local classifier weighting by quadratic programming it has been widely accepted that the classification accuracy can be improved by combining outputs of multiple classifiers however how to combine multiple classifiers with various potentially conflicting decisions is still an open problem a rich collection of classifier combination procedures many of which are heuristic in nature have been developed for this goal in this brief we describe a dynamic approach to combine classifiers that have expertise in different regions of the input space to this end we use local classifier accuracy estimates to weight classifier outputs specifically we estimate local recognition accuracies of classifiers near a query sample by utilizing its nearest neighbors and then use these estimates to find the best weights of classifiers to label the query the problem is formulated as a convex quadratic optimization problem which returns optimal nonnegative classifier weights with respect to the chosen objective function and the weights ensure that locally most accurate classifiers are weighted more heavily for labeling the query sample experimental results on several data sets indicate that the proposed weighting scheme outperforms other popular classifier combination schemes particularly on problems with complex decision boundaries hence the results indicate that local classification accuracy based combination techniques are well suited for decision making when the classifiers are trained by focusing on different regions of the input space

local linear perceptrons for classification a structure composed of local linear perceptrons for approximating global class discriminants is investigated such local linear models may be combined in a cooperative or competitive way in the cooperative model a weighted sum of the outputs of the local perceptrons is computed where the weight is a function of the distance between the input and the position of the local perceptron in the competitive model the cost function dictates a mixture model where only one of the local perceptrons give output learning of the local models positions and the linear mappings they implement are coupled and both supervised we show that this is preferable to the uncoupled case where the positions are trained in an unsupervised manner before the separate supervised training of mappings we use goodness criteria based on the cross entropy and give learning equations for both the cooperative and competitive cases the coupled and uncoupled versions of cooperative and competitive approaches are compared among themselves and with multilayer perceptrons of sigmoidal hidden units and radial basis functions rbfs of gaussian units on the application of recognition of handwritten digits the criteria of comparison are the generalization accuracy learning time and the number of free parameters we conclude that even on such a high dimensional problem such local models are promising they generalize much better than rbf s and use much less memory when compared with multilayer perceptrons we note that local models learn much faster and generalize as well and sometimes better with comparable number of parameters

assessing generalization ability of majority vote point classifiers classification algorithms have been traditionally designed to simultaneously reduce errors caused by bias as well by variance however there occur many situations where low generalization error becomes extremely crucial to getting tangible classification solutions and even slight overfitting causes serious consequences in the test results in such situations classifiers with low vapnik chervonenkis vc dimension can bring out positive differences due to two main advantages 1 the classifier manages to keep the test error close to training error and 2 the classifier learns effectively with small number of samples this paper shows that a class of classifiers named majority vote point mvp classifiers on account of very low vc dimension can exhibit a generalization error that is even lower than that of linear classifiers this paper proceeds by theoretically formulating an upper bound on the vc dimension of the mvp classifier later through empirical analysis the trend of exact values of vc dimension is estimated finally case studies on machine fault diagnosis problems and prostate tumor detection problem revalidate the fact that an mvp classifier can achieve a lower generalization error than most other classifiers

using measures of similarity and inclusion for multiple classifier fusion by decision templates abstract decision templates dt are a technique for classifier fusion for continuous valued individual classifier outputs the individual outputs considered here sum up to the same value e g statistical classifiers yielding some estimates of the posterior probabilities for the classes first the dt fusion algorithm is explained second we show that two similarity measures s 1 and s 2 and two inclusion indices i 1 and i 2 between fuzzy sets see dubois and prade fuzzy sets and systems theory and applications academic press new york 1980 produce the same dt classifier the equivalence is proven by showing that for every object submitted for classification all four measures induce the same ordering on the set of class labels through dt fusion thereby assigning the object to the same class

factorization theorems and the structure of operators on hilbert space soit 7b h un espace de hilbert complexe et soit 7b l 7b h l algebre des operateurs lineaires bornes agissant sur 7b h on demontre des theoremes de factorisation on etudie la structure des operateurs sur 7b h

on polynomially bounded operators acting on a banach space abstract by the von neumann inequality every contraction on a hilbert space is polynomially bounded a simple example shows that this result does not extend to banach space contractions in this paper we give general conditions under which an arbitrary banach space contraction is polynomially bounded these conditions concern the thinness of the spectrum and the behaviour of the resolvent or the sequence of negative powers to do this we use techniques from harmonic analysis in particular results concerning thin sets such as helson sets kronecker sets and sets that satisfy spectral synthesis

a unifying approximate dynamic programming model for the economic lot scheduling problem we formulate the well known economic lot scheduling problem elsp with sequence dependent setup times and costs as a semi markov decision process using an affine approximation of the bias function we obtain a semi infinite linear program determining a lower bound for the minimum average cost rate under a very mild condition we can reduce this problem to a relatively small convex quadratically constrained linear problem by exploiting the structure of the objective function and the state space this problem is equivalent to the lower bound problem derived by dobson dobson g 1992 the cyclic lot scheduling problem with sequence dependent setups oper res 40 736 749 and reduces to the well known lower bound problem introduced in bomberger bomberger ee 1966 a dynamic programming approach to a lot size scheduling problem management sci 12 778 784 for sequence dependent setups we thus provide a framework that unifies previous work and opens new paths for future research on tighter lower bounds

classifier combination based on confidence transformation this paper investigates the effects of confidence transformation in combining multiple classifiers using various combination rules the combination methods were tested in handwritten digit recognition by combining varying classifier sets the classifier outputs are transformed to confidence measures by combining three scaling functions global normalization gaussian density modeling and logistic regression and three confidence types linear sigmoid and evidence the combination rules include fixed rules sum rule product rule median rule etc and trained rules linear discriminants and weighted combination with various parameter estimation techniques the experimental results justify that confidence transformation benefits the combination performance of either fixed rules or trained rules trained rules mostly outperform fixed rules especially when the classifier set contains weak classifiers among the trained rules the support vector machine with linear kernel linear svm performs best while the weighted combination with optimized weights performs comparably well i have also attempted the joint optimization of confidence parameters and combination weights but its performance was inferior to that of cascaded confidence transformation combination this justifies that the cascaded strategy is a right way of multiple classifier combination

the average cost optimality equation for markov control processes on borel spaces abstract this paper deals with discrete time markov control processes with borel state space allowing unbounded costs and noncompact control sets for these models the existence of average optimal stationary policies has been recently established under very general assumptions using an optimality inequality here we give a condition which is a strengtened version of a variant of the vanishing discount factor approach for the optimality equation to hold

how do correlation and variance of base experts affect fusion in biometric authentication tasks combining multiple information sources such as subbands streams with different features and multimodal data has been shown to be a very promising trend both in experiments and to some extents in real life biometric authentication applications despite considerable efforts in fusions there is a lack of understanding on the roles and effects of correlation and variance of both the client and impostor scores of base classifiers experts often scores are assumed to be independent in this paper we explicitly consider this factor using a theoretical model called variance reduction equal error rate vr eer analysis assuming that client and impostor scores are approximately gaussian distributed we showed that equal error rate eer can be modeled as a function of f ratio which itself is a function of 1 correlation 2 variance of base experts and 3 difference of client and impostor means to achieve lower eer smaller correlation and average variance of base experts and larger mean difference are desirable furthermore analysing any of these factors independently e g focusing on correlation alone could be miss leading experimental results on the banca multimodal database confirm our findings using vr eer analysis we analyzed four commonly encountered scenarios in biometric authentication which include fusing correlated uncorrelated base experts of similar different performances the analysis explains and shows that fusing systems of different performances is not always beneficial one of the most important findings is that positive correlation hurts fusion while negative correlation greater diversity which measures the spread of prediction score with respect to the fused score improves fusion however by linking the concept of ambiguity decomposition to classification problem it is found that diversity is not sufficient to be an evaluation criterion to compare several fusion systems unless measures are taken to normalize the class dependent variance moreover by linking the concept of bias variance covariance decomposition to classification using eer it is found that if the inherent mismatch between training and test sessions can be learned from the data such mismatch can be incorporated into the fusion system as a part of training parameters

optimality inequalities for average cost markov decision processes and the stochastic cash balance problem for general state and action space markov decision processes we present sufficient conditions for the existence of solutions of the average cost optimality inequalities these conditions also imply the convergence of both the optimal discounted cost value function and policies to the corresponding objects for the average costs per unit time case inventory models are natural applications of our results we describe structural properties of average cost optimal policies for the cash balance problem an inventory control problem where the demand may be negative and the decision maker can produce or scrap inventory we also show the convergence of optimal thresholds in the finite horizon case to those under the expected discounted cost criterion and those under the expected discounted costs to those under the average costs per unit time criterion

average cost optimal policies for markov control processes with borel state space and unbounded costs abstract we show the existence of average cost optimal stationary policies for markov control processes with borel state space and unbounded costs per stage under a set of assumptions recently introduced by l i sennott 1989 for control processes with countable state space and finite control sets

enhancing decision combination of face and fingerprint by exploitation of individual classifier space an approach to multi modal biometry this paper presents a new approach to combine decisions from face and fingerprint classifiers for multi modal biometry by exploiting the individual classifier space on the basis of availability of class specific information present in the classifier space we exploit the prior knowledge by training the face classifier using response vectors on a validation set enhancing class separability using parametric and nonparametric linear discriminant analysis in the classifier output space and thereby improving the performance of the face classifier fingerprint classifier often does not provide this information due to high sensitivity of available minutiae points producing partial matches across subjects the enhanced face and fingerprint classifiers are combined using a sum rule we also propose a generalized algorithm for multiple classifier combination mcc based on our approach experimental results show superiority of the proposed method over other existing fusion techniques such as sum product max min rules decision template and dempster shafer theory

a theoretical study on six classifier fusion strategies we look at a single point in feature space two classes and l classifiers estimating the posterior probability for class spl omega sub 1 assuming that the estimates are independent and identically distributed normal or uniform we give formulas for the classification error for the following fusion methods average minimum maximum median majority vote and oracle

a novel combining classifier method based on variational inference in this paper we propose a combining classifier method based on the bayesian inference framework specifically the outputs of base classifiers called level1 data or meta data are utilized in a combiner to produce the final classification in our ensemble system each class in the training set induces a distribution on the level1 data which is modeled by a multivariate gaussian distribution traditionally the parameters of the gaussian are estimated using a maximum likelihood approach however maximum likelihood estimation cannot be applied since the covariance matrix of level1 data of each class is not full rank instead we propose to estimate the multivariate gaussian distribution of level1 data of each class by using the variational inference method experiments conducted on eighteen uci machine learning repository datasets and a selected 10 class clef2009 medical imaging database demonstrated the advantage of our method compared with several well known ensemble methods we proposed a variational inference method for multivariate gaussian distribution estimation we proposed a novel combining classifier method by employing variational inference on base classifiers outputs the proposed method is highly competitive to many state of the arts ensemble classifier methods

data dependency in multiple classifier systems in this paper the data dependency of aggregation modules in multiple classifier system is being investigated we first propose a new categorization scheme in which combining methods are grouped into data independent implicitly data dependent and explicitly data dependent it is argued that data dependent approaches present the highest potential for improved performance in this study we intend to provide a comprehensive investigation of this argument and explore the impact of data dependency on the performance of multiple classifiers we evaluate this impact based on two criteria prediction accuracy and stability in addition we examine the effect of class imbalance and uneven data distribution on these two criteria this paper presents the findings of an extensive set of comparative experiments based on the findings it can be concluded that data dependent aggregation methods are generally more stable and less sensitive to class imbalance in addition data dependent methods exhibited superior or identical generalization ability for most of the data sets

cyclicity of bicyclic operators and completeness of translates we study cyclicity of operators on a separable banach space which admit a bicyclic vector such that the norms of its images under the iterates of the operator satisfy certain growth conditions a simple consequence of our main result is that a bicyclic unitary operator on a banach space with separable dual is cyclic our results also imply that if s a n n in mathbb z longmapsto a n 1 n in mathbb z is the shift operator acting on the weighted space of sequences ell omega 2 mathbb z if the weight satisfies some regularity conditions and n 1 for nonnegative n then s is cyclic if rm lim n rightarrow infty rm log omega n sqrt n 0 on the other hand one can see that s is not cyclic if the series sum n geq 1 rm log omega n n 2 diverges we show that the question of herrero whether either s or s is cyclic on ell omega 2 mathbb z admits a positive answer when the series sum n in mathbb z rm log s n n 2 1 is convergent we also prove completeness results for translates in certain banach spaces of functions on mathbb r

fuzzy versus nonfuzzy in combining classifiers designed by boosting boosting is recognized as one of the most successful techniques for generating classifier ensembles typically the classifier outputs are combined by the weighted majority vote the purpose of this study is to demonstrate the advantages of some fuzzy combination methods for ensembles of classifiers designed by boosting we ran two fold cross validation experiments on six benchmark data sets to compare the fuzzy and nonfuzzy combination methods on the fuzzy side we used the fuzzy integral and the decision templates with different similarity measures on the nonfuzzy side we tried the weighted majority vote as well as simple combiners such as the majority vote minimum maximum average product and the naive bayes combination in our experiments the fuzzy combination methods performed consistently better than the nonfuzzy methods the weighted majority vote showed a stable performance though slightly inferior to the performance of the fuzzy combiners

theorems of katznelson tzafriri type for contractions for t a contraction on a hilbert space and a function in the disc algebra we show that if 0 on spt then limn t tn 0 the same method gives a new proof of recent results of katznelson tzafriri several applications are given

average cost optimal stationary policies in infinite state markov decision processes with unbounded costs we deal with infinite state markov decision processes with unbounded costs three simple conditions based on the optimal discounted value function guarantee the existence of an expected average cost optimal stationary policy sufficient conditions are the existence of a distinguished state of smallest discounted value and a single stationary policy inducing an irreducible ergodic markov chain for which the average cost of a first passage from any state to the distinguished state is finite a result to verify this is also given two examples illustrate the ease of applying the criteria

on the optimality equation for average cost markov control processes with feller transition probabilities we consider markov control processes with borel state space and feller transition probabilities satisfying some generalized geometric ergodicity conditions we provide a new theorem on the existence of a solution to the average cost optimality equation

a note on order statistics based parametric pattern classification recently a novel classification paradigm is proposed named classification by moments of order statistics cmos which is shown to attain the optimal bayesian bound for symmetric distributions and a near optimal accuracy for asymmetric distributions 13 9 however in the process of deriving the order statistics based classification scheme the authors use a plausible relation e x k n k n 1 s e x k n 1 k n 1 where is the cumulative distribution function of random variable x and x k n is the k th order statistics of a sample of size n from x therefore the new approach actually should be viewed as the classification scheme based on the percentiles of distribution instead of the so called order statistics based classification in this paper we will build the cmos using 2 os criteria in its true sense furthermore we show that the order statistics based classification reaches the optimal bayesian bound for symmetric distributions and compare the accuracy of cmos bayesian classification median based classifier and percentiles based classification for non symmetric distributions the theoretical results are verified by rigorous experiments as well highlightswe present the os based classification scheme for distributions in the exponential family we show that cmos using 2 os attains the optimal bayesian bound for symmetric distributions we compare cmos with the existing classification paradigms for asymmetric distributions

a genetic fuzzy linguistic combination method for fuzzy rule based multiclassifiers fuzzy set theory has been widely and successfully used as a mathematical tool to combine the outputs provided by the individual classifiers in a multiclassification system by means of a fuzzy aggregation operator however to the best of our knowledge no fuzzy combination method has been proposed which is composed of a fuzzy rule based system we think this can be a very promising research line as it allows us to benefit from the key advantage of fuzzy systems i e their interpretability by using a fuzzy linguistic rule based classification system as a combination method the resulting classifier ensemble would show a hierarchical structure and the operation of the latter component would be transparent to the user moreover for the specific case of fuzzy multiclassification systems the new approach could also become a smart way to allow standard fuzzy classifiers to deal with high dimensional problems avoiding the curse of dimensionality as the chance to perform classifier selection at class level is also incorporated into the method we conduct comprehensive experiments considering 20 uci datasets with different dimensionality where our approach improves or at least maintains accuracy while reducing complexity of the system and provides some interpretability insight into the multiclassification system reasoning mechanism the results obtained show that this approach is able to compete with the state of the art multiclassification system selection and fusion methods in terms of accuracy thus providing a good interpretability accuracy tradeoff

a multilayered neuro fuzzy classifier with self organizing properties a novel self organizing neuro fuzzy multilayered classifier sonefmuc is suggested in this paper which is composed of small scale interconnected fuzzy neuron classifiers fncs arranged in layers the model provides a different perspective for generating a new class of hierarchical classifiers with multilevel classifiers combination at each layer parent fncs are combined to construct a descendant fnc at the next layer with enhanced classification qualities the generic fncs exhibit an original structure including four modules 1 the fuser aggregates the decision support outputs of the parent fncs using a fusion operator 2 the data splitting module divides data into correctly classified patterns with high degree of confidence which are handled by the fuser and ambiguous ones 3 the last two modules are realized by fuzzy rule based systems and implement a neuro fuzzy classifier within each fnc used to improve the classification accuracy of ambiguous patterns the former performs feature transformations to an intermediate output space while the latter provides the decision supports of non confident patterns unlike traditional classifiers the classification mapping is accomplished in sonefmuc by performing successive decision fusions and feature transformations sonefmuc structure is determined sequentially via a self constructing learning algorithm structure learning inherently implements feature selection considering the most informative attributes as model inputs to improve classification accuracy the models obtained after structure learning are optimized using a parameter learning scheme based on genetic algorithms the effectiveness of our approach is tested on a set of benchmark classification problems experimental results show that the proposed neuro fuzzy classifier is favorably compared to other well known classification techniques of the literature

some results of katznelson tzafriri type abstract for semigroups s r z and z k we show that if t is a representation of s by contractions on a hilbert space then inf t s t t f t sup f sp u t s where f l 1 s and sp u t s is the unitary spectrum of t with respect to s for t a representation of a suitable semigroup s by contractions on a banach space we give sharp conditions on sp u t s which guarantee that the equality above holds these conditions concern the thinness of sp u t s in the harmonic analysis sense these results are related to theorems of katznelson tzafriri type which give conditions guaranteeing that inf t s t t f t vanishes

zero sum stochastic games in borel spaces average payoff criteria this paper is concerned with two person zero sum dynamic stochastic games in borel spaces with possibly unbounded payoff function and several average or ergodic payoff criteria we give conditions under which the long run expected average payoff criterion the sample path average criterion the existence of solutions to the average payoff shapley equations and a certain martingale condition are all equivalent

robust markov control processes abstract we examine the average minimax control problem on a general state space with an unbounded cost function the controller is uncertain about his model in the sense that he deals with a range of alternative models as possibly true the aim of this paper is to establish the optimality inequality and to provide a minimax strategy for the controller a new feature in our approach is an application of a generalised tauberian relation that in turn allows us to impose relatively weak assumptions

a matrix method of basic belief assignment s negation in dempster shafer theory negation is a new perspective to represent knowledge the negation of probability distribution has been proposed and it has a lot of interesting properties which can reach a maximum entropy because of the defects of the classical probability theory in the expression of uncertainty the basic belief assignment bba in the dempster shafer theory d s theory are widely used in decision theory thus negation provides a new perspective for d s theory to measure fuzziness in this paper a new definition of negation of bba is presented in the proposed negation bbas are represented as vectors and negation is realized by matrix operators this method has a good interpretation of the matrix operators and has the merit of simplifying the problem with several different definitions of entropy to determinate the uncertainty of bba the proposed negation of bba can reach a maximum belief entropy when the entropies satisfy a certain property

on the estimation of independent binomial random variables using occurrence and sequential information we re visit the age old problem of estimating the parameters of a distribution from its observations traditionally scientists and statisticians have attempted to obtain strong estimates by extracting the information contained in the observations taken as a set however generally speaking the information contained in the sequence in which the observations have appeared has been ignored i e except to consider dependence information as in the case of markov models and n gram statistics in this paper we present results which to the best of our knowledge are the first reported results which consider how estimation can be enhanced by utilizing both the information in the observations and in their sequence of appearance the strategy known as sequence based estimation sbe works as follows we first quickly allude to the results pertaining to computing the maximum likelihood estimates mle of the data when the samples are taken individually we then derive the corresponding mle results when the samples are taken two at a time and then extend these for the cases when they are processed three at a time four at a time etc in each case we also experimentally demonstrate the convergence of the corresponding estimates we then suggest various avenues for future research including those by which these estimates can be fused to yield a superior overall cumulative estimate of the parameter of the distribution in pattern recognition pr and in other internet and compression applications we believe that our new estimates have great potential for practitioners especially when the cardinality of the observation set is small

necessary and sufficient conditions for a bounded solution to the optimality equation in average reward markov decision chains abstract we consider average reward markov decision processes with discrete time parameter and denumerable state space we are concerned with the following problem find necessary and sufficient conditions so that for arbitrary bounded reward function the corresponding average reward optimality equation has a bounded solution this problem is solved for a class of systems including the case in which under the action of any stationary policy the state space is an irreducible positive recurrent class

on the structure of contraction operators ii soit 7b h un espace de hilbert complexe separable de dimension infinie et 7b l 7b h l algebre de tous les operateurs lineaires bornes sur 7b h soit d le disque unite ouvert dans c d et n est l ensemble des entiers positifs il existe r 6 tel que chaque contraction t dans 7b l 7b h avec c t soit a un sous espace hyperinvariant non trivial soit appartient a la classe a 1 r

control of markov chains with long run average cost criterion the dynamic programming equations the long run average cost control problem for discrete time markov chains on a countable state space is studied in a very general framework necessary and sufficient conditions for optimality in terms of the dynamic programming equations are given when an optimal stable stationary strategy is known to exist e g for the situations studied in stochastic differential systems stochastic control theory and applications ima vol math app 10 springer verlag new york berlin 1988 pp 57 77 a characterization of the desired solution of the dynamic programming equations is given in a special case also included is a novel convex analytic argument for deducing the existence of an optimal stable stationary strategy when that of a randomized one is known

ssc a classifier combination method based on signal strength we propose a new classifier combination method the signal strength based combining ssc approach to combine the outputs of multiple classifiers to support the decision making process in classification tasks as ensemble learning methods have attracted growing attention from both academia and industry recently it is critical to understand the fundamental issues of the combining rule motivated by the signal strength concept our proposed ssc algorithm can effectively integrate the individual vote from different classifiers in an ensemble learning system comparative studies of our method with nine major existing combining rules namely geometric average rule arithmetic average rule median value rule majority voting rule borda count max and min rule weighted average and weighted majority voting rules is presented furthermore we also discuss the relationship of the proposed method with respect to margin based classifiers including the boosting method adaboost m1 and adaboost m2 and support vector machines by margin analysis detailed analyses of margin distribution graphs are presented to discuss the characteristics of the proposed method simulation results for various real world datasets illustrate the effectiveness of the proposed method

average optimality in dynamic programming on borel spaces unbounded costs and controls abstract we show the existence of average cost optimal stationary policies in a class of discrete time markov control processes with borel state space unbounded costs and non compact control sets

average cost markov decision processes with weakly continuous transition probabilities this paper presents sufficient conditions for the existence of stationary optimal policies for average cost markov decision processes with borel state and action sets and weakly continuous transition probabilities the one step cost functions may be unbounded and the action sets may be noncompact the main contributions of this paper are i general sufficient conditions for the existence of stationary discount optimal and average cost optimal policies and descriptions of properties of value functions and sets of optimal actions ii a sufficient condition for the average cost optimality of a stationary policy in the form of optimality inequalities and iii approximations of average cost optimal actions by discount optimal actions

anti bayesian parametric pattern classification using order statistics criteria for some members of the exponential family this paper submits a comprehensive report of the use of order statistics os for parametric pattern recognition pr for various distributions within the exponential family although the field of parametric pr has been thoroughly studied for over five decades the use of the os of the distributions to achieve this has not been reported the pioneering work on using os for classification was presented earlier for the uniform distribution and for some members of the exponential family where it was shown that optimal pr can be achieved in a counter intuitive manner diametrically opposed to the bayesian paradigm i e by comparing the testing sample to a few samples distant from the mean apart from the results for the gaussian and doubly exponential which are merely cited here our new results include the rayleigh gamma and certain beta distributions the new scheme referred to as classification by moments of order statistics cmos has an accuracy that attains bayes bound for symmetric distributions and is otherwise very close to the optimal bayes bound as has been shown both theoretically and by rigorous experimental testing the results here also give a theoretical foundation for the families of border identification bi algorithms reported in the literature highlights we present the results concerning anti bayesian optimal pr for the exponential family these new techniques use order statistics os criteria in classification these results have been proven for symmetric and asymmetric distributions the experimental results justify the claims

a counterexample on the optimality equation in markov decision chains with the average cost criterion abstract we consider markov decision processes with denumerable state space and finite control sets the performance index of a control policy is a long run expected average cost criterion and the cost function is bounded below for these models the existence of average optimal stationary policies was recently established in 11 under very general assumptions such a result was obtained via an optimality inequality here we use a simple example to prove that the conditions in 11 do not imply the existence of a solution to the average cost optimality equation

a multiplicative formula for aggregating probability assessments this paper presents an axiomatic approach to the problem of aggregating expert assessments of an event s probability into some group probability assessment a multiplicative formula is derived

solutions of the average cost optimality equation for markov decision processes with weakly continuous kernel the fixed point approach revisited abstract this paper shows the existence of lower semicontinuous solutions of the average cost optimality equation for markov decision processes with borel spaces possible unbounded cost function and weakly continuous transition kernel this is done imposing a growth condition on the cost function a lyapunov stability condition on the transition kernel and a set of standard compactness continuity conditions the solution of the average cost optimality equation is obtained by means of the banach fixed point theorem

on power bounded operators abstract the main result asserts that for any contraction t on an arbitrary banach space x t n t n 1 0 as n if and only if the spectrum of t has no points on the unit circle except perhaps z 1 this theorem is extended for t t n where is a function of spectral synthesis on the unit circle as an application we generalize the so called zero two law of ornstein and sucheston and zaharopol to positive contraction on a very large class of banach lattices

double bagging combining classifiers by bootstrap aggregation the combination of classifiers leads to substantial reduction of misclassification error in a wide range of applications and benchmark problems we suggest using an out of bag sample for combining different classifiers in our setup a linear discriminant analysis is performed using the observations in the out of bag sample and the corresponding discriminant variables computed for the observations in the bootstrap sample are used as additional predictors for a classification tree two classifiers are combined and therefore method and variable selection bias is no problem for the corresponding estimate of misclassification error the need of an additional test sample disappears moreover the procedure performs comparable to the best classifiers used in a number of artificial examples and applications

a note on optimality conditions for continuous time markov decision processes with average cost criterion this note deals with continuous time markov decision processes with a denumerable state space and the average cost criterion the transition rates are allowed to be unbounded and the action set is a borel space we give a new set of conditions under which the existence of optimal stationary policies is ensured by using the optimality inequality our results are illustrated with a controlled queueing model moreover we use an example to show that our conditions do not imply the existence of a solution to the optimality equations in the previous literature

examples concerning abel and cesaro limits abstract this note describes examples of all possible equality and strict inequality relations between upper and lower abel and cesaro limits of sequences bounded above or below it also provides applications to markov decision processes

overtaking and almost sure optimality for infinite horizon markov decision processes we consider infinite horizon optimal control of markov chains on complete metric spaces we employ the overtaking optimality criterion which is either applied to the expected cost flow or to the individual sample paths yielding almost sure optimality results we use the existence of a solution pair to the optimality equation l x to establish and characterize optimal strategies for finite state spaces we derive sufficient as well as necessary conditions for overtaking optimality

order statistics based parametric classification for multi dimensional distributions traditionally in the field of pattern recognition pr the moments of the class conditional densities of the respective classes have been used to perform classification however the use of phenomena that utilized the properties of the order statistics os were not reported recently in 10 8 we proposed a new paradigm named cmos classification by the moments of order statistics which specifically used these quantifiers it is fascinating that cmos is essentially anti bayesian in its nature because the classification is performed in a counter intuitive manner i e by comparing the testing sample to a few samples distant from the mean as opposed to the bayesian approach in which the task is based on the central points of the distributions in our initial works we proposed the foundational theory of cmos for the uni dimensional uniform and some other distributions these results were extended for various symmetric and asymmetric uni dimensional distributions within the exponential family in 8 in this paper we generalize these results for multi dimensional distributions the multi dimensional generalization is particularly non trivial because there is no well established method for achieving the ordering of multi dimensional data specified in terms of its uni dimensional components the strategy is analogous to a naive bayes approach although it really is of an anti naive bayes paradigm we provide here the analytical and experimental results for the 2 dimensional uniform doubly exponential and gaussian distributions and also clearly specify the way by which one should extend the results for higher dimensions the analogous results for the other distributions in the exponential family which were discussed in 10 8 are alluded to but omitted to avoid repetition

singular inner functions and biinvariant subspaces for dissymetric weighted shifts abstract we consider dissymetric weights on z i e nonincreasing unbounded weights z 1 such that n 1 for n 0 and such that lim n n 1 n 1 where n sup p z n p p a dissymetric weight is said to be quasianalytic if n log n n 2 denote by the unit circle and by d the open unit disc set l 2 f l 2 f n z f n 2 2 n 1 2 we identify the usual hardy space h 2 d to the set f l 2 f n 0 n s f e it e it f e it the usual shift on l 2 if u is a singular inner function denote by e u the closure of span s n u n z in l 2 we show that if is a dissymetric weight such that log n n n then e u is a proper subspace of l 2 for every singular inner function u also if is any dissymetric weight then there exists some singular inner function u such that e u is a proper subspace of l 2 so that s always has nontrivial biinvariant subspaces no nontrivial biinvariant subspaces of s were known so far in the quasianalytic case

the fundamental theory of optimal anti bayesian parametric pattern classification using order statistics criteria the gold standard for a classifier is the condition of optimality attained by the bayesian classifier within a bayesian paradigm if we are allowed to compare the testing sample with only a single point in the feature space from each class the optimal bayesian strategy would be to achieve this based on the mahalanobis distance from the corresponding means the reader should observe that in this context the mean in one sense is the most central point in the respective distribution in this paper we shall show that we can obtain optimal results by operating in a diametrically opposite way i e a so called anti bayesian manner indeed we assert a completely counter intuitive result that by working with a very few points distant from the mean one can obtain remarkable classification accuracies the number of points can sometimes be as small as two further if these points are determined by the order statistics of the distributions the accuracy of our method referred to as classification by moments of order statistics cmos attains the optimal bayes bound this claim which is totally counter intuitive has been proven for many uni dimensional and some multi dimensional distributions within the exponential family and the theoretical results have been verified by rigorous experimental testing apart from the fact that these results are quite fascinating and pioneering in their own right they also give a theoretical foundation for the families of border identification bi algorithms reported in the literature

weak conditions for average optimality in markov control processes abstract in this paper we study the existence of average cost optimal policies for markov control processes on borel spaces and with possibly unbounded costs and controls under assumptions weaker than those used in the previous literature we show that the optimality inequality holds everywhere and that there exists a stationary policy which is optimal whenever the initial state lies in a possibly proper subset of the state space this is in contrast to previous works where an implicit unichain assumption ensures optimality for all initial states

the existence of minimum pair of state and policy for markov decision processes under the hypothesis of doeblin this paper studies the average cost markov decision process with compact state and action spaces and bounded lower semicontinuous cost functions following the idea of borkar s excellent papers siamj control optim 21 1983 pp 652 666 22 1984 pp 965 978 the general case where irreducibility is not assumed is considered under the hypothesis of doeblin and the existence of a minimum pair of state and policy which attains the infimum of the average expected cost over all initial states and policies is established further it is proved that under additional weak conditions there exists an optimal stationary policy in the usual sense

optimal stationary policies in general state space markov decision chains with finite action sets the result of sennott 9 on the existence of optimal stationary policies in countable state markov decision chains with finite action sets is generalized to arbitrary state space markov decision chains the assumption of finite action sets occurring in a global countable action space allows a particularly simple theoretical structure for the general state space markov decision chain two examples illustrate the results example 1 is a system of parallel queues with stochastic work requirements a movable server with controllable service rate and a reject option example 2 is a system of parallel queues with stochastic controllable inputs a movable server with fixed service rates and a reject option

average control of markov decision processes with feller transition probabilities and general action spaces abstract this paper studies the average control problem of discrete time markov decision processes mdps for short with general state space feller transition probabilities and possibly non compact control constraint sets a x two hypotheses are considered either the cost function c is strictly unbounded or the multifunctions a r x a a x c x a r are upper semicontinuous and compact valued for each real r for these two cases we provide new results for the existence of a solution to the average cost optimality equality and inequality using the vanishing discount approach we also study the convergence of the policy iteration approach under these conditions it should be pointed out that we do not make any assumptions regarding the convergence and the continuity of the limit function generated by the sequence of relative difference of the discounted value functions and the poisson equations as often encountered in the literature

svm fuzcoc a novel svm based feature selection method using a fuzzy complementary criterion an efficient filter feature selection fs method is proposed in this paper the svm fuzcoc approach achieving a satisfactory trade off between classification accuracy and dimensionality reduction additionally the method has reasonably low computational requirements even in high dimensional feature spaces to assess the quality of features we introduce a local fuzzy evaluation measure with respect to patterns that embraces fuzzy membership degrees of every pattern in their classes accordingly the above measure reveals the adequacy of data coverage provided by each feature the required membership grades are determined via a novel fuzzy output kernel based support vector machine applied on single features based on a fuzzy complementary criterion fuzcoc the fs procedure iteratively selects features with maximum additional contribution in regard to the information content provided by previously selected features this search strategy leads to small subsets of powerful and complementary features alleviating the feature redundancy problem we also devise different svm fuzcoc variants by employing seven other methods to derive fuzzy degrees from svm outputs based on probabilistic or fuzzy criteria our method is compared with a set of existing fs methods in terms of performance capability dimensionality reduction and computational speed via a comprehensive experimental setup including synthetic and real world datasets

decision templates for multiple classifier fusion an experimental comparison abstract multiple classifier fusion may generate more accurate classification than each of the constituent classifiers fusion is often based on fixed combination rules like the product and average only under strict probabilistic conditions can these rules be justified we present here a simple rule for adapting the class combiner to the application c decision templates one per class are estimated with the same training set that is used for the set of classifiers these templates are then matched to the decision profile of new incoming objects by some similarity measure we compare 11 versions of our model with 14 other techniques for classifier fusion on the satimage and phoneme datasets from the database elena our results show that decision templates based on integral type measures of similarity are superior to the other schemes on both data sets