negative holomorphic curvature and positive canonical bundle in this note we show that if a projective manifold admits a kahler metric with negative holomorphic sectional curvature then the canonical bundle of the manifold is ample this confirms a conjecture of the second author

a new sequential classifier using information criterion window abstract we propose a model based parametric unsupervised sequential classifier with an information criterion window icw based on the assumption that the number of clusters changes smoothly from a stage to the following stage to determine the number of clusters at each stage and to perform classification on the observed mixture data the proposed approach provides possible solutions for two problems of pattern recognition adaptive classification and sequential clustering validation simulation results demonstrate that the proposed algorithm provides good results for pure mixed data and successfully performs clustering for the mixed gaussian data in the large sample limit

testing in normal mixture models when the proportions are known summary the aim of this paper is to study the behaviour of the likelihood ratio test statistic in mixture models when the proportions of the distributions are known a priori the results depend on the value of the proportion the dimensionality of the problem and whether or not the variance of the distributions is known

finite mixture models for proportions summary six data sets recording fetal control mortality in mouse litters are presented the data are clearly overdispersed and a standard approach would be to describe the data by means of a beta binomial model or to use quasi likelihood methods for five of the examples we show that the beta binomial model provides a reasonable description but that the fit can be significantly improved by using a mixture of a beta binomial model with a binomial distribution this mixture provides two alternative solutions in one of which the binomial component indicates a high probability of death but is selected infrequently this accounts for outlying litters with high mortality the influence of the outliers on the beta binomial fits is also demonstrated the location and nature of the two main maxima to the likelihood are investigated through profile log likelihoods comparisons are made with the performance of finite mixtures of binomial distributions data describing fetal deaths in litters are frequently overdispersed relative to the binomial distribution due to differential litter effects in some cases sample sizes may be too small for a significant effect of overdispersion to be detected in others however data sets are certainly large enough and six illustrations of such data sets are given in tables 1 6 the data of tables 3 6 have been published before while those of tables 1 and 2 have been formed by pooling smaller sets of data that have previously been analyzed by james and smith 1982 we shall refer to the data sets in order as el e2 hs1 hs2 hs3 avss different data sets highlight different aspects of the work of this paper statisticians analyzing such data might adopt a parametric approach for example by fitting a beta binomial or a correlated binomial distribution the more robust approach provided by quasilikelihood is an alternative see liang and hanfelt 1994 the various options are described in morgan 1992 chapter 6 and model details are given in section 2 also shiown in tables 1 6 are the expected values from fitting the beta binomial distribution the fits appear to be reasonably good except for the small numbers of litters with high mortality because of small cell frequencies we use simulation to test goodness of fit taking the el data set as an example we can simulate from the fitted beta binomial model a data set that matches el with regard to numbers of litters of the various different sizes observed and that uses as parameter values the maximum likelihood estimates resulting from fitting the model to the real data the model can then be fitted to the simulated data and the maximum log likelihood recorded this process may then be repeated many times to provide a goodness of fit reference for the maximum

mixture densities maximum likelihood and the em algorithm the problem of estimating the parameters which determine a mixture density has been the subject of a large diverse body of literature spanning nearly ninety years during the last two decades the

conjugate mixture models for clustering multimodal data the problem of multimodal clustering arises whenever the data are gathered with several physically different sensors observations from different modalities are not necessarily aligned in the sense there there is no obvious way to associate or compare them in some common space a solution may consist in considering multiple clustering tasks independently for each modality the main difficulty with such an approach is to guarantee that the unimodal clusterings are mutually consistent in this letter we show that multimodal clustering can be addressed within a novel framework conjugate mixture models these models exploit the explicit transformations that are often available between an unobserved parameter space objects and each of the observation spaces sensors we formulate the problem as a likelihood maximization task and derive the associated conjugate expectation maximization algorithm the convergence properties of the proposed algorithm are thoroughly investigated several local and global optimization techniques are proposed in order to increase its convergence speed two initialization strategies are proposed and compared a consistent model selection criterion is proposed the algorithm and its variants are tested and evaluated within the task of 3d localization of several speakers using both auditory and visual data

application of the em algorithm for the multitarget multisensor tracking problem an important problem in surveillance and reconnaissance systems is the tracking of multiple moving targets in cluttered noise environments using outputs from a number of sensors possessing wide variations in individual characteristics and accuracies a number of approaches have been proposed for this multitarget multisensor tracking problem ranging from reasonably simple though ad hoc schemes to fairly complex but theoretically optimum approaches in this paper we describe an iterative procedure for time recursive multitarget multisensor tracking based on use of the expectation maximization em algorithm more specifically we pose the multitarget multisensor tracking problem as an incomplete data problem with the observable sensor outputs representing the incomplete data whereas the target associated sensor outputs constitute the complete data target updates at each time use an em based approach that calculates the maximum a posteriori map estimate of the target states under the assumption of appropriate motion models based on the outputs of disparate sensors the approach uses a markov random field mrf model of the associations between observations and targets and allows for estimation of joint association probabilities without explicit enumeration the advantage of this em based approach is that it provides a computationally efficient means for approaching the performance offered by theoretically optimum approaches that use explicit enumeration of the joint association probabilities we provide selected results illustrating the performance complexity characteristics of this em based approach compared with competing schemes

assessing a mixture model for clustering with the integrated completed likelihood we propose an assessing method of mixture model in a cluster analysis setting with integrated completed likelihood for this purpose the observed data are assigned to unknown clusters using a maximum a posteriori operator then the integrated completed likelihood icl is approximated using the bayesian information criterion bic numerical experiments on simulated and real data of the resulting icl criterion show that it performs well both for choosing a mixture model and a relevant number of clusters in particular icl appears to be more robust than bic to violation of some of the mixture model assumptions and it can select a number of dusters leading to a sensible partitioning of the data

convex clustering via l1 fusion penalization summary we study the large sample behaviour of a convex clustering framework which minimizes the sample within cluster sum of squares under an l1 fusion constraint on the cluster centroids this recently proposed approach has been gaining in popularity however its asymptotic properties have remained mostly unknown our analysis is based on a novel representation of the sample clustering procedure as a sequence of cluster splits determined by a sequence of maximization problems we use this representation to provide a simple and intuitive formulation for the population clustering procedure we then demonstrate that the sample procedure consistently estimates its population analogue and we derive the corresponding rates of convergence the proof conducts a careful simultaneous analysis of a collection of m estimation problems whose cardinality grows together with the sample size on the basis of the new perspectives gained from the asymptotic investigation we propose a key post processing modification of the original clustering framework we show both theoretically and empirically that the resulting approach can be successfully used to estimate the number of clusters in the population using simulated data we compare the proposed method with existing number of clusters and modality assessment approaches and obtain encouraging results we also demonstrate the applicability of our clustering method to the detection of cellular subpopulations in a single cell virology study

a maximum likelihood method for latent class regression involving a censored dependent variable the standard tobit or censored regression model is typically utilized for regression analysis when the dependent variable is censored this model is generalized by developing a conditional mixture maximum likelihood method for latent class censored regression the proposed method simultaneously estimates separate regression functions and subject membership in k latent classes or groups given a censored dependent variable for a cross section of subjects maximum likelihood estimates are obtained using an em algorithm the proposed method is illustrated via a consumer psychology application

a latent class mixture model for incomplete longitudinal gaussian data in the analyses of incomplete longitudinal clinical trial data there has been a shift away from simple methods that are valid only if the data are missing completely at random to more principled ignorable analyses which are valid under the less restrictive missing at random assumption the availability of the necessary standard statistical software nowadays allows for such analyses in practice while the possibility of data missing not at random mnar cannot be ruled out it is argued that analyses valid under mnar are not well suited for the primary analysis in clinical trials rather than either forgetting about or blindly shifting to an mnar framework the optimal place for mnar analyses is within a sensitivity analysis context one such route for sensitivity analysis is to consider next to selection models pattern mixture models or shared parameter models the latter can also be extended to a latent class mixture model the approach taken in this article the performance of the so obtained flexible model is assessed through simulations and the model is applied to data from a depression trial

numerical characterization of the kahler cone of a compact kahler manifold the goal of this work is to give a precise numerical description of the kahler cone of a compact kahler manifold our main result states that the kahler cone depends only on the intersection form of the cohomology ring the hodge structure and the homology classes of analytic cycles if x is a compact kahler manifold the kahler cone k of x is one of the connected components of the set p of real 1 1 cohomology classes which are numerically positive on analytic cycles i e y p 0 for every irreducible analytic set y in x p dim y this result is new even in the case of projective manifolds where it can be seen as a generalization of the well known nakai moishezon criterion and it also extends previous results by campana peternell and eyssidieux the principal technical step is to show that every nef class which has positive highest self intersection numberx n 0 contains a kahler current this is done by using the calabi yau theorem and a mass concentration technique for monge ampere equations the main result admits a number of variants and corollaries including a description of the cone of numerically effective 1 1 classes and their dual cone another important consequence is the fact that for an arbitrary deformation x s of compact kahler manifolds the kahler cone of a very general fibre xt is independent of t i e invariant by parallel transport under the 1 1 component of the gauss manin connection

influence based diagnostics for finite mixture models summary in the fitting of finite mixtures of distributions to empirical data it is often felt necessary to exclude certain observations in order to achieve a satisfactory fit this is particularly true of fisheries lengthfrequency data where the object is to model a discrete number of age classes by a mixture of normal components and the presence of outliers in the sample can have a large effect on the parameter estimates and the fit this paper develops diagnostic tools to measure the effect of individual observations on the parameter estimates and the fit in order to make the data rejection decision of the data analyst less ad hoc specifically we show how to compute the parameter influence curves and introduce a statistic similar to cook s distance used in regression diagnostics

bayesian winner take all reconstruction of intermediate views from stereoscopic images this paper presents a new algorithm for the reconstruction of intermediate views from a pair of still stereoscopic images the algorithm is designed to address the issue of blur caused by linear filtering often employed in such reconstruction the proposed algorithm is block based and to reconstruct the intermediate views employs nonlinear disparity compensated filtering by means of a winner take all strategy the reconstructed image is modeled as a tiling by fixed size blocks coming from various positions disparity compensation of either the left or right images while the tiling map itself is modeled by a binary decision field in addition to that an observation model relating the left and right images via a disparity field and a disparity field model are used all models are probabilistic and are combined into a maximum a posteriori probability criterion the intermediate intensities disparities and the binary decision field are estimated jointly using the expectation maximization algorithm the new approach is compared experimentally on complex natural images with a reference block based algorithm employing linear filtering although the improvements are localized and often subtle they demonstrate that a high quality intermediate view reconstruction for complex scenes is feasible

maximum likelihood estimation of the multivariate normal mixture model the hessian of the multivariate normal mixture model is derived and estimators of the information matrix are obtained thus enabling consistent estimation of all parameters and their precisions the usefulness of the new theory is illustrated with two examples and some simulation experiments the newly proposed estimators appear to be superior to the existing ones

the analysis of repeated measures data on schizophrenic reaction times using mixture models reaction times for schizophrenic individuals in a simple visual tracking experiment can be substantially more variable than for non schizophrenic individuals current psychological theory suggests that at least some of this extra variability arises from an attentional lapse that delays some but not all of each schizophrenic s reaction times based on this theory we pursue models in which measurements from non schizophrenics arise from a normal linear model with a separate mean for each individual whereas measurements from schizophrenics arise from a mixture of i a component analogous to the distribution of response times for non schizophrenics and ii a mean shifted component we fit four mixture models within this framework where the distinctions between models arise from assumptions about the variance of the shifted observations and the exchangeability of schizophrenic individuals some of these models can be fit by maximum likelihood using the em algorithm and all can be fit using the ecm algorithm where the covariance matrices associated with the parameters are calculated by the sem and secm algorithms respectively bayesian model monitoring using posterior predictive checks is invoked to discard models that fail to reproduce certain observed features of the data and to stimulate the development of better models

calibrating the excess mass and dip tests of modality summary nonparametric tests of modality are a distribution free way of assessing evidence about inhomogeneity in a population provided that the potential subpopulations are sufficiently well separated they include the excess mass and dip tests which are equivalent in univariate settings and are alternatives to the bandwidth test only very conservative forms of the excess mass and dip tests are available at present however and for that reason they are generally not competitive with the bandwidth test in the present paper we develop a practical approach to calibrating the excess mass and dip tests to improve their level accuracy and power substantially our method exploits the fact that the limiting distribution of the excess mass statistic under the null hypothesis depends on unknowns only through a constant which may be estimated our calibrated test exploits this fact and is shown to have greater power and level accuracy than the bandwidth test has the latter tends to be quite conservative even in an asymptotic sense moreover the calibrated test avoids difficulties that the bandwidth test has with spurious modes in the tails which often must be discounted through subjective intervention of the experimenter

holomorphic sectional curvature nefness and miyaoka yau type inequality on a compact kahler manifold we introduce a notion of almost nonpositivity for the holomorphic sectional curvature which by definition is weaker than the existence of a kahler metric with semi negative holomorphic sectional curvature we prove that a compact kahler manifold of almost nonpositive holomorphic sectional curvature has a nef canonical line bundle contains no rational curves and satisfies some miyaoka yau type inequalities in the course of the discussions we attach a real value to any fixed kahler class which up to a constant factor depending only on the dimension of manifold turns out to be an upper bound for the nef threshold

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

estimation and hypothesis testing in finite mixture models summary finite mixture models are a useful class of models for application to data when sample sizes are not large and the number of underlying densities is in question likelihood ratio tests based on joint maximum likelihood estimation of the mixing parameter x and the parameter of the underlying densities 0 are problematical our approach places a prior distribution on x and estimates 0 by maximizing the likelihood of the data given 0 with x integrated out advantages of this approach computational issues using the em algorithm and directions for further work are discussed the technique is applied to two examples

a finite mixture of nonlinear random coefficient models for continuous repeated measures data nonlinear random coefficient models nrcms for continuous longitudinal data are often used for examining individual behaviors that display nonlinear patterns of development or growth over time in measured variables as an extension of this model this study considers the finite mixture of nrcms that combine features of nrcms with the idea of finite mixture or latent class models the efficacy of this model is that it allows the integration of intrinsically nonlinear functions where the data come from a mixture of two or more unobserved subpopulations thus allowing the simultaneous investigation of intra individual within person variability inter individual between person variability and subpopulation heterogeneity effectiveness of this model to work under real data analytic conditions was examined by executing a monte carlo simulation study the simulation study was carried out using an r routine specifically developed for the purpose of this study the r routine used maximum likelihood with the expectation maximization algorithm the design of the study mimicked the output obtained from running a two class mixture model on task completion data

maximum likelihood estimation for mixed continuous and categorical data with missing values summary maximum likelihood procedures for analysing mixed continuous and categorical data with missing values are presented the general location model of olkin tate 1961 and extensions introduced by krzanowski 1980 1982 form the basis for our methods maximum likelihood estimation with incomplete data is achieved by an application of the em algorithm dempster laird rubin 1977 special cases of the algorithm include orchard woodbury s 1972 algorithm for incomplete normal samples fuchs s 1982 algorithms for log linear modelling of partially classified contingency tables and day s 1969 algorithm for multivariate normal mixtures applications include a imputation of missing values b logistic regression and discriminant analysis with missing predictors and unclassified observations c linear regression with missing continuous and categorical predictors and d parametric cluster analysis with incomplete data methods are illustrated using data from the st louis risk research project some key word8 cluster analysis discriminant analysis em algorithm incomplete data linear regression logistic regression log linear model mixture model

maximin effects in inhomogeneous large scale data large scale data are often characterized by some degree of inhomogeneity as data are either recorded in different time regimes or taken from multiple sources we look at regression models and the effect of randomly changing coefficients where the change is either smoothly in time or some other dimension or even without any such structure fitting varying coefficient models or mixture models can be appropriate solutions but are computationally very demanding and often return more information than necessary if we just ask for a model estimator that shows good predictive properties for all regimes of the data then we are aiming for a simple linear model that is reliable for all possible subsets of the data we propose the concept of maximin effects and a suitable estimator and look at its prediction accuracy from a theoretical point of view in a mixture model with known or unknown group structure under certain circumstances the estimator can be computed orders of magnitudes faster than standard penalized regression estimators making computations on large scale data feasible empirical examples complement the novel methodology and theory

a method for calibrating false match rates in record linkage abstract specifying a record linkage procedure requires both 1 a method for measuring closeness of agreement between records typically a scalar weight and 2 a rule for deciding when to classify records as matches or nonmatches based on the weights here we outline a general strategy for the second problem that is for accurately estimating false match rates for each possible cutoff weight the strategy uses a model where the distribution of observed weights are viewed as a mixture of weights for true matches and weights for false matches an em algorithm for fitting mixtures of transformed normal distributions is used to find posterior modes associated posterior variability is due to uncertainty about specific normalizing transformations as well as uncertainty in the parameters of the mixture model the latter being calculated using the sem algorithm this mixture model calibration method is shown to perform well in an applied setting with census data further a simulation experiment reveals that

an extension of a theorem of wu yau we show that a compact kahler manifold with nonpositive holomorphic sectional curvature has nef canonical bundle if the holomorphic sectional curvature is negative then it follows that the canonical bundle is ample confirming a conjecture of yau the key ingredient is the recent solution of this conjecture in the projective case by wu yau

on the regression analysis of tumour recurrence rates regression models with mixture random components are proposed for the statistical analysis of recurrent events when waiting times between successive events are unknown these models allow adjustment of parameter estimates for unobserved heterogeneity in the population due for example to missing covariates or overdispersion resulting from inexact distributional assumptions the models are illustrated by a study of recurrence rates of superficial bladder cancer in men

cluster validation for unsupervised stochastic model based image segmentation image segmentation is an important and early processing stage in many image analysis problems often this must be done in an unsupervised fashion in that training data is not available and the class conditioned feature vectors must be estimated directly from the data a major problem in such applications is the determination of the number of classes actually present in an image this problem called the cluster validation problem remains essentially unsolved we investigate the cluster validation problem associated with the use of a previously developed unsupervised segmentation algorithm based upon the expectation maximization em algorithm more specifically we consider several well known information theoretic criteria ics as candidate solutions to the validation problem when used in conjunction with this em based segmentation scheme we show that these criteria generally provide inappropriate solutions due to the domination of the penalty term by the associated log likelihood function as an alternative we propose a model fitting technique in which the complete data log likelihood functional is modeled as an exponential function in the number of classes acting the estimated number of classes are then determined in a manner similar to finding the rise time of the exponential function this new validation technique is shown to be robust and outperform the ics in our experiments experimental results for both synthetic and real world imagery are detailed

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

density estimation with confidence sets exemplified by superclusters and voids in the galaxies abstract a method is presented for forming both a point estimate and a confidence set of semiparametric densities the final product is a three dimensional figure that displays a selection of density estimates for a plausible range of smoothing parameters the boundaries of the smoothing parameter are determined by a nonparametric goodness of fit test that is based on the sample spacings for each value of the smoothing parameter our estimator is selected by choosing the normal mixture that maximizes a function of the sample spacings a point estimate is selected from this confidence set by using the method of cross validation an algorithm to find the mixing distribution that maximizes the spacings functional is presented these methods are illustrated with a data set from the astronomy literature the measurements are velocities at which galaxies in the corona borealis region are moving away from our galaxy if the galaxies are clustered the velocity density will be multimodal with clusters correspond

bayesian model selection in finite mixtures by marginal density decompositions we consider the problem of estimating the number of components d and the unknown mixing distribution in a finite mixture model in which d is bounded by some fixed finite number n our approach relies on the use of a prior over the space of mixing distributions with at most n components by decomposing the resulting marginal density under this prior we discover a weighted bayes factor method for consistently estimating d that can be implemented by an iid generalized weighted chinese restaurant gwcr monte carlo algorithm we also discuss a gibbs sampling method the blocked gibbs sampler for estimating d and also the mixing distribution we show that our resulting posterior is consistent and achieves the frequentist optimal op n 1 4 rate of estimation we compare the performance of the new gwcr model selection procedure with that of the akaike information criterion and the bayes information criterion implemented through an em algorithm applications of our methods to five real datasets and simulation

segmentation of textured images using a multiresolution gaussian autoregressive model we present a new algorithm for segmentation of textured images using a multiresolution bayesian approach the new algorithm uses a multiresolution gaussian autoregressive mgar model for the pyramid representation of the observed image and assumes a multiscale markov random field model for the class label pyramid the models used in this paper incorporate correlations between different levels of both the observed image pyramid and the class label pyramid the criterion used for segmentation is the minimization of the expected value of the number of misclassified nodes in the multiresolution lattice the estimate which satisfies this criterion is referred to as the multiresolution maximization of the posterior marginals mmpm estimate and is a natural extension of the single resolution maximization of the posterior marginals mpm estimate previous multiresolution segmentation techniques have been based on the maximum a posterior map estimation criterion which has been shown to be less appropriate for segmentation than the mpm criterion it is assumed that the number of distinct textures in the observed image is known the parameters of the mgar model the means prediction coefficients and prediction error variances of the different textures are unknown a modified version of the expectation maximization em algorithm is used to estimate these parameters the parameters of the gibbs distribution for the label pyramid are assumed to be known experimental results demonstrating the performance of the algorithm are presented

testing the number of components in a normal mixture we demonstrate that under a theorem proposed by vuong the likelihood ratio statistic based on the kullback leibler information criterion of the null hypothesis that a random sample is drawn from a k 0 component normal mixture distribution against the alternative hypothesis that the sample is drawn from a k 1 component normal mixture distribution is asymptotically distributed as a weighted sum of independent chi squared random variables with one degree of freedom under general regularity conditions we report simulation studies of two cases where we are testing a single normal versus a two component normal mixture and a two component normal mixture versus a three component normal mixture an empirical adjustment to the likelihood ratio statistic is proposed that appears to improve the rate of convergence to the limiting distribution