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Multi-Hop Network With Multiple Decision Centers Under Expected-Rate Constraints

IEEE TRANSACTIONS ON INFORMATION THEORY 2023年第7期69卷 4255-4283页

作者： Hamad, Mustapha Wigger, Michele Sarkiss, Mireille Inst Polytech Paris LTCI Telecom Paris F-91120 Palaiseau France Paris Res Ctr Huawei Math & Algorithm Sci Lab F-92100 Boulogne Billancourt France Inst Polytech Paris SAMOVAR Telecom Sud Paris F-91120 Palaiseau France

We consider a multi-hop distributed hypothesis testing problem with multiple decision centers (DCs) for testing against independence and where the observations obey some Markov chain. For this system, we characterize the fundamental type-II error exponents region, i.e., the type-II error exponents that the various DCs can achieve simultaneously, under expected rate constraints. Our results show that this fundamental exponents region is boosted compared to the region under maximum rate constraints, and that it depends on the permissible type-I error probabilities. When all DCs have equal permissible type-I error probabilities, the exponents region is rectangular and all DCs can simultaneously achieve their optimal type-II error exponents. When the DCs have different permissible type-I error probabilities, a tradeoff between the type-II error exponents at the different DCs arises. New achievability and converse proofs are presented. For the achievability, a new multiplexing and rate-sharing strategy is proposed. The converse proof is based on applying different change of measure arguments in parallel and on proving asymptotic Markov chains. For the special cases K is an element of {2, 3}, and for arbitrary K >= 2 when all permissible type-I error probabilities at the various DCs are equal, we provide simplified expressions for the exponents region;a similar simplification is conjectured for the general case.

关键词： Multi-hop distributed hypothesis testing error exponents expected-rate constraints variable-length coding

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Evolution of distributed detection performance over balanced binary relay tree networks with bit errors

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NONLINEAR DYNAMICS 2022年第4期107卷 3903-3917页

作者： Tian, Yu-Ping Zhu, Wenbo Hangzhou Dianzi Univ Sch Automat Hangzhou 310018 Peoples R China Southeast Univ Sch Automat Nanjing 210096 Peoples R China

Target detection based on wireless sensor networks can be considered as a distributed binary hypothesis testing problem. In this paper, the evolution of detection error probability with the increase in the network scale is studied for the balanced binary relay tree network with channel noise. Firstly, the iterative expressions of false-alarm probability and missed-detection probability depending on the number of tree network layers are given. Then, the iterative process of two types of error probabilities in the network space is described as a discrete nonlinear switched dynamic system, and the dynamic properties of two types of error probabilities are analyzed in a plane rectangular coordinate system. A globally attractive invariant set of the state of the dynamic system, which is not related to the channel noise, is derived. The switching mode of the system and the total error probability in the invariant set are further analyzed, and a necessary and sufficient convergence condition of the total error probability is provided. Based on this condition, the following detection properties of the network are revealed: (1) as long as the channel bit error probability is not zero, the total error probability does not tend to zero as the network size grows to infinity;(2) when the channel bit error probability is greater than 2-root 3/2, the total error probability will continue to increase with the increase in the network size.

关键词： distributed detection distributed hypothesis testing Nonlinear switched system Invariant set Channel noise

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On hypothesis testing Against Conditional Independence With Multiple Decision Centers

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IEEE TRANSACTIONS ON COMMUNICATIONS 2018年第6期66卷 2409-2420页

作者： Salehkalaibar, Sadaf Wigger, Michele Timo, Roy Univ Tehran Dept Elect & Comp Engn Coll Engn Tehran *** Iran Univ Paris Saclay LTCI Telecom ParisTech F-75013 Paris France Ericsson Res S-16483 Stockholm Sweden

A distributed binary hypothesis testing problem is studied with one observer and two decision centers. Achievable type-II error exponents are derived for testing against conditional independence when the observer communicates with the two decision centers over one common and two individual noise-free bit pipes and when it communicates with them over a noisy broadcast channel. The results are based on a coding and testing scheme that splits the observations into subblocks, so that transmitter and receivers can independently apply to each subblock either Gray-Wyner coordination coding with side-information or hybrid joint source-channel coding with side-information, followed by a Neyman-Pearson test over the subblocks at the receivers. This approach allows to avoid introducing further error exponents that one would expect from the receivers' decoding operations related to binning or the noisy transmission channel. The derived exponents are shown to be optimal in some special cases when communication is over noise-free links. The results reveal a tradeoff between the type-II error exponents at the two decision centers.

关键词： distributed hypothesis testing broadcast channel testing against conditional independence Gray-Wyner network

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distributed Learning Over Networks: Effect of Using Historical Observations

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2020年第12期65卷 5503-5509页

作者： Shi, Chong-Xiao Yang, Guang-Hong Northeastern Univ Coll Informat Sci & Engn Shenyang 110819 Liaoning Peoples R China Northeastern Univ Minist Educ Key Lab Integrated Automat Proc Ind Shenyang 110819 Peoples R China

This article investigates the problem of distributed hypothesis testing over networks. By introducing double and triple cumulations of historical observations, two novel distributed learning algorithms are developed to solve the considered problem. Within this framework, we study the convergence rates of the proposed algorithms. More specifically: 1) It is proven that the algorithm with double cumulation of historical observations has a faster convergence rate than those of the existing algorithms. 2) Furthermore, it is proven that the algorithm with triple cumulation of historical observations can be further accelerated. Especially, based on the theoretical results, this article shows that a tradeoff among convergence rate, transient performance, and memory burden exists in the proposed algorithms. Finally, simulation examples verify the theoretical results.

关键词： Convergence testing Bayes methods Silicon Acceleration Transient analysis Knowledge engineering Convergence rate distributed hypothesis testing historical observations non-Bayesian learning

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distributed Inference With Sparse and Quantized Communication

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2021年 69卷 3906-3921页

作者： Mitra, Aritra Richards, John Bagchi, Saurabh Sundaram, Shreyas Purdue Univ Sch Elect & Comp Engn W Lafayette IN 47907 USA Sandia Natl Labs Albuquerque NM 87123 USA

We consider the problem of distributed inference where agents in a network observe a stream of private signals generated by an unknown state, and aim to uniquely identify this state from a finite set of hypotheses. We focus on scenarios where communication between agents is costly, and takes place over channels with finite bandwidth. To reduce the frequency of communication, we develop a novel event-triggered distributed learning rule that is based on the principle of diffusing low beliefs on each false hypothesis. Building on this principle, we design a trigger condition under which an agent broadcasts only those components of its belief vector that have adequate innovation, to only those neighbors that require such information. We prove that our rule guarantees convergence to the true state exponentially fast almost surely despite sparse communication, and that it has the potential to significantly reduce information flow from uninformative agents to informative agents. Next, to deal with finite-precision communication channels, we propose a distributed learning rule that leverages the idea of adaptive quantization. We show that by sequentially refining the range of the quantizers, every agent can learn the truth exponentially fast almost surely, while using just 1 bit to encode its belief on each hypothesis. For both our proposed algorithms, we rigorously characterize the trade-offs between communication-efficiency and the learning rate.

关键词： Laboratories Distance learning Convergence Computer aided instruction Quantization (signal) testing Technological innovation distributed inference bayesian learning distributed hypothesis testing communication-efficiency

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Bayesian Learning Without Recall

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IEEE TRANSACTIONS ON SIGNAL AND INFORMATION PROCESSING OVER NETWORKS 2017年第3期3卷 592-606页

作者： Rahimian, M. Amin Jadbabaie, Ali Univ Penn Dept Elect & Syst Engn Philadelphia PA 19104 USA MIT Inst Data Syst & Soc Cambridge MA 02139 USA

We analyze a model of learning and belief formation in networks in which agents follow Bayes rule yet they do not recall their history of past observations and cannot reason about how other agents' beliefs are formed. They do so by making rational inferences about their observations which include a sequence of independent and identically distributed private signals as well as the actions of their neighboring agents at each time. Successive applications of Bayes rule to the entire history of past observations lead to forebodingly complex inferences: due to lack of knowledge about the global network structure, and unavailability of private observations, as well as third party interactions preceding every decision. Such difficulties make Bayesian updating of beliefs an implausible mechanism for social learning. To address these complexities, we consider a Bayesian without Recall model of inference. On the one hand, this model provides a tractable framework for analyzing the behavior of rational agents in social networks. On the other hand, this model also provides a behavioral foundation for the variety of non-Bayesian update rules in the literature. We present the implications of various choices for the structure of the action space and utility functions for such agents and investigate the properties of learning, convergence, and consensus in special cases.

关键词： Adaptation and learning over graphs Bayesian learning distributed detection distributed hypothesis testing distributed learning learning models and methods non-Bayesian learning observational learning rational learning sequential decision methods sequential learning social learning statistical learning

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Online Design of Optimal Precoders for High Dimensional Signal Detection

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2019年第15期67卷 4122-4135页

作者： Khanduri, Prashant Theagarajan, Lakshmi Narasimhan Varshney, Pramod K. Syracuse Univ Dept Elect Engn & Comp Sci Syracuse NY 13244 USA Indian Inst Technol Palakkad Dept Elect Engn Kozhippara 678557 Kerala India

In this paper, we propose a novel methodology to design optimal precoders for distributed detection of high-dimensional signals. We consider a wireless sensor network (WSN) that consists of multiple sensors that are spatially distributed in a region of interest and a fusion center (FC). The sensors observe an unknown high-dimensional signal and forward their observations to the FCafter precoding. The sensors collect data over both temporal and spatial domains. The FC performs a binary hypothesis test based on the data received fromthe sensors over noisy channels. In this setup, we present a technique to design optimal online linear precoding strategies with transmit power constraints. We show analytically that the error exponents achieved by the proposed precoders are independent of the signal dimension. In contrast, the error exponents of the state-of-the-art precoding strategies deteriorate with the increase in signal dimension. We verify our analysis via numerical simulations and show that the proposed precoders achieve better detection performance compared to those of other state-of-the-art techniques known in the literature.

关键词： Spatio-temporal data distributed hypothesis testing precoder design dimensionality reduction

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Decision fusion approach for multitemporal classification

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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 1999年第3期37卷 1227-1233页

作者： Jeon, B Landgrebe, DA Sungkyunkwan Univ Sch Elect & Comp Engn Suwon South Korea Purdue Univ Sch Elect & Comp Engn W Lafayette IN 47907 USA

This paper proposes two decision fusion-based multitemporal classifiers, namely, the jointly likelihood and the weighted majority fusion classifiers, that are derived using two different definitions of the minimum expected cost. Without any overhead incurred by multitemporal processing, a user-selected conventional pixelwise classifier makes local class decisions separately using each temporal data set, and the proposed multitemporal classifiers make the global class decisions by optimally summarizing those local class decisions. The proposed weighted majority decision fusion classifier can handle not only the data set reliabilities but also the classwise reliabilities of each data set. Classification experiment using the jointly likelihood decision fusion with three remotely sensed Thematic Mapper (TM) data sets shows more than 10% overall classification accuracy improvement over the pixelwise maximum likelihood classifier.

关键词： decision fusion distributed detection distributed hypothesis testing multitemporal classifier reliability

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Social Opinion Formation and Decision Making Under Communication Trends

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2024年 72卷 506-520页

作者： Kayaalp, Mert Bordignon, Virginia Sayed, Ali H. Ecole Polytech Fed Lausanne Adapt Syst Lab CH-1015 Lausanne Switzerland

This work studies the learning process over social networks under partial and random information sharing. In traditional social learning models, agents exchange full belief information with each other while trying to infer the true state of nature. We study the case where agents share information about only one hypothesis, namely, the trending topic, which can be randomly changing at every iteration. We show that agents can learn the true hypothesis even if they do not discuss it, at rates comparable to traditional social learning. We also show that using one's own belief as a prior for estimating the neighbors' non-transmitted beliefs might create opinion clusters that prevent learning with full confidence. This phenomenon occurs when a single hypothesis corresponding to the truth is exchanged exclusively during all times. Such a practice, however, avoids the complete rejection of the truth under any information exchange procedure - something that could happen if priors were uniform.

关键词： Social networking (online) Information sharing Bayes methods Decision making Behavioral sciences Optimization Blogs Social learning distributed inference distributed hypothesis testing diffusion strategy trending topics partial information sharing

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On distributed Learning With Constant Communication Bits

IEEE JOURNAL ON SELECTED AREAS IN INFORMATION THEORY

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IEEE JOURNAL ON SELECTED AREAS IN INFORMATION THEORY 2022年第1期3卷 125-134页

作者： Xu, Xiangxiang Huang, Shao-Lun Tsinghua Berkeley Shenzhen Inst Data Sci & Informat Technol Res Ctr Shenzhen 518055 Peoples R China

In this paper, we study a distributed learning problem constrained by constant communication bits. Specifically, we consider the distributed hypothesis testing (DHT) problem where two distributed nodes are constrained to transmit a constant number of bits to a central decoder. In such settings, we show that in order to achieve the optimal error exponents, it suffices to consider the empirical distributions of observed data sequences and encode them to the transmission bits. With such a coding strategy, we develop a geometric approach in the distribution spaces and establish an inner bound of error exponent regions. In particular, we show the optimal achievable error exponents and coding schemes for the following cases: (i) both nodes can transmit log(2)(3) bits;(ii) one of the nodes can transmit 1 bit, and the other node is not constrained;(iii) the joint distribution of the nodes are conditionally independent given one hypothesis. Furthermore, we provide several numerical examples for illustrating the theoretical results. Our results provide theoretical guidance for designing practical distributed learning rules, and the developed approach also reveals new potentials for establishing error exponents for DHT with more general communication constraints.

关键词： distributed learning distributed hypothesis testing communication constraints multiterminal data compression error exponent statistical inference

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