed. In this model, latent factors are like summary objects that has latent factor scores in each modality, and the observed objects are represented in terms of such summary objects. This potentially brings about a significant dimensionality reduction. It also naturally enables a powerful means of clustering based on a diverse set of observations. An expectation-maximization (EM) algorithm to find the model parameters is provided. The algorithm is tested on a Twitter dataset which consists of the counts and geographical coordinates of hashtag occurrences, together with the bag of words for each hashtag. The resultant factors successfully localizes the hashtags in all dimensions: counts, coordinates, topics. The algorithm is also extended to accommodate von Mises-Fisher distribution, which is used to model the spherical coordinates.

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Asymptotically Optimal Decision Rules for Joint Detection and Source Coding

Merhav

2014

IEEE Trans. Inform. Theory

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The problem of joint detection and lossless source coding is considered. We derive asymptotically optimal decision rules for deciding whether or not a sequence of observations has emerged from a desired information source, and to compress it if has. In particular, our decision rules asymptotically minimize the cost of compression in the case that the data has been classified as 'desirable', subject to given constraints on the two kinds of the probability of error. In another version of this performance criterion, the constraint on the false alarm probability is replaced by the a constraint on the cost of compression in the false alarm event. We then analyze the asymptotic performance of these decision rules and demonstrate that they may exhibit certain phase transitions. We also derive universal decision rules for the case where the underlying sources (under either hypothesis or both) are unknown, and training sequences from each source may or may not be available. Finally, we discuss how our framework can be extended in several directions.

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Sequential joint detection and estimation

Cited by 4 publications

References 15 publications

Sequential Joint Detection and Estimation: Optimum Tests and Applications

Sequential Joint Detection and Estimation: Optimum Tests and Applications

Multimodal factor analysis

Asymptotically Optimal Decision Rules for Joint Detection and Source Coding

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