eigenfaces vs fisherfaces recognition using class specific linear projection we develop a face recognition algorithm which is insensitive to large variation in lighting direction and facial expression taking a pattern classification approach we consider each pixel in an image as a coordinate in a high dimensional space we take advantage of the observation that the images of a particular face under varying illumination but fixed pose lie in a 3d linear subspace of the high dimensional image space if the face is a lambertian surface without shadowing however since faces are not truly lambertian surfaces and do indeed produce self shadowing images will deviate from this linear subspace rather than explicitly modeling this deviation we linearly project the image into a subspace in a manner which discounts those regions of the face with large deviation our projection method is based on fisher s linear discriminant and produces well separated classes in a low dimensional subspace even under severe variation in lighting and facial expressions the eigenface technique another method based on linearly projecting the image space to a low dimensional subspace has similar computational requirements yet extensive experimental results demonstrate that the proposed fisherface method has error rates that are lower than those of the eigenface technique for tests on the harvard and yale face databases

bivariate survival models induced by frailties abstract when two observed survival times depend via a proportional hazards model on the same unobserved variable called a frailty this common dependence induces an association between the observed times this article considers the class of bivariate survival distributions that can arise in this way extends it to allow negative association and shows that the observable bivariate distribution determines the unobserved frailty distribution up to a scale parameter a cross ratio function easily estimated even from censored data is the key to both the characterization results and inferential procedures and diagnostic plots that are introduced and illustrated by real examples the models considered are the natural counterpart for survival data of the latent variable models that have long been used in factor analysis for continuous data or in latent structure analysis for binary data the main distinguishing feature of survival data is the possibility of censoring which makes the standard methods difficu

power transformation toward a linear regression quantile in this article we consider the linear quantile regression model with a power transformation on the dependent variable like the classical box cox transformation approach it extends the applicability of linear models without resorting to nonparametric smoothing but transformations on the quantile models are more natural due to the equivariance property of the quantiles under monotone transformations we propose an estimation procedure and establish its consistency and asymptotic normality under some regularity conditions the objective function employed in the estimation can also be used to check inadequacy of a power transformed linear quantile regression model and to obtain inference on the transformation parameter the proposed approach is shown to be valuable through illustrative examples

correlation curves as local measures of variance explained by regression abstract we call a model for an experiment heterocorrelatious if the strength of the relationship between a response variable y and a covariate x is different in different regions of the covariate space for such experiments we introduce a correlation curve that measures heter ocorrelaticity in terms of the variance explained by regression locally at each covariate value more precisely the squared correlation curve is obtained by first expressing the usual linear model variance explained to total variance formula in terms of the residual variance and the regression slope and then replacing these by the conditional residual variance depending on x and the slope of the conditional mean of y given x x the correlation curve x satisfies the invariance properties of correlation it reduces to the galton pearson correlation in linear models it is between 1 and 1 it is 0 when x and y are independent and it is 1 when y is a function of x we introduce estimates of the correlation curve based on

global validity of the boltzmann equation for two and three dimensional rare gas in vacuum erratum and improved result we point out an error in our earlier papers 1 and 2 and present a more direct and natural proof which although based on the same physical ideas of the previous ones saves and actually improves the validity results for the boltzmann equation given in 1 and 2

graph embedding and extensions a general framework for dimensionality reduction a large family of algorithms supervised or unsupervised stemming from statistics or geometry theory has been designed to provide different solutions to the problem of dimensionality reduction despite the different motivations of these algorithms we present in this paper a general formulation known as graph embedding to unify them within a common framework in graph embedding each algorithm can be considered as the direct graph embedding or its linear kernel tensor extension of a specific intrinsic graph that describes certain desired statistical or geometric properties of a data set with constraints from scale normalization or a penalty graph that characterizes a statistical or geometric property that should be avoided furthermore the graph embedding framework can be used as a general platform for developing new dimensionality reduction algorithms by utilizing this framework as a tool we propose a new supervised dimensionality reduction algorithm called marginal fisher analysis in which the intrinsic graph characterizes the intraclass compactness and connects each data point with its neighboring points of the same class while the penalty graph connects the marginal points and characterizes the interclass separability we show that mfa effectively overcomes the limitations of the traditional linear discriminant analysis algorithm due to data distribution assumptions and available projection directions real face recognition experiments show the superiority of our proposed mfa in comparison to lda also for corresponding kernel and tensor extensions

feature space locality constraint for kernel based nonlinear discriminant analysis subspace learning is an important approach in pattern recognition nonlinear discriminant analysis nda due to its capability of describing nonlinear manifold structure of samples is considered to be more powerful to undertake classification tasks in image related problems in kernel based nda representation there are three spaces involved i e original data space implicitly mapped high dimension feature space and the target low dimension subspace existing methods mainly focus on the information in original data space to find the most discriminant low dimension subspace the implicit high dimension feature space plays a role that connects the original space and the target subspace to realize the nonlinear dimension reduction but the sample geometric structure information in feature space is not involved in this work we try to utilize and explore this information specifically the locality information of samples in feature space is modeled and integrated into the traditional kernel based nda methods in this way both the sample distributions in original data space and the mapped high dimension feature space are modeled and more information is expected to be explored to improve the discriminative ability of the subspace two algorithms named fslc kda and fslc ksr are presented extensive experiments on orl extended yaleb pie multi pie and frgc databases validate the efficacy of the proposed method

dependence calibration in conditional copulas a nonparametric approach summary the study of dependence between random variables is a mainstay in statistics in many cases the strength of dependence between two or more random variables varies according to the values of a measured covariate we propose inference for this type of variation using a conditional copula model where the copula function belongs to a parametric copula family and the copula parameter varies with the covariate in order to estimate the functional relationship between the copula parameter and the covariate we propose a nonparametric approach based on local likelihood of importance is also the choice of the copula family that best represents a given set of data the proposed framework naturally leads to a novel copula selection method based on cross validated prediction errors we derive the asymptotic bias and variance of the resulting local polynomial estimator and outline how to construct pointwise confidence intervals the finite sample performance of our method is investigated using simulation studies and is illustrated using a subset of the matched multiple birth data

on assessing the strength of dependency between failure time variates summary the correlation p between cumulative hazard variates is considered as a measure of dependence between pairs of failure time variates such correlation is readily estimated in the absence of censorship but modelling assumptions are required for its estimation in the presence of independent right censorship a semiparametric class of bivariate failure time models in which a dependence parameter 0 is in one to one correspondence with the cumulative hazard variate correlation p is considered for this purpose a simple estimating function consisting of a weighted sum over the grid formed by the observed failure times of differences between nonparametric and model restricted estimates of covariance rates is proposed for estimation and corresponding asymptotic distribution theory is given this estimation procedure is shown to lack robustness under conditions of moderate to heavy censorship motivating consideration of dependency measures that can be defined on the support of the observed failure times two such measures the correlation between marginal martingales and a cumulative cross ratio statistic are discussed and corresponding nonparametric estimators are proposed

a lack of fit test for quantile regression we propose an omnibus lack of fit test for linear or nonlinear quantile regression based on a cusum process of the gradient vector the test does not involve nonparametric smoothing but is consistent for all nonparametric alternatives without any moment conditions on the regression error in addition the test is suitable for detecting the local alternatives of any order arbitrarily close to n 1 2 from the null hypothesis the limiting distribution of the proposed test statistic is non gaussian but can be characterized by a gaussian process we propose a simple sequential resampling scheme to carry out the test whose nominal levels are well approximated in our empirical study for

checking the cox model with cumulative sums of martingale based residuals summary this paper presents a new class of graphical and numerical methods for checking the adequacy of the cox regression model the procedures are derived from cumulative sums of martingale based residuals over follow up time and or covariate values the distributions of these stochastic processes under the assumed model can be approximated by zero mean gaussian processes each observed process can then be compared both visually and analytically with a number of simulated realizations from the approximate null distribution these comparisons enable the data analyst to assess objectively how unusual the observed residual patterns are special attention is given to checking the functional form of a covariate the form of the link function and the validity of the proportional hazards assumption an omnibus test consistent against any model misspecification is also studied the proposed techniques are illustrated with two real data sets

quantile association regression models it is often important to study the association between two continuous variables in this work we propose a novel regression framework for assessing conditional associations on quantiles we develop general methodology which permits covariate effects on both the marginal quantile models for the two variables and their quantile associations the proposed quantile copula models have straightforward interpretation facilitating a comprehensive view of association structure which is much richer than that based on standard product moment and rank correlations we show that the resulting estimators are uniformly consistent and weakly convergent as a process of the quantile index simple variance estimators are presented which perform well in numerical studies extensive simulations and a real data example demonstrate the practical utility of the methodology supplementary materials for this article are available online

global validity of the boltzmann equation for a three dimensional rare gas in vacuum we consider a system ofn hard disks in 2 in the boltzmann grad limit i e n d 0 n d 1 0 whered is the diameter of the disks if is sufficiently small and if the joint distribution densities factorize at time zero we prove that the time evolved one particle distribution converges for all times to the solution of the boltzmann equation with the same initial datum

nonlinear component analysis as a kernel eigenvalue problem a new method for performing a nonlinear form of principal component analysis is proposed by the use of integral operator kernel functions one can efficiently compute principal components in high dimensional feature spaces related to input space by some nonlinear map for instance the space of all possible five pixel products in 16 16 images we give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition

kinetic limits for a class of interacting particle systems we study one dimensional particle systems in which particles travel as independent random walks and collide stochastically the collision rates are chosen so that each particle experiences finitely many collisions per unit time we establish the kinetic limit and derive the discrete boltzmann equation for the macroscopic particle density

standard errors and covariance matrices for smoothed rank estimators a pseudo bayesian interpretation of standard errors yields a natural induced smoothing of statistical estimating functions when applied to rank estimation the lack of smoothness which prevents standard error estimation is remedied efficiency and robustness are preserved while the smoothed estimation has excellent computational properties in particular convergence of the iterative equation for standard error is fast and standard error calculation becomes asymptotically a one step procedure this property also extends to covariance matrix calculation for rank estimates in multi parameter problems examples and some simple explanations are given

robust inference for univariate proportional hazards frailty regression models we consider a class of semiparametric regression models which are one parameter extensions of the cox j roy statist soc ser b 34 1972 187 220 model for right censored univariate failure times these models assume that the hazard given the covariates and a random frailty unique to each individual has the proportional hazards form multiplied by the frailty the frailty is assumed to have mean 1 within a known one parameter family of distributions inference is based on a nonparametric likelihood the behavior of the likelihood maximizer is studied under general conditions where the fitted model may be misspecified the joint estimator of the regression and frailty parameters as well as the baseline hazard is shown to be uniformly consistent for the pseudo value maximizing the asymptotic limit of the likelihood appropriately standardized the estimator converges weakly to a gaussian process when the model is correctly specified the procedure is semiparametric efficient achieving the semiparametric information bound for all parameter components it is also proved that the bootstrap gives valid inferences for all parameters even under misspecification we demonstrate analytically the importance of the robust inference in several examples in a randomized clinical trial a valid test of the treatment effect is possible when other prognostic factors and the frailty distribution are both misspecified under certain conditions on the covariates the ratios of the regression parameters are still identifiable the practical utility of the procedure is illustrated on a non hodgkin s lymphoma dataset

a stochastic model associated with enskog equation and its kinetic limit we examine a system of particles in which the particles travel deterministically in between stochastic collisions the collisions are elastic and occur with probability d when two particles are at a distance when the number of particles n goes to infinity and n d goes to a nonzero constant we show that the particle density converges to a solution of the enskog equation

time dependent association measures for bivariate survival distributions abstract we propose time dependent association measures for application to bivariate survival analysis such association measures provide informative summaries for data on twins ophthalmic and auditory studies and for other matched pair designs we develop several desirable properties of time dependent association measures and study three measures motivated by these properties we examine the measures from a general bivariate survival perspective and for the proportional hazards frailty model we use monozygotic mz and dizygotic dz twin data from the danish twin registry to illustrate how these measures depend on the specification of the proportional hazards frailty model this model consists of two components a baseline hazard function and a frailty distribution we produce gamma and nonparametric maximum likelihood estimates of the frailty distribution and estimate a gompertz baseline hazard function for two of the measures a nonparametric estimate provides a comparison to the model based estim

face recognition using kernel direct discriminant analysis algorithms techniques that can introduce low dimensional feature representation with enhanced discriminatory power is of paramount importance in face recognition fr systems it is well known that the distribution of face images under a perceivable variation in viewpoint illumination or facial expression is highly nonlinear and complex it is therefore not surprising that linear techniques such as those based on principle component analysis pca or linear discriminant analysis lda cannot provide reliable and robust solutions to those fr problems with complex face variations in this paper we propose a kernel machine based discriminant analysis method which deals with the nonlinearity of the face patterns distribution the proposed method also effectively solves the so called small sample size sss problem which exists in most fr tasks the new algorithm has been tested in terms of classification error rate performance on the multiview umist face database results indicate that the proposed methodology is able to achieve excellent performance with only a very small set of features being used and its error rate is approximately 34 and 48 of those of two other commonly used kernel fr approaches the kernel pca kpca and the generalized discriminant analysis gda respectively

dimensionality reduction of multimodal labeled data by local fisher discriminant analysis reducing the dimensionality of data without losing intrinsic information is an important preprocessing step in high dimensional data analysis fisher discriminant analysis fda is a traditional technique for supervised dimensionality reduction but it tends to give undesired results if samples in a class are multimodal an unsupervised dimensionality reduction method called locality preserving projection lpp can work well with multimodal data due to its locality preserving property however since lpp does not take the label information into account it is not necessarily useful in supervised learning scenarios in this paper we propose a new linear supervised dimensionality reduction method called local fisher discriminant analysis lfda which effectively combines the ideas of fda and lpp lfda has an analytic form of the embedding transformation and the solution can be easily computed just by solving a generalized eigenvalue problem we demonstrate the practical usefulness and high scalability of the lfda method in data visualization and classification tasks through extensive simulation studies we also show that lfda can be extended to non linear dimensionality reduction scenarios by applying the kernel trick

face recognition using laplacianfaces we propose an appearance based face recognition method called the laplacianface approach by using locality preserving projections lpp the face images are mapped into a face subspace for analysis different from principal component analysis pca and linear discriminant analysis lda which effectively see only the euclidean structure of face space lpp finds an embedding that preserves local information and obtains a face subspace that best detects the essential face manifold structure the laplacianfaces are the optimal linear approximations to the eigenfunctions of the laplace beltrami operator on the face manifold in this way the unwanted variations resulting from changes in lighting facial expression and pose may be eliminated or reduced theoretical analysis shows that pca lda and lpp can be obtained from different graph models we compare the proposed laplacianface approach with eigenface and fisherface methods on three different face data sets experimental results suggest that the proposed laplacianface approach provides a better representation and achieves lower error rates in face recognition

local linear quantile regression abstract in this article we study nonparametric regression quantile estimation by kernel weighted local linear fitting two such estimators are considered one is based on localizing the characterization of a regression quantile as the minimizer of e pp y a x x where p is the appropriate check function the other follows by inverting a local linear conditional distribution estimator and involves two smoothing parameters rather than one our aim is to present fully operational versions of both approaches and to show that each works quite well although either might be used in practice we have a particular preference for the second our automatic smoothing parameter selection method is novel the main regression quantile smoothing parameters are chosen by rule of thumb adaptations of state of the art methods for smoothing parameter selection for regression mean estimation the techniques are illustrated by application to two datasets and compared in simulations

boltzmann grad limits for stochastic hard sphere models we study a d dimensional stochastic particle system in which the particles travel deterministically in between stochastic collisions the collisions are elastic and occur with a probability of order when two particles are at a distance less than when the number of particles n goes to infinity and n d 1 goes to a nonzero constant we show that the particle density converges to a solution of the boltzmann equation provided that d 1

an approach to multivariate covariate dependent quantile contours with application to bivariate conditional growth charts multivariate quantile contours are useful in numerous applications and have been studied in different contexts however no easy solutions exist when dynamic and conditional quantile contours are needed without strong distributional assumptions in this article we propose a new form of bivariate quantile contours and a two stage estimation procedure to take time effect into account the proposed procedure relies on quantile regression for longitudinal data and is flexible to include potentially important covariates as necessary in addition we propose a visual model assessment tool and discuss a practical guideline for model selection the performance of the proposed methodology is demonstrated by a simulation study as well as an application to joint height weight screening of young children in the united states we construct bivariate growth charts by a nested sequence of age dependent and covariate varying quantile contours of height and weight and use it to locate an individual subject s percentile

a new lda based face recognition system which can solve the small sample size problem a new lda based face recognition system is presented in this paper linear discriminant analysis lda is one of the most popular linear projection techniques for feature extraction the major drawback of applying lda is that it may encounter the small sample size problem in this paper we propose a new lda based technique which can solve the small sample size problem we also prove that the most expressive vectors derived in the null space of the within class scatter matrix using principal component analysis pca are equal to the optimal discriminant vectors derived in the original space using lda the experimental results show that the new lda process improves the performance of a face recognition system signi cantly 2000 pattern recognition society published by elsevier science ltd all rights reserved

on the cauchy problem for boltzmann equations global existence and weak stability we study the large data cauchy problem for boltzmann equations with general collision kernels we prove that sequences of solutions which satisfy only the physically natural a priori bounds converge weakly in l to a solution from this stability result we deduce global existence of a solution to the cauchy problem our method relies upon recent compactness results for velocity averages a new formulation of the boltzmann equation which involves nonlinear normalization and an analysis of subsolutions and supersolutions it allows us to overcome the lack of strong a priori estimates and define a meaningful collision operator for general configurations

analyzing bivariate continuous data grouped into categories defined by empirical quantiles of marginal distributions epidemiologists sometimes study the association between two measurements of exposure on the same subjects by grouping the original bivariate continuous data into categories that are defined by the empirical quantiles of the two marginal distributions although such grouped data are presented in a two way contingency table the cell counts in this table do not have a multinomial distribution we describe the joint distribution of counts in such a table by the term empirical bivariate quantile partitioned ebqp distribution blomqvist 1950 annals of mathematical statistics 21 539 600 gave an asymptotic ebqp theory for bivariate data partitioned by the sample medians we demonstrate that his asymptotic theory is not correct however except in special cases we present a general asymptotic theory for tables of arbitrary dimensions and apply this theory to construct confidence intervals for the kappa statistic we show by simulations that the confidence interval procedures we propose have near nominal coverage for sample sizes exceeding 60 for both 2 x 2 and 3 x 3 tables these simulations also illustrate that the asymptotic theory of blomqvist 1950 and the methods that fleiss cohen and everitt 1969 psychological bulletin 72 323 327 give for multinomial tables can yield subnominal coverage for kappa calculated from ebqp tables although in some cases the coverage for these procedures is near nominal levels

regularity of the moments of the solution of a transport equation let u u x v satisfy the transport equation u v xu f x rn v rnwhere f belongs to some space of type lp dx d v where is a positive bounded measure on rn we study the resulting regularity of the moment u x v d v in terms of fractional sobolev spaces for example counter examples are given in order to test the optimality of our results

correlation curves measures of association as functions of covariate values for experiments where the strength of association between a response variable y and a covariate x is different over different regions of values for the covariate x we propose local nonparametric dependence functions which measure the strength of association between y and x as a function of x x our dependence functions are extensions of galton s idea of strength of co relation from the bivariate normal case to the nonparametric case in particular a dependence function is obtained by expressing the usual galton pearson correlation coefficient in terms of the regression line slope 3 and the residual variance o 2 and then replacing 3 and 72 by a nonparametric regression slope 13 x and a nonparametric residual variance o 2 x var yix respectively our local dependence functions are standardized nonparametric regression curves which provide universal scale free measures of the strength of the relationship between variables in nonlinear models they share most of the properties of the correlation coefficient and they reduce to the usual correlation coefficient in the bivariate normal case for this reason we call them correlation curves we show that in a certain sense they quantify lehmann s notion of regression dependence finally the correlation curve concept is illustrated using data from a study of the relationship between cholesterol levels x and triglyceride concentrations y of heart patients