optimal grouping for group minimax hypothesis testing bayesian hypothesis testing and minimax hypothesis testing represent extreme instances of detection in which the prior probabilities of the hypotheses are either completely and precisely known or are completely unknown group minimax also known as gamma minimax is a robust intermediary between bayesian and minimax hypothesis testing that allows for coarse or partial advance knowledge of the hypothesis priors by using information on sets in which the prior lies existing work on group minimax however does not consider the question of how to define the sets or groups of priors it is assumed that the groups are given in this paper we propose a novel intermediate detection scheme formulated through the quantization of the space of prior probabilities that optimally determines groups and also representative priors within the groups we show that when viewed from a quantization perspective group minimax amounts to determining centroids with a minimax bayes risk error divergence distortion criterion the appropriate bregman divergence for this task in addition the optimal partitioning of the space of prior probabilities is a bregman voronoi diagram together the optimal grouping and representation points are an epsilon net with respect to bayes risk error divergence and permit a rate distortion type asymptotic analysis of detection performance with the number of groups examples of detecting signals corrupted by additive white gaussian noise and of distinguishing exponentially distributed signals are presented

energy to peak state estimation for markov jump rnns with time varying delays via nonsynchronous filter with nonstationary mode transitions in this paper the problem of energy to peak state estimation for a class of discrete time markov jump recurrent neural networks rnns with randomly occurring nonlinearities rons and time varying delays is investigated a practical phenomenon of nonsynchronous jumps between rnns modes and desired mode dependent filters is considered and a nonstationary mode transition among the filters is used to model the nonsynchronous jumps to different degrees that are also mode dependent the rons are used to model a class of sector like nonlinearities that occur in a probabilistic way according to a bernoulli sequence the time varying delays are supposed to be mode dependent and unknown but with known lower and upper bounds a priori sufficient conditions on the existence of the nonsynchronous filters are obtained such that the filtering error system is stochastically stable and achieves a prescribed energy to peak performance index further to the recent study on the class of nonsynchronous estimation problem a monotonicity is observed in obtaining filtering performance index while changing the degree of nonsynchronous jumps a numerical example is presented to verify the theoretical findings

on the choice of norms in system identification in this paper we discuss smooth and sensitive norms for prediction error system identification when the disturbances are magnitude bounded formal conditions for sensitive norms which give an order of magnitude faster convergence of the parameter estimate variance are developed however it also is shown that the parameter estimate variance convergence rate of sensitive norms is arbitrarily bad for certain distributions a necessary condition for a norm to be statistically robust with respect to the family f c of distributions with support c c for some arbitrary c 0 is that its second derivative does not vanish on the support a direct consequence of this observation is that the quadratic norm is statistically robust among all l sub p norms p spl les 2 spl infin for f c

multiterminal source coding with high resolution we consider separate encoding and joint decoding of correlated continuous information sources subject to a difference distortion measure we first derive a multiterminal extension of the shannon lower bound for the rate region then we show that this shannon outer bound is asymptotically tight for small distortions these results imply that the loss in the sum of the coding rates due to the separation of the encoders vanishes in the limit of high resolution furthermore lattice quantizers followed by slepian wolf lossless encoding are asymptotically optimal we also investigate the high resolution rate region in the remote coding case where the encoders observe only noisy versions of the sources for the quadratic gaussian case we establish a separation result to the effect that multiterminal coding aimed at reconstructing the noisy sources subject to the rate constraints followed by estimation of the remote sources from these reconstructions is optimal under certain regularity conditions on the structure of the coding scheme

the non regular ceo problem we consider the ceo problem for non regular source distributions such as uniform or truncated gaussian a group of agents observe independently corrupted versions of data and transmit coded versions over rate limited links to a ceo the ceo then estimates the underlying data based on the received coded observations agents are not allowed to convene before transmitting their observations this formulation is motivated by the practical problem of a firm s ceo estimating non regular beliefs about a sequence of events before acting on them agents observations are modeled as jointly distributed with the underlying data through a given conditional probability density function we study the asymptotic behavior of the minimum achievable mean squared error distortion at the ceo in the limit when the number of agents l and the sum rate r tend to infinity we establish a 1 r 2 convergence of the distortion an intermediate regime of performance between the exponential behavior in discrete ceo problems berger zhang and viswanathan 1996 and the 1 r behavior in gaussian ceo problems viswanathan and berger 1997 achievability is proved by a layered architecture with scalar quantization distributed entropy coding and midrange estimation the converse is proved using the bayesian chazan zakai ziv bound

extended ziv zakai lower bound for vector parameter estimation the bayesian ziv zakai bound on the mean square error mse in estimating a uniformly distributed continuous random variable is extended for arbitrarily distributed continuous random vectors and for distortion functions other than mse the extended bound is evaluated for some representative problems in time delay and bearing estimation the resulting bounds have simple closed form expressions and closely predict the simulated performance of the maximum likelihood estimator in all regions of operation

rate region of the quadratic gaussian two encoder source coding problem we determine the rate region of the quadratic gaussian two encoder source coding problem this rate region is achieved by a simple architecture that separates the analog and digital aspects of the compression furthermore this architecture requires higher rates to send a gaussian source than it does to send any other source with the same covariance our techniques can also be used to determine the sum rate of some generalizations of this classical problem our approach involves coupling the problem to a quadratic gaussian ldquoceo problem rdquo

h_ infty state estimation for discrete time complex networks with randomly occurring sensor saturations and randomly varying sensor delays in this paper the state estimation problem is investigated for a class of discrete time delay nonlinear complex networks with randomly occurring phenomena from sensor measurements the randomly occurring phenomena include randomly occurring sensor saturations rosss and randomly varying sensor delays rvsds that result typically from networked environments a novel sensor model is proposed to describe the rosss and the rvsds within a unified framework via two sets of bernoulli distributed white sequences with known conditional probabilities rather than employing the commonly used lipschitz type function a more general sector like nonlinear function is used to describe the nonlinearities existing in the network the purpose of the addressed problem is to design a state estimator to estimate the network states through available output measurements such that for all probabilistic sensor saturations and sensor delays the dynamics of the estimation error is guaranteed to be exponentially mean square stable and the effect from the exogenous disturbances to the estimation accuracy is attenuated at a given level by means of an h norm in terms of a novel lyapunov krasovskii functional and the kronecker product sufficient conditions are established under which the addressed state estimation problem is recast as solving a convex optimization problem via the semidefinite programming method a simulation example is provided to show the usefulness of the proposed state estimation conditions

quantization of prior probabilities for hypothesis testing in this paper bayesian hypothesis testing is investigated when the prior probabilities of the hypotheses taken as a random vector are quantized nearest neighbor and centroid conditions are derived using mean bayes risk error mbre as a distortion measure for quantization a high resolution approximation to the distortion rate function is also obtained human decision making in segregated populations is studied assuming bayesian hypothesis testing with quantized priors

quantization of prior probabilities for collaborative distributed hypothesis testing this paper studies the quantization of prior probabilities drawn from an ensemble in distributed detection with data fusion by combination of binary local decisions design and performance equivalences between a team of n agents and a more powerful single agent are obtained effects of identical quantization and diverse quantization on mean bayes risk are compared it is shown that when agents using diverse quantizers interact to agree on a perceived common risk the effective number quantization levels is increased with this collaboration optimal diverse regular quantization with k cells per quantizer performs as well as optimal identical quantization with n k 1 1 cells per quantizer similar results are obtained for the maximum bayes risk error criterion

delay slope dependent stability results of recurrent neural networks by using the fact that the neuron activation functions are sector bounded and nondecreasing this brief presents a new method named the delay slope dependent method for stability analysis of a class of recurrent neural networks with time varying delays this method includes more information on the slope of neuron activation functions and fewer matrix variables in the constructed lyapunov krasovskii functional then some improved delay dependent stability criteria with less computational burden and conservatism are obtained numerical examples are given to illustrate the effectiveness and the benefits of the proposed method

analytic groups and pushing small sets apart we say that a space x has the separation property provided that if a and b are subsets of x with a countable and b first category then there is a homeomorphism f x x such that f a b o we prove that a borel space with this property is polish our main result is that if the homeomorphisms needed in the separation property for the space x come from the homeomorphisms given by an action of an analytic group then x is polish several examples are also presented 2009 american mathematical society

on the midrange estimator an error criterion for the design of an estimator based on extreme order statistics namely the midrange is defined this approach is taken to overcome the fact that the variance of the midrange estimate is strongly dependent on the input distribution moreover under this performance criterion nonparametric characteristics for the design of these estimators are found

sum rate of the vacationing ceo problem the vacationing chief executive officer ceo problem combines the salient features of the so called ceo problem and the multiple description md problem in this setting noisy versions of a source are observed by two encoders as in the ceo problem in addition we require that each encoder generate mds of the source as in the md problem the vacationing ceo problem arises in asynchronous multicast networks and solving it is an essential step in developing a general theory for multiencoder and multidecoder lossy compression in this paper an achievable sum rate and two sum rate lower bounds are presented for the quadratic gaussian vacationing ceo problem these bounds exactly determine the optimal sum rate over a wide range of parameters

statistical inference under multiterminal data compression this paper presents a survey of the literature on the information theoretic problems of statistical inference under multiterminal data compression with rate constraints significant emphasis is put on problems 1 multiterminal hypothesis testing 2 multiterminal parameter estimation and 3 multiterminal pattern classification in either case of positive rates or zero rates in addition the paper includes three new results i e the converse theorems for all problems of multiterminal hypothesis testing multiterminal parameter estimation and multiterminal pattern classification at the zero rate

on the generalized gaussian ceo problem this paper considers a distributed source coding dsc problem where l encoders observe noisy linear combinations of k correlated remote gaussian sources and separately transmit the compressed observations to the decoder to reconstruct the remote sources subject to a sum distortion constraint this dsc problem is referred to as the generalized gaussian ceo problem since it can be viewed as a generalization of the quadratic gaussian ceo problem where the number of remote source k 1 first we provide a new outer region obtained using the entropy power inequality and an equivalent argument in the sense of having the same rate distortion region and berger tung inner region among a certain class of generalized gaussian ceo problems we then give two sufficient conditions for our new outer region to match the inner region achieved by berger tung schemes where the second matching condition implies that in the low distortion regime the berger tung inner rate region is always tight while in the high distortion regime the same region is tight if a certain condition holds the sum rate part of the outer region is also studied and shown to meet the berger tung sum rate upper bound under a certain condition which is obtained using the karush kuhn tucker conditions of the underlying convex semidefinite optimization problem and is in general weaker than the aforesaid two for rate region tightness

the rate distortion function for the quadratic gaussian ceo problem a new multiterminal source coding problem called the ceo problem was presented and investigated by berger zhang and viswanathan recently viswanathan and berger have investigated an extension of the ceo problem to gaussian sources and call it the quadratic gaussian ceo problem they considered this problem from a statistical viewpoint deriving some interesting results in this paper we consider the quadratic gaussian ceo problem from a standpoint of multiterminal rate distortion theory we regard the ceo problem as a certain multiterminal remote source coding problem with infinitely many separate encoders whose observations are conditionally independent if the remote source is given this viewpoint leads us to a complete solution to the problem we determine the tradeoff between the total amount of rate and squared distortion deriving an explicit formula of the rate distortion function the derived function has the form of a sum of two nonnegative functions one is a classical rate distortion function for single gaussian source and the other is a new rate distortion function which dominates the performance of the system for a relatively small distortion it follows immediately from our result that the conjecture of viswanathan and berger on the asymptotic behavior of minimum squared distortion for large rates is true

communicating probability distributions a rate distortion problem is solved that is motivated by a quantum data compression problem the goal is to send information about a source string x so that a receiver can construct a second string y for which the joint empirical probability distribution of x and y is close to some desired distribution the problem differs from the usual rate distortion problems in that one must consider both remote sources and distortion functions that are not averages of per letter distortion functions

rate distortion theory for gaussian multiterminal source coding systems with several side informations at the decoder in this paper we consider the separate coding problem for l 1 correlated gaussian memoryless sources we deal with the case where l sources work as partial side information at the decoder for the reconstruction of the remaining source the determination problem of the rate distortion region for this system is the so called many help one problem and it has been known as a highly challenging problem for almost 20 years in this paper we give a partial solution to this problem we determine the rate distortion region in the case where the l sources working as partial side information are conditionally independent if the remaining source we wish to reconstruct is given the additive white gaussian noise ceo problem is a special case of this we also discuss the relation of the result previous results of ours

vector gaussian multiterminal source coding we derive an outer bound of the rate region of the vector gaussian l terminal ceo problem by establishing a lower bound on each supporting hyperplane of the rate region to this end we prove a new extremal inequality by exploiting the connection between differential entropy and fisher information as well as some fundamental estimation theoretic inequalities it is shown that the outer bound matches the berger tung inner bound in the high resolution regime we then derive a lower bound on each supporting hyperplane of the rate region of the direct vector gaussian l terminal source coding problem by coupling it with the ceo problem through a limiting argument the tightness of this lower bound in the high resolution regime and the weak dependence regime is also proved

probabilistic coherence and proper scoring rules this paper provides self contained proof of a theorem relating probabilistic coherence of forecasts to their non domination by rival forecasts with respect to any proper scoring rule the theorem recapitulates insights achieved by other investigators and clarifies the connection of coherence and proper scoring rules to bregman divergence

the ceo problem multiterminal source coding we consider a new problem in multiterminal source coding motivated by the following decentralized communication estimation task a firm s chief executive officer ceo is interested in the data sequence x t sub t 1 sup spl infin which cannot be observed directly perhaps because it represents tactical decisions by a competing firm the ceo deploys a team of l agents who observe independently corrupted versions of x t sub t 1 sup spl infin because x t is only one among many pressing matters to which the ceo must attend the combined data rate at which the agents may communicate information about their observations to the ceo is limited to say r bits per second if the agents were permitted to confer and pool their data then in the limit as l spl rarr spl infin they usually would be able to smooth out their independent observation noises entirely then they could use their r bits per second to provide the ceo with a representation of x t with fidelity d r where d spl middot is the distortion rate function of x t in particular with such data pooling d can be made arbitrarily small if r exceeds the entropy rate h of x t suppose however that the agents are not permitted to convene agent i having to send data based solely on his own noisy observations y sub i t we show that then there does not exist a finite value of r for which even infinitely many agents can make d arbitrarily small furthermore in this isolated agents case we determine the asymptotic behavior of the minimal error frequency in the limit as l and then r tend to infinity