the em algorithm an old folk song sung to a fast new tune celebrating the 20th anniversary of the presentation of the paper by dempster laird and rubin which popularized the em algorithm we investigate after a brief historical account strategies that aim to make the em algorithm converge faster while maintaining its simplicity and stability e g automatic monotone convergence in likelihood first we introduce the idea of a working parameter to facilitate the search for efficient data augmentation schemes and thus fast em implementations second summarizing various recent extensions of the em algorithm we formulate a general alternating expectation conditional maximization algorithm aecm that couples flexible data augmentation schemes with model reduction schemes to achieve efficient computations we illustrate these methods using multivariate t models with known or unknown degrees of freedom and poisson models for image reconstruction we show through both empirical and theoretical evidence the potential for a dramatic reduction in computational time with little increase in human effort we also discuss the intrinsic connection between em type algorithms and the gibbs sampler and the possibility of using the techniques presented here to speed up the latter the main conclusion of the paper is that with the help of statistical considerations it is possible to construct algorithms that are simple stable and fast

sur le theoreme d atiyah singer on donne une version simplifiee de la demonstration probabiliste du theoreme de l indice pour l operateur de dirac donnee par j m bismut au lieu d utiliser la construction du mouvement brownien au moyen du fibre des reperes on utilise la construction de schwartz en plongeant la variete ambiante dans un espace vectoriel de dimension plus grande on evite aussi l utilisation de la decomposition de l espace de wiener en deux utilisee par j m bismut le calcul des variations stochastiques etant notre outil principal de ce fait on perd la relation avec la cohomologie de l espace des lacets

analytic torsion and holomorphic determinant bundles in this paper we prove that in the case of holomorphic locally kahler fibrations the analytic and algebraic geometry constructions of determinant bundles for direct images coincide we calculate the curvature of the holomorphic hermitian connection for the quillen metric on the determinant bundle we study the behavior of the quillen metric under change of metrics in the fibers and also on the twisting vector bundles we thus generalize the conformal anomaly formula to kahler manifolds of arbitrary dimension we also study the quillen metrics on determinants associated with exact sequences of vector bundles we prove that the quillen metric is smooth on the grothendieck knudsen mumford determinant for arbitrary holomorphic fibrations

determinant bundles manifolds with boundary and surgery we define determinant bundles associated to the following data i a family of generalized dirac operators on even dimensional manifolds with boundary ii the choice of a spectral section for the family of dirac operators induced on the boundary under the assumption that the operators of the boundary family have null spaces of constant dimension we define through the notion ofb zeta function a quillen metric we also introduce the analogue of the bismut freed connection we prove that the curvature of a natural perturbation of the bismut freed connection equals the 2 form piece in the right hand side of the family index formula thus extending to manifolds with boundary results of quillen bismut and freed given a closed fibration we investigate the behaviour of the quillen metric and of the bismut freed connection under the operation of surgery along a fibering hypersurface we prove in particular additivity formulae for the curvature and for the logarithm of the holonomy

etale groupoids eta invariants and index theory let g be a discrete finitely generated group let m t be a g equivariant fibration with fibers dieomorphic to a fixed even dimensional manifold with boundary z we assume that g m m g is a galois covering of a compact manifold with boundary letd y ya t be a g equivariant family of dirac type operators under the assumption that the boundary family is l 2 invertible we define an index class in k0 c 0 t zr g if in addition g is of polynomial growth we define higher indices by pairing the index class with suitable cyclic cocycles our main result is then a formula for these higher indices the structure of the formula is as in the seminal work of atiyah patodi and singer with an interior geometric contribution and a boundary contribution in the form of a higher eta invariant associated to the boundary family under similar assump tions we extend our theorem to any g proper manifold with g an etale groupoid we employ this generalization in order to establish a higher atiyah patodi singer index formula on certain foliations with boundary fundamental to our work is a suitable generalization of melrose b pseudodierential calculus as well as the superconnection proof of the index theorem on g proper manifolds recently given by gorokhovsky and lott in 10

manifold regularization a geometric framework for learning from labeled and unlabeled examples we propose a family of learning algorithms based on a new form of regularization that allows us to exploit the geometry of the marginal distribution we focus on a semi supervised framework that incorporates labeled and unlabeled data in a general purpose learner some transductive graph learning algorithms and standard methods including support vector machines and regularized least squares can be obtained as special cases we use properties of reproducing kernel hilbert spaces to prove new representer theorems that provide theoretical basis for the algorithms as a result in contrast to purely graph based approaches we obtain a natural out of sample extension to novel examples and so are able to handle both transductive and truly semi supervised settings we present experimental evidence suggesting that our semi supervised algorithms are able to use unlabeled data effectively finally we have a brief discussion of unsupervised and fully supervised learning within our general framework

the higher twisted index theorem for foliations abstract given a gerbe l on the holonomy groupoid g of the foliation m f whose pull back to m is torsion we construct a connes map from the twisted dupont sullivan bicomplex of g to the cyclic complex of the l projective leafwise smoothing operators on m f our construction allows to couple the k theory analytic indices of l projective leafwise elliptic operators with the twisted cohomology of b g producing scalar higher invariants finally by adapting the bismut quillen superconnection approach we compute these higher twisted indices as integrals over the ambient manifold of the expected twisted characteristic classes

on family rigidity theorems i note that ind p is a virtual g representation let chg ind p with g g be the equivariant chern character of ind p evaluated at g in this paper we first prove a family fixed point formula that expresses chg ind p in terms of the geometric data on the fixed points x of the fiber of then by applying this formula we generalize the witten rigidity theorems and several vanishing theorems proved in liu3 for elliptic genera to the family case let g s1 a family elliptic operator p is called rigid on the equivariant chern character level with respect to this s1 action if chg ind p h b is independent of g s1 when the base b is a point we recover the classical rigidity and vanishing theorems when b is a manifold we get many nontrivial higher order rigidity and vanishing theorems by taking the coefficients of certain expansion of chg for the history of the witten rigidity theorems we refer the reader to t bt k l2 h liu1 and liu4 the family vanishing theorems that generalize those vanishing theorems in liu3 which in turn give us many higher order vanishing theorems in the family case in a forthcoming paper we extend our results to general loop group representations and prove much more general family vanishing theorems that generalize the results in liu3 we believe there should be some applications of our results to topology and geometry which we hope to report on a later occasion this paper is organized as follows in section 1 we prove the equivariant family index theorem in section 2 we prove the family rigidity theorem in the last part of section 2 motivated by the family rigidity theorem we state a conjecture in section 3 we generalize the family rigidity theorem to the nonzero anomaly case as corollaries we derive several vanishing theorems

eta invariants torsion forms and flat vector bundles we present a new proof as well as a c q extension and also certain c z extension of the riemann roch grothendieck theorem of bismut lott for flat vector bundles the main techniques used are the computations of the adiabatic limits of invariants associated to the so called sub signature operators we further show that the bismut lott analytic torsion form can be derived naturally from transgressions of forms appearing in the adiabatic limit computations

differential k theory and localization formula for eta invariants in this paper we obtain a localization formula in differential k theory for s 1 actions we establish a localization formula for equivariant eta invariants by combining this result with our extension of goette s result on the comparison of two types of equivariant eta invariants an important step in our approach is to construct a pre lambda ring structure in differential k theory

diffusions conditionnelles i hypoellipticite partielle this paper is devoted to the proof of certain results on conditional diffusions by using the malliavin calculus of variations it is shown that under minimal conditions on the vectors fields which define a two component diffusion xt zt and their lie brackets a s for any t 0 the conditional law of xt t 0 given b zs s t a c density

higher spectral flow for a continuous curve of families of dirac type operators we define a higher spectral flow as ak group element we show that this higher spectral flow can be computed analytically by forms and is related to the family index in the same way as the spectral flow is related to the index we introduce a notion of toeplitz family and relate its index to the higher spectral flow applications to family indices for manifolds with boundary are also given

the atiyah singer theorems a probabilistic approach ii the lefschetz fixed point formulas abstract in this paper the lefschetz fixed point formulas of m f atiyah and i m singer ann of math 87 1968 484 530 546 604 for classical elliptic complexes are proved by using probabilistic methods

pseudodifferential operators on supermanifolds and the atiyah singer index theorem fermionic quantization or clifford algebra is combined with pseudodifferential operators to simplify the proof of the atiyah singer index theorem for the dirac operator on a spin manifold

the infinitesimal lefschetz formulas a heat equation proof abstract in this paper the lefschetz formulas of atiyah and bott ann of math 86 1967 374 407 88 1968 451 491 and atiyah and singer ann of math 87 1968 546 604 93 1971 119 138 are proved by heat equation methods in infinitesimal form i e without using the usual localization on the fixed point set the proof is obtained by a homotopic deformation of the dirac operator and uses probabilistic methods the main applications are potentially in noncompact situations where fixed point formulas do not always hold while their infinitesimal analogues are still valid

openness stability and implicit multifunction theorems applications to variational systems abstract in this paper we aim to present two general results regarding on one hand the openness stability of set valued maps and on the other hand the metric regularity behavior of the implicit multifunction related to a generalized variational system then these results are applied in order to obtain in a natural way and in a widely studied case several relations between the metric regularity moduli of the field maps defining the variational system and the solution map our approach allows us to complete and extend several very recent results from the literature

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

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

z k manifolds and families of dirac operators the index of a family of a family of dirac operators is ak theory element in the parameter space sullivan s k manifolds are used to detect this index completely for the first chern class this gives a topological interpretation of witten s global anomaly the relationship with the geometry of the index bundle is considered

ekeland s inverse function theorem in graded frechet spaces revisited for multifunctions abstract in this paper we present some inverse function theorems and implicit function theorems for set valued mappings between frechet spaces the proof relies on lebesgue s dominated convergence theorem and on ekeland s variational principle an application to the existence of solutions of differential equations in frechet spaces with non smooth data is given

index theorem and equivariant cohomology on the loop space in this paper extending ideas of witten and atiyah we describe some relations of equivariant cohomology on the loop space of a manifold to the path integral representation of the index of the dirac operator on a twisted spin complex in particular the natural extension of the chern character to the whole loop space is described also it is shown that the non zero free homotopy classes of the loop space have 0 measure for the index measures associated to the index problem

an inverse map result and some applications to sensitivity of generalized equations abstract this work deals with non global inverse map results for the sum of two maps we prove two theorems which shed some new light on this aspect some implications in terms of sensitivity of parametric generalized equations are investigated finally a class of well conditioned operators is identified

local index theory over etale groupoids we give a superconnection proof of connes index theorem for proper cocompact actions of etale groupoids this includes connes general foliation index theo rem for foliations with hausdorholonomy groupoid

aps boundary conditions eta invariants and adiabatic limits we prove an adiabatic limit formula for the eta invariant of a manifold with boundary the eta invariant is defined using the atiyah patodisinger boundary condition and the underlying manifold is fibered over a manifold with boundary our result extends the work of bismut cheeger to manifolds with boundary

zeta forms and the local family index theorem for a family f of elliptic pseudodifferential operators we show there is a natural zeta form f s and zeta determinant form dot f in the ring of smooth differential forms on the parameterizing manifold generalizing the classical single operator zeta function and zeta determinant we show that the zeta forms extend the atiyah bott seeley formula for the index of an elliptic operator to a family of elliptic operators while the zeta determinant form leads to a graded chern class form for the index bundle globally the zeta form and zeta determinant form exist only at the level of k theory as maps to cohomology

on the full asymptotics of analytic torsion abstract the purpose of this article is to study the asymptotic expansion of ray singer analytic torsion associated with powers p of a given positive line bundle over a compact n dimensional complex manifold as p here we prove that the asymptotic expansion contains only the terms of the form p n i log p p n i for i n for the first two leading terms it was proved by bismut vasserot we calculate the coefficients of the terms p n 1 log p p n 1 in the kahler case and thus answer the question posed in the recent work of klevtsov ma marinescu wiegmann about quantum hall effect our second result concerns the general asymptotic expansion of the analytic torsion for a compact complex orbifold

homology of algebras of families of pseudodifferential operators abstract we compute the hochschild cyclic and periodic cyclic homology groups of algebras of families of laurent complete symbols on manifolds with corners we show in particular that the spectral sequence associated with hochschild homology degenerates at e 2 and converges to hochschild homology as a byproduct we identify the space of residue traces on fibrations by manifolds with corners in the process we prove some structural results about algebras of complete symbols on manifolds with corners

real embedding and equivariant eta forms bismut and zhang math ann 295 4 661 684 1993 establish a mathrm mod mathbb z embedding formula of atiyah patodi singer reduced eta invariants in this paper we explain the hidden mathrm mod mathbb z term as a spectral flow and extend this embedding formula to the equivariant family case in this case the spectral flow is generalized to the equivariant chern character of some equivariant dai zhang higher spectral flow

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

higher degree analogs of the determinant line bundle in the first part of this paper given a smooth family of dirac type operators on an odd dimensional closed manifold we construct an abelian gerbe with connection whose curvature is the three form component of the atiyah singer families index the orem in the second part of the paper given a smooth family of dirac type operators whose index lies in the subspace b of the reduced k theory of the parametrizing space we construct a set of deligne cohomology classes of degree i whose curvatures are the i form component of the atiyah singer families index theorem

on semiregularity of mappings abstract there are two basic ways of weakening the definition of the well known metric regularity property by fixing one of the points involved in the definition the first resulting property is called metric subregularity and has attracted a lot of attention during the last decades on the other hand the latter property which we call semiregularity can be found under several names and the corresponding results are scattered in the literature we provide a self contained material gathering and extending the existing theory on the topic we demonstrate a clear relationship with other regularity properties for example the equivalence with the so called openness with a linear rate at the reference point is shown in particular cases we derive necessary and or sufficient conditions of both primal and dual type we illustrate the importance of semiregularity in the convergence analysis of an inexact newton type scheme for generalized equations with not necessarily differentiable single valued part

the atiyah singer index theorem for families of dirac operators two heat equation proofs the purpose of this paper is to give two heat equation proofs of the index theorem of atiyah singer for a family of dirac operators

the atiyah singer theorems a probabilistic approach i the index theorem abstract the atiyah singer index theorem for classical elliptic complexes is proved by using probabilistic methods the general idea is to use a probabilistic construction of the heat equation kernel which permits the direct derivation of the index formulas without using the theory of invariants of gilkey stochastic calculus on the exterior algebra is then used to find the classical local formula for the index theorem the lefschetz fixed point formulas of atiyah singer will be proved in part ii

space alternating generalized expectation maximization algorithm the expectation maximization em method can facilitate maximizing likelihood functions that arise in statistical estimation problems in the classical em paradigm one iteratively maximizes the conditional log likelihood of a single unobservable complete data space rather than maximizing the intractable likelihood function for the measured or incomplete data em algorithms update all parameters simultaneously which has two drawbacks 1 slow convergence and 2 difficult maximization steps due to coupling when smoothness penalties are used the paper describes the space alternating generalized em sage method which updates the parameters sequentially by alternating between several small hidden data spaces defined by the algorithm designer the authors prove that the sequence of estimates monotonically increases the penalized likelihood objective derive asymptotic convergence rates and provide sufficient conditions for monotone convergence in norm two signal processing applications illustrate the method estimation of superimposed signals in gaussian noise and image reconstruction from poisson measurements in both applications the sage algorithms easily accommodate smoothness penalties and converge faster than the em algorithms

the analysis of elliptic families ii dirac operators eta invariants and the holonomy theorem in this paper we specialize the results obtained in bf1 to the case of a family of dirac operators we first calculate the curvature of the unitary connection on the determinant bundle which we introduced in bf1

universal bundle for gravity local index theorem and covariant gravitational anomalies consistent and covariant lorentz and diffeomorphism anomalies are investigated in terms of the geometry of the universal bundle for gravity this bundle is explicitly constructed and its geometrical structure will be studied by means of the local index theorem for families of bismut and freed the consistent gravitational anomalies are calculated covariant gravitational anomalies are shown to be related with secondary characteristic classes of the universal bundle and a new set of descent equations which also contains the covariant schwinger terms is derived the relation between consistent and covariant anomalies is studied finally a geometrical realization of the gravitational brs anti brs transformations is presented which enables the formulation of a kind of covariance condition for covariant gravitational anomalies

a hilbert bundle description of differential k theory abstract we give an infinite dimensional description of the differential k theory of a manifold m the generators are triples h a where h is a z 2 graded hilbert bundle on m a is a superconnection on h and is a differential form on m the relations involve eta forms we show that the ensuing group is the differential k group k 0 m in addition we construct the pushforward of a finite dimensional cocycle under a proper submersion with a riemannian structure we give the analogous description of the odd differential k group k 1 m finally we give a model for twisted differential k theory

adiabatic limit bismut freed connection and the real analytic torsion form for a complex flat vector bundle over a fibered manifold we consider the 1 parameter family of certain deformed sub signature operators introduced by ma zhang in mz we compute the adiabatic limit of the bismut freed connection associated to this family and show that the bismut lott analytic torsion form shows up naturally under this procedure

chain rules for linear openness in general banach spaces this paper is devoted to the investigation of the linear openness of a general type of set valued composition in banach spaces as an application of the main result we study an important issue recently brought into attention by a paper of arutyunov the relation between some assertions on fixed points of set valued compositions and linear openness results of lyusternik graves type then we show on one hand that the chain rule for linear openness we obtain here covers several well known and recent results in the field and on the other hand that it generates new interesting conclusions

diffusions conditionnelles ii generateur conditionnel application au filtrage abstract this paper is a continuation of diffusions conditionelles i if x t z t is a two component diffusion process it is shown that under appropriate conditions the process x t t t given z s s t is a nonhomogeneous strong markov process whose generator is explicitly found by using the theory of stochastic flows the filtering equation is reduced to an ordinary partial differential equation

fourier mukai transform and adiabatic curvature of spectral bundles for landau hamiltonians on riemann surfaces we study the family of landau hamiltonians on a riemann surface s by means of a nahm transform and an integral functor related to the fourier mukai transform associated to its jacobian variety j s this approach allows us to explicitly determine the spectral bundles associated to the holomorphic landau levels as a first main result we prove that these spectral bundles are holomorphic stable bundles with respect to the canonical polarization of j s determined by the theta divisor the spectral bundles are endowed with a natural connection and the adiabatic charge transport properties of the corresponding landau levels are determined by the adiabatic curvature of which coincides with the curvature of the determinant bundle det by means of the theory of analytic torsion and determinant bundles developed by bismut gillet and soule we compute the adiabatic curvature of the spectral bundles on an arbitrary riemann surface we prove that all the holomorphic landau levels have the same charge transport coefficients but their adiabatic curvatures differ by a term which involves the relative analytic torsion of different powers of the canonical bundle of s twisted by a fixed line bundle

improved generative semisupervised learning based on finely grained component conditional class labeling we introduce new inductive generative semisupervised mixtures with more finely grained class label generation mechanisms than in previous work our models combine advantages of semisupervised mixtures which achieve label extrapolation over a component and nearest neighbor nn nearest prototype np classification which achieve accurate classification in the vicinity of labeled samples or prototypes for our nn based method we propose a novel two stage stochastic data generation with all samples first generated using a standard finite mixture and then all class labels generated conditioned on the samples and their components of origin this mechanism entails an underlying markov random field specific to each mixture component or cluster we invoke the pseudo likelihood formulation which forms the basis for an approximate generalized expectation maximization model learning algorithm our np based model overcomes a problem with the nn based model that manifests at very low labeled fractions both models are advantageous when within component class proportions are not constant over the feature space region owned by a component the practicality of this scenario is borne out by experiments on uc irvine data sets which demonstrate significant gains in classification accuracy over previous semisupervised mixtures and also overall gains over knn classification moreover for very small labeled fractions our methods overall outperform supervised linear and nonlinear kernel support vector machines

transgressed chern forms for dirac operators abstract we apply the results of connes moscovici on transgressed chern forms we also establish certain uniform estimates for such chern forms

a study of gaussian mixture models of color and texture features for image classification and segmentation the aims of this paper are two fold to define gaussian mixture models gmms of colored texture on several feature spaces and to compare the performance of these models in various classification tasks both with each other and with other models popular in the literature we construct gmms over a variety of different color and texture feature spaces with a view to the retrieval of textured color images from databases we compare supervised classification results for different choices of color and texture features using the vistex database and explore the best set of features and the best gmm configuration for this task in addition we introduce several methods for combining the color and structure information in order to improve the classification performances we then apply the resulting models to the classification of texture databases and to the classification of man made and natural areas in aerial images we compare the gmm model with other models in the literature and show an overall improvement in performance

localization formulas superconnections and the index theorem for families in this paper we give a new proof of the localization formulas of berline and vergne 9 and duistermaat and heckman 18 when interpreted in the framework of atiyah 2 the probabilistic heat equation proof of the index theorem given in our paper 12 appears as the rigorous infinite dimensional version of this new proof of the localization formulas in finite dimensions the results of quillen 25 on superconnections are briefly presented the heat equation proofs 15 of the index theorem for families are described it is shown that in this framework the superconnections formalism is the operator theoretic description of integration along the fiber in the loop space

nonlocal invariants in index theory in its original form the atiyah singer index theorem equates two global quantities of a closed manifold one analytic the index of an elliptic operator and one topological a characteristic number because it relates invariants from different branches of mathematics the index theorem has many applications and extensions to differential geometry k theory mathematical physics and other fields this report focuses on advances in geometric aspects of index theory for operators naturally associated to a riemannian metric on a closed manifold the topological side of the index theorem can often be expressed as the integral of local i e pointwise curvature expression we will first discuss these local refinements in 1 which arise naturally in heat equation proofs of the index theorem in 2 3 we discuss further developments in index theory which lead to spectral invariants the eta invariant and the determinant of an elliptic operator that are definitely nonlocal finally in 4 we point out some recent connections among these nonlocal invariants and classical index theory

unsupervised learning of parsimonious mixtures on large spaces with integrated feature and component selection estimating the number of components the order in a mixture model is often addressed using criteria such as the bayesian information criterion bic and minimum message length however when the feature space is very large use of these criteria may grossly underestimate the order here it is suggested that this failure is not mainly attributable to the criterion e g bic but rather to the lack of structure in standard mixtures these models trade off data fitness and model complexity only by varying the order the authors of the present paper propose mixtures with a richer set of tradeoffs the proposed model allows each component its own informative feature subset with all other features explained by a common model shared by all components parameter sharing greatly reduces complexity at a given order since the space of these parsimonious modeling solutions is vast this space is searched in an efficient manner integrating the component and feature selection within the generalized expectation maximization gem learning for the mixture parameters the quality of the proposed unsupervised solutions is evaluated using both classification error and test set data likelihood on text data the proposed multinomial version learned without labeled examples without knowing the true number of topics and without feature preprocessing compares quite favorably with both alternative unsupervised methods and with a supervised naive bayes classifier a gaussian version compares favorably with a recent method introducing feature saliency in mixtures

mixture modeling with pairwise instance level class constraints the goal of semisupervised clustering mixture modeling is to learn the underlying groups comprising a given data set when there is also some form of instance level supervision available usually in the form of labels or pairwise sample constraints most prior work with constraints assumes the number of classes is known with each learned cluster assumed to be a class and hence subject to the given class constraints when the number of classes is unknown or when the one cluster per class assumption is not valid the use of constraints may actually be deleterious to learning the ground truth data groups we address this by 1 allowing allocation of multiple mixture components to individual classes and 2 estimating both the number of components and the number of classes we also address new class discovery with components void of constraints treated as putative unknown classes for both real world and synthetic data our method is shown to accurately estimate the number of classes and to give favorable comparison with the recent approach of shental bar hillel hertz and weinshall 2003

on certain infinite dimensional aspects of arakelov intersection theory letk y x be an embedding of compact complex manifolds bismut and lebeau have calculated the quillen norm of the canonical isomorphism identifying the determinant of the cohomology of a holomorphic vector bundle overy and the determinant of the cohomology of a resolution by a complex of holomorhic vector bundles overx the purpose of this paper is to show that the formula of bismut lebeau can be viewed as an equivariant intersection formula over the loop space of the considered manifolds in the presence of an infinite dimensional excess normal bundle this excess normal bundle is responsible for the appearance of the additive genusr of gillet and soule in the formula of bismut and lebeau