a study on h state estimation of static neural networks with time varying delays this paper studies the problem of h state estimation for static neural networks with time varying delay by construction of a suitable lyapunov krasovskii functional some improved delay dependent conditions are established such that the error system is globally exponentially stable with a decay rate and a prescribed h performance is guaranteed in order to get less conservative results of the state estimation condition zero equalities and reciprocally convex approach are employed the estimator gain matrix can be obtained in terms of the solution to linear matrix inequalities numerical examples are provided to illustrate the effectiveness and performance of the developed method

comparison of model selection for regression we discuss empirical comparison of analytical methods for model selection currently there is no consensus on the best method for finite sample estimation problems even for the simple case of linear estimators this article presents empirical comparisons between classical statistical methods akaike information criterion aic and bayesian information criterion bic and the structural risk minimization srm method based on vapnik chervonenkis vc theory for regression problems our study is motivated by empirical comparisons in hastie tibshirani and friedman 2001 which claims that the srm method performs poorly for model selection and suggests that aic yields superior predictive performance hence we present empirical comparisons for various data sets and different types of estimators linear subset selection and k nearest neighbor regression our results demonstrate the practical advantages of vc based model selection it consistently outperforms aic for all data sets in our study srm and bic methods show similar predictive performance this discrepancy between empirical results obtained using the same data is caused by methodological drawbacks in hastie et al 2001 especially in their loose interpretation and application of srm method hence we discuss methodological issues important for meaningful comparisons and practical application of srm method we also point out the importance of accurate estimation of model complexity vc dimension for empirical comparisons and propose a new practical estimate of model complexity for k nearest neighbors regression

exponential synchronization of a class of neural networks with sampled data control abstract this paper investigates the problem of the master slave synchronization for a class of neural networks with discrete and distributed delays under sampled data control by introducing some new terms a novel piecewise time dependent lyapunov krasovskii functional lkf is constructed to fully capture the available characteristics of real sampling information and nonlinear function vector of the system based on the lkf and wirtinger based inequality less conservative synchronization criteria are obtained to guarantee the exponential stability of the error system and then the slave system is synchronized with the master system the designed sampled data controller can be obtained by solving a set of linear matrix inequalities lmis which depend on the maximum sampling period and the decay rate the criteria are less conservative than the ones obtained in the existing works a numerical example is presented to illustrate the effectiveness and merits of the proposed method

sampled data synchronization of chaotic lur e systems with time delays this paper studies the problem of sampled data control for master slave synchronization schemes that consist of identical chaotic lur e systems with time delays it is assumed that the sampling periods are arbitrarily varying but bounded in order to take full advantage of the available information about the actual sampling pattern a novel lyapunov functional is proposed which is positive definite at sampling times but not necessarily positive definite inside the sampling intervals based on the lyapunov functional an exponential synchronization criterion is derived by analyzing the corresponding synchronization error systems the desired sampled data controller is designed by a linear matrix inequality approach the effectiveness and reduced conservatism of the developed results are demonstrated by the numerical simulations of chua s circuit and neural network

a smoothing filter based on fuzzy transform this paper is devoted to the smoothing of discrete functions using the fuzzy transform introduced by perfilieva we generalize a smoothing filter based on the fuzzy transform recently proposed by us to obtain a better control on the smoothed functions for this purpose a generalization of the concept of fuzzy partition is suggested and the smoothing filter is defined as a combination of the direct discrete fuzzy transform and a slightly modified inverse continuous fuzzy transform an approximation behavior total variation of smoothed functions and statistical properties including the description of the white noise reduction and the asymptotic expression of bias and variance are investigated and discussed the proposed filter is compared with the nadaraya watson estimator and the results are illustrated assuming financial data

stochastic complexity and modeling on demontre un theoreme fondamental qui donne une borne inferieure pour la longueur de code et donc pour les erreurs de prediction on definit les notions d information a priori et d information utile dans les donnees

model selection for regression with continuous kernel functions using the modulus of continuity this paper presents a new method of model selection for regression problems using the modulus of continuity for this purpose we suggest the prediction risk bounds of regression models using the modulus of continuity which can be interpreted as the complexity of functions we also present the model selection criterion referred to as the modulus of continuity information criterion mcic which is derived from the suggested prediction risk bounds the suggested mcic provides a risk estimate using the modulus of continuity for a trained regression model or an estimation function while other model selection criteria such as the aic and bic use structural information such as the number of training parameters as a result the suggested mcic is able to discriminate the performances of trained regression models even with the same structure of training models to show the effectiveness of the proposed method the simulation for function approximation using the multilayer perceptrons mlps was conducted through the simulation for function approximation it was demonstrated that the suggested mcic provides a good selection tool for nonlinear regression models even with the limited size of data

stability analysis of uncertain sampled data systems with incremental delay using looped functionals the robust stability analysis of asynchronous and uncertain sampled data systems with constant incremental input delay is addressed in the looped functional framework these functionals have been shown to be suitable for the analysis of impulsive systems as they allow one to express discrete time stability conditions in an affine way enabling then the consideration of uncertain and time varying systems the stability conditions are obtained by first reformulating the sampled data system as an impulsive system and by then considering a tailored looped functional along with wirtinger s inequality a recently introduced inequality that has been shown to be less conservative than jensen s inequality several examples are given for illustration

wirtinger based integral inequality application to time delay systems in the last decade the jensen inequality has been intensively used in the context of time delay or sampled data systems since it is an appropriate tool to derive tractable stability conditions expressed in terms of linear matrix inequalities lmis however it is also well known that this inequality introduces an undesirable conservatism in the stability conditions and looking at the literature reducing this gap is a relevant issue and always an open problem in this paper we propose an alternative inequality based on the fourier theory more precisely on the wirtinger inequalities it is shown that this resulting inequality encompasses the jensen one and also leads to tractable lmi conditions in order to illustrate the potential gain of employing this new inequality with respect to the jensen one two applications on time delay and sampled data stability analysis are provided

passivity analysis for discrete time stochastic markovian jump neural networks with mixed time delays in this paper passivity analysis is conducted for discrete time stochastic neural networks with both markovian jumping parameters and mixed time delays the mixed time delays consist of both discrete and distributed delays the markov chain in the underlying neural networks is finite piecewise homogeneous by introducing a lyapunov functional that accounts for the mixed time delays a delay dependent passivity condition is derived in terms of the linear matrix inequality approach the case of markov chain with partially unknown transition probabilities is also considered all the results presented depend upon not only discrete delay but also distributed delay a numerical example is included to demonstrate the effectiveness of the proposed methods

reciprocally convex approach to stability of systems with time varying delays whereas the upper bound lemma for matrix cross product introduced by park 1999 and modified by moon park kwon and lee 2001 plays a key role in guiding various delay dependent criteria for delayed systems the jensen inequality has become an alternative as a way of reducing the number of decision variables it directly relaxes the integral term of quadratic quantities into the quadratic term of the integral quantities resulting in a linear combination of positive functions weighted by the inverses of convex parameters this paper suggests the lower bound lemma for such a combination which achieves performance behavior identical to approaches based on the integral inequality lemma but with much less decision variables comparable to those based on the jensen inequality lemma

the risk inflation criterion for multiple regression a new criterion is proposed for the evaluation of variable selection procedures in multiple regression this criterion which we call the risk inflation is based on an adjustment to the risk essentially the risk inflation is the maximum increase in risk due to selecting rather than knowing the correct predictors a new variable selection procedure is obtained which in the case of orthogonal predictors substantially improves on aic c p and bic and is close to optimal in contrast to aic c p and bic which use dimensionality penalties of 2 2 and log n respectively this new procedure uses a penalty 2 log p where p is the number of available predictors for the case of nonorthogonal predictors bounds for the optimal penalty are obtained

exponential synchronization of neural networks with discrete and distributed delays under time varying sampling this paper investigates the problem of master slave synchronization for neural networks with discrete and distributed delays under variable sampling with a known upper bound on the sampling intervals an improved method is proposed which captures the characteristic of sampled data systems some delay dependent criteria are derived to ensure the exponential stability of the error systems and thus the master systems synchronize with the slave systems the desired sampled data controller can be achieved by solving a set of linear matrix inequalitys which depend upon the maximum sampling interval and the decay rate the obtained conditions not only have less conservatism but also have less decision variables than existing results simulation results are given to show the effectiveness and benefits of the proposed methods

adapting to unknown smoothness via wavelet shrinkage abstract we attempt to recover a function of unknown smoothness from noisy sampled data we introduce a procedure sureshrink that suppresses noise by thresholding the empirical wavelet coefficients the thresholding is adaptive a threshold level is assigned to each dyadic resolution level by the principle of minimizing the stein unbiased estimate of risk sure for threshold estimates the computational effort of the overall procedure is order n log n as a function of the sample size n sureshrink is smoothness adaptive if the unknown function contains jumps then the reconstruction essentially does also if the unknown function has a smooth piece then the reconstruction is essentially as smooth as the mother wavelet will allow the procedure is in a sense optimally smoothness adaptive it is near minimax simultaneously over a whole interval of the besov scale the size of this interval depends on the choice of mother wavelet we know from a previous paper by the authors that traditional smoot

model selection beyond the bayesian frequentist divide the principle of parsimony also known as ockham s razor has inspired many theories of model selection yet such theories all making arguments in favor of parsimony are based on very different premises and have developed distinct methodologies to derive algorithms we have organized challenges and edited a special issue of jmlr and several conference proceedings around the theme of model selection in this editorial we revisit the problem of avoiding overfitting in light of the latest results we note the remarkable convergence of theories as different as bayesian theory minimum description length bias variance tradeoff structural risk minimization and regularization in some approaches we also present new and interesting examples of the complementarity of theories leading to hybrid algorithms neither frequentist nor bayesian or perhaps both frequentist and bayesian

model complexity control for regression using vc generalization bounds it is well known that for a given sample size there exists a model of optimal complexity corresponding to the smallest prediction generalization error hence any method for learning from finite samples needs to have some provisions for complexity control existing implementations of complexity control include penalization or regularization weight decay in neural networks and various greedy procedures aka constructive growing or pruning methods there are numerous proposals for determining optimal model complexity aka model selection based on various asymptotic analytic estimates of the prediction risk and on resampling approaches nonasymptotic bounds on the prediction risk based on vapnik chervonenkis vc theory have been proposed by vapnik this paper describes application of vc bounds to regression problems with the usual squared loss an empirical study is performed for settings where the vc bounds can be rigorously applied i e linear models and penalized linear models where the vc dimension can be accurately estimated and the empirical risk can be reliably minimized empirical comparisons between model selection using vc bounds and classical methods are performed for various noise levels sample size target functions and types of approximating functions our results demonstrate the advantages of vc based complexity control with finite samples

the minimum description length principle in coding and modeling we review the principles of minimum description length and stochastic complexity as used in data compression and statistical modeling stochastic complexity is formulated as the solution to optimum universal coding problems extending shannon s basic source coding theorem the normalized maximized likelihood mixture and predictive codings are each shown to achieve the stochastic complexity to within asymptotically vanishing terms we assess the performance of the minimum description length criterion both from the vantage point of quality of data compression and accuracy of statistical inference context tree modeling density estimation and model selection in gaussian linear regression serve as examples

new approaches on stability criteria for neural networks with interval time varying delays abstract this paper concerns the problem of delay dependent stability criteria for neural networks with interval time varying delays first by constructing a newly augmented lyapunov krasovskii functional and combining with a reciprocally convex combination technique less conservative stability criterion is established in terms of linear matrix inequalities lmis which will be introduced in theorem 1 second by taking different interval of integral terms of lyapunov krasovskii functional utilized in theorem 1 further improved stability criterion is proposed in theorem 2 third a novel approach which divides the bounding of activation function into two subinterval are proposed in theorem 3 to reduce the conservatism of stability criterion finally through two well known numerical examples used in other literature it will be shown the proposed stability criteria achieves the improvements over the existing ones and the effectiveness of the proposed idea

stability and dissipativity analysis of distributed delay cellular neural networks in this brief the problems of delay dependent stability analysis and strict q s dissipativity analysis are investigated for cellular neural networks cnns with distributed delay first by introducing an integral partitioning technique two new forms of lyapunov krasovskii functionals are constructed and improved distributed delay dependent stability conditions are established in terms of linear matrix inequalities based on this criterion a new sufficient delay and dependent condition is given to guarantee that the cnns with distributed delay are strictly q s dissipative the results developed in this brief can tolerate larger allowable delay than existing ones in the literature which is demonstrated by several examples

synchronization criteria for coupled neural networks with interval time varying delays and leakage delay abstract this paper considers the synchronization problem for coupled neural networks with interval time varying delays and leakage delay by construction of a suitable lyapunov krasovskii s functional and utilization of finsler s lemma novel delay dependent criteria for the synchronization of the networks are established in terms of linear matrix inequalities lmis which can be easily solved by various effective optimization algorithms two numerical examples are given to illustrate the effectiveness of the proposed methods

finite dimensional filters part i the wei norman technique this two part paper deals with necessary or sufficient conditions for the existence of finite dimensional filters in this first part we set the problem and propose a construction of such filters by the wei norman technique after having formulated the problem of finite dimensional filters in terms of finite dimensional realizations of input output mappings we specify the dependence with respect to the initial measure we show how different notions of dependence imply different properties of the so called estimation algebra cal e cal e is homomorphic to a lie algebra of vector fields cal e contains only operators of order less than or equal to two cal e is finite dimensional and contains only operators of order less than or equal to two these results depend on a precise definition of a finite dimensional realization especially on what concerns the domain of the output function the last and most stringent condition on cal e will be shown to be almost sufficient to recover a family of finite dimensional realizations thanks to the proof of a baker campbell hausdorff formula which allows us to apply the wei norman technique in a quite general setting