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On the Optimality of Binning for distributed hypothesis testing

IEEE TRANSACTIONS ON INFORMATION THEORY 2012年第10期58卷 6282-6303页

作者： Rahman, Md Saifur Wagner, Aaron B. Cornell Univ Sch Elect & Comp Engn Ithaca NY 14853 USA

We study a hypothesis testing problem in which data are compressed distributively and sent to a detector that seeks to decide between two possible distributions for the data. The aim is to characterize all achievable encoding rates and exponents of the type 2 error probability when the type 1 error probability is at most a fixed value. For related problems in distributed source coding, schemes based on random binning perform well and are often optimal. For distributed hypothesis testing, however, the use of binning is hindered by the fact that the overall error probability may be dominated by errors in the binning process. We show that despite this complication, binning is optimal for a class of problems in which the goal is to "test against conditional independence." We then use this optimality result to give an outer bound for a more general class of instances of the problem.

关键词： Binning distributed hypothesis testing Gaussian many-help-one hypothesis testing against independence Gel'fand and Pinsker hypothesis testing against independence outer bound Quantize-Bin-Test scheme rate-exponent region test against conditional independence

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Private Two-Terminal hypothesis testing

Private Two-Terminal Hypothesis Testing

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IEEE International Symposium on Information Theory (ISIT)

作者： Narayanan, Varun Mishra, Manoj Prabhakaran, Vinod M. Tata Inst Fundamental Res Mumbai Maharashtra India Homi Bhabha Natl Inst NISER Bhubaneswar India

ISBN: (纸本)9781728164328

We study private two-terminal hypothesis testing with simple hypotheses where the privacy goal is to ensure that participating in the testing protocol reveals little additional information about the other user's observation when a user is told what the correct hypothesis is. We show that, in general, meaningful correctness and privacy cannot be achieved if the users do not have access to correlated (but, not common) randomness. We characterize the optimal correctness and privacy error exponents when the users have access to non-trivial correlated randomness (those that permit secure multiparty computation).

关键词： distributed hypothesis testing secure multiparty computation privacy error exponents

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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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New Results on testing Against Independence with Rate-Limited Constraints 7

New Results on Testing Against Independence with Rate-Limite...

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7th IEEE Global Conference on Signal and Information Processing (IEEE GlobalSIP)

作者： Espinosa, Sebastian Silva, Jorge F. Piantanida, Pablo Univ Chile Dept Elect Engn Santiago Chile Univ Paris Sud CNRS Cent Supelec Lab Signaux & Syst L2S Orsay France Univ Montreal Montreal Inst Learning Algorithms MILA Montreal PQ Canada

ISBN: (纸本)9781728127231

This work studies error exponent limits in hypothesis testing (HT) in a distributed scenario with partial communication constraints. We derive general conditions on the Type I error restriction under which the error exponent of the optimal Type II error has a closed-form characterization for the task of testing against independence. We show that the error exponent is preserved for a family of decreasing Type I error restrictions. Complementing this analysis, new expressions are derived to bound the optimal Type II error probability for a finite number of observations. These bounds shed light about the velocity at which error exponent limits are attained with the number of samples.

关键词： distributed hypothesis testing multi-terminal source coding error exponent information bottleneck

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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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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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Complexity of Bayesian Belief Exchange over a Network 56

Complexity of Bayesian Belief Exchange over a Network

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56th Annual IEEE Conference on Decision and Control (CDC)

作者： Rahimian, M. Amin Jadbabaie, Ali Mossel, Elchanan MIT IDSS 77 Massachusetts Ave Cambridge MA 02139 USA

ISBN: (纸本)9781509028733

Many important real-world decision making problems involve group interactions among individuals with purely informational externalities, such situations arise for example in jury deliberations, expert committees, medical diagnosis, etc. In this paper, we will use the framework of iterated eliminations to model the decision problem as well as the thinking process of a Bayesian agent in a group decision/discussion scenario. We model the purely informational interactions of rational agents in a group, where they receive private information and act based upon that information while also observing other people's beliefs. As the Bayesian agent attempts to infer the true state of the world from her sequence of observations which include her neighbors' beliefs as well as her own private signal, she recursively refines her belief about the signals that other players could have observed and beliefs that they would have hold given the assumption that other players are also rational. We further analyze the computational complexity of the Bayesian belief formation in groups and show that it is NP-hard. We also investigate the factors underlying this computational complexity and show how belief calculations simplify in special network structures or cases with strong inherent symmetries. We finally give insights about the statistical efficiency (optimality) of the beliefs and its relations to computational efficiency.

关键词： Rational Choice theory Computational social choice distributed hypothesis testing Bayesian inference Computational complexity Bayesian computations

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Information Centrality and Ordering of Nodes for Accuracy in Noisy Decision-Making Networks

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2016年第4期61卷 1040-1045页

作者： Poulakakis, Ioannis Young, George F. Scardovi, Luca Leonard, Naomi Ehrich Univ Delaware Dept Mech Engn Newark DE 19711 USA Princeton Univ Dept Mech & Aerosp Engn Princeton NJ 08544 USA Univ Toronto Dept Elect & Comp Engn Toronto ON M5S 3G4 Canada

This technical note considers a network of stochastic evidence accumulators, each represented by a drift-diffusion model accruing evidence towards a decision in continuous time by observing a noisy signal and by exchanging information with other units according to a fixed communication graph. These network dynamics model distributed sequential hypothesis testing as well as collective decision making. We prove the relationship between the location of each unit in the graph and its certainty as measured by the inverse of the variance of its state. Under mild connectivity assumptions, we show that only in balanced directed graphs do the node variances remain within a bounded constant from the minimum possible variance. We then prove that, for these digraphs, node ranking based on certainty is governed by information centrality, which depends on the notion of effective resistance suitably generalized to directed graphs. Our results, which describe the certainty of each unit as a function of the structural properties of the graph, can guide the selection of leaders in problems that involve the observation of noisy external signals by a cooperative multi-agent network.

关键词： Decision making distributed hypothesis testing drift diffusion information centrality leader selection noisy networks

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distributed Estimation and Learning over Heterogeneous Networks

Distributed Estimation and Learning over Heterogeneous Netwo...

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54th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

作者： Rahimian, M. Amin Jadbabaie, Ali MIT Inst Data Syst & Soc 77 Massachusetts Ave Cambridge MA 02139 USA

ISBN: (纸本)9781509045501

We consider several estimation and learning problems that networked agents face when making decisions given their uncertainty about an unknown variable. Our methods are designed to efficiently deal with heterogeneity in both size and quality of the observed data, as well as heterogeneity over time (intermittence). The goal of the studied aggregation schemes is to efficiently combine the observed data that is spread over time and across several network nodes, accounting for all the network heterogeneities. Moreover, we require no form of coordination beyond the local neighborhood of every network agent or sensor node. The three problems that we consider are (i) maximum likelihood estimation of the unknown given initial data sets, (ii) learning the true model parameter from streams of data that the agents receive intermittently over time, and (iii) minimum variance estimation of a complete sufficient statistic from several data points that the networked agents collect over time. In each case, we rely on an aggregation scheme to combine the observations of all agents;moreover, when the agents receive streams of data over time, we modify the update rules to accommodate the most recent observations. In every case, we demonstrate the efficiency of our algorithms by proving convergence to the globally efficient estimators given the observations of all agents. We supplement these results by investigating the rate of convergence and providing finite-time performance guarantees.

关键词： Statistical Learning distributed Learning distributed hypothesis testing distributed Detection distributed Estimation Online Learning

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Learning without Recall from Actions of Neighbors

Learning without Recall from Actions of Neighbors

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American Control Conference (ACC)

作者： Rahimian, M. Amin Jadbabaie, Ali Univ Penn Dept Elect & Syst Engn Philadelphia PA 19104 USA

ISBN: (纸本)9781467386821

Under the Bayesian without Recall ( BWR) model of inference, the agents behave rationally with respect to their most recent observations and yet they do not recall their history of past observations and cannot reason about how other agents are making their decisions. This model avoids the complexities of fully rational inference and also provides a behavioral foundation for non-Bayesian updating. We present the implications of the choice of signal and action space and utility structures for such agents, leading us to familiar update forms including the linear updates and the DeGroot model. We show that for a wide class of distributions from the exponential family with their conjugate priors, the BWR action updates take the form of a linear update in the self and neighboring actions. Furthermore, if the agents begin with noninformative priors then these action updates take the form of a convex combination as in the DeGroot model: agents who start from noninformative priors follow the DeGroot update and reach a consensus.

关键词： Social Learning Bayesian Learning Non-Bayesian Learning Rational Learning Observational Learning Statistical Learning distributed Learning distributed hypothesis testing distributed Detection DeGroot Model Linear Regression Conjugate Priors Exponential families

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