estimating semiparametric panel data models by marginal integration abstract we propose an alternative method for estimating the nonlinear component in semiparametric panel data models our method is based on marginal integration that allows us to recover the nonlinear component from an additive regression structure that results from the first differencing transformation we characterize the asymptotic behavior of our estimator we also extend the methodology to treat panel data models with two way effects monte carlo simulations show that our estimator behaves well in finite samples in both random effects and fixed effects settings

root n consistent semiparametric regression on considere une variable aleatoire x z dans 7b r p 7b r q on construit un estimateur generalisant l estimateur des moindres carres ordinaires en inserant des estimateurs non parametriques de la regression dans la projection orthogonale non lineaire sur z

higher rank support tensor machines for visual recognition this work addresses the two class classification problem within the tensor based large margin classification paradigm to this end we formulate the higher rank support tensor machines stms in which the parameters defining the separating hyperplane form a tensor tensorplane that is constrained to be the sum of rank one tensors subsequently we propose two extensions in which the separating tensorplanes take into consideration the spread of the training data along the different tensor modes more specifically we first propose the higher rank s s w stms that use the total or the within class covariance matrix in order to whiten the data and thus provide invariance to affine transformations second we propose the higher rank relative margin support tensor machines rmstms that bound from above the distance of the data samples from the separating tensorplane while maximizing the margin from it the corresponding optimization problem is solved in an iterative manner utilizing the candecomp parafac cp decomposition where at each iteration the parameters corresponding to the projections along a single tensor mode are estimated by solving a typical support vector machine svm type optimization problem the efficiency of the proposed method is illustrated on the problems of gait and action recognition where we report results that improve in some cases considerably the state of the art

testing additivity in generalized nonparametric regression models with estimated parameters we develop several kernel based consistent tests of an hypothesis of additivity in nonparametric regression we allow for discrete covariates and parameters estimated from a semiparametric gmm criterion function the additivity hypothesis is of interest because it delivers interpretability and reasonably fast convergence rates for nonparametric estimators the asymptotic distribution of the parameter estimators are found we also derive the asymptotic distribution of the additivity test statistics under a sequence of local alternatives we give a ranking of the different tests based on local asymptotic power the practical performance is investigated through simulations based on the data set used in linton and hardle 1996

efficient estimates in semiparametric additive regression models with unknown error distribution several authors have shown how to efficiently estimate beta in the semiparametric additive model y x beta g t text error g t smooth but unknown when the error distribution is normal however the general theory suggests that efficient estimation should be possible for general error distributions with finite fisher information even when the error distribution is unknown in this note we construct a sequence of estimators which achieves this goal under technical assumptions

identification and nonparametric estimation of a transformed additively separable model let r x z be a function that along with its derivatives can be consistently estimated nonparametrically this paper discusses the identification and consistent estimation of the unknown functions h m g and f where r x z h m x z m x z g x f z and h is strictly monotonic an estimation algorithm is proposed for each of the model s unknown components when r x z represents a conditional mean function the resulting estimators use marginal integration to separate the components g and f our estimators are shown to have a limiting normal distribution with a faster rate of convergence than unrestricted nonparametric alternatives their small sample performance is studied in a monte carlo experiment we apply our results to estimate generalized homothetic production functions for four industries in the chinese economy

the brezis nirenberg problem for the laplacian with a singular drift in rn and sn abstract we consider the brezis nirenberg problem for the laplacian with a singular drift for a geodesic ball in both r n and s n 3 n 5 the singular drift we consider derives from a potential which is symmetric around the center of the geodesic ball here the potential is given by a parameter say times the logarithm of the distance to the center of the ball in both cases we determine the exact region in the parameter space for which positive smooth solutions of this problem exist and the exact region for which there are no solutions the parameter space is characterized by the geodesic radius of the ball and the coupling constant of the linear term of the brezis nirenberg problem

unsupervised learning of human action categories using spatial temporal words we present a novel unsupervised learning method for human action categories a video sequence is represented as a collection of spatial temporal words by extracting space time interest points the algorithm automatically learns the probability distributions of the spatial temporal words and the intermediate topics corresponding to human action categories this is achieved by using latent topic models such as the probabilistic latent semantic analysis plsa model and latent dirichlet allocation lda our approach can handle noisy feature points arisen from dynamic background and moving cameras due to the application of the probabilistic models given a novel video sequence the algorithm can categorize and localize the human action s contained in the video we test our algorithm on three challenging datasets the kth human motion dataset the weizmann human action dataset and a recent dataset of figure skating actions our results reflect the promise of such a simple approach in addition our algorithm can recognize and localize multiple actions in long and complex video sequences containing multiple motions

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

asymptotic separation for independent trajectories of markov processes we say that n independent trajectories 1 t n t of a stochastic process t on a metric space are asymptotically separated if for some 0 the distance between i ti and j tj is at least for some indices i j and for all large enough t1 tn with probability 1 we prove sufficient conitions for asymptotic separationin terms of the green function and the transition function for a wide class of markov processes in particular if is the diffusion on a riemannian manifold generated by the laplace operator and the heat kernel p t x y satisfies the inequality p t x x ct 2 then n trajectories of are asymptotically separated provided moreover if for some 0 2 then n trajectories of are asymptotically separated where is the process generated by 2

toward dynamic image mosaic generation with robustness to parallax mosaicing is largely dependent on the quality of registration among the constituent input images parallax and object motion present challenges to image registration leading to artifacts in the result to reduce the impact of these artifacts traditional image mosaicing approaches often impose planar scene constraints or rely on purely rotational camera motion or dense sampling however these requirements are often impractical or fail to address the needs of all applications instead taking advantage of depth cues and a smooth transition criterion we achieve significantly improved mosaicing results for static scenes coping effectively with nontrivial parallax in the input we extend this approach to the synthesis of dynamic video mosaics incorporating foreground background segmentation and a consistent motion perception criterion although further additions are required to cope with unconstrained object motion our algorithm can synthesize a perceptually convincing output conveying the same appearance of motion as seen in the input sequences

human action recognition using shape and clg motion flow from multi view image sequences in this paper we present a method for human action recognition from multi view image sequences that uses the combined motion and shape flow information with variability consideration a combined local global clg optic flow is used to extract motion flow feature and invariant moments with flow deviations are used to extract the global shape flow feature from the image sequences in our approach human action is represented as a set of multidimensional clg optic flow and shape flow feature vectors in the spatial temporal action boundary actions are modeled by using a set of multidimensional hmms for multiple views using the combined features which enforce robust view invariant operation we recognize different human actions in daily life successfully in the indoor and outdoor environment using the maximum likelihood estimation approach the results suggest robustness of the proposed method with respect to multiple views action recognition scale and phase variations and invariant analysis of silhouettes

local polynomial kernel regression for generalized linear models and quasi likelihood functions abstract we investigate the extension of the nonparametric regression technique of local polynomial fitting with a kernel weight to generalized linear models and quasi likelihood contexts in the ordinary regression case local polynomial fitting has been seen to have several appealing features in terms of intuitive and mathematical simplicity one noteworthy feature is the better performance near the boundaries compared to the traditional kernel regression estimators these properties are shown to carry over to generalized linear model and quasi likelihood settings we also derive the asymptotic distributions of the proposed class of estimators that allow for straightforward interpretation and extensions of state of the art bandwidth selection methods

specification and structural break tests for additive models with applications to realized variance data we study two types of testing problems in a nonparametric additive model setting we develop methods to test i whether an additive component function has a given parametric form and ii whether an additive component has a structural break we apply the theory to a nonparametric extension of the linear heterogeneous autoregressive model which is widely employed to describe realized variance data we find that the linearity assumption is often rejected but actual deviations from linearity are mild

analytic and geometric background of recurrence and non explosion of the brownian motion on riemannian manifolds we provide an overview of such properties of the brownian motion on complete non compact riemannian manifolds as recurrence and non explosion it is shown that both properties have various analytic characterizations in terms of the heat kernel green function liouville properties etc on the other hand we consider a number of geometric conditions such as the volume growth isoperimetric inequalities curvature bounds etc which are related to recurrence and non explosion

estimation of additive regression models with known links summary we consider estimation of an additive nonparametric regression model with known link function the asymptotic distribution of this regression estimate is given the practical performance is investigated via an application to the study of migration between east and west germany

a universal prior for integers and estimation by minimum description length of the number of bits required to write down the observed data has been reformulated to extend the classical maximum likelihood principle the principle permits estimation of the number of the parameters in statistical models in addition to their values and even of the way the parameters appear in the models i e of the model structures the principle rests on a new way to interpret and construct a universal prior distribution for the integers which makes sense even when the parameter is an individual object truncated realvalued parameters are converted to integers by dividing them by their precision and their prior is determined from the universal prior for the integers by optimizing the precision 1 introduction in this paper we study estimation based upon the principle of minimizing the total number of binary digits required to rewrite the observed data when each observation is given with some precision instead of attempting at an absolutely shortest description which would be futile we look for the optimum relative to a class of parametrically given distributions this minimum description length mdl principle which we introduced in a less comprehensive form in 25 turns out to degenerate to the more familiar maximum likelihood ml principle in case the number of parameters in the models is fixed so that the description length of the parameters themselves can be ignored in another extreme case where the parameters determine the data it similarly degenerates to jaynes s principle of maximum entropy 14 but the main power of the new criterion is that it permits estimates of the entire model its parameters their number and even the way the parameters appear in the model i e the model structure hence there will be no need to supplement the estimated parameters with a separate hypothesis test to decide whether a model is adequately parameterized or perhaps over parameterized

hardy littlewood theory for semigroups soit t t t 0 un semi groupe symetrique sousmarkovien et soit n 2 alors on a les proprietes equivalentes a dim t t n b il existe c 2 0 s t t t f c 2 t n 2 f 1 f l 1 x t 0 en fait a b meme dans le cas n 2

estimation and testing for varying coefficients in additive models with marginal integration we propose marginal integration estimation and testing methods for the coefficients of varying coefficient multivariate regression models asymptotic distribution theory is developed for the estimation method which enjoys the same rate of convergence as univariate function estimation for the test statistic asymptotic normal theory is established these theoretical results are derived under the fairly general conditions of absolute regularity mixing application of the test procedure to west german real gnp gross national product data reveals that a partially linear varying coefficient model is best parsimonious in fitting the data dynamics a fact that is also confirmed with residual diagnostics

linear smoothers and additive models we study linear smoothers and their use in building nonparametric regression models in the first part of this paper we examine certain aspects of linear smoothers for scatterplots examples of these are the running mean and running line kernel and cubic spline smoothers the eigenvalue and singular value decompositions of the corresponding smoother matrix are used to describe qualitatively a smoother and several other topics such as the number of degrees of freedom of a smoother are discussed in the second part of the paper we describe how linear smoothers can be used to estimate the additive model a powerful nonparametric regression model using the backfitting algorithm we show that backfitting is the gauss seidel iterative method for solving a set of normal equations associated with the additive model we provide conditions for consistency and nondegeneracy and prove convergence for the backfitting and related algorithms for a class of smoothers that includes cubic spline smoothers

on the parabolic kernel of the schrodinger operator etude des equations paraboliques du type q x t t u x t 0 sur une variete riemannienne generale introduction estimations de gradients inegalites de harnack majorations et minorations des solutions fondamentales equation de la chaleur et noyau de green operateur de schrodinger

invariant image recognition by zernike moments the problem of rotation scale and translation invariant recognition of images is discussed a set of rotation invariant features are introduced they are the magnitudes of a set of orthogonal complex moments of the image known as zernike moments scale and translation invariance are obtained by first normalizing the image with respect to these parameters using its regular geometrical moments a systematic reconstruction based method for deciding the highest order zernike moments required in a classification problem is developed the quality of the reconstructed image is examined through its comparison to the original one the orthogonality property of the zernike moments which simplifies the process of image reconstruction make the suggest feature selection approach practical features of each order can also be weighted according to their contribution to the reconstruction process the superiority of zernike moment features over regular moments and moment invariants was experimentally verified

spline backfitted kernel smoothing of nonlinear additive autoregression model application of nonparametric and semiparametric regression techniques to high dimensional time series data has been hampered due to the lack of effective tools to address the curse of dimensionality under rather weak conditions we propose spline backfitted kernel estimators of the component functions for the nonlinear additive time series data that are both computationally expedient so they are usable for analyzing very high dimensional time series and theoretically reliable so inference can be made on the component functions with confidence simulation experiments have provided strong evidence that corroborates the asymptotic theory

view invariant representation and recognition of actions analysis of human perception of motion shows that information for representing the motion is obtained from the dramatic changes in the speed and direction of the trajectory in this paper we present a computational representation of human action to capture these dramatic changes using spatio temporal curvature of 2 d trajectory this representation is compact view invariant and is capable of explaining an action in terms of meaningful action units called dynamic instants and intervals a dynamic instant is an instantaneous entity that occurs for only one frame and represents an important change in the motion characteristics an interval represents the time period between two dynamic instants during which the motion characteristics do not change starting without a model we use this representation for recognition and incremental learning of human actions the proposed method can discover instances of the same action performed by different people from different view points experiments on 47 actions performed by 7 individuals in an environment with no constraints shows the robustness of the proposed method

estimates for functions of the laplace operator on homogeneous trees in this paper we study the heat equation on a homogeneous graph relative to the natural nearest neighbour laplacian we find pointwise estimates for the heat and resolvent kernels and the lp lq mapping properties of the corresponding operators in recent years random walks on graphs have been studied as analogues of diffusions on manifolds see e g t coulhon cn m kanai k1 k2 and n th varopoulos v1 v2 more recently i chavel and e a feldman cf and m m h pang p considered the semigroup e t 0 in this paper we consider the heat semigroup associated to the canonical laplace operator on a homogeneous tree which is perhaps the basic example of a graph where the cardinality of the ball of radius r grows exponentially in r we study the properties of the heat and resolvent operators and discover very close analogies with diffusions on hyperbolic spaces in line with the philosophy of the above mentioned authors a homogeneous tree x of degree q 1 is defined to be a connected graph with no loops in which every vertex is adjacent to q 1 other vertices we denote by d the natural distance on x d x y being the number of edges between the vertices x and y and by l x the lebesgue space with respect to counting measure on x on x the canonical laplace operator l is defined thus lf x f x 1 q 1 y x d x y 1 f y x x it is easily seen to be bounded on l x for every p in 1 and self adjoint on l x denote by 2 l the l x spectrum of l and by p the associated spectral resolution of the identity such that lf 2 l dp f f l x and denote inf 2 l by b2 for in 0 1 and with re 0 the heat operator and the resolvent of l are the operators defined by the formulae htf 2 l e t dp f t r received by the editors october 4 1996 1991 mathematics subject classification primary 43a85 secondary 20e08 43a90 22e35

manifolds and graphs with slow heat kernel decay we give upper estimates on the long time behavior of the heat kernel on noncompact riemannian manifolds and infinite graphs which only depend on a lower bound of the volume growth we also show that these estimates are sharp

isoperimetric inequalities and markov chains soit a i j i j n la matrice stochastique d une chaine de markov reversible sur n 1 2 soit n 2 tel que f r c f d f c 0 n ou r 2n n 2 ou c 0 est independant de f et ou r indique la norme dans l r n d pour la mesure i i alors on a sup i j j 1 a i j 0 n 2

discovering motion primitives for unsupervised grouping and one shot learning of human actions gestures and expressions this paper proposes a novel representation of articulated human actions and gestures and facial expressions the main goals of the proposed approach are 1 to enable recognition using very few examples i e one or k shot learning and 2 meaningful organization of unlabeled datasets by unsupervised clustering our proposed representation is obtained by automatically discovering high level subactions or motion primitives by hierarchical clustering of observed optical flow in four dimensional spatial and motion flow space the completely unsupervised proposed method in contrast to state of the art representations like bag of video words provides a meaningful representation conducive to visual interpretation and textual labeling each primitive action depicts an atomic subaction like directional motion of limb or torso and is represented by a mixture of four dimensional gaussian distributions for one shot and k shot learning the sequence of primitive labels discovered in a test video are labeled using kl divergence and can then be represented as a string and matched against similar strings of training videos the same sequence can also be collapsed into a histogram of primitives or be used to learn a hidden markov model to represent classes we have performed extensive experiments on recognition by one and k shot learning as well as unsupervised action clustering on six human actions and gesture datasets a composite dataset and a database of facial expressions these experiments confirm the validity and discriminative nature of the proposed representation

unsupervised learning of finite mixture models this paper proposes an unsupervised algorithm for learning a finite mixture model from multivariate data the adjective unsupervised is justified by two properties of the algorithm 1 it is capable of selecting the number of components and 2 unlike the standard expectation maximization em algorithm it does not require careful initialization the proposed method also avoids another drawback of em for mixture fitting the possibility of convergence toward a singular estimate at the boundary of the parameter space the novelty of our approach is that we do not use a model selection criterion to choose one among a set of preestimated candidate models instead we seamlessly integrate estimation and model selection in a single algorithm our technique can be applied to any type of parametric mixture model for which it is possible to write an em algorithm in this paper we illustrate it with experiments involving gaussian mixtures these experiments testify for the good performance of our approach

on the discreteness of the spectrum of the laplacian on noncompact riemannian manifolds necessary and sufficient conditions for the discreteness of the laplacian on a noncompact riemannian manifold m are established in terms of the isocapacitary function of m the relevant capacity takes a different form according to whether m has finite or infinite volume conditions involving the more standard isoperimetric function of m can also be derived but they are only sufficient in general as we demonstrate by concrete examples

action categorization with modified hidden conditional random field in this paper we present a method for action categorization with a modified hidden conditional random field hcrf specifically effective silhouette based action features are extracted using motion moments and spectrum of chain code we formulate a modified hcrf mhcrf to have a guaranteed global optimum in the modelling of the temporal action dependencies after the hmm pathing stage experimental results on action categorization using this model are compared favorably against several existing model based methods including gmm svm logistic regression hmm crf and hcrf

spatiotemporal localization and categorization of human actions in unsegmented image sequences in this paper we address the problem of localization and recognition of human activities in unsegmented image sequences the main contribution of the proposed method is the use of an implicit representation of the spatiotemporal shape of the activity which relies on the spatiotemporal localization of characteristic ensembles of feature descriptors evidence for the spatiotemporal localization of the activity is accumulated in a probabilistic spatiotemporal voting scheme the local nature of the proposed voting framework allows us to deal with multiple activities taking place in the same scene as well as with activities in the presence of clutter and occlusion we use boosting in order to select characteristic ensembles per class this leads to a set of class specific codebooks where each codeword is an ensemble of features during training we store the spatial positions of the codeword ensembles with respect to a set of reference points as well as their temporal positions with respect to the start and end of the action instance during testing each activated codeword ensemble casts votes concerning the spatiotemporal position and extend of the action using the information that was stored during training mean shift mode estimation in the voting space provides the most probable hypotheses concerning the localization of the subjects at each frame as well as the extend of the activities depicted in the image sequences we present classification and localization results for a number of publicly available datasets and for a number of sequences where there is a significant amount of clutter and occlusion

a discriminative model of motion and cross ratio for view invariant action recognition action recognition is very important for many applications such as video surveillance human computer interaction and so on view invariant action recognition is hot and difficult as well in this field in this paper a new discriminative model is proposed for video based view invariant action recognition in the discriminative model motion pattern and view invariants are perfectly fused together to make a better combination of invariance and distinctiveness we address a series of issues including interest point detection in image sequence motion feature extraction and description and view invariant calculation first motion detection is used to extract motion information from videos which is much more efficient than traditional background modeling and tracking based methods second as for feature representation we exact variety of statistical information from motion and view invariant feature based on cross ratio last in the action modeling we apply a discriminative probabilistic model hidden conditional random field to model motion patterns and view invariants by which we could fuse the statistics of motion and projective invariability of cross ratio in one framework experimental results demonstrate that our method can improve the ability to distinguish different categories of actions with high robustness to view change in real circumstances

view invariant analysis of cyclic motion this paper presents a general framework for image based analysis of 3d repeating motions that addresses two limitations in the state of the art first the assumption that a motion be perfectly even from one cycle to the next is relaxed real repeating motions tend not to be perfectly even i e the length of a cycle varies through time because of physically important changes in the scene a generalization of period is defined for repeating motions that makes this temporal variation explicit this representation called the period trace is compact and purely temporal describing the evolution of an object or scene without reference to spatial quantities such as position or velocity second the requirement that the observer be stationary is removed observer motion complicates image analysis because an object that undergoes a 3d repeating motion will generally not produce a repeating sequence of images using principles of affine invariance we derive necessary and sufficient conditions for an image sequence to be the projection of a 3d repeating motion accounting for changes in viewpoint and other camera parameters unlike previous work in visual invariance however our approach is applicable to objects and scenes whose motion is highly non rigid experiments on real image sequences demonstrate how the approach may be used to detect several types of purely temporal motion features relating to motion trends and irregularities applications to athletic and medical motion analysis are discussed

action recognition using linear dynamic systems in this paper we propose a novel approach based on linear dynamic systems ldss for action recognition our main contributions are two fold first we introduce ldss to action recognition ldss describe the dynamic texture which exhibits certain stationarity properties in time they are adopted to model the spatiotemporal patches which are extracted from the video sequence because the spatiotemporal patch is more analogous to a linear time invariant system than the video sequence notably ldss do not live in the euclidean space so we adopt the kernel principal angle to measure the similarity between ldss and then the multiclass spectral clustering is used to generate the codebook for the bag of features representation second we propose a supervised codebook pruning method to preserve the discriminative visual words and suppress the noise in each action class the visual words which maximize the inter class distance and minimize the intra class distance are selected for classification our approach yields the state of the art performance on three benchmark datasets especially the experiments on the challenging ucf sports and feature films datasets demonstrate the effectiveness of the proposed approach in realistic complex scenarios

oracally efficient two step estimation of generalized additive model the generalized additive model gam is a multivariate nonparametric regression tool for non gaussian responses including binary and count data we propose a spline backfitted kernel sbk estimator for the component functions and the constant which are oracally efficient under weak dependence the sbk technique is both computationally expedient and theoretically reliable thus usable for analyzing high dimensional time series inference can be made on component functions based on asymptotic normality simulation evidence strongly corroborates the asymptotic theory the method is applied to estimate insolvent probability and to obtain higher accuracy ratio than a previous study supplementary materials for this article are available online

exploring sparseness and self similarity for action recognition we propose that the dynamics of an action in video data forms a sparse self similar manifold in the space time volume which can be fully characterized by a linear rank decomposition inspired by the recurrence plot theory we introduce the concept of joint self similarity volume joint ssv to model this sparse action manifold and hence propose a new optimized rank 1 tensor approximation of the joint ssv to obtain compact low dimensional descriptors that very accurately characterize an action in a video sequence we show that these descriptor vectors make it possible to recognize actions without explicitly aligning the videos in time in order to compensate for speed of execution or differences in video frame rates moreover we show that the proposed method is generic in the sense that it can be applied using different low level features such as silhouettes tracked points histogram of oriented gradients and so forth therefore our method does not necessarily require explicit tracking of features in the space time volume our experimental results on five public data sets demonstrate that our method produces promising results and outperforms many baseline methods

an analysis of transformations for additive nonparametric regression abstract we consider a nonparametric regression model with a parametric family of dependent variable transformations one of which induces additive covariate effects we estimate the additive regression effects using the integration method and estimate the transformation parameter from a profiled instrumental variable and pseudolikelihood criterion the asymptotic distributions of the parameter and regression estimates are given the practical performance is investigated via an application

smooth backfitting in generalized additive models generalized additive models have been popular among statisticians and data analysts in multivariate nonparametric regression with non gaussian responses including binary and count data in this paper a new likelihood approach for fitting generalized additive models is proposed it aims to maximize a smoothed likelihood the additive functions are estimated by solving a system of nonlinear integral equations an iterative algorithm based on smooth backfitting is developed from the newton kantorovich theorem asymptotic properties of the estimator and convergence of the algorithm are discussed it is shown that our proposal based on local linear fit achieves the same bias and variance as the oracle estimator that uses knowledge of the other components numerical comparison with the recently proposed two stage estimator ann statist 32 2004 2412 2443 is also made

large margin cost sensitive learning of conditional random fields we tackle the structured output classification problem using the conditional random fields crfs unlike the standard 0 1 loss case we consider a cost sensitive learning setting where we are given a non 0 1 misclassification cost matrix at the individual output level although the task of cost sensitive classification has many interesting practical applications that retain domain specific scales in the output space e g hierarchical or ordinal scale most crf learning algorithms are unable to effectively deal with the cost sensitive scenarios as they merely assume a nominal scale hence 0 1 loss in the output space in this paper we incorporate the cost sensitive loss into the large margin learning framework by large margin learning the proposed algorithm inherits most benefits from the svm like margin based classifiers such as the provable generalization error bounds moreover the soft max approximation employed in our approach yields a convex optimization similar to the standard crf learning with only slight modification in the potential functions we also provide the theoretical cost sensitive generalization error bound we demonstrate the improved prediction performance of the proposed method over the existing approaches in a diverse set of sequence image structured prediction problems that often arise in pattern recognition and computer vision domains

modeling and classifying human activities from trajectories using a class of space varying parametric motion fields many approaches to trajectory analysis such as clustering or classification use probabilistic generative models thus not requiring trajectory alignment registration switched linear dynamical models e g hmms have been used in this context due to their ability to describe different motion regimes however these models are not suitable for handling space dependent dynamics that are more naturally captured by nonlinear models as is well known these are more difficult to identify in this paper we propose a new way of modeling trajectories based on a mixture of parametric motion vector fields that depend on a small number of parameters switching among these fields follows a probabilistic mechanism characterized by a field of stochastic matrices this approach allows representing a wide variety of trajectories and modeling space dependent behaviors without using global nonlinear dynamical models experimental evaluation is conducted in both synthetic and real scenarios the latter concerning with human trajectory modeling for activity classification a central task in video surveillance

local likelihood estimation abstract a scatterplot smoother is applied to data of the form x 1 y 1 x 2 y 2 xn yn and uses local fitting to estimate the dependence of y on x a simple example is the running lines smoother which fits a least squares line to the y values falling in a window around each x value the value of the estimated function at x is given by the value of the least squares line at x a smoother generalizes the least squares line which assumes that the dependence of y on x is linear in this article we extend the idea of local fitting to likelihood based regression models one such application is to the class of generalized linear models nelder and wedderburn 1972 we enlarge this class by replacing the covariate form 0 x 1 with an unspecified smooth function s x this function is estimated from the data by a technique we call local likelihood estimation the method consists of maximum likelihood estimation for 0 and 1 applied in a window around each x value multiple covariates are incor

human action recognition based on graph embedded spatio temporal subspace human action recognition is an important issue in the pattern recognition field with applications ranging from remote surveillance to the indexing of commercial video content however human actions are characterized by non linear dynamics and are therefore not easily learned and recognized accordingly this study proposes a silhouette based human action recognition system in which a three step procedure is used to construct an efficient discriminant spatio temporal subspace for k nn classification purposes in the first step an adaptive locality preserving projection alpp method is proposed to obtain a low dimensional spatial subspace in which the linearity in the local data structure is preserved to resolve the problem of overlaps in the spatial subspace resulting from the ambiguity of the human body shape among different action classes temporal data are extracted using a non base central difference action vector ncdav method finally the large margin nearest neighbor lmnn metric learning method is applied to construct an efficient spatio temporal subspace for classification purposes the experimental results show that the proposed system accurately recognizes a variety of human actions in real time and outperforms most existing methods in addition a robustness test with noisy data indicates that our system is remarkably robust toward noise in the input images

design adaptive nonparametric regression abstract in this article we study the method of nonparametric regression based on a weighted local linear regression this method has advantages over other popular kernel methods moreover such a regression procedure has the ability of design adaptation it adapts to both random and fixed designs to both highly clustered and nearly uniform designs and even to both interior and boundary points it is shown that the local linear regression smoothers have high asymptotic efficiency i e can be 100 with a suitable choice of kernel and bandwidth among all possible linear smoothers including those produced by kernel orthogonal series and spline methods the finite sample property of the local linear regression smoother is illustrated via simulation studies nonparametric regression is frequently used to explore the association between covariates and responses there are many versions of kernel regression smoothers some estimators are not good for random designs such as in observational studies and

view invariant action recognition based on artificial neural networks in this paper a novel view invariant action recognition method based on neural network representation and recognition is proposed the novel representation of action videos is based on learning spatially related human body posture prototypes using self organizing maps fuzzy distances from human body posture prototypes are used to produce a time invariant action representation multilayer perceptrons are used for action classification the algorithm is trained using data from a multi camera setup an arbitrary number of cameras can be used in order to recognize actions using a bayesian framework the proposed method can also be applied to videos depicting interactions between humans without any modification the use of information captured from different viewing angles leads to high classification performance the proposed method is the first one that has been tested in challenging experimental setups a fact that denotes its effectiveness to deal with most of the open issues in action recognition

3d motion recovery via affine epipolar geometry algorithms to perform point based motion estimation under orthographic and scaled orthographic projection abound in the literature a key limitation of many existing algorithms is that they operate on the minimum amount of data required often requiring the selection of a suitable minimal set from the available data to serve as a local coordinate frame such approaches are extremely sensitive to errors and noise in the minimal set and forfeit the advantages of using the full data set furthermore attention is seldom paid to the statistical performance of the algorithms

local polynomial estimation of nonparametric simultaneous equations models abstract we define a new procedure for consistent estimation of nonparametric simultaneous equations models under the conditional mean independence restriction of newey et al 1999 nonparametric estimation of triangular simultaneous equation models econometrica 67 565 603 it is based upon local polynomial regression and marginal integration techniques we establish the asymptotic distribution of our estimator under weak data dependence conditions simulation evidence suggests that our estimator may significantly outperform the estimators of pinkse 2000 nonparametric two step regression estimation when regressors and errors are dependent canadian journal of statistics 28 289 300 and newey and powell 2003 instrumental variable estimation of nonparametric models econometrica 71 1565 1578

difference equations isoperimetric inequality and transience of certain random walks the difference laplacian on a square lattice in rn has been stud ied by many authors in this paper an analogous difference operator is studied for an arbitrary graph it is shown that many properties of the laplacian in the continuous setting e g the maximum principle the harnack inequality and cheeger s bound for the lowest eigenvalue hold for this difference oper ator the difference laplacian governs the random walk on a graph just as the laplace operator governs the brownian motion as an application of the theory of the difference laplacian it is shown that the random walk on a class of graphs is transient the random walks we consider are defined as follows let k be a connected graph i e a one dimensional simplicial complex for a vertex x e k let m x denote the number of edges emanating from x the probability that a particle moves from x to another vertex y e k is l m x if x and y are connected by an edge and it is zero otherwise as observed by courant friedrichs and lewy cfl for the case of a square lattice in the plane this random walk is intimately related to the difference analog of the laplacian

bounds for eigenfunctions of the laplacian on noncompact riemannian manifolds we deal with eigenvalue problems for the laplacian on noncompact riemannian manifolds m of finite volume sharp conditions ensuring l q m and l infinity m bounds for eigenfunctions are exhibited

miscellanea efficient estimation of additive nonparametric regression models summary we define a new procedure for estimating additive nonparametric regression models we use the integration method of linton nielsen 1995 to provide starting values that are then used in a one step backfitting procedure we show that our new method is efficient in a certain sense and dominates the straight integration method according to mean squared error

identification and n consistent estimation of a nonlinear panel data model with correlated unobserved effects abstract this paper investigates identification and root n consistent estimation of a class of single index panel data models in which the link function is unknown the unobserved individual effects may be correlated with all the explanatory variables and all the explanatory variables may be predetermined we propose two sets of sufficient conditions one in which link function is assumed to be strictly increasing and the other in which it is not we propose simple kernel based estimators for the models and derive consistency and asymptotic normality results for the proposed estimators finally we present results of two monte carlo studies of the estimators

large time behavior of the heat kernel in this paper we study the large time behavior of the minimal heat kernel kpm x y t of a general time independent parabolic operator lu ut p x x u which is defined on a noncompact manifold m more precisely we prove that limt e 0tkpm x y t always exists here 0 is the generalized principal eigenvalue of the operator p in m

shape matching and object recognition using shape contexts we present a novel approach to measuring similarity between shapes and exploit it for object recognition in our framework the measurement of similarity is preceded by 1 solving for correspondences between points on the two shapes 2 using the correspondences to estimate an aligning transform in order to solve the correspondence problem we attach a descriptor the shape context to each point the shape context at a reference point captures the distribution of the remaining points relative to it thus offering a globally discriminative characterization corresponding points on two similar shapes will have similar shape contexts enabling us to solve for correspondences as an optimal assignment problem given the point correspondences we estimate the transformation that best aligns the two shapes regularized thin plate splines provide a flexible class of transformation maps for this purpose the dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points together with a term measuring the magnitude of the aligning transform we treat recognition in a nearest neighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image results are presented for silhouettes trademarks handwritten digits and the coil data set

matching shape sequences in video with applications in human movement analysis we present an approach for comparing two sequences of deforming shapes using both parametric models and nonparametric methods in our approach kendall s definition of shape is used for feature extraction since the shape feature rests on a non euclidean manifold we propose parametric models like the autoregressive model and autoregressive moving average model on the tangent space and demonstrate the ability of these models to capture the nature of shape deformations using experiments on gait based human recognition the nonparametric model is based on dynamic time warping we suggest a modification of the dynamic time warping algorithm to include the nature of the non euclidean space in which the shape deformations take place we also show the efficacy of this algorithm by its application to gait based human recognition we exploit the shape deformations of a person s silhouette as a discriminating feature and provide recognition results using the nonparametric model our analysis leads to some interesting observations on the role of shape and kinematics in automated gait based person authentication

generalised structured models summary we present a general class of nonlinear regression and time series models that we call generalised structured models the class is a natural generalisation of generalised additive models and it includes generalised interaction models structured volatility models visual garch generalised autoregressive conditional heteroscedasticity models and varying coefficient models we discuss estimation principles including smoothing splines and a generalisation of the projection approach of mammen et al 1999 we finish the paper with some theoretical considerations about the asymptotic performance of the estimator for the general class of generalised structured models

flexible modelling of discrete failure time including time varying smooth effects discrete survival models have been extended in several ways more flexible models are obtained by including time varying coefficients and covariates which determine the hazard rate in an additive but not further specified form in this paper a general model is considered which comprises both types of covariate effects an additional extension is the incorporation of smooth interaction between time and covariates thus in the linear predictor smooth effects of covariates which may vary across time are allowed it is shown how simple duration models produce artefacts which may be avoided by flexible models for the general model which includes parametric terms time varying coefficients in parametric terms and time varying smooth effects estimation procedures are derived which are based on the regularized expansion of smooth effects in basis functions the approach is used to model the sojourn time in a psychiatric hospital it is demonstrated how initial conditions which have non linear influence are damped over time

support vector machines for histogram based image classification traditional classification approaches generalize poorly on image classification tasks because of the high dimensionality of the feature space this paper shows that support vector machines svm can generalize well on difficult image classification problems where the only features are high dimensional histograms heavy tailed rbf kernels of the form k x y e sup spl rho spl sigma sub i sup xia yia b with a spl les 1 and b spl les 2 are evaluated on the classification of images extracted from the corel stock photo collection and shown to far outperform traditional polynomial or gaussian radial basis function rbf kernels moreover we observed that a simple remapping of the input x sub i spl rarr x sub i sup a improves the performance of linear svm to such an extend that it makes them for this problem a valid alternative to rbf kernels

explicit constants for gaussian upper bounds on heat kernels on utilise des inegalites logarithmiques de sobolev pour obtenir des bornes superieures gaussiennes sur les noyaux de la chaleur associes a des operateurs d ordre 2 elliptiques et hypoelliptiques

lucas kanade meets horn schunck combining local and global optic flow methods differential methods belong to the most widely used techniques for optic flow computation in image sequences they can be classified into local methods such as the lucas kanade technique or bigun s structure tensor method and into global methods such as the horn schunck approach and its extensions often local methods are more robust under noise while global techniques yield dense flow fields the goal of this paper is to contribute to a better understanding and the design of novel differential methods in four ways i we juxtapose the role of smoothing regularisation processes that are required in local and global differential methods for optic flow computation ii this discussion motivates us to describe and evaluate a novel method that combines important advantages of local and global approaches it yields dense flow fields that are robust against noise iii spatiotemporal and nonlinear extensions as well as multiresolution frameworks are presented for this hybrid method iv we propose a simple confidence measure for optic flow methods that minimise energy functionals it allows to sparsify a dense flow field gradually depending on the reliability required for the resulting flow comparisons with experiments from the literature demonstrate the favourable performance of the proposed methods and the confidence measure

action recognition by spatio temporal oriented energies in this paper we present a unified representation based on the spatio temporal steerable pyramid stsp for the holistic representation of human actions a video sequence is viewed as a spatio temporal volume preserving all the appearance and motion information of an action in it by decomposing the spatio temporal volumes into band passed sub volumes the spatio temporal laplacian pyramid provides an effective technique for multi scale analysis of video sequences and spatio temporal patterns with different scales could be well localized and captured to efficiently explore the underlying local spatio temporal orientation structures at multiple scales a bank of three dimensional separable steerable filters are conducted on each of the sub volume from the laplacian pyramid the outputs of the quadrature pair of steerable filters are squared and summed to yield a more robust oriented energy representation to be further invariant and compact a spatio temporal max pooling operation is performed between responses of the filtering at adjacent scales and over spatio temporal neighbourhoods in order to capture the appearance local geometric structure and motion of an action we apply the stsp on the intensity 3d gradients and optical flow of video sequences yielding a unified holistic representation of human actions taking advantage of multi scale multi orientation analysis and feature pooling stsp produces a compact but informative and invariant representation of human actions we conduct extensive experiments on the kth ucf sports and hmdb51 datasets which shows the unified stsp achieves comparable results with the state of the art methods

translation invariants of zernike moments moment functions defined using a polar coordinate representation of the image space such as radial moments and zernike moments are used in several recognition tasks requiring rotation invariance however this coordinate representation does not easily yield translation invariant functions which are also widely sought after in pattern recognition applications this paper presents a mathematical framework for the derivation of translation invariants of radial moments defined in polar form using a direct application of this framework translation invariant functions of zernike moments are derived algebraically from the corresponding central moments both derived functions are developed for non symmetrical as well as symmetrical images they mitigate the zero value obtained for odd order moments of the symmetrical images vision applications generally resort to image normalization to achieve translation invariance the proposed method eliminates this requirement by providing a translation invariance property in a zernike feature set the performance of the derived invariant sets is experimentally confirmed using a set of binary latin and english characters

consistent model selection for marginal generalized additive model for correlated data we consider the generalized additive model when responses from the same cluster are correlated incorporating correlation in the estimation of nonparametric components for the generalized additive model is important because it improves estimation efficiency and increases statistical power for model selection in our setting there is no specified likelihood function for the generalized additive model because the outcomes could be nonnormal and discrete which makes estimation and model selection very challenging problems we propose consistent estimation and model selection that incorporate the correlation structure we establish an asymptotic property with l2 norm consistency for the nonparametric components which achieves the optimal rate of convergence in addition the proposed model selection strategy is able to select the correct generalized additive model consistently that is with probability approaching to 1 the estimators for the zero function components converge to 0 almost surely we illus

a new proof of moser s parabolic harnack inequality using the old ideas of nash in 1958 nash published his fundamental work on the local holder continuity of solutions of second order parabolic equations with coefficients which need not be smooth 8 the primary purpose of that work was to study the properties of the fundamental solution corresponding to the parabolic operator and from these properties to derive regularity for a general solution though the work is often cited in the literature about weak solutions of elliptic and parabolic equations one feels that nash s ideas were never fully understood and maybe still are not and that because of this the more understandable and seemingly more fruitful ideas of de giorgi 4 and moser 6 7 were subsequently adopted

nonparametric identification of nonlinear time series projections abstract we study the possibility of identifying general linear and nonlinear time series models using nonparametric methods the kernel estimators of the conditional mean and variance are used as a basis and the properties of these quantities as model indicators are briefly discussed some drawbacks are pointed out and motivated by these we introduce projections as tools of identification the projections are especially useful for additive modeling expressions for the asymptotic bias and variance are obtained the projection of the conditional variance is suggested as a tool for identifying heteroscedastic time series the results are illustrated by simulations for both the estimators of the projections and the estimators of the conditional mean and variance

shape and motion from image streams under orthography a factorization method inferring scene geometry and camera motion from a stream of images is possible in principle but is an ill conditioned problem when the objects are distant with respect to their size we have developed a factorization method that can overcome this difficulty by recovering shape and motion under orthography without computing depth as an intermediate step an image stream can be represented by the 2fxp measurement matrix of the image coordinates of p points tracked through f frames we show that under orthographic projection this matrix is of rank 3 based on this observation the factorization method uses the singular value decomposition technique to factor the measurement matrix into two matrices which represent object shape and camera rotation respectively two of the three translation components are computed in a preprocessing stage the method can also handle and obtain a full solution from a partially filled in measurement matrix that may result from occlusions or tracking failures the method gives accurate results and does not introduce smoothing in either shape or motion we demonstrate this with a series of experiments on laboratory and outdoor image streams with and without occlusions

noncommutative riemann integration and novikov shubin invariants for open manifolds given a c algebra a with a semicontinuous semifinite trace acting on the hilbert space h we define the family ar of bounded riemann measurable elements w r t as a suitable closure a la dedekind of a in analogy with one of the classical characterizations of riemann measurable functions and show that ar is a c algebra and extends to a semicontinuous semifinite trace on ar then unbounded riemann measurable operators are defined as the closed operators on h which are affiliated to a and can be approximated in measure by operators in ar in analogy with unbounded riemann integration unbounded riemann measurable operators form a a e bimodule on ar denoted by ar and such a bimodule contains the functional calculi of selfadjoint elements of ar under unbounded riemann measurable functions besides extends to a bimodule trace on ar type ii1 singular traces for c algebras can be defined on the bimodule of unbounded riemann measurable operators noncommutative riemann integration and singular traces for c algebras are then used to define novikov shubin numbers for amenable open manifolds to show their invariance under quasi isometries and to prove that they are noncommutative asymptotic dimensions

rate optimal estimation for a general class of nonparametric regression models with unknown link functions this paper discusses a nonparametric regression model that naturally generalizes neural network models the model is based on a finite number of one dimensional transformations and can be estimated with a one dimensional rate of convergence the model contains the generalized additive model with unknown link function as a special case for this case it is shown that the additive components and link function can be estimated with the optimal rate by a smoothing spline that is the solution of a penalized least squares criterion

semiparametric estimation of a panel data proportional hazards model with fixed effects this paper considers a panel duration model that has a proportional hazards specification with fixed effects the paper shows how to estimate the baseline and integrated baseline hazard functions without assuming that they belong to known finite dimensional families of functions existing estimators assume that the baseline hazard function belongs to a known parametric family therefore the estimators presented here are more general than existing ones this paper also presents a method for estimating the parametric part of the proportional hazards model with dependent right censoring under which the partial likelihood estimator is inconsistent the paper presents some monte carlo evidence on the small sample performance of the new estimators

nonparametric estimation of an additive model with a link function this paper describes an estimator of the additive components of a nonparametric additive model with a known link function when the additive components are twice continuously differentiable the estimator is asymptotically normally distributed with a rate of convergence in probability of 2 5 n this is true regardless of the finite dimension of the explanatory variable thus in contrast to the existing asymptotically normal estimator the new estimator has no curse of dimensionality moreover the asymptotic distribution of each additive component is the same as it would be if the other components were known with certainty

silhouette analysis based gait recognition for human identification human identification at a distance has recently gained growing interest from computer vision researchers gait recognition aims essentially to address this problem by identifying people based on the way they walk in this paper a simple but efficient gait recognition algorithm using spatial temporal silhouette analysis is proposed for each image sequence a background subtraction algorithm and a simple correspondence procedure are first used to segment and track the moving silhouettes of a walking figure then eigenspace transformation based on principal component analysis pca is applied to time varying distance signals derived from a sequence of silhouette images to reduce the dimensionality of the input feature space supervised pattern classification techniques are finally performed in the lower dimensional eigenspace for recognition this method implicitly captures the structural and transitional characteristics of gait extensive experimental results on outdoor image sequences demonstrate that the proposed algorithm has an encouraging recognition performance with relatively low computational cost

cyclic motion detection for motion based recognition the motion of a walking person is analyzed by examining cycles in the movement cycles are detected using autocorrelation and fourier transform techniques of the smoothed spatio temporal curvature function of trajectories created by specific points on the object as it performs cyclic motion a large impulse in the fourier magnitude plot indicates the frequency at which cycles are occurring both synthetically generated and real walking sequences are analyzed for cyclic motion the real sequences are then used in a motion based recognition application in which one complete cycle is stored as a model and a matching process is performed using one cycle of an input trajectory

nonparametric estimation of a generalized additive model with an unknown link function mean of a random scalar y conditional on a random vector x e rd let h x e yix x denote the conditional mean function this paper is concerned with estimating h under weak assumptions about its functional form when x is a multidimensional continuous random variable the paper describes a model that nests single index additive and multiplicative models and that can be estimated with a faster rate of convergence in probability than can a fully nonparametric model nonparametric estimation of h is usually unattractive when x is multidimensional the rate of convergence of nonparametric estimators decreases rapidly as the dimension of x increases and nonparametric estimates can be very imprecise with samples of practical size when x is multidimensional the curse of dimensionality this problem can be overcome through the use of dimension reduction methods they reduce the effective dimension of the estimation problem by making assumptions about the functional form of h that are stronger than those of a fully nonparametric estimator but weaker than those of a finite dimensional parametric model one method of dimension reduction is semiparametric single index modeling the best known and most easily estimated semiparametric single index model assumes that 1 1 h x g 3 x where 3 is an unknown d x 1 vector and g is an unknown function the vector 3 can be estimated with an n 1 2 rate of convergence in probability which is the rate that would be obtained if g were known han 1987 hardle and stoker 1989 horowitz and hardle 1996 ichimura 1993 klein and spady 1993 newey and stoker 1993 powell stock and stoker 1989 sherman 1993 stoker 1991 g can be estimated with the rate of convergence n r 2r 1 where r is an integer that depends on the smoothness of g but not on d dimension reduction can also be achieved by using a nonparametric generalized additive model in such a model