k polystability of q fano varieties admitting kahler einstein metrics it is shown that any possibly singular fano variety x admitting a kahler einstein metric is k polystable thus confirming one direction of the yau tian donaldson conjecture in the setting of mathbb q fano varieties equipped with their anti canonical polarization the proof is based on a new formula expressing the donaldson futaki invariants in terms of the slope of the ding functional along a geodesic ray in the space of all bounded positively curved metrics on the anti canonical line bundle of x one consequence is that a toric fano variety x is k polystable iff it is k polystable along toric degenerations iff 0 is the barycenter of the canonical weight polytope p associated to x the results also extend to the logarithmic setting and in particular to the setting of kahler einstein metrics with edge cone singularities applications to geodesic stability bounds on the ricci potential and perelman s lambda entropy functional on k unstable fano manifolds are also given

global stabilization for a class of switched nonlinear feedforward systems abstract the problem of global stabilization for a class of switched nonlinear feedforward systems under arbitrary switchings is investigated in this paper based on the integrator forwarding technique and the common lyapunov function method we design bounded state feedback controllers of individual subsystems to guarantee asymptotic stability of the closed loop system a common coordinate transformation of all subsystems is exploited to avoid individual coordinate transformations for subsystems that are required when applying the forwarding recursive design scheme an example is provided to demonstrate the effectiveness of the proposed design method

openness results for uniform k stability assume that a projective variety together with a polarization is uniformly k stable if the polarization is canonical or anti canonical then the projective variety is uniformly k stable with respects to any polarization sufficiently close to the original polarization

ideal spatial adaptation by wavelet shrinkage summary with ideal spatial adaptation an oracle furnishes information about how best to adapt a spatially variable estimator whether piecewise constant piecewise polynomial variable knot spline or variable bandwidth kernel to the unknown function estimation with the aid of an oracle offers dramatic advantages over traditional linear estimation by nonadaptive kernels however it is a priori unclear whether such performance can be obtained by a procedure relying on the data alone we describe a new principle for spatially adaptive estimation selective wavelet reconstruction we show that variable knot spline fits and piecewise polynomial fits when equipped with an oracle to select the knots are not dramatically more powerful than selective wavelet reconstruction with an oracle we develop a practical spatially adaptive method riskshrink which works by shrinkage of empirical wavelet coefficients riskshrink mimics the performance of an oracle for selective wavelet reconstruction as well as it is possible to do so a new inequality in multivariate normal decision theory which we call the oracle inequality shows that attained performance differs from ideal performance by at most a factor of approximately 2 log n where n is the sample size moreover no estimator can give a better guarantee than this within the class of spatially adaptive procedures riskshrink is essentially optimal relying only on the data it comes within a factor log 2 n of the performance of piecewise polynomial and variableknot spline methods equipped with an oracle in contrast it is unknown how or if piecewise polynomial methods could be made to function this well when denied access to an oracle and forced to rely on data alone

large scale multiple kernel learning while classical kernel based learning algorithms are based on a single kernel in practice it is often desirable to use multiple kernels lanckriet et al 2004 considered conic combinations of kernel matrices for classification leading to a convex quadratically constrained quadratic program we show that it can be rewritten as a semi infinite linear program that can be efficiently solved by recycling the standard svm implementations moreover we generalize the formulation and our method to a larger class of problems including regression and one class classification experimental results show that the proposed algorithm works for hundred thousands of examples or hundreds of kernels to be combined and helps for automatic model selection improving the interpretability of the learning result in a second part we discuss general speed up mechanism for svms especially when used with sparse feature maps as appear for string kernels allowing us to train a string kernel svm on a 10 million real world splice data set from computational biology we integrated multiple kernel learning in our machine learning toolbox shogun for which the source code is publicly available at http www fml tuebingen mpg de raetsch projects shogun

data driven rank breaking for efficient rank aggregation rank aggregation systems collect ordinal preferences from individuals to produce a global ranking that represents the social preference rank breaking is a common practice to reduce the computational complexity of learning the global ranking the individual preferences are broken into pairwise comparisons and applied to efficient algorithms tailored for independent paired comparisons however due to the ignored dependencies in the data naive rank breaking approaches can result in inconsistent estimates the key idea to produce accurate and consistent estimates is to treat the pairwise comparisons unequally depending on the topology of the collected data in this paper we provide the optimal rank breaking estimator which not only achieves consistency but also achieves the best error bound this allows us to characterize the fundamental tradeoff between accuracy and complexity further the analysis identies how the accuracy depends on the spectral gap of a corresponding comparison graph

the ubiquitous kronecker product abstract the kronecker product has a rich and very pleasing algebra that supports a wide range of fast elegant and practical algorithms several trends in scientific computing suggest that this important matrix operation will have an increasingly greater role to play in the future first the application areas where kronecker products abound are all thriving these include signal processing image processing semidefinite programming and quantum computing second sparse factorizations and kronecker products are proving to be a very effective way to look at fast linear transforms researchers have taken the kronecker methodology as developed for the fast fourier transform and used it to build exciting alternatives third as computers get more powerful researchers are more willing to entertain problems of high dimension and this leads to kronecker products whenever low dimension techniques are tensored together

a markov chain approximation to choice modeling assortment planning is an important problem that arises in many industries such as retailing and airlines one of the key challenges in an assortment planning problem is to identify the right model for the substitution behavior of customers from the data error in model selection can lead to highly suboptimal decisions in this paper we consider a markov chain based choice model and show that it provides a simultaneous approximation for all random utility based discrete choice models including the multinomial logit mnl the probit the nested logit and mixtures of multinomial logit models in the markov chain model substitution from one product to another is modeled as a state transition in the markov chain we show that the choice probabilities computed by the markov chain based model are a good approximation to the true choice probabilities for any random utility based choice model under mild conditions moreover they are exact if the underlying model is a generalized attraction model gam of wh

fast fourier transforms for symmetric groups theory and implementation recently it has been proved that a fourier transform for the symmetric group s based on young s seminormal form can be evaluated in less than 0 5 n3 n2 n arithmetic operations we look at this algorithm in more detail and show that it allows an efficient software implementation using appropriate data structures we also describe a similarly efficient algorithm for the inverse fourier transform we compare the time and memory requirements of our program to those of other existing implementations

an extended mallows model for ranked data aggregation in this article we study the rank aggregation problem which aims to find a consensus ranking by aggregating multiple ranking lists to address the problem probabilistically we formulate an elabo

quadratic stability of a class of switched nonlinear systems quadratic stability of a class of switched nonlinear systems is studied in this note we first transform quadratic stability problem into an equivalent nonlinear programming problem then we derive a necessary and sufficient condition for quadratic stability of this class of switched systems by using karush kuhn tucker condition for nonlinear programming problems the necessary and sufficient condition is given in terms of the strict completeness of a certain set of functions on a subset of the state space which is much easier to check

multivariate spearman s ρ for aggregating ranks using copulas we study the problem of rank aggregation given a set of ranked lists we want to form a consensus ranking furthermore we consider the case of extreme lists i e only the rank of the best or worst elements are known we impute missing ranks and generalise spearman s to extreme ranks our main contribution is the derivation of a non parametric estimator for rank aggregation based on multivariate extensions of spearman s which measures correlation between a set of ranked lists multivariate spearman s is defined using copulas and we show that the geometric mean of normalised ranks maximises multivariate correlation motivated by this we propose a weighted geometric mean approach for learning to rank which has a closed form least squares solution when only the best top k or worst bottom k elements of a ranked list are known we impute the missing ranks by the average value allowing us to apply spearman s we discuss an optimistic and pessimistic imputation of missing values which respectively maximise and minimise correlation and show its effect on aggregating university rankings finally we demonstrate good performance on the rank aggregation benchmarks mq2007 and mq2008

multistage ranking models abstract suppose that a sample of people independently examines a fixed set of k items and then ranks these items according to personal judgment the process of ranking the items is decomposed into k 1 stages in the forward model the most preferred item is selected at the first stage the best of the remaining items is selected at the second stage and so on until the least preferred item is selected by default various probability models are adopted at each stage and properties of the resulting models for randomly sampled rankings are investigated luce 1959 first proposed such a modeling scheme where each item i was thought to have an intrinsic value i and the probability of choosing a particular item i at any stage conditional on the set s of items not previously chosen was given by i i s i j s j where i is an indicator function plackett 1975 began with the same model but added interaction terms that would theoretically extend the usefulness of this approach when the basic m

scalar curvature and stability of toric varieties we define a stability condition for a polarised algebraic variety and state a conjecture relating this to the existence of a kahler metric of constant scalar curvature the main result of the paper goes some way towards verifying this conjecture in the case of toric surfaces we prove that under the stability hypothesis the mabuchi functional is bounded below on invariant metrics and that minimising sequences have a certain convergence property in the reverse direction we give new examples of polarised surfaces which do not admit metrics of constant scalar curvature the proofs use a general framework developed by guillemin and abreu in which invariant kahler metrics correspond to convex functions on the moment polytope of a toric variety this paper is a step towards the solution of the general problem of finding conditions under which a complex projective variety admits a kahler metric of constant scalar curvature the pattern of the answer one expects is that this differential geometric condition should be equivalent to some notion of stability in the sense of geometric invariant theory this expectation is probably now an item of folklore going back to suggestions put forward by yau in the case of kahlereinstein metrics and the many results of tian and others in this case reinforced by a detailed formal picture which makes clear the analogy with the well established relation between the stability of vector bundles and yang mills connections 5 here we begin the investigation of

robust fuzzy control of nonlinear systems with parametric uncertainties addresses the robust fuzzy control problem for nonlinear systems in the presence of parametric uncertainties the takagi sugeno t s fuzzy model is adopted for fuzzy modeling of the nonlinear system two cases of the t s fuzzy system with parametric uncertainties both continuous time and discrete time cases are considered in both continuous time and discrete time cases sufficient conditions are derived for robust stabilization in the sense of lyapunov asymptotic stability for the t s fuzzy system with parametric uncertainties the sufficient conditions are formulated in the format of linear matrix inequalities the t s fuzzy model of the chaotic lorenz system which has complex nonlinearity is developed as a test bed the effectiveness of the proposed controller design methodology is finally demonstrated through numerical simulations on the chaotic lorenz system

a nonparametric clustering algorithm with a quantile based likelihood estimator clustering is a representative of unsupervised learning and one of the important approaches in exploratory data analysis by its very nature clustering without strong assumption on data distribution is desirable information theoretic clustering is a class of clustering methods that optimize information theoretic quantities such as entropy and mutual information these quantities can be estimated in a nonparametric manner and information theoretic clustering algorithms are capable of capturing various intrinsic data structures it is also possible to estimate information theoretic quantities using a data set with sampling weight for each datum assuming the data set is sampled from a certain cluster and assigning different sampling weights depending on the clusters the cluster conditional information theoretic quantities are estimated in this letter a simple iterative clustering algorithm is proposed based on a nonparametric estimator of the log likelihood for weighted data sets the clustering algorithm is also derived from the principle of conditional entropy minimization with maximum entropy regularization the proposed algorithm does not contain a tuning parameter the algorithm is experimentally shown to be comparable to or outperform conventional nonparametric clustering methods

least squares quantization in pcm it has long been realized that in pulse code modulation pcm with a given ensemble of signals to handle the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall it has been shown by panter and dite that in the limit as the number of quanta becomes infinite the asymptotic fractional density of quanta per unit voltage should vary as the one third power of the probability density per unit voltage of signal amplitudes in this paper the corresponding result for any finite number of quanta is derived that is necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy the optimization criterion used is that the average quantization noise power be a minimum it is shown that the result obtained here goes over into the panter and dite result as the number of quanta become large the optimum quautization schemes for 2 b quanta b 1 2 cdots 7 are given numerically for gaussian and for laplacian distribution of signal amplitudes

on stability l2 gain and h control for switched systems this paper addresses the issues of stability l 2 gain analysis and h control for switched systems via multiple lyapunov function methods a concept of general lyapunov like functions is presented a necessary and sufficient condition for stability of switched systems is given in terms of multiple generalized lyapunov like functions which enables derivation of improved stability tests an l 2 gain characterization and a design method for stabilizing switching laws a solution to the h control problem for switched systems is also provided

aggregating inconsistent information ranking and clustering we address optimization problems in which we are given contradictory pieces of input information and the goal is to find a globally consistent solution that minimizes the extent of disagreement with the respective inputs specifically the problems we address are rank aggregation the feedback arc set problem on tournaments and correlation and consensus clustering we show that for all these problems and various weighted versions of them we can obtain improved approximation factors using essentially the same remarkably simple algorithm additionally we almost settle a long standing conjecture of bang jensen and thomassen and show that unless np bpp there is no polynomial time algorithm for the problem of minimum feedback arc set in tournaments

mercer kernel based clustering in feature space the article presents a method for both the unsupervised partitioning of a sample of data and the estimation of the possible number of inherent clusters which generate the data this work exploits the notion that performing a nonlinear data transformation into some high dimensional feature space increases the probability of the linear separability of the patterns within the transformed space and therefore simplifies the associated data structure it is shown that the eigenvectors of a kernel matrix which defines the implicit mapping provides a means to estimate the number of clusters inherent within the data and a computationally simple iterative procedure is presented for the subsequent feature space partitioning of the data

birational superrigidity and k stability of fano complete intersections of index 1 we prove that every smooth fano complete intersection of index 1 and codimension r in pn r is birationally superrigid and k stable if n 10r we also propose a generalization of tian s criterion of k stability and as an application prove the k stability of the complete intersection of a quadric and a cubic in p5 in the appendix written jointly with c stibitz we prove the conditional birational superrigidity of fano complete intersections of higher index in large dimension

classification by pairwise coupling we discuss a strategy for polychotomous classification that involves estimating class probabilities for each pair of classes and then coupling the estimates together the coupling model is similar to the bradley terry method for paired comparisons we study the nature of the class probability estimates that arise and examine the performance of the procedure in real and simulated data sets classifiers used include linear discriminants nearest neighbors adaptive nonlinear methods and the support vector machine

an approach to fuzzy control of nonlinear systems stability and design issues presents a design methodology for stabilization of a class of nonlinear systems first the authors represent a nonlinear plant with a takagi sugeno fuzzy model then a model based fuzzy controller design utilizing the concept of the so called parallel distributed compensation is employed the main idea of the controller design is to derive each control rule so as to compensate each rule of a fuzzy system the design procedure is conceptually simple and natural moreover the stability analysis and control design problems can be reduced to linear matrix inequality lmi problems therefore they can be solved efficiently in practice by convex programming techniques for lmis the design methodology is illustrated by application to the problem of balancing and swing up of an inverted pendulum on a cart

stability analysis and state feedback control of continuous time t s fuzzy systems via anew switched fuzzy lyapunov function approach this paper deals with stability analysis and control design problems for continuous time takagi sugeno t s fuzzy systems first a new membership function dependent switching law is proposed and a relaxation parameter is introduced into this switching law to guarantee a minimal dwell time between two consecutive switching compared to the existing methods the most important point is that with the help of the dwell time the discretized lyapunov function dlf technique can be adopted then a new stability criterion of the t s fuzzy system with less conservatism is derived based on a fuzzy discretized lyapunov function fdlf second to estimate the domain of attraction da an algorithm with less iteration steps is proposed based on the proposed switching method sufficient conditions for existence of the state feedback controllers are presented via the switched non parallel distributed compensation non pdc scheme the effectiveness of the proposed method is illustrated through three simulation examples

kahler einstein metrics and volume minimization abstract we prove that if a polarized q fano variety admits a kahler einstein metric then the normalized volume functional over the associated affine cone is globally minimized at the canonical divisorial valuation obtained by blowing up the vertex this is also generalized to the logarithmic and the orbifold settings a refinement of this result together with the result in 41 gives an equivalent characterization of k semistability for any smooth fano manifold we also prove that the valuation associated to the reeb vector field of a smooth sasaki einstein metric minimizes the normalized volume over the corresponding kahler cone these results strengthen and generalize the minimization result of martelli sparks yau

a survey of kernel and spectral methods for clustering clustering algorithms are a useful tool to explore data structures and have been employed in many disciplines the focus of this paper is the partitioning clustering problem with a special interest in two recent approaches kernel and spectral methods the aim of this paper is to present a survey of kernel and spectral clustering methods two approaches able to produce nonlinear separating hypersurfaces between clusters the presented kernel clustering methods are the kernel version of many classical clustering algorithms e g k means som and neural gas spectral clustering arise from concepts in spectral graph theory and the clustering problem is configured as a graph cut problem where an appropriate objective function has to be optimized an explicit proof of the fact that these two paradigms have the same objective is reported since it has been proven that these two seemingly different approaches have the same mathematical foundation besides fuzzy kernel clustering methods are presented as extensions of kernel k means clustering algorithm

the kendall and mallows kernels for permutations we show that the widely used kendall tau correlation coefficient and the related mallows kernel are positive definite kernels for permutations they offer computationally attractive alternatives to more complex kernels on the symmetric group to learn from rankings or learn to rank we show how to extend these kernels to partial rankings multivariate rankings and uncertain rankings examples are presented on how to formulate typical problems of learning from rankings such that they can be solved with state of the art kernel algorithms we demonstrate promising results on clustering heterogeneous rank data and high dimensional classification problems in biomedical applications

a signal processing approach to fourier analysis of ranking data the importance of phase ranking data is a type of data obtained in some elections in customer surveys as well as from web search results such data may be considered as a type of signal defined on the group of permutations of n objects denoted sn there exists a fourier transform for sn obtained from group representation theory which is well known in the mathematics literature however previous work has not approached the transform from a signal processing perspective in particular there is no discussion of what constitutes magnitude and phase nor any analysis of what phase information might tell us beyond a well known connection to group translation this paper explores the properties of the phase spectrum of ranking data in particular a novel contribution is the formulation of the bispectrum for ranking data which may be used for studying phase linearity analysis of two well known ranking data sets shows that they are surprisingly well fit by linear phase approximations

an efficient implementation of reid s multiple hypothesis tracking algorithm and its evaluation for the purpose of visual tracking an efficient implementation of reid s multiple hypothesis tracking mht algorithm is presented in which the k best hypotheses are determined in polynomial time using an algorithm due to murly 1968 the mht algorithm is then applied to several motion sequences the mht capabilities of track initiation termination and continuation are demonstrated together with the latter s capability to provide low level support of temporary occlusion of tracks between 50 and 150 corner features are simultaneously tracked in the image plane over a sequence of up to 51 frames each corner is tracked using a simple linear kalman filter and any data association uncertainty is resolved by the mht kalman filter parameter estimation is discussed and experimental results show that the algorithm is robust to errors in the motion model an investigation of the performance of the algorithm as a function of look ahead tree depth indicates that high accuracy can be obtained for tree depths as shallow as three experimental results suggest that a real time mht solution to the motion correspondence problem is possible for certain classes of scenes

the efficient computation of fourier transforms on the symmetric group this paper introduces new techniques for the efficient computation of fourier transforms on symmetric groups and their homogeneous spaces we replace the matrix multiplications in clausen s algorithm with sums indexed by combinatorial objects that generalize young tableaux and write the result in a form similar to horner s rule the algorithm we obtain computes the fourier transform of a function on s n in no more than 3 4n n 1 s n multiplications and the same number of additions analysis of our algorithm leads to several combinatorial problems that generalize path counting we prove corresponding results for inverse transforms and transforms on homogeneous spaces

k stability of constant scalar curvature kahler manifolds abstract we show that a polarised manifold with a constant scalar curvature kahler metric and discrete automorphisms is k stable this refines the k semistability proved by s k donaldson

a grouped ranking model for item preference parameter given a set of rating data for a set of items determining preference levels of items is a matter of importance various probability models have been proposed to solve this task one such model is the plackett luce model which parameterizes the preference level of each item by a real value in this letter the plackett luce model is generalized to cope with grouped ranking observations such as movie or restaurant ratings since it is difficult to maximize the likelihood of the proposed model directly a feasible approximation is derived and the em algorithm is adopted to find the model parameter by maximizing the approximate likelihood which is easily evaluated the proposed model is extended to a mixture model and two applications are proposed to show the effectiveness of the proposed model numerical experiments with real world data are carried out

thresholds valuations and k stability abstract let x be a normal complex projective variety with at worst klt singularities and l a big line bundle on x we use valuations to study the log canonical threshold of l as well as another invariant the stability threshold the latter generalizes a notion by fujita and odaka and can be used to characterize when a q fano variety is k semistable or uniformly k stable it can also be used to generalize volume bounds due to fujita and liu the two thresholds can be written as infima of certain functionals on the space of valuations on x when l is ample we prove that these infima are attained in the toric case toric valuations achieve these infima and we obtain simple expressions for the two thresholds in terms of the moment polytope of l

the repeated insertion model for rankings missing link between two subset choice models several probabilistic models for subset choice have been proposed in the literature for example to explain approval voting data we show that marley et al s latent scale model is subsumed by falmagne and regenwetter s size independent model in the sense that every choice probability distribution generated by the former can also be explained by the latter our proof relies on the construction of a probabilistic ranking model which we label the repeated insertion model this model is a special case of marden s orthogonal contrast model class and in turn includes the classical mallows model as a special case we explore its basic properties as well as its relationship to fligner and verducci s multistage ranking model

the state complexity of random dfas the state complexity of a deterministic finite state automaton dfa is the number of states in its minimal equivalent dfa we study the state complexity of random n state dfas over a k symbol alphabet drawn uniformly from the set n n k 2 n of all such automata we show that with high probability the latter is k n o n log n for a certain explicit constant k

bayesian decision process for cost efficient dynamic ranking via crowdsourcing rank aggregation based on pairwise comparisons over a set of items has a wide range of applications although considerable research has been devoted to the development of rank aggregation algorithms one basic question is how to efficiently collect a large amount of high quality pairwise comparisons for the ranking purpose because of the advent of many crowdsourcing services a crowd of workers are often hired to conduct pairwise comparisons with a small monetary reward for each pair they compare since different workers have different levels of reliability and different pairs have different levels of ambiguity it is desirable to wisely allocate the limited budget for comparisons among the pairs of items and workers so that the global ranking can be accurately inferred from the comparison results to this end we model the active sampling problem in crowdsourced ranking as a bayesian markov decision process which dynamically selects item pairs and workers to improve the ranking accuracy under a budget constraint we further develop a computationally efficient sampling policy based on knowledge gradient as well as a moment matching technique for posterior approximation experimental evaluations on both synthetic and real data show that the proposed policy achieves high ranking accuracy with a lower labeling cost

confidence intervals for population ranks in the presence of ties and near ties frequentist confidence intervals for population ranks and their statistical justifications are not well established even though there is a great need for such procedures in practice how do we assign confidence bounds for the ranks of health care facilities schools and financial institutions based on data that do not clearly separate the performance of different entities apart the commonly used bootstrap based frequentist confidence intervals and bayesian intervals for population ranks may not achieve the intended coverage probability in the frequentist sense especially in the presence of unknown ties or near ties among the populations to be ranked given random samples from k populations we propose confidence bounds for population ranking parameters and develop rigorous frequentist theory and nonstandard bootstrap inference for population ranks which allow ties and near ties in the process a notion of modified population rank is introduced that appears quite suitable for dealing with the popul

non parametric modeling of partially ranked data statistical models on full and partial rankings of n items are often of limited practical use for large n due to computational consideration we explore the use of non parametric models for partially ranked data and derive computationally ef cient procedures for their use for large n the derivations are largely possible through combinatorial and algebraic manipulations based on the lattice of partial rankings a bias variance analysis and an experimental study demonstrate the applicability of the proposed method

consistency of support vector machines and other regularized kernel classifiers it is shown that various classifiers that are based on minimization of a regularized risk are universally consistent i e they can asymptotically learn in every classification task the role of the loss functions used in these algorithms is considered in detail as an application of our general framework several types of support vector machines svms as well as regularization networks are treated our methods combine techniques from stochastics approximation theory and functional analysis

reductivity of the automorphism group of k polystable fano varieties we prove that k polystable log fano pairs have reductive automorphism groups in fact we deduce this statement by establishing more general results concerning the s completeness and theta reductivity of the moduli of k semistable log fano pairs assuming the conjecture that k semistability is an open condition we prove that the artin stack parametrizing k semistable fano varieties admits a separated good moduli space

using the bootstrap to quantify the authority of an empirical ranking the bootstrap is a popular and convenient method for quantifying the authority of an empirical ordering of attributes for example of a ranking of the performance of institutions or of the influence of genes on a response variable in the first of these examples the number p of quantities being ordered is sometimes only moderate in size in the second it can be very large often much greater than sample size however we show that in both types of problem the conventional bootstrap can produce inconsistency moreover the standard n out of n bootstrap estimator of the distribution of an empirical rank may not converge in the usual sense the estimator may converge in distribution but not in probability nevertheless in many cases the bootstrap correctly identifies the support of the asymptotic distribution of ranks in some contemporary problems bootstrap prediction intervals for ranks are particularly long and in this context we also quantify the accuracy of bootstrap methods showing that the standard bootstrap gets the order of magnitude of the interval right but not the constant multiplier of interval length the m out of n bootstrap can improve performance and produce statistical consistency but it requires empirical choice of m we suggest a tuning solution to this problem we show that in genomic examples where it might be expected that the standard synchronous bootstrap will successfully accommodate non independence of vector components that approach can produce misleading results an independent component bootstrap can overcome these difficulties even in cases where components are not strictly independent

moderate deviation based inference for random degeneration in paired rank lists consider a problem where n items objects or individuals are judged by assessors using their perceptions of a set of performance criteria or alternatively by technical devices in particular two assessors might rank the items between 1 and n on the basis of relative performance independently of each other we can aggregate the rank lists by assigning one if the two assessors agree and zero otherwise and we can modify this approach to make it robust against irregularities in this article we consider methods and algorithms that can be used to address this problem we study their theoretical properties in the case of a model based on nonstationary bernoulli trials and we report on their numerical properties for both simulated and real data

observer based robust fuzzy control of nonlinear systems with parametric uncertainties this paper addresses the robust fuzzy control problem for nonlinear systems in the presence of parametric uncertainties and the state variables unavailable for measurement the takagi sugeno t s fuzzy model system with parametric uncertainties is adopted for modeling the nonlinear system and establishing fuzzy state observer sufficient conditions are derived for robust stabilization in the sense of lyapunov asymptotic stability and are formulated in the format of linear matrix inequalities lmis the effectiveness of the proposed fuzzy controller and fuzzy observer design methodology is finally demonstrated through numerical simulations on an inverted pendulum system

fourier theoretic probabilistic inference over permutations permutations are ubiquitous in many real world problems such as voting ranking and data association representing uncertainty over permutations is challenging since there are n possibilities and typical compact and factorized probability distribution representations such as graphical models cannot capture the mutual exclusivity constraints associated with permutations in this paper we use the low frequency terms of a fourier decomposition to represent distributions over permutations compactly we present kronecker conditioning a novel approach for maintaining and updating these distributions directly in the fourier domain allowing for polynomial time bandlimited approximations low order fourier based approximations however may lead to functions that do not correspond to valid distributions to address this problem we present a quadratic program defined directly in the fourier domain for projecting the approximation onto a relaxation of the polytope of legal marginal distributions we demonstrate the effectiveness of our approach on a real camera based multi person tracking scenario

the p norm push a simple convex ranking algorithm that concentrates at the top of the list we are interested in supervised ranking algorithms that perform especially well near the top of the ranked list and are only required to perform sufficiently well on the rest of the list in this work we provide a general form of convex objective that gives high scoring examples more importance this push near the top of the list can be chosen arbitrarily large or small based on the preference of the user we choose lp norms to provide a specific type of push if the user sets p larger the objective concentrates harder on the top of the list we derive a generalization bound based on the p norm objective working around the natural asymmetry of the problem we then derive a boosting style algorithm for the problem of ranking with a push at the top the usefulness of the algorithm is illustrated through experiments on repository data we prove that the minimizer of the algorithm s objective is unique in a specific sense furthermore we illustrate how our objective is related to quality measurements for information retrieval

a generalized multiple lyapunov functions method based non fragile guaranteed cost control for uncertain switched fuzzy systems abstract this paper is concerned with a non fragile guaranteed cost control problem for a class of uncertain switched fuzzy systems which are described by switched takagi sugeno t s fuzzy models by employing the generalized multiple lyapunov functions method we present a sufficient condition to guarantee the closed loop system asymptotically stable and possess an upper bound of the non fragile guaranteed cost function meanwhile a non fragile state feedback control law and a switching law are designed moreover an optimization problem in which the minimal non fragile guaranteed cost can be obtained is solved finally a simulation example is given to verify the feasibility and effectiveness of the proposed method

modeling the variability of rankings for better or for worse rankings of institutions such as universities schools and hospitals play an important role today in conveying information about relative performance they inform policy decisions and budgets and are often reported in the media while overall rankings can vary markedly over relatively short time periods it is not unusual to find that the ranks of a small number of highly performing institutions remain fixed even when the data on which the rankings are based are extensively revised and even when a large number of new institutions are added to the competition in the present paper we endeavor to model this phenomenon in particular we interpret as a random variable the value of the attribute on which the ranking should ideally be based more precisely if p items are to be ranked then the true but unobserved attributes are taken to be values of p independent and identically distributed variates however each attribute value is observed only with noise and via a sample of size roughly equal to n say these noisy approximations to the true attributes are the quantities that are actually ranked we show that if the distribution of the true attributes is light tailed e g normal or exponential then the number of institutions whose ranking is correct even after recalculation using new data and even after many new institutions are added is essentially fixed formally p is taken to be of order n c for any fixed c 0 and the number of institutions whose ranking is reliable depends very little on p on the other hand cases where the number of reliable rankings increases significantly when new institutions are added are those for which the distribution of the true attributes is relatively heavy tailed for example with tails that decay like x for some 0 these properties and others are explored analytically under general conditions a numerical study links the results to outcomes for real data problems

wavelet shrinkage asymptopia much recent effort has sought asymptotically minimax methods for recovering infinite dimensional objects curves densities spectral densities images from noisy data a now rich and complex body of work develops nearly or exactly minimax estimators for an array of interesting problems unfortunately the results have rarely moved into practice for a variety of reasons among them being similarity to known methods computational intractability and lack of spatial adaptivity we discuss a method for curve estimation based on n noisy data translate the empirical wavelet coefficients towards the origin by an amount 2 log n n the proposal differs from those in current use is computationally practical and is spatially adaptive it thus avoids several of the previous objections further the method is nearly minimax both for a wide variety of loss functions pointwise error global error measured in l p norms pointwise and global error in estimation of derivatives and for a wide range of smoothness classes including standard holder and sobolev classes and bounded variation this is a much broader near optimality than anything previously proposed we draw loose parallels with near optimality in robustness and also with the broad near eigenfunction properties of wavelets themselves finally the theory underlying the method is interesting as it exploits a correspondence between statistical questions and questions of optimal recovery and information based complexity

seshadri constants diophantine approximation and roth s theorem for arbitrary varieties in this paper we associate an invariant alpha x l to an algebraic point x on an algebraic variety x with an ample line bundle l the invariant alpha measures how well x can be approximated by rational points on x with respect to the height function associated to l we show that this invariant is closely related to the seshadri constant epsilon x l measuring local positivity of l at x and in particular that roth s theorem on mathbb p 1 generalizes as an inequality between these two invariants valid for arbitrary projective varieties

special test configuration and k stability of fano varieties for any at projective family x l c such that the generic bre x is a klt q fano variety and ljx q kx we use the techniques from the minimal model program mmp to modify the total family the end product is a family such that every ber is a klt q fano variety moreover we can prove that the donaldson futaki invariants of the appearing models decrease when the family is a test conguration of a xed fano variety x kx this implies tian s conjecture given x a fano manifold to test its k semi poly stability we only need to test on the special test congurations

conjugacy class prior distributions on metric based ranking models summary a new class of prior distributions for metric based models in the analysis of fully and partially ranked data is developed this class is attractive because it provides a meaningful way to encapsulate prior information about the parameters of the model three examples illustrate the ideas developed in the paper

effective sampling and learning for mallows models with pairwise preference data learning preference distributions is a critical problem in many areas e g recommender systems ir social choice however many existing learning and inference methods impose restrictive assumptions on the form of user preferences that can be admitted as evidence we relax these restrictions by considering as data arbitrary pairwise comparisons of alternatives which represent the fundamental building blocks of ordinal rankings we develop the first algorithms for learning mallows models and mixtures thereof from pairwise comparison data at the heart of our technique is a new algorithm the generalized repeated insertion model grim which allows sampling from arbitrary ranking distributions and conditional mallows models in particular while we show that sampling from a mallows model with pairwise evidence is computationally difficult in general we develop approximate samplers that are exact for many important special cases and have provable bounds with pairwise evidence and derive algorithms for evaluating log likelihood learning mallows mixtures and non parametric estimation experiments on real world data sets demonstrate the effectiveness of our approach

mm algorithms for generalized bradley terry models the bradley terry model for paired comparisons is a simple and muchstudied means to describe the probabilities of the possible outcomes when individuals are judged against one another in pairs among the many studies of the model in the past 75 years numerous authors have generalized it in several directions sometimes providing iterative algorithms for obtaining maximum likelihood estimates for the generalizations building on a theory of algorithms known by the initials mm for minorization maximization this paper presents a powerful technique for producing iterative maximum likelihood estimation algorithms for a wide class of generalizations of the bradley terry model while algorithms for problems of this type have tended to be custom built in the literature the techniques in this paper enable their mass production simple conditions are stated that guarantee that each algorithm described will produce a sequence that converges to the unique maximum likelihood estimator several of the algorithms and convergence results herein are new

kahler einstein metrics with positive scalar curvature in this paper we prove that the existence of kahler einstein metrics implies the stability of the underlying kahler manifold in a suitable sense in particular this disproves a long standing conjecture that a compact kahler manifold admits kahler einstein metrics if it has positive first chern class and no nontrivial holomorphic vector fields we will also establish an analytic criterion for the existence of kahler einstein metrics our arguments also yield that the analytic criterion is satisfied on stable kahler manifolds provided that the partial c 0 estimate posed in t6 is true

k stability and kahler einstein metrics we prove that if a fano manifold m is k stable then it admits a kahler einstein metric it affirms a longstanding conjecture for fano manifolds 2015 wiley periodicals inc

stability and stabilizability of switched linear systems a survey of recent results during the past several years there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems this paper aims to briefly survey recent results in this field first the stability analysis for switched systems is reviewed we focus on the stability analysis for switched linear systems under arbitrary switching and we highlight necessary and sufficient conditions for asymptotic stability after a brief review of the stability analysis under restricted switching and the multiple lyapunov function theory the switching stabilization problem is studied and a variety of switching stabilization methods found in the literature are outlined then the switching stabilizability problem is investigated that is under what condition it is possible to stabilize a switched system by properly designing switching control laws note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature a necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here

an estimation of generalized bradley terry models based on the em algorithm the bradley terry model is a statistical representation for one s preference or ranking data by using pairwise comparison results of items for estimation of the model several methods based on the sum of weighted kullback leibler divergences have been proposed from various contexts the purpose of this letter is to interpret an estimation mechanism of the bradley terry model from the viewpoint of flatness a fundamental notion used in information geometry based on this point of view a new estimation method is proposed on a framework of the em algorithm the proposed method is different in its objective function from that of conventional methods especially in treating unobserved comparisons and it is consistently interpreted in a probability simplex an estimation method with weight adaptation is also proposed from a viewpoint of the sensitivity experimental results show that the proposed method works appropriately and weight adaptation improves accuracy of the estimate

learning the kernel matrix with semidefinite programming kernel based learning algorithms work by embedding the data into a euclidean space and then searching for linear relations among the embedded data points the embedding is performed implicitly by specifying the inner products between each pair of points in the embedding space this information is contained in the so called kernel matrix a symmetric and positive semidefinite matrix that encodes the relative positions of all points specifying this matrix amounts to specifying the geometry of the embedding space and inducing a notion of similarity in the input space classical model selection problems in machine learning in this paper we show how the kernel matrix can be learned from data via semidefinite programming sdp techniques when applied to a kernel matrix associated with both training and test data this gives a powerful transductive algorithm using the labeled part of the data one can learn an embedding also for the unlabeled part the similarity between test points is inferred from training points and their labels importantly these learning problems are convex so we obtain a method for learning both the model class and the function without local minima furthermore this approach leads directly to a convex method for learning the 2 norm soft margin parameter in support vector machines solving an important open problem

a new correlation coefficient for comparing and aggregating non strict and incomplete rankings abstract we introduce a correlation coefficient that is designed to deal with a variety of ranking formats including those containing non strict i e with ties and incomplete i e unknown preferences the correlation coefficient is designed to enforce a neutral treatment of incompleteness whereby no assumptions are made about individual preferences involving unranked objects the new measure which can be regarded as a generalization of the seminal kendall tau correlation coefficient is proven to satisfy a set of metric like axioms and to be equivalent to a recently developed ranking distance function associated with kemeny aggregation in an effort to further unify and enhance both robust ranking methodologies this work proves the equivalence of an additional distance and correlation coefficient pairing in the space of non strict incomplete rankings these connections induce new exact optimization methodologies a specialized branch and bound algorithm and an exact integer programming formulation moreover the bridging of these complementary theories reinforces the singular suitability of the featured correlation coefficient to solve the general consensus ranking problem the latter premise is bolstered by an accompanying set of experiments on random instances which are generated via a herein developed sampling technique connected with the classic mallows distribution of ranking data associated experiments with the branch and bound algorithm demonstrate that as data becomes noisier the featured correlation coefficient yields relatively fewer alternative optimal solutions and that the aggregate rankings tend to be closer to an underlying ground truth shared by a majority

delay dependent and decay rate dependent conditions for exponential mean stability and non fragile controller design of positive markov jump linear systems with time delay abstract this paper proposes some new sufficient conditions and necessary conditions for exponential mean stability with prescribed decay rate and sufficient conditions for non fragile controller design of both continuous time and discrete time positive markov jump linear systems with time delay first sufficient stability conditions are derived by constructing novel linear stochastic co positive lyapunov krasovskii functionals second the corresponding necessary conditions are established by applying a model transformation technique and analyzing the relationship between stochastic stability of the transformed systems and exponential mean stability with given decay rate of the original systems compared with the existing conditions the proposed stability conditions are not only delay dependent but also decay rate dependent and the sufficient conditions plus the necessary conditions can be used to judge the system stability more precisely third based on the new sufficient conditions non fragile controllers are designed by solving linear programming problems such that the closed loop systems are positive and exponentially mean stable with an expected decay rate finally by numerical examples the effects of both time delay and decay rate on exponential mean stability are exploited and the validity of the non fragile controller design conditions is demonstrated

learning permutations with exponential weights we give an algorithm for the on line learning of permutations the algorithm maintains its uncertainty about the target permutation as a doubly stochastic weight matrix and makes predictions using an efficient method for decomposing the weight matrix into a convex combination of permutations the weight matrix is updated by multiplying the current matrix entries by exponential factors and an iterative procedure is needed to restore double stochasticity even though the result of this procedure does not have a closed form a new analysis approach allows us to prove an optimal up to small constant factors bound on the regret of our algorithm this regret bound is significantly better than that of either kalai and vempala s more efficient follow the perturbed leader algorithm or the computationally expensive method of explicitly representing each permutation as an expert

label ranking by learning pairwise preferences preference learning is an emerging topic that appears in different guises in the recent literature this work focuses on a particular learning scenario called label ranking where the problem is to learn a mapping from instances to rankings over a finite number of labels our approach for learning such a mapping called ranking by pairwise comparison rpc first induces a binary preference relation from suitable training data using a natural extension of pairwise classification a ranking is then derived from the preference relation thus obtained by means of a ranking procedure whereby different ranking methods can be used for minimizing different loss functions in particular we show that a simple weighted voting strategy minimizes risk with respect to the well known spearman rank correlation we compare rpc to existing label ranking methods which are based on scoring individual labels instead of comparing pairs of labels both empirically and theoretically it is shown that rpc is superior in terms of computational efficiency and at least competitive in terms of accuracy

distance based ranking models on examine le modele de type mallows pour une distance generale et on etudie ensuite les distances pour lesquelles le modele peut etre decompose en facteurs representant des etapes independantes dans le processus de classement

filtrations and test configurations we introduce a strengthening of k stability based on filtrations of the homogeneous coordinate ring this allows for considering certain limits of families of test configurations which arise naturally in several settings we prove that if a manifold with no automorphisms admits a csck metric then it satisfies this stronger stability notion we also discuss the relation with the birational transformations in the definition of b stability

multiple kernel learning algorithms in recent years several methods have been proposed to combine multiple kernels instead of using a single one these different kernels may correspond to using different notions of similarity or may be using information coming from multiple sources different representations or different feature subsets in trying to organize and highlight the similarities and differences between them we give a taxonomy of and review several multiple kernel learning algorithms we perform experiments on real data sets for better illustration and comparison of existing algorithms we see that though there may not be large differences in terms of accuracy there is difference between them in complexity as given by the number of stored support vectors the sparsity of the solution as given by the number of used kernels and training time complexity we see that overall using multiple kernels instead of a single one is useful and believe that combining kernels in a nonlinear or data dependent way seems more promising than linear combination in fusing information provided by simple linear kernels whereas linear methods are more reasonable when combining complex gaussian kernels