optimality approximation and complexity in set membership h sub spl infin identification investigates the set membership identification of time invariant discrete time exponentially stable possibly infinite dimensional linear systems from time or frequency domain data corrupted by deterministic noise the aim is to deliver not a single model but a set of models whose size in h sub spl infin norm measures the uncertainty in the identification the main focus of the note is on the optimality properties for finite data and on the tradeoff between optimality and complexity of approximated low order model sets a method is given for evaluating convergent and computationally efficient inner and outer approximations of the value set for a given frequency such approximations allow one to compute within any desired accuracy the identification error of any identified model and to evaluate an optimal model at any given number of frequencies by suitably approximating these values model sets with nominal models in rh sub spl infin are then derived whose order is selected by trading off between model set complexity and identification accuracy degradation this degradation is evaluated by computing the optimality level defined as the ratio between the reduced model identification error and the optimal one a numerical example demonstrates the effectiveness of the presented results

scale sensitive dimensions uniform convergence and learnability learnability in valiant s pac learning model has been shown to be strongly related to the existence of uniform laws of large numbers these laws define a distribution free convergence property of means to expectations uniformly over classes of random variables classes of real valued functions enjoying such a property are also known as uniform glivenko cantelli classes in this paper we prove through a generalization of sauer s lemma that may be interesting in its own right a new characterization of uniform glivenko cantelli classes our characterization yields dudley gine and zinn s previous characterization as a corollary furthermore it is the first based on a gine and zinn s previous characterization as a corollary furthermore it is the first based on a simple combinatorial quantity generalizing the vapnik chervonenkis dimension we apply this result to obtain the weakest combinatorial condition known to imply pac learnability in the statistical regression or agnostic framework furthermore we find a characterization of learnability in the probabilistic concept model solving an open problem posed by kearns and schapire these results show that the accuracy parameter plays a crucial role in determining the effective complexity of the learner s hypothesis class

exponential strong converse for content identification with lossy recovery we revisit the high dimensional content identification with lossy recovery problem tuncel and gunduz 2014 and establish an exponential strong converse theorem as a corollary of the exponential strong converse theorem we derive an upper bound on the joint identification error and excess distortion exponent for the problem our main results can be specialized to the biometrical identification problem willems 2003 and the content identification problem tuncel 2009 since these two problems are both special cases of the content identification with lossy recovery problem we leverage the information spectrum method introduced by oohama and adapt the strong converse techniques therein to be applicable to the problem at hand

quantum achievability proof via collision relative entropy in this paper we provide a simple framework for deriving one shot achievable bounds for some problems in quantum information theory our framework is based on the joint convexity of the exponential of the collision relative entropy and is a partial quantum generalization of the technique of yassaee et al from classical information theory based on this framework we derive one shot achievable bounds for the problems of communication over classical quantum channels quantum hypothesis testing and classical data compression with quantum side information we argue that our one shot achievable bounds are strong enough to give the asymptotic achievable rates of these problems even up to the second order

minimum complexity regression estimation with weakly dependent observations the minimum complexity regression estimation framework barron 1991 barron and cover 1991 and rissanen 1989 is a general data driven methodology for estimating a regression function from a given list of parametric models using independent and identically distributed i i d observations we extend barron s regression estimation framework to m dependent observations and to strongly mixing observations in particular we propose abstract minimum complexity regression estimators for dependent observations which may be adapted to a particular list of parametric models and establish upper bounds on the statistical risks of the proposed estimators in terms of certain deterministic indices of resolvability assuming that the regression function satisfies a certain fourier transform type representation we examine minimum complexity regression estimators adapted to a list of parametric models based on neural networks and by using the upper bounds for the abstract estimators we establish rates of convergence for the statistical risks of these estimators also as a key tool we extend the classical bernstein inequality from i i d random variables to m dependent processes and to strongly mixing processes

renyi divergence and kullback leibler divergence renyi divergence is related to renyi entropy much like kullback leibler divergence is related to shannon s entropy and comes up in many settings it was introduced by renyi as a measure of information that satisfies almost the same axioms as kullback leibler divergence and depends on a parameter that is called its order in particular the renyi divergence of order 1 equals the kullback leibler divergence we review and extend the most important properties of renyi divergence and kullback leibler divergence including convexity continuity limits of sigma algebras and the relation of the special order 0 to the gaussian dichotomy and contiguity we also show how to generalize the pythagorean inequality to orders different from 1 and we extend the known equivalence between channel capacity and minimax redundancy to continuous channel inputs for all orders and present several other minimax results

coordination capacity we develop elements of a theory of cooperation and coordination in networks rather than considering a communication network as a means of distributing information or of reconstructing random processes at remote nodes we ask what dependence can be established among the nodes given the communication constraints specifically in a network with communication rates ri j between the nodes we ask what is the set of all achievable joint distributions p x1 xm of actions at the nodes of the network several networks are solved including arbitrarily large cascade networks distributed cooperation can be the solution to many problems such as distributed games distributed control and establishing mutual information bounds on the influence of one part of a physical system on another

construction of fuzzy σ algebras using triangular norms abstract generalizing the definitions given by the author fuzzy sets and systems4 1980 83 93 we introduce and study t fuzzy algebras t being any triangular norm the main result is that for a large class of triangular norms each t fuzzy algebra is generated i e consists of all functions x 0 1 being measurable with respect to some algebra on x

brief finite sample properties of system identification of arx models under mixing conditions the asymptotic convergence properties of system identification methods are well known but comparatively little is known about the practical situation where only a finite number of data points are available in this paper we consider the finite sample properties of prediction error methods for system identification we consider arx models and uniformly bounded criterion functions the problem we pose is how many data points are required in order to guarantee with high probability that the expected value of the identification criterion is close to its empirical mean value the sample sizes are obtained using generalisations of risk minimisation theory to weakly dependent processes we obtain uniform probabilistic bounds on the difference between the expected value of the identification criterion and the empirical value evaluated on the observed data points the bounds are very general in particular no assumption is made about the true system belonging to the model class further analysis shows that in order to maintain a given bound on the difference the number of data points required grows at most at a polynomial rate in the model order and in many cases no faster than quadratically the results obtained here generalise previous results derived for the case where the observed data was independent and identically distributed

analysis of remaining uncertainties and exponents under various conditional renyi entropies we analyze the asymptotics of the normalized remaining uncertainty of a source when a compressed or hashed version of it and correlated side information is observed for this system commonly known as slepian wolf source coding we establish the optimal minimum rate of compression of the source to ensure that the remaining uncertainties vanish we also study the exponential rate of decay of the remaining uncertainty to zero when the rate is above the optimal rate of compression in this paper we consider various classes of random universal hash functions instead of measuring remaining uncertainties using traditional shannon information measures we do so using two forms of the conditional renyi entropy among other techniques we employ new one shot bounds and the moments of type class enumerator method see merhav for these evaluations we show that these asymptotic results are generalizations of the strong converse exponent and the error exponent of the slepian wolf problem under maximum a posteriori decoding

brief non asymptotic confidence ellipsoids for the least squares estimate in this paper we consider the finite sample properties of least squares system identification and derive non asymptotic confidence ellipsoids for the estimate the shape of the confidence ellipsoids is similar to the shape of the ellipsoids derived using asymptotic theory but unlike asymptotic theory they are valid for a finite number of data points the probability that the estimate belongs to a certain ellipsoid has a natural dependence on the volume of the ellipsoid the data generating mechanism the model order and the number of data points available

corrections to wyner s common information under renyi divergence measures in this correspondence we correct an erroneous result on the achievability part of the renyi common information with order 1 s in 1 2 in l yu and v y f tan wyner s common information under renyi divergence measures ieee trans inf theory vol 64 no 5 pp 3616 3632 may 2018 the new achievability result upper bound of the renyi common information no longer coincides with wyner s common information we also provide a new converse result lower bound in this correspondence for the renyi common information with order 1 s in 1 infty numerical results show that for doubly symmetric binary sources the new upper and lower bounds coincide for the order 1 s in 1 2 and they are both strictly larger than wyner s common information for this case

distributed channel synthesis two familiar notions of correlation are rediscovered as the extreme operating points for distributed synthesis of a discrete memoryless channel in which a stochastic channel output is generated based on a compressed description of the channel input wyner s common information is the minimum description rate needed however when common randomness independent of the input is available the necessary description rate reduces to shannon s mutual information this paper characterizes the optimal tradeoff between the amount of common randomness used and the required rate of description we also include a number of related derivations including the effect of limited local randomness rate requirements for secrecy applications to game theory and new insights into common information duality our proof makes use of a soft covering lemma known in the literature for its role in quantifying the resolvability of a channel the direct proof achievability constructs a feasible joint distribution over all parts of the system using a soft covering from which the behavior of the encoder and decoder is inferred with no explicit reference to joint typicality or binning of auxiliary interest this paper also generalizes and strengthens this soft covering tool

efficient agnostic learning of neural networks with bounded fan in we show that the class of two layer neural networks with bounded fan in is efficiently learnable in a realistic extension to the probably approximately correct pac learning model in this model a joint probability distribution is assumed to exist on the observations and the learner is required to approximate the neural network which minimizes the expected quadratic error as special cases the model allows learning real valued functions with bounded noise learning probabilistic concepts and learning the best approximation to a target function that cannot be well approximated by the neural network the networks we consider have real valued inputs and outputs an unlimited number of threshold hidden units with bounded fan in and a bound on the sum of the absolute values of the output weights the number of computation steps of the learning algorithm is bounded by a polynomial in 1 spl epsiv 1 spl delta n and b where spl epsiv is the desired accuracy spl delta is the probability that the algorithm fails n is the input dimension and b is the bound on both the absolute value of the target which may be a random variable and the sum of the absolute values of the output weights in obtaining the result we also extended some results on iterative approximation of functions in the closure of the convex hull of a function class and on the sample complexity of agnostic learning with the quadratic loss function

non asymptotic quality assessment of generalised fir models with periodic inputs in any real life identification problem only a finite number of data points is available on the other hand almost all results in stochastic identification pertain to asymptotic properties that is they tell us what happens when the number of data points tends to infinity in this paper we consider the problem of assessing the quality of the estimates identified from a finite number of data points we focus on least squares identification of generalised fir models and develop a method to produce a bound on the uncertainty in the parameter estimate the method is data driven and based on tests involving permuted data sets moreover it does not require that the true system is in the model class

finite sample properties of linear model identification in this paper we consider the finite sample properties of prediction error methods using a quadratic criterion function for system identification the problem we pose is how many data points are required to guarantee with high probability that the expected value of the quadratic identification criterion is close to its empirical mean value the sample sizes are obtained using risk minimization theory which provides uniform probabilistic bounds on the difference between the expected value of the squared prediction error and its empirical mean evaluated on a finite number of data points the bounds are very general no assumption is made about the true system belonging to the model class and the noise sequence is not assumed to be uniformly bounded further analysis shows that in order to maintain a given bound on the deviation the number of data points needed grows no faster than quadratically with the number of parameters for fir and arx models

on the renyi divergence joint range of relative entropies and a channel coding theorem this paper starts by considering the minimization of the renyi divergence subject to a constraint on the total variation distance based on the solution of this optimization problem the exact locus of the points bigl d q p 1 d q p 2 bigr is determined when p 1 p 2 and q are arbitrary probability measures which are mutually absolutely continuous and the total variation distance between p 1 and p 2 is not below a given value it is further shown that all the points of this convex region are attained by probability measures which are defined on a binary alphabet this characterization yields a geometric interpretation of the minimal chernoff information subject to a constraint on the variational distance this paper also derives an exponential upper bound on the performance of binary linear block codes or code ensembles under maximum likelihood decoding its derivation relies on the gallager bounding technique and it reproduces the shulman feder bound as a special case the bound is expressed in terms of the renyi divergence from the normalized distance spectrum of the code or the average distance spectrum of the ensemble to the binomially distributed distance spectrum of the capacity achieving ensemble of random block codes this exponential bound provides a quantitative measure of the degradation in performance of binary linear block codes or code ensembles as a function of the deviation of their distance spectra from the binomial distribution an efficient use of this bound is considered

convex linear t s functions a generalization of frank s equation abstract the main purpose of this paper is to solve the functional equation t s min max for 0 and a pair t s of a t norm t and a t conorm s this equation arises when we consider a convex linear combination of a t norm and a t conorm and set out the problem of finding the intersection of the segments determined by the pairs min max and t s

discrete lossy gray wyner revisited second order asymptotics large and moderate deviations in this paper we revisit the discrete lossy gray wyner problem in particular we derive its optimal second order coding rate region its error exponent reliability function and its moderate deviations constant under mild conditions on the source to obtain the second order asymptotics we extend some ideas from watanabe s work in particular we leverage the properties of an appropriate generalization of the conditional distortion tilted information density which was first introduced by kostina and verdu the converse part uses a perturbation argument by gu and effros in their strong converse proof of the discrete gray wyner problem the achievability part uses two novel elements 1 a generalization of various type covering lemmas and 2 the uniform continuity of the conditional rate distortion function in both the source joint distribution and the distortion level to obtain the error exponent for the achievability part we use the same generalized type covering lemma and for the converse we use the strong converse together with a change of measure technique finally to obtain the moderate deviations constant we apply the moderate deviations theorem to probabilities defined in terms of information spectrum quantities

probabilistic optimal estimation with uniformly distributed noise the classical approach to system identification is based on stochastic assumptions about the measurement error and provides estimates that have random nature worst case identification on the other hand only assumes the knowledge of deterministic error bounds and establishes guaranteed estimates thus being in principle better suited for the use in control design however a main limitation of such deterministic bounds lies in their potential conservatism thus leading to estimates of restricted use in this paper we propose a rapprochement between the stochastic and worst case system identification viewpoints which is based on the probabilistic setting of information based complexity the main idea in this line of research is to discard sets of measure at most where is a probabilistic accuracy from the set of deterministic estimates therefore we are decreasing the so called worst case radius of information at the expense of a given probabilistic risk in the case of uniformly distributed noise we derive new computational results and in particular we compute a trade off curve called violation function which shows how the radius of information decreases as a function of the accuracy to this end we construct randomized and deterministic algorithms which provide approximations of this function we report extensive simulations showing numerical comparisons between the stochastic worst case and probabilistic approaches thus demonstrating the efficacy of the methods proposed in this paper

memory universal prediction of stationary random processes we consider the problem of one step ahead prediction of a real valued stationary strongly mixing random process xi sub i spl infin sup spl infin the best mean square predictor of x sub 0 is its conditional mean given the entire infinite past x sub i sub i spl infin sup 1 given a sequence of observations x sub 1 x sub 2 x sub n we propose estimators for the conditional mean based on sequences of parametric models of increasing memory and of increasing dimension for example neural networks and legendre polynomials the proposed estimators select both the model memory and the model dimension in a data driven fashion by minimizing certain complexity regularized least squares criteria when the underlying predictor function has a finite memory we establish that the proposed estimators are memory universal the proposed estimators which do not know the true memory deliver the same statistical performance rates of integrated mean squared error as that delivered by estimators that know the true memory furthermore when the underlying predictor function does not have a finite memory we establish that the estimator based on legendre polynomials is consistent

principles of inclusion and exclusion for fuzzy sets abstract many previous papers have presented generalizations of the principle of inclusion and exclusion to fuzzy sets or if sets atanassov s intuitionistic fuzzy sets with godel or product operations we clarify for which fuzzy intersections and unions based on continuous triangular norms and conorms the principle of inclusion and exclusion holds

vapnik chervonenkis generalization bounds for real valued neural networks we show how lower bounds on the generalization ability of feedforward neural nets with real outputs can be derived within a formalism based directly on the concept of vc dimension and vapnik s theorem on uniform convergence of estimated probabilities

second order region for gray wyner network the coding problem over the gray wyner network is studied from the second order coding rates perspective a tilted information density for this network is introduced in the spirit of kostina verdu and under a certain regularity condition the second order region is characterized in terms of the variance of this tilted information density and the tangent vector of the first order region the second order region is proved by the type method the achievability part is proved by the type covering argument and the converse part is proved by a refinement of the perturbation approach that was used by gu effros to show the strong converse of the gray wyner network this is the first instance that the second order region is characterized for a multi terminal problem where the characterization of the first order region involves an auxiliary random variable

strong secrecy from channel resolvability we analyze physical layer security based on the premise that the coding mechanism for secrecy over noisy channels is tied to the notion of channel resolvability instead of considering capacity based constructions which associate to each message a subcode that operates just below the capacity of the eavesdropper s channel we consider channel resolvability based constructions which associate to each message a subcode that operates just above the resolvability of the eavesdropper s channel building upon the work of csiszar and hayashi we provide further evidence that channel resolvability is a powerful and versatile coding mechanism for secrecy by developing results that hold for strong secrecy metrics and arbitrary channels specifically we show that at least for symmetric wiretap channels random capacity based constructions fail to achieve the strong secrecy capacity while channel resolvability based constructions achieve it we then leverage channel resolvability to establish the secrecy capacity region of arbitrary broadcast channels with confidential messages and a cost constraint for strong secrecy metrics finally we specialize our results to study the secrecy capacity of wireless channels with perfect channel state information csi mixed channels and compound channels with receiver csi as well as the secret key capacity of source models for secret key agreement by tying secrecy to channel resolvability we obtain achievable rates for strong secrecy metrics with simple proofs

rates of convergence for empirical processes of stationary mixing sequences classical empirical process theory for vapnik cervonenkis classes deals mainly with sequences of independent variables this paper extends the theory to stationary sequences of dependent variables it establishes rates of convergence for mixing and mixing empirical processes indexed by classes of functions the method of proof depends on a coupling of the dependent sequence with sequences of independent blocks to which the classical theory can be applied a uniform o ns 1 s rate of convergence over v c classes is established for sequences whose mixing coefficients decay slightly faster than o n s

a large deviation analysis of the maximum likelihood learning of markov tree structures the problem of maximum likelihood ml estimation of discrete tree structured distributions is considered chow and liu established that ml estimation reduces to the construction of a maximum weight spanning tree using the empirical mutual information quantities as the edge weights using the theory of large deviations we analyze the exponent associated with the error probability of the event that the ml estimate of the markov tree structure differs from the true tree structure given a set of independently drawn samples by exploiting the fact that the output of ml estimation is a tree we establish that the error exponent is equal to the exponential rate of decay of a single dominant crossover event we prove that in this dominant crossover event a non neighbor node pair replaces a true edge of the distribution that is along the path of edges in the true tree graph connecting the nodes in the non neighbor pair using ideas from euclidean information theory we then analyze the scenario of ml estimation in the very noisy learning regime and show that the error exponent can be approximated as a ratio which is interpreted as the signal to noise ratio snr for learning tree distributions we show via numerical experiments that in this regime our snr approximation is accurate

mixing coefficients between discrete and real random variables computation and properties in this paper we study the problem of estimating the alpha beta and phi mixing coefficients between two random variables that can either assume values in a finite set or the set of real numbers in either case explicit closed form formulas for the beta mixing coefficient are already known therefore for random variables assuming values in a finite set our contributions are twofold 1 in the case of the alpha mixing coefficient we show that determining whether or not it exceeds a prespecified threshold is np complete and provide efficiently computable upper and lower bounds 2 we derive an exact closed form formula for the phi mixing coefficient next we prove analogs of the data processing inequality from information theory for each of the three kinds of mixing coefficients then we move on to real valued random variables and show that by using percentile binning and allowing the number of bins to increase more slowly than the number of samples we can generate empirical estimates that are consistent i e converge to the true values as the number of samples approaches infinity

finite sample properties of system identification methods in this paper we study the quality of system identification models obtained using the standard quadratic prediction error criterion for a general linear model class the main feature of our results is that they hold true for a finite data sample and they are not asymptotic the main theorems bound the difference between the expected value of the identification criterion evaluated at the estimated parameters and at the optimal parameters the bound depends naturally on the model and system order the pole locations and the noise variance and it shows that although these variables often do not enter in asymptotic convergence results they do play an important role when the data sample is finite

on exact and renyi common informations recently two extensions of wyner s common information exact and renyi common informations were introduced respectively by kumar li and el gamal kle and the present authors the class of common information problems involves determining the minimum rate of the common input to two independent processors needed to exactly or approximately generate a target joint distribution for the exact common information problem exact generation of the target distribution is required while for wyner s and alpha renyi common informations the relative entropy and renyi divergence with order alpha were respectively used to quantify the discrepancy between the synthesized and target distributions the exact common information is larger than or equal to wyner s common information however it was hitherto unknown whether the former is strictly larger than the latter for some joint distributions in this paper we first establish the equivalence between the exact and infty renyi common informations and then provide single letter upper and lower bounds for these two quantities for doubly symmetric binary sources we show that the upper and lower bounds coincide which implies that for such sources the exact and infty renyi common informations are completely characterized interestingly we observe that for such sources these two common informations are strictly larger than wyner s this answers an open problem posed by kle furthermore we extend wyner s infty renyi and exact common informations to sources with countably infinite or continuous alphabets including gaussian sources

wyner s common information under renyi divergence measures we study a generalized version of wyner s common information problem also coined the distributed source simulation problem the original common information problem consists in understanding the minimum rate of the common input to independent processors to generate an approximation of a joint distribution when the distance measure used to quantify the discrepancy between the synthesized and target distributions is the normalized relative entropy our generalization involves changing the distance measure to the unnormalized and normalized renyi divergences of order alpha 1 s in 0 2 we show that the minimum rate needed to ensure the renyi divergences between the distribution induced by a code and the target distribution vanishes remains the same as the one in wyner s setting except when the order alpha 1 s 0 this implies that wyner s common information is rather robust to the choice of distance measure employed as a byproduct of the proofs used to the establish the above results the exponential strong converse for the common information problem under the total variation distance measure is established

exact random coding secrecy exponents for the wiretap channel we analyze the exact exponential decay rate of the expected amount of information leaked to the wiretapper in wyner s wiretap channel setting using wiretap channel codes constructed from both i i d and constant composition random codes our analysis for those sampled from i i d random coding ensemble shows that the previously known achievable secrecy exponent using this ensemble is indeed the exact exponent for an average code in the ensemble furthermore our analysis on wiretap channel codes constructed from the ensemble of constant composition random codes leads to an exponent which in addition to being the exact exponent for an average code is larger than the achievable secrecy exponent that has been established so far in the literature for this ensemble which in turn was known to be smaller than that achievable by wiretap channel codes sampled from i i d random coding ensemble we show examples where the exact secrecy exponent for the wiretap channel codes constructed from random constant composition codes is larger than that of those constructed from i i d random codes and examples where the exact secrecy exponent for the wiretap channel codes constructed from i i d random codes is larger than that of those constructed from constant composition random codes we hence conclude that unlike the error correction problem there is no general ordering between the two random coding ensembles in terms of their secrecy exponent

exact channel synthesis we consider the exact channel synthesis problem this problem concerns the determination of the minimum amount of information required to create exact correlation remotely when there is a certain rate of randomness shared by two terminals this problem generalizes an existing approximate version in which the generated joint distribution is required to be close to a target distribution under the total variation tv distance measure instead being exactly equal to the target distribution we provide single letter inner and outer bounds on the admissible region of the shared randomness rate and the communication rate for the exact channel synthesis problem these two bounds coincide for doubly symmetric binary sources we observe that for such sources the admissible rate region for exact channel synthesis is strictly included in that for the tv approximate version we also extend the exact and tv approximate channel synthesis problems to sources with countably infinite alphabets and continuous sources the latter includes gaussian sources as by products lemmas concerning soft covering under renyi divergence measures are derived

local algorithms for pattern recognition and dependencies estimation in previous publications bottou and vapnik 1992 vapnik 1992 we described local learning algorithms which result in performance improvements for real problems we present here the theoretical framework on which these algorithms are based first we present a new statement of certain learning problems namely the local risk minimization we review the basic results of the uniform convergence theory of learning and extend these results to local risk minimization we also extend the structural risk minimization principle for both pattern recognition problems and regression problems this extended induction principle is the basis for a new class of algorithms

decision theoretic generalizations of the pac model for neural net and other learning applications we describe a generalization of the pac learning model that is based on statistical decision theory in this model the learner receives randomly drawn examples each example consisting of an instance x in x and an outcome y in y and tries to find a hypothesis h x a where h in h that specifies the appropriate action a in a to take for each instance x in order to minimize the expectation of a loss l y a here x y and a are arbitrary sets l is a real valued function and examples are generated according to an arbitrary joint distribution on x times y special cases include the problem of learning a function from x into y the problem of learning the conditional probability distribution on y given x regression and the problem of learning a distribution on x density estimation we give theorems on the uniform convergence of empirical loss estimates to true expected loss rates for certain hypothesis spaces h and show how this implies learnability with bounded sample size disregarding computational complexity as an application we give distribution independent upper bounds on the sample size needed for learning with feedforward neural networks our theorems use a generalized notion of vc dimension that applies to classes of real valued functions adapted from pollard s work and a notion of capacity and metric dimension for classes of functions that map into a bounded metric space supersedes 89 30 and 90 52 also in information and computation vol 100 no 1 september 1992

a note on a generalized frank functional equation abstract we study a generalized frank functional equation in the broader framework of associative aggregation functions and show that up to the two projections we obtain exactly the same set of solutions as in the original paper by m j frank aequationes mathematicae 19 1979

brief new identification approaches for disturbed models recently much research has been conducted in the field of identification of the linear models in general these methods use a time domain estimate or a frequency domain estimate in this paper the time domain estimate and the frequency domain estimate were combined to identify the autoregressive exogenous noise arx interference model the concept of a general prediction error criterion is introduced for the time domain estimate an optimal frequency estimation is introduced for the frequency domain estimate a new identification method called the empirical frequency domain optimal parameter estimate is proposed for disturbed systems it is fully applied and developed for the output error model and a specific case or the arx model the algorithm theoretically provides the globally optimum frequency domain estimate of the model some simulations are included to illustrate the new identification method

general nonasymptotic and asymptotic formulas in channel resolvability and identification capacity and their application to the wiretap channel several nonasymptotic formulas are established in channel resolvability and identification capacity and they are applied to the wiretap channel by using these formulas the epsi capacities of the above three problems are considered in the most general setting where no structural assumptions such as the stationary memoryless property are made on a channel as a result we solve an open problem proposed by han and verduacute moreover we obtain lower bounds of the exponents of error probability and the wiretapper s information in the wiretap channel

triangular norm based measures and their markov kernel representation abstract we approach the problem whether left continuous triangular norm based valuations called t measures or t probability measures defined on triangular normbased tribes of the unit cube can be disintegrated by markov kernels we prove that each t measure based on a fundamental triangular norm these triangular norms t together with their corresponding triangular conorms s satisfy the functional equation t x y s x y x y can be uniquely represented as a sum of a disintegrable t measure and a hard core which is either identically zero or which is monotonically irreducible i e cannot be disintegrated

exponential decreasing rate of leaked information in universal random privacy amplification we derive a new upper bound for eve s information in secret key generation from a common random number without communication this bound improves on bennett s bound based on the renyi entropy of order 2 because the bound obtained here uses the renyi entropy of order 1 s for s 0 1 this bound is applied to a wire tap channel then we derive an exponential upper bound for eve s information our exponent is compared with hayashi s exponent for the additive case the bound obtained here is better the result is applied to secret key agreement by public discussion

learning dynamical systems in a stationary environment abstract we consider the problem of learning the input output relation of a dynamical system from noisy data our method rests on the use of a smooth simultaneous estimator which generalizes the standard empirical estimator in a stationary environment our algorithm is shown to select a model which exhibits the probably approximately correct pac property under very mild conditions this contribution should be thought of as a first attempt to extend concepts developed in learning theory to the field of system identification where due to the presence of the system dynamics the typical i i d assumption on the data made in learning theory is not satisfied