sufficient dimension reduction via squared loss mutual information estimation the goal of sufficient dimension reduction in supervised learning is to find the low dimensional subspace of input features that contains all of the information about the output values that the input features possess in this letter we propose a novel sufficient dimension reduction method using a squared loss variant of mutual information as a dependency measure we apply a density ratio estimator for approximating squared loss mutual information that is formulated as a minimum contrast estimator on parametric or nonparametric models since cross validation is available for choosing an appropriate model our method does not require any prespecified structure on the underlying distributions we elucidate the asymptotic bias of our estimator on parametric models and the asymptotic convergence rate on nonparametric models the convergence analysis utilizes the uniform tail bound of a u process and the convergence rate is characterized by the bracketing entropy of the model we then develop a natural gradient algorithm on the grassmann manifold for sufficient subspace search the analytic formula of our estimator allows us to compute the gradient efficiently numerical experiments show that the proposed method compares favorably with existing dimension reduction approaches on artificial and benchmark data sets

direct learning of sparse changes in markov networks by density ratio estimation we propose a new method for detecting changes in markov network structure between two sets of samples instead of naively fitting two markov network models separately to the two data sets and figuring out their difference we directly learn the network structure change by estimating the ratio of markov network models this density ratio formulation naturally allows us to introduce sparsity in the network structure change which highly contributes to enhancing interpretability furthermore computation of the normalization term a critical bottleneck of the naive approach can be remarkably mitigated we also give the dual formulation of the optimization problem which further reduces the computation cost for large scale markov networks through experiments we demonstrate the usefulness of our method

f divergence estimation and two sample homogeneity test under semiparametric density ratio models a density ratio is defined by the ratio of two probability densities we study the inference problem of density ratios and apply a semiparametric density ratio estimator to the two sample homogeneity test in the proposed test procedure the f divergence between two probability densities is estimated using a density ratio estimator the f divergence estimator is then exploited for the two sample homogeneity test we derive an optimal estimator of f divergence in the sense of the asymptotic variance in a semiparametric setting and provide a statistic for two sample homogeneity test based on the optimal estimator we prove that the proposed test dominates the existing empirical likelihood score test through numerical studies we illustrate the adequacy of the asymptotic theory for finite sample inference

ridge regression biased estimation for nonorthogonal problems in multiple regression it is shown that parameter estimates based on minimum residual sum of squares have a high probability of being unsatisfactory if not incorrect if the prediction vectors are not orthogonal proposed is an estimation procedure based on adding small positive quantities to the diagonal of x x introduced is the ridge trace a method for showing in two dimensions the effects of nonorthogonality it is then shown how to augment x x to obtain biased estimates with smaller mean square error

an extended pressure finite element space for two phase incompressible flows with surface tension we consider a standard model for incompressible two phase flows in which a localized force at the interface describes the effect of surface tension if a level set or vof method is applied then the interface which is implicitly given by the zero level of the level set function is in general not aligned with the triangulation that is used in the discretization of the flow problem this non alignment causes severe difficulties w r t the discretization of the localized surface tension force and the discretization of the flow variables in cases with large surface tension forces the pressure has a large jump across the interface in standard finite element spaces due to the non alignment the functions are continuous across the interface and thus not appropriate for the approximation of the discontinuous pressure in many simulations these effects cause large oscillations of the velocity close to the interface so called spurious velocities in this paper for a simplified model problem we give an analysis that explains why known standard methods for discretization of the localized force term and for discretization of the pressure variable often yield large spurious velocities in the paper s grosz a reusken finite element discretization error analysis of a surface tension force in two phase incompressible flows preprint 262 igpm rwth aachen siam j numer anal accepted for publication we introduce a new and accurate method for approximation of the surface tension force in the present paper we use the extended finite element space xfem presented in n moes j dolbow t belytschko a finite element method for crack growth without remeshing int j numer meth eng 46 1999 131 150 t belytschko n moes s usui c parimi arbitrary discontinuities in finite elements int j numer meth eng 50 2001 993 1013 for the discretization of the pressure we show that the size of spurious velocities is reduced substantially provided we use both the new treatment of the surface tension force and the extended pressure finite element space

bayesian regularization and pruning using a laplace prior standard techniques for improved generalization from neural networks include weight decay and pruning weight decay has a bayesian interpretation with the decay function corresponding to a prior over weights the method of transformation groups and maximum entropy suggests a laplace rather than a gaussian prior after training the weights then arrange themselves into two classes 1 those with a common sensitivity to the data error and 2 those failing to achieve this sensitivity and that therefore vanish since the critical value is determined adaptively during training pruning in the sense of setting weights to exact zeros becomes an automatic consequence of regularization alone the count of free parameters is also reduced automatically as weights are pruned a comparison is made with results of mackay using the evidence framework and a gaussian regularizer

a face oriented stabilized nitsche type extended variational multiscale method for incompressible two phase flow a novel extended variational multiscale method for incompressible two phase flow is proposed in this approach the level set method which allows for accurately representing complex interface evolutions is combined with an extended finite element method for the fluid field sharp representation of the discontinuities at the interface related to surface tension effects and large material parameter ratios are enabled by this approach to capture the discontinuities jump enrichments are applied for both velocity and pressure field nitsche s method is then used to weakly impose the continuity of the velocity field for a stable formulation on the entire domain residual based variational multiscale terms are supported by appropriate face oriented ghost penalty and fluid stabilization terms in the region of enriched elements both face oriented terms as well as interfacial terms related to nitsche s method are introduced such that it is accounted for viscous and convection dominated transient flows as a result stability and wellconditioned systems are guaranteed independent of the interface location the proposed method is applied to four numerical examples of increasing complexity two dimensional rayleigh taylor instabilities a twodimensional collapsing water column three dimensional rising bubbles as well as a three dimensional bubble coalescence excellent agreement with either analytical solutions or numerical and experimental reference data as well as robustness for all flow regimes is demonstrated for all examples

a linear conceptual subsurface storm flow model a zero dimensional lumped linear conceptual model of the subsurface storm flow from hillslopes has been developed by integrating over the length of the hillslope the linearized one dimensional dupuit forchheimer approximation discharge relationship for saturated flow over an inclined plane the derived two term storage function accounts for gravity and gradient driven flow coupled with the storage balance equation for the plane the model allows direct analytical computation of the outflow hydrograph at the foot of the hill in response to an infiltration step input the model is the conceptual counterpart of the linear advection diffusion lad flow equation derived from the extended boussinesq equation through linearization in contrast to the kinematic wave approximation the outflows normalized by their equilibrium values are properly given as functions of the infiltration rate the outflow hydrographs computed by the conceptual lad model approximate nonlinear behavior closely over a wide range of conditions encountered in field applications

the entire regularization path for the support vector machine the support vector machine svm is a widely used tool for classification many efficient implementations exist for fitting a two class svm model the user has to supply values for the tuning parameters the regularization cost parameter and the kernel parameters it seems a common practice is to use a default value for the cost parameter often leading to the least restrictive model in this paper we argue that the choice of the cost parameter can be critical we then derive an algorithm that can fit the entire path of svm solutions for every value of the cost parameter with essentially the same computational cost as fitting one svm model we illustrate our algorithm on some examples and use our representation to give further insight into the range of svm solutions

adaptively weighted numerical integration in the finite cell method abstract with adaptively weighted aw numerical integration for a given set of quadrature nodes order and domain of integration the quadrature weights are obtained by solving a system of suitable moment fitting equations in least square sense the moments in the moment equations are approximated over a simplified domain that is homeomorphic to the original domain and then are corrected for the deviation from the original domain using shape sensitivity analysis in this paper we demonstrate the application of aw integration scheme in the context of the finite cell method which must perform numerical integration over arbitrary domains without meshing the standard integration technique employed in fcm is the characteristic function method that converts the continuous integrand over a complex domain into a discontinuous integrand over a simple box domain then well known integrand adaptivity techniques are employed to integrate the resulting discontinuous integrand over the box domain although this method is simple to implement it becomes computationally very expensive for realistic complex 3d domains such as sculptures bones and engines in contrast in aw scheme the quadrature weights directly adapt to the complex geometric domain without the need to making the integrand discontinuous leading to superior computational properties in this paper we demonstrate the computational efficiency of aw over the characteristic function method as it requires fewer subdivisions and less time to achieve a given accuracy in both two and three dimensions in addition aw offers a number of advantages including flexibility in the choice of quadrature points and basis functions

linear theory of subsurface storm flow a solution to the subsurface storm flow problem is developed through linearization of the complete one dimensional governing equation water surface profiles and outflow hydrographs obtained from this approximate theory are compared with the exact solution and with the kinematic approximation to this problem for a number of cases characterized by the parameter 4 i cos k sin2 the accuracy and range of applicability of the proposed theory are greater than that of the kinematic theory its results may be considered satisfactory for the cases with 1 however the kinematic theory is a preferable substitute for 0 25

finite analytic numerical method for unsteady two dimensional navier stokes equations abstract the main purpose of this paper is to develop a finite analytic fa numerical solution for unsteady two dimensional navier stokes equations the fa method utilizes the analytic solution in a small local element to formulate the algebraic representation of partial differential equations in this study the combination of linear and exponential functions that satisfy the governing equation is adopted as the boundary function thereby improving the accuracy of the finite analytic solution two flows one a starting cavity flow and the other a vortex shedding flow behind a rectangular block are solved by the fa method the starting square cavity flow is solved for reynolds numbers of 400 1000 and 2000 to show the accuracy and stability of the fa solution the fa solution for flow over a rectangular block h h 4 predicts the strouhal number for reynolds numbers of 100 and 500 to be 0 156 and 0 125 details of the flow patterns are given in addition to streamlines and vorticity distribution rest streamlines are given to illustrate the vortex motion downstream of the block

information based objective functions for active data selection learning can be made more efficient if we can actively select particularly salient data points within a bayesian learning framework objective functions are discussed that measure the expected informativeness of candidate measurements three alternative specifications of what we want to gain information about lead to three different criteria for data selection all these criteria depend on the assumption that the hypothesis space is correct which may prove to be their main weakness

sub domain adaptation learning methodology regarded as global methods maximum mean discrepancy mmd based transfer learning frameworks only reflect the global distribution discrepancy and structural differences between domains they can reflect neither the inner local distribution discrepancy nor the structural differences between domains to address this problem a novel transfer learning framework with local learning ability a sub domain adaptation learning framework sdal is proposed in this framework a projected maximum local weighted mean discrepancy pmlmd is constructed by integrating the theory and method of local weighted mean lwm into mmd pmlmd reflects global distribution discrepancy between domains through accumulating local distribution discrepancies between the local sub domains in domains in particular we formulate in theory that pmlmd is one of the generalized measures of mmd on the basis of sdal two novel methods are proposed by using multi label classifiers mlc and support vector machine svm finally tests on artificial data sets high dimensional text data sets and face data sets show the sdal based transfer learning methods are superior to or at least comparable with benchmarking methods

four types of learning curves if machines are learning to make decisions given a number of examples the generalization error e t is defined as the average probability that an incorrect decision is made for a new example by a machine when trained with t examples the generalization error decreases as t increases and the curve e t is called a learning curve the present paper uses the bayesian approach to show that given the annealed approximation learning curves can be classified into four asymptotic types if the machine is deterministic with noiseless teacher signals then 1 e at 1 when the correct machine parameter is unique and 2 e at 2 when the set of the correct parameters has a finite measure if the teacher signals are noisy then 3 e at 1 2 for a deterministic machine and 4 e c at 1 for a stochastic machine

online direct density ratio estimation applied to inlier based outlier detection many machine learning problems such as nonstationarity adaptation outlier detection dimensionality reduction and conditional density estimation can be effectively solved by using the ratio of probability densities since the naive two step procedure of first estimating the probability densities and then taking their ratio performs poorly methods to directly estimate the density ratio from two sets of samples without density estimation have been extensively studied recently however these methods are batch algorithms that use the whole data set to estimate the density ratio and they are inefficient in the online setup where training samples are provided sequentially and solutions are updated incrementally without storing previous samples in this letter we propose two online density ratio estimators based on the adaptive regularization of weight vectors through experiments on inlier based outlier detection we demonstrate the usefulness of the proposed methods

an efficient implementation of an active set method for svms we propose an active set algorithm to solve the convex quadratic programming qp problem which is the core of the support vector machine svm training the underlying method is not new and is based on the extensive practice of the simplex method and its variants for convex quadratic problems however its application to large scale svm problems is new until recently the traditional active set methods were considered impractical for large svm problems by adapting the methods to the special structure of svm problems we were able to produce an efficient implementation we conduct an extensive study of the behavior of our method and its variations on svm problems we present computational results comparing our method with joachims svmlight see joachims 1999 the results show that our method has overall better performance on many svm problems it seems to have a particularly strong advantage on more difficult problems in addition this algorithm has better theoretical properties and it naturally extends to the incremental mode since the proposed method solves the standard svm formulation as does svmlight the generalization properties of these two approaches are identical and we do not discuss them in the paper

on the optimality of prediction based selection criteria and the convergence rates of estimators several estimators of squared prediction error have been suggested for use in model and bandwidth selection problems among these are cross validation generalized cross validation and a number of related techniques based on the residual sum of squares for many situations with squared error loss e g nonparametric smoothing these estimators have been shown to be asymptotically optimal in the sense that in large samples the estimator minimizing the selection criterion also minimizes squared error loss however cross validation is known not to be asymptotically optimal for some easy location problems we consider selection criteria based on estimators of squared prediction risk for choosing between location estimators we show that criteria based on adjusted residual sum of squares are not asymptotically optimal for choosing between asymptotically normal location estimators that converge at rate n 1 2 but are when the rate of convergence is slower we also show that leave one out cross validation is not asymptotically optimal for choosing between n differentiable statistics but leave d out cross validation is optimal when d oo at the appropriate rate

an unfitted finite element method based on nitsche s method for elliptic interface problems in this paper we propose a method for the finite element solution of elliptic interface problem using an approach due to nitsche the method allows for discontinuities internal to the elements in the approximation across the interface we show that optimal order of convergence holds without restrictions on the location of the interface relative to the mesh further we derive a posteriori error estimates for the purpose of controlling functionals of the error and present some numerical examples

on minimum distribution discrepancy support vector machine for domain adaptation domain adaptation learning dal is a novel and effective technique to address pattern classification problems where the prior information for training is unavailable or insufficient its effectiveness depends on the discrepancy between the two distributions that respectively generate the training data for the source domain and the testing data for the target domain however dal may not work so well when only the distribution mean discrepancy between source and target domains is considered and minimized in this paper we first construct a generalized projected maximum distribution discrepancy gpmdd metric for dal on reproducing kernel hilbert space rkhs based domain distributions by simultaneously considering both the projected maximum distribution mean and the projected maximum distribution scatter discrepancy between the source and the target domain in the sequel based on both the structure risk and the gpmdd minimization principle we propose a novel domain adaptation kernelized support vector machine daksvm with respect to the classical svm and its two extensions called ls daksvm and m daksvm with respect to the least square svm and the v svm respectively moreover our theoretical analysis justified that the proposed gpmdd metric could effectively measure the consistency not only between the rkhs embedding domain distributions but also between the scatter information of source and target domains hence the proposed methods are distinctive in that the more consistency between the scatter information of source and target domains can be achieved by tuning the kernel bandwidth the better the convergence of gpmdd metric minimization is and thus improving the scalability and generalization capability of the proposed methods for dal experimental results on artificial and real world problems indicate that the performance of the proposed methods is superior to or at least comparable with existing benchmarking methods

active learning in approximately linear regression based on conditional expectation of generalization error the goal of active learning is to determine the locations of training input points so that the generalization error is minimized we discuss the problem of active learning in linear regression scenarios traditional active learning methods using least squares learning often assume that the model used for learning is correctly specified in many practical situations however this assumption may not be fulfilled recently active learning methods using importance weighted least squares learning have been proposed which are shown to be robust against misspecification of models in this paper we propose a new active learning method also using the weighted least squares learning which we call alice active learning using the importance weighted least squares learning based on conditional expectation of the generalization error an important difference from existing methods is that we predict the conditional expectation of the generalization error given training input points while existing methods predict the full expectation of the generalization error due to this difference the training input design can be fine tuned depending on the realization of training input points theoretically we prove that the proposed active learning criterion is a more accurate predictor of the single trial generalization error than the existing criterion numerical studies with toy and benchmark data sets show that the proposed method compares favorably to existing methods

sharp interface immersed boundary level set method for wave body interactions a sharp interface cartesian grid method for the large eddy simulation of two phase turbulent flows interacting with moving bodies is presented the overall approach uses a sharp interface immersed boundary formulation and a level set ghost fluid method for solid fluid and fluid fluid interface treatments respectively a four step fractional step method is used for velocity pressure coupling and a lagrangian dynamic smagorinsky subgrid scale model is adopted for large eddy simulations a simple contact angle boundary condition treatment that conforms to the immersed boundary formulation is developed a variety of test cases of different scales ranging from bubble dynamics water entry and exit landslide generated waves to ship hydrodynamics are performed for validation extensions for high reynolds number ship flows using wall layer models are also considered

blending in the extended finite element method by discontinuous galerkin and assumed strain methods summary in the extended finite element method xfem errors are caused by parasitic terms in the approximation space of the blending elements at the edge of the enriched subdomain a discontinuous galerkin dg formulation is developed which circumvents this source of error a patch based version of the dg formulation is developed which decomposes the domain into enriched and unenriched subdomains continuity between patches is enforced with an internal penalty method an element based form is also developed where each element is considered a patch the patch based dg is shown to have similar accuracy to the element based dg for a given discretization but requires significantly fewer degrees of freedom the method is applied to material interfaces cracks and dislocation problems for the dislocations a contour integral form of the internal forces that only requires integration over the patch boundaries is developed a previously developed assumed strain as method is also developed further and compared with the dg method for weak discontinuities and linear elastic cracks the dg method is shown to be significantly more accurate than the standard xfem for a given element size and to converge optimally even where the standard xfem does not the accuracy of the dg method is similar to that of the as method but requires less application specific coding copyright q 2007 john wiley sons ltd

on spurious velocities in incompressible flow problems with interfaces we show that a non physical velocity may appear in the finite element calculation of incompressible two phase flows subjected to an external local force there are different sources responsible for this phenomenon approximation of the incompressibility constraint the interface and the local external force furthermore we demonstrate that this non physical velocity does not vanish with the expected order of convergence we evaluate different concepts and give recommendations for a proper handling of this phenomenon

a level set approach for computing solutions to incompressible two phase flow a level set approach for computing solutions to incompressible two phase flow is presented the interface between the two fluids is considered to be sharp and is described as the zero level set of a smooth function a new treatment of the level set method allows us to efficiently maintain the level set function as the signed distance from the interface we never have to explicitly reconstruct or find the zero level set consequently we are able to handle arbitrarily complex topologies large density and viscosity ratios and surface tension on relatively coarse grids we use a second order projection method along with a second order upwinded procedure for advecting the momentum and level set equations we consider the motion of air bubbles and water drops we also compute flows with multiple fluids such as air oil and water

the extended generalized finite element method an overview of the method and its applications an overview of the extended generalized finite element method gefm xfem with emphasis on methodological issues is presented this method enables the accurate approximation of solutions that involve jumps kinks singularities and other locally non smooth features within elements this is achieved by enriching the polynomial approximation space of the classical finite element method the gefm xfem has shown its potential in a variety of applications that involve non smooth solutions near interfaces among them are the simulation of cracks shear bands dislocations solidification and multi field problems copyright 2010 john wiley sons ltd

a stable generalized finite element method sgfem of degree two for interface problems abstract generalized or extended finite element methods gfem xfem of degree 1 for interface problems have been reported in the literature they i yield optimal order of convergence i e o h h is a discretization parameter ii are stable in a sense that conditioning is not worse than that of the standard fem and iii are robust in that the conditioning does not deteriorate as interface curves are close to boundaries of underlying elements however higher order gfem xfem with the properties i iii have not been successfully addressed yet various enrichment schemes for gfem xfem based on d or d p k d is a distance function or the absolute value of level set function and p k is the polynomial basis of degree k have been reported recently to obtain higher order convergence but they are not stable or robust in general in fact they even may not yield the optimal orders of convergence in this paper we propose a stable gfem xfem of degree 2 sgfem2 for the interface problems where we used the enrichment scheme based on d 1 x y instead of d or d 1 x y x 2 x y y 2 in the literature we prove that the sgfem2 yields the optimal order of convergence i e o h 2 for the interface problems with curved smooth interfaces a local principal component analysis technique has been proposed which ensures that the sgfem2 is stable and robust numerical experiments for straight and curved interfaces have been presented to illuminate these properties

a semi lagrangean time integration approach for extended finite element methods many computational problems incorporate discontinuities that evolve in time the extendend finite element method xfem is able to represent discontinuities sharply on fixed arbitrary meshes but numerical difficulties arise if these discontinuities move in time we point out that this issue is crucial for interface problems with strongly discontinuous fields on fixed grids a method using semi lagrangean techniques is proposed to adequately handle time integration based on finite difference schemes in the context of the xfem the basic idea is to adapt previous numerical solutions to the current interface position by tracking back virtual lagrangean particles to their previous positions where an appropriate solution can be extrapo lated from a smooth field convergence properties of the proposed method in time and space are thoroughly studied for two one dimensional model problems finally the method is applied to the particularly challenging problem of premixed combustion where the discontinuity appears at the flame front separating the burnt from the unburnt gases a two dimensional and a three dimensional expanding flame demonstrates that the method is sufficiently accurate to retain the properties of the overall nitsche type formulation for interface problems with embedded strong discontinuities

sufficient dimension reduction via direct estimation of the gradients of logarithmic conditional densities sufficient dimension reduction sdr is aimed at obtaining the low rank projection matrix in the input space such that information about output data is maximally preserved among various approaches to sdr a promising method is based on the eigendecomposition of the outer product of the gradient of the conditional density of output given input in this letter we propose a novel estimator of the gradient of the logarithmic conditional density that directly fits a linear in parameter model to the true gradient under the squared loss thanks to this simple least squares formulation its solution can be computed efficiently in a closed form then we develop a new sdr method based on the proposed gradient estimator we theoretically prove that the proposed gradient estimator as well as the sdr solution obtained from it achieves the optimal parametric convergence rate finally we experimentally demonstrate that our sdr method compares favorably with existing approaches in both accuracy and computational efficiency on a variety of artificial and benchmark data sets

a corrected xfem approximation without problems in blending elements the extended finite element method xfem enables local enrichments of approximation spaces standard finite elements are used in the major part of the domain and enriched elements are employed where special solution properties such as discontinuities and singularities shall be captured in elements that blend the enriched areas with the rest of the domain problems arise in general these blending elements often require a special treatment in order to avoid a decrease in the overall convergence rate a modification of the xfem approximation is proposed in this work the enrichment functions are modified such that they are zero in the standard elements unchanged in the elements with all their nodes being enriched and varying continuously in the blending elements all nodes in the blending elements are enriched the modified enrichment function can be reproduced exactly everywhere in the domain and no problems arise in the blending elements the corrected xfem is applied to problems in linear elasticity and optimal convergence rates are achieved copyright 2007 john wiley sons ltd

the intrinsic xfem a method for arbitrary discontinuities without additional unknowns a new method for treating arbitrary discontinuities in a finite element fe context is presented unlike the standard extended fe method xfem no additional unknowns are introduced at the nodes whose supports are crossed by discontinuities the method constructs an approximation space consisting of mesh based enriched moving least squares mls functions near discontinuities and standard fe shape functions elsewhere there is only one shape function per node and these functions are able to represent known characteristics of the solution such as discontinuities singularities etc the mls method constructs shape functions based on an intrinsic basis by minimizing a weighted error functional thereby weight functions are involved and special mesh based weight functions are proposed in this work the enrichment is achieved through the intrinsic basis the method is illustrated for linear elastic examples involving strong and weak discontinuities and matches optimal rates of convergence even for crack tip applications copyright 2006 john wiley sons ltd

a locally extended finite element method for the simulation of multi fluid flows using the particle level set method abstract the simulation of immiscible two phase flows on eulerian meshes requires the use of special techniques to guarantee a sharp definition of the evolving fluid interface this work describes the combination of two distinct technologies with the goal of improving the accuracy of the target simulations first of all a spatial enrichment is employed to improve the approximation properties of the eulerian mesh this is done by injecting into the solution space new features to make it able to correctly resolve the solution in the vicinity of the moving interface then the lagrangian particle level set pls method is employed to keep trace of the evolving solution and to improve the mass conservation properties of the resulting method while the local enrichment can be understood in the general context of the xfem we employ an element local variant which allows preserving the matrix graph and hence highly improving the computational efficiency

a new face oriented stabilized xfem approach for 2d and 3d incompressible navier stokes equations abstract we develop a new stabilized xfem based fixed grid approach for the transient incompressible navier stokes equations using cut elements our framework is based on a new flexible strategy to handle several degrees of freedom dofs at nodes required for complex shaped embedded meshes as they occur for fixed grid fluid structure interaction problems boundary conditions on embedded boundaries are imposed weakly using a nitsche type approach ghost penalty terms for velocity and pressure are added for stability reasons and to improve the conditioning of the system matrix the idea of ghost penalties previously developed for stokes problems is extended to the incompressible navier stokes equations by using face oriented fluid stabilizations for both viscous and convective dominated flows furthermore the need for additional terms to enforce boundary conditions for non viscous flows is addressed a detailed numerical study of our stabilized fluid formulation including studies of nitsche s parameter and the ghost penalty parameter shows optimal error convergence and a good system conditioning in the viscous and the convective dominated cases compared to other fixed grid fluid formulations our method is much more accurate and less sensitive to the location of the interface regarding the accuracy and the sensitivity with respect to the interface position a clear improvement could be observed for the viscous and pressure fluxes as well as for the imposition of the boundary condition results of a transient two dimensional high reynolds number flow over a cylinder and the flow over a thick plate in 3d confirm the applicability of the proposed method

a computational approach to handle complex microstructure geometries in multiscale analysis of components there is usually a need to solve microstructures with complex geometries in this paper we use the extended finite element method x fem to solve scales involving complex geometries the x fem allows one to use meshes not necessarily matching the physical surface of the problem while retaining the accuracy of the classical finite element approach for material interfaces this is achieved by introducing a new enrichment strategy although the mesh does not need to conform to the physical surfaces it needs to be fine enough to capture the geometry of these surfaces a simple algorithm is described to adaptively refine the mesh to meet this geometrical requirement numerical experiments on the periodic homogenization of two phase complex cells demonstrate the accuracy and simplicity of the x fem c 2003 elsevier b v all rights reserved

finite analytic numerical solution for two dimensional groundwater solute transport a new numerical method called the finite analytic fa method is used to solve a groundwater solute transport problem the basic idea of the finite analytic method is the incorporation of local analytic solution in the numerical solution of the partial differential equation when the local analytic solution is evaluated at a given nodal point it gives an algebraic relationship between a nodal value in an element and its neighboring nodal points the assemble of the linear system equations results in a tridiagonal matrix like most finite difference method the advantages of using efficient iterative techniques for solving tridiagonal matrices are equally applicable to fa method the automatic localized upstream shift and the analytic property of the fa method eliminates the difficulty of numerical dispersion locally and suppresses the overall numerical dispersion for large peclet number for small peclet number fa method yields excellent results in comparison with the analytic solution for large peclet number fa solutions are oscillation free with some degree of numerical dispersion the results are comparable with those obtained using upstream weighted finite element method

free surface flow simulations in the presence of inclined walls difficulties associated with free surface finite element flow simulations are related to a nonlinear and advective nature of most hydrodynamic flows b requirements for compatibility between velocity and pressure interpolation c maintaining a valid computational mesh in the presence of moving boundaries and d enforcement of the kinematic conditions at the free surface focusing on the last issue we present an extension of the free surface elevation equation to cases where the prescribed direction of the surface node motion is not uniformly vertical the resulting hyperbolic generalized elevation equation is discretized using a galerkin least squares formulation applied on the surface mesh the elevation field so obtained is then used to impose displacement boundary conditions on the elastic mesh update scheme that governs the movement of interior mesh nodes the proposed method is used to solve a two dimensional problem of sloshing in a trapezoidal tank and a three dimensional application involving flow in a trapezoidal channel with bridge supports

covariate shift adaptation for discriminative 3d pose estimation discriminative or structured prediction methods have proved effective for variety of problems in computer vision a notable example is 3d monocular pose estimation all methods to date however relied on an assumption that training source and test target data come from the same underlying joint distribution in many real cases including standard data sets this assumption is flawed in the presence of training set bias the learning results in a biased model whose performance degrades on the target test set under the assumption of covariate shift we propose an unsupervised domain adaptation approach to address this problem the approach takes the form of training instance reweighting where the weights are assigned based on the ratio of training and test marginals evaluated at the samples learning with the resulting weighted training samples alleviates the bias in the learned models we show the efficacy of our approach by proposing weighted variants of kernel regression kr and twin gaussian processes tgp we show that our weighted variants outperform their unweighted counterparts and improve on the state of the art performance in the public humaneva data set

modeling holes and inclusions by level sets in the extended finite element method a methodology to model arbitrary holes and material interfaces inclusions without meshing the internal boundaries is proposed the numerical method couples the level set method s osher j a sethian j comput phys 79 1 1988 12 to the extended finite element method x fem n moes j dolbow t belytschko int j numer methods engrg 46 1 1999 131 in the x fem the finite element approximation is enriched by additional functions through the notion of partition of unity the level set method is used for representing the location of holes and material interfaces and in addition the level set function is used to develop the local enrichment for material interfaces numerical examples in two dimensional linear elastostatics are presented to demonstrate the accuracy and potential of the new technique

inferences for case control and semiparametric two sample density ratio models summary we consider inference in general binary response regression models under retrospective sampling plans prentice pyke 1979 discovered that inference for the odds ratio parameter in a logistic model can be based on a prospective likelihood even though the sampling scheme is retrospective we show that the estimating function obtained from the prospective likelihood is optimal in a class of unbiased estimating functions also we link casecontrol sampling with a two sample biased sampling problem where the ratio of two densities is assumed to take a known parametric form connections between this model and the cox proportional hazards model are pointed out large and small sample size behaviour of the proposed estimators is studied

an enriched finite element method and level sets for axisymmetric two phase flow with surface tension a finite element method for axisymmetric two phase flow problems is presented the method uses an enriched finite element formulation in which the interface can move arbitrarily through the mesh without remeshing the enrichment is implemented by the extended finite element method x fem which models the discontinuity in the velocity gradient at the interface by a local partition of unity it provides an accurate representation of the velocity field at interfaces on an eulerian grid that is not conformal to the weak discontinuity the interface is represented by a level set which is also used in the construction of the element enrichment surface tension effects are considered and the interface curvature is computed from the level set field the method is demonstrated by several examples copyright 2003 john wiley sons ltd

arbitrary branched and intersecting cracks with the extended finite element method summary extensions of a new technique for the nite element modelling of cracks with multiple branches multiple holes and cracks emanating from holes are presented this extended nite element method x fem allows the representation of crack discontinuities and voids independently of the mesh a standard displacementbased approximation is enriched by incorporating discontinuous elds through a partition of unity method a methodology that constructs the enriched approximation based on the interaction of the discontinuous geometric features with the mesh is developed computation of the stress intensity factors sif in dierent examples involving branched and intersecting cracks as well as cracks emanating from holes are presented to demonstrate the accuracy and the robustness of the proposed technique copyright 2000 john wiley sons ltd

algebraic analysis for nonidentifiable learning machines this article clarifies the relation between the learning curve and the algebraic geometrical structure of a nonidentifiable learning machine such as a multilayer neural network whose true parameter set is an analytic set with singular points by using a concept in algebraic analysis we rigorously prove that the bayesian stochastic complexity or the free energy is asymptotically equal to 1 log n m1 1 log log n constant where n is the number of training samples and 1 and m1 are the rational number and the natural number which are determined as the birational invariant values of the singularities in the parameter space also we show an algorithm to calculate 1 and m1 based on the resolution of singularities in algebraic geometry in regular statistical models 2 1 is equal to the number of parameters and m1 1 whereas in nonregular models such as multilayer networks 2 1 is not larger than the number of parameters and m1 1 since the increase of the stochastic complexity is equal to the learning curve or the generalization error the nonidentifiable learning machines are better models than the regular ones if bayesian ensemble learning is applied

the extended finite element method for two phase and free surface flows a systematic study in immiscible two phase flows jumps or kinks are present in the velocity and pressure fields across the interfaces of the two fluids the extended finite element method xfem is able to reproduce such discontinuities within elements robust and accurate interface capturing schemes with no restrictions on the interface topology are thereby enabled this paper investigates different enrichment schemes and time integration schemes within the xfem test cases with and without surface tension on moving or stationary meshes are studied and compared to interface tracking results when possible a particularly useful setting is extracted which is recommended for two phase flows an extension of this formulation for the simulation of free surface flows and of floating objects is proposed

a positivity preserving and conservative variational scheme for phase field modeling of two phase flows abstract we present a positivity preserving variational scheme for the phase field modeling of incompressible two phase flows with high density ratio the variational finite element technique relies on the allen cahn phase field equation for capturing the phase interface on a fixed eulerian mesh with mass conservative and energy stable discretization the mass conservation is achieved by enforcing a lagrange multiplier which has both temporal and spatial dependence on the underlying solution of the phase field equation to make the scheme energy stable in a variational sense we discretize the spatial part of the lagrange multiplier in the phase field equation by the mid point approximation the proposed variational technique is designed to reduce the spurious and unphysical oscillations in the solution while maintaining the second order accuracy of both spatial and temporal discretizations we integrate the allen cahn phase field equation with the incompressible navier stokes equations for modeling a broad range of two phase flow and fluid fluid interface problems the coupling of the implicit discretizations corresponding to the phase field and the incompressible flow equations is achieved via nonlinear partitioned iterative procedure comparison of results between the standard linear stabilized finite element method and the present variational formulation shows a remarkable reduction of oscillations in the solution while retaining the boundedness of the phase indicator field we perform a standalone test to verify the accuracy and stability of the allen cahn two phase solver we examine the convergence and accuracy properties of the coupled phase field solver through the standard benchmarks of the laplace young law and a sloshing tank problem two and three dimensional dam break problems are simulated to assess the capability of the phase field solver for complex air water interfaces involving topological changes on unstructured meshes finally we demonstrate the phase field solver for a practical offshore engineering application of wave structure interaction

a new finite element formulation for computational fluid dynamics x the compressible euler and navier stokes equations a space time element method is presented for solving the compressible euler and navier stokes equations the proposed formulation includes the variational equation predictor multi corrector algorithms and boundary conditions the variational equation is based on the time discontinuous galerkin method in which the physical entropy variables are employed a least squares operator and a discontinuity capturing operator are added resulting in a high order accurate and unconditionally stable method implicit explicit predictor multi corrector algorithms applicable to steady as well as unsteady problems are presented techniques are developed to enhance their efficiency implementation of boundary conditions is addressed in particular a technique is introduced to satisfy nonlinear essential boundary conditions and a consistent method is presented to calculate boundary fluxes numerical results are presented to demonstrate the performance of the method

improved implementation and robustness study of the x fem for stress analysis around cracks numerical crack propagation schemes were augmented in an elegant manner by the x fem method the use of special tip enrichment functions as well as a discontinuous function along the sides of the crack allows one to do a complete crack analysis virtually without modifying the underlying mesh which is of industrial interest especially when a numerical model for crack propagation is desired this paper improves the implementation of the x fem method for stress analysis around cracks in three ways first the enrichment strategy is revisited the conventional approach uses a topological enrichment only the elements touching the front are enriched we suggest a geometrical enrichment in which a given domain size is enriched the improvements obtained with this enrichment are discussed second the conditioning of the x fem both for topological and geometrical enrichments is studied a preconditioner is introduced so that off the shelf iterative solver packages can be used and perform as well on x fem matrices as on standard fem matrices the preconditioner uses a local nodal cholesky based decomposition third the numerical integration scheme to build the x fem stiffness matrix is dramatically improved for tip enrichment functions by the use of an ad hoc integration scheme a 2d benchmark problem is designed to show the improvements and the robustness

generalised information criteria in model selection summary the problem of evaluating the goodness of statistical models is investigated from an information theoretic point of view information criteria are proposed for evaluating models constructed by various estimation procedures when the specified family of probability distributions does not contain the distribution generating the data the proposed criteria are applied to the evaluation of models estimated by maximum likelihood robust penalised likelihood bayes procedures etc we also discuss the use of the bootstrap in model evaluation problems and present a variance reduction technique in the bootstrap simulation

hybrid finite analytic solution of lateral subsurface flow a hybrid finite analytic method a numerical technique was used to solve lateral subsurface storm flow described by the extended dupuit forchheimer equation in subregions the local linearized one dimensional dupuit forchheimer equation was solved analytically in space and discretized in time by a simple difference formula this is called a hybrid finite analytic approach the system of algebraic equations obtained by the hybrid finite analytic approach can approximately preserve the overall nonlinear effect because the term h x 2 and the coefficient of diffusion are treated as constants only in the local regions a four point numerical formula can provide results that are stable and acceptably accurate without complex calculation and without small time steps the comparison between steady state profiles of the water table provided by this study with profiles provided by previous investigations shows that the method performs very well in the analysis of lateral subsurface storm flow

strongly stable generalized finite element method ssgfem for a non smooth interface problem ii a simplified algorithm abstract the solution of interface problems with non smooth interfaces having corners connected by straight lines exhibit weak singularity along the interface and may have singularities at the corners in an earlier paper zhang et al 2019 a strongly stable generalized finite element method ssgfem was proposed to approximate solution of such problems the method required two separate enrichment functions at o h 1 number of nodes h is the mesh parameter and a local orthogonalization technique requiring additional operations was used to ensure its stability and robustness in this paper we present a simplified ssgfem that does not require two enrichment functions at any of the nodes as a result we obtain an optimally converging gfem that is stable i e its scaled condition number is of the same order that of a standard fem and robust i e the conditioning is independent of the position of meshes relative to the interface these properties are illuminated by well designed experiments the simplified ssgfem does not require lot and requires less degrees of freedom and is easier to implement in contrast to the ssgfem proposed in zhang et al 2019 we also proved the optimal convergence for the simplified ssgfem in this paper that required a more involved analysis based on a smart observation on approximation of weak singularities near the corner

connectivity free front tracking method for multiphase flows with free surfaces in this study a connectivity free front tracking method is developed to simulate multiphase flows with free surfaces this method is based on the point set method which does not require any connectivities between interfacial points to represent the interface the main advantage of the connectivity free approach is the easiness in re constructing the interface when large topology change occurs it requires an indicator field to be constructed first based on the existing interface and the surface curvature and normal are then computed using the indicator field here we adopt the reproducing kernel particle method rkpm interpolation function that provides the ability to deal with free surface flows and the flexibility of using non uniform meshes when local fine resolution is needed a points regeneration scheme is developed to construct smooth interfaces and to automatically handle topology changes the mass conservation is verified by performing a single vortex advection test several 2 d and 3 d numerical tests including an oscillating droplet dam breaking two droplet impacting and multi bubble merging are presented to show the accuracy and the robustness of the method

analysis of an xfem discretization for stokes interface problems we consider a stationary stokes interface problem in the discretization the interface is not aligned with the triangulation for the discretization we use the p 1 extended finite element space p 1 xfem for the pressure and the standard conforming p 2 finite element space for the velocity since this pair is not necessarily lbb stable a consistent stabilization term known from the literature is added for the discrete bilinear form an inf sup stability result is derived which is uniform with respect to h mesh size parameter the viscosity quotient mu 1 mu 2 and the position of the interface in the triangulation based on this discretization error bounds are derived an optimal preconditioner for the stiffness matrix corresponding to this pair p 1 xfe for pressure and p 2 fe for velocity is presented the preconditioner has block diagonal form with a multigrid preconditioner for the velocity block and a new schur complement preconditioner optimality of this block preconditioner

a fictitious domain approach for a mixed finite element method solving the two phase stokes problem with surface tension forces abstract in this article we study a mixed finite element formulation for solving the stokes problem with general surface forces that induce a jump of the normal trace of the stress tensor on an interface that splits the domain into two subdomains equality of velocities is assumed at the interface the interface conditions are taken into account with multipliers a suitable lagrangian functional is introduced for deriving a weak formulation of the problem a specificity of this work is the consideration of the interface with a fictitious domain approach the latter is inspired by the xfem approach in the sense that cut off functions are used but it is simpler to implement since no enrichment by singular functions is provided in that context getting convergence for the dual variables defined on the interface is non trivial for that purpose an augmented lagrangian technique stabilizes the convergence of the multipliers which is important because their value would determine the dynamics of the interface in an unsteady framework theoretical analysis is provided where we show that a discrete inf sup condition independent of the mesh size is satisfied for the stabilized formulation this guarantees optimal convergence rates that we observe with numerical tests the capacity of the method is demonstrated with robustness tests and with an unsteady model tested for deformations of the interface that correspond to ellipsoidal shapes in dimension 2

direct density derivative estimation estimating the derivatives of probability density functions is an essential step in statistical data analysis a naive approach to estimate the derivatives is to first perform density estimation and then compute its derivatives however this approach can be unreliable because a good density estimator does not necessarily mean a good density derivative estimator to cope with this problem in this letter we propose a novel method that directly estimates density derivatives without going through density estimation the proposed method provides computationally efficient estimation for the derivatives of any order on multidimensional data with a hyperparameter tuning method and achieves the optimal parametric convergence rate we further discuss an extension of the proposed method by applying regularized multitask learning and a general framework for density derivative estimation based on bregman divergences applications of the proposed method to nonparametric kullback leibler divergence approximation and bandwidth matrix selection in kernel density estimation are also explored

interface stabilised finite element method for moving domains and free surface flows abstract a recently developed stabilised finite element method which draws upon features of both continuous and discontinuous finite element methods is generalised for the incompressible navier stokes equations on moving domains and for free surface problems the approach allows the natural incorporation of upwinding of the advective flux and the formulation is stable when using equal order lagrange basis functions for the velocity and pressure fields particular attention is paid to the formulation of a fractional step algorithm for moving domain problems numerous applications to environmental free surface flows are presented ranging from simple test cases to simulations of sophisticated laboratory experiments it is shown that the formulation which contains no flow dependent stabilisation parameters is able to model a wide range of flow conditions stably without user intervention and it is shown that negligible numerical dissipation is introduced the physics of the considered numerical examples involves sensitive free surface wave behaviour which has been accurately captured due to the stability of the model together with negligible introduced numerical dissipation

covariate shift adaptation by importance weighted cross validation a common assumption in supervised learning is that the input points in the training set follow the same probability distribution as the input points that will be given in the future test phase however this assumption is not satisfied for example when the outside of the training region is extrapolated the situation where the training input points and test input points follow different distributions while the conditional distribution of output values given input points is unchanged is called the covariate shift under the covariate shift standard model selection techniques such as cross validation do not work as desired since its unbiasedness is no longer maintained in this paper we propose a new method called importance weighted cross validation iwcv for which we prove its unbiasedness even under the covariate shift the iwcv procedure is the only one that can be applied for unbiased classification under covariate shift whereas alternatives to iwcv exist for regression the usefulness of our proposed method is illustrated by simulations and furthermore demonstrated in the brain computer interface where strong non stationarity effects can be seen between training and test sessions

on time integration in the xfem the extended finite element method xfem is often used in applications that involve moving interfaces examples are the propagation of cracks or the movement of interfaces in two phase problems this work focuses on time integration in the xfem the performance of the discontinuous galerkin method in time space time finite elements fes and time stepping schemes are analyzed by convergence studies for different model problems it is shown that space time fe achieve optimal convergence rates special care is required for time stepping in the xfem due to the time dependence of the enrichment functions in each time step the enrichment functions have to be evaluated at different time levels this has important consequences in the quadrature used for the integration of the weak form a time stepping scheme that leads to optimal or only slightly sub optimal convergence rates is systematically constructed in this work copyright 2009 john wiley sons ltd

an extended finite element method for a diffuse interface model this work presents an extended finite element method xfem for a diffuse interface model which describes interfacial phenomena of multi phase flow the diffuse interface has a non zero thickness over which the phase field variable changes continuously the diffuse interface thickness is typically very small compared to the observed domain size resulting in a high gradient solution in this work the finite element approximation of the phase field variable is locally enriched with a tangent hyperbolic function which characterizes a high gradient solution of the diffuse interface model we study a one dimensional advection and two diffusion problems and demonstrate the remarkable improvement of the solution by the local enrichment

stable generalized finite element method sgfem for parabolic interface problems abstract we study a stable generalized finite element method sgfem for parabolic interface problems with smooth interfaces the standard finite element fe space based on a simple mesh is enriched by a one side distance function to simulate gradient jumps of exact solutions on the interfaces the mesh is quasi uniform and independent of the interfaces so that mesh matching or refinement along the interfaces is not needed the main idea to derive the sgfem is to modify the one side distance function by subtracting its fe interpolant the sgfem approximates the parabolic interface problem with an optimal convergence rate and is stable in that its scaled condition number is of the same order as the fem o h 2 h is a mesh size parameter and does not depend on the relative positions of the mesh and interfaces the proposed sgfem is a conforming method and is free from any penalty parameters or stability schemes moreover the components of the approximation functions of the sgfem are independent when extended to vector valued interface problems the optimal convergence rates of sgfem for curved interfaces are proven theoretically for the backward euler and crank nicolson formulations the convergence and conditioning are tested by numerical experiments

strongly stable generalized finite element method ssgfem for a non smooth interface problem abstract in this paper we propose a strongly stable generalized finite element method ssgfem for a non smooth interface problem where the interface has a corner the ssgfem employs enrichments of 2 types the nodes in a neighborhood of the corner are enriched by singular functions characterizing the singularity of the unknown solution while the nodes close to the interface are enriched by a distance based function characterizing the jump in the gradient of the unknown solution along the interface thus nodes in the neighborhood of the corner and close to the interface are enriched with two enrichment functions both types of enrichments have been modified by a simple local procedure of subtracting the interpolant a simple local orthogonalization technique lot also has been used at the nodes enriched with both enrichment functions we prove that the ssgfem yields the optimal order of convergence the numerical experiments presented in this paper indicate that the conditioning of the ssgfem is not worse than that of the standard finite element method and the conditioning is robust with respect to the position of the mesh relative to the interface

on the construction of blending elements for local partition of unity enriched finite elements for computational efficiency partition of unity enrichments are preferably localized to the sub domains where they are needed it is shown that an appropriate construction of the elements in the blending area the regionwhere the enriched elements blend to unenriched elements is often crucial for good performance of local partition of unity enrichments an enhanced strain formulation is developed which leads to good performance the optimal rate of convergence is achieved for polynomial enrichments it is shown that a proper choice of the finite element shape functions and partition of unity shape functions also improves the accuracy and convergence the methods are illustrated by several examples the examples deal primarily with the signed distance function enrichment for treating discontinuous derivatives inside an element but other enrichments are also considered results show that both methods provide optimal rates of convergence

regularization path for nu support vector classification the v support vector classification v svc proposed by scholkopf has the advantage of using a regularization parameter v for controlling the number of support vectors and margin errors however compared to c svc its formulation is more complicated and to date there are no effective methods for computing its regularization path in this paper we propose a new regularization path algorithm which is designed on the basis of a modified formulation of v svc and traces the solution path with respect to the parameter v through theoretical analysis and confirmatory experiments we show that our algorithm can avoid the infeasible updating path under several assumptions i e assumptions 1 and 2 and fit the entire solution path in a finite number of steps when the regularization path of v svc is available a novel approach proposed by yang and ong can be applied to obtain the global optimal solution of common validation functions for v svc and the computation for the whole process is minimal numerical experiments show that it is more efficient than various kinds of grid search methods for selecting the optimal regularization parameter v

high order extended finite element method for cracked domains the aim of the paper is to study the capabilities of the extended finite element method xfem to achieve accurate computations in non smooth situations such as crack problems although the xfem method ensures a weaker error than classical nite element methods the rate of convergence is not improved when the mesh parameter h is going to zero because of the presence of a singularity the di culty can be overcome by modifying the enrichment of the nite element basis with the asymptotic crack tip displacement solutions as well as with the heaviside function numerical simulations show that the modi ed xfem method achieves an optimal rate of convergence i e like in a standard nite element method for a smooth problem

analysis of backward euler extended finite element discretization of parabolic problems with moving interfaces abstract numerical experiments performed by several authors repeatedly confirmed that the extended finite element method combined with classical time stepping schemes such as backward euler or crank nicolson provides optimal rates of convergence when applied to problems with moving interfaces in spite of the rapid spread of this discretization approach a complete space and time error analysis is not available yet the objective of this work is to contribute to closing the gap between observations and rigorous analysis more precisely we preform a thorough space and time error analysis of different variants of the extended finite element method combined with backward euler time advancing scheme when applied to problems with moving interfaces our results prove that the discretization error measured in the natural norms decreases with the expected rate when space and time discretization steps are refined we also show that the space and time approximation properties are fully decoupled as a consequence high order approximation schemes could be developed and analyzed within the theoretical framework proposed here numerical experiments are finally addressed for the verification of the algorithms besides the interest of providing rigorous error bounds we believe that a general theoretical framework is extremely helpful as a guide for further developing and refining extended finite element methods for free interface problems

estimating the support of a high dimensional distribution suppose you are given some data set drawn from an underlying probability distribution p and you want to estimate a simple subset s of input space such that the probability that a test point drawn from p lies outside of s equals some a priori specified value between 0 and 1 we propose a method to approach this problem by trying to estimate a function f that is positive on s and negative on the complement the functional form of f is given by a kernel expansion in terms of a potentially small subset of the training data it is regularized by controlling the length of the weight vector in an associated feature space the expansion coefficients are found by solving a quadratic programming problem which we do by carrying out sequential optimization over pairs of input patterns we also provide a theoretical analysis of the statistical performance of our algorithm the algorithm is a natural extension of the support vector algorithm to the case of unlabeled data

on semi supervised linear regression in covariate shift problems semi supervised learning approaches are trained using the full training labeled data and available testing unlabeled data demonstrations of the value of training with unlabeled data typically depend on a smoothness assumption relating the conditional expectation to high density regions of the marginal distribution and an inherent missing completely at random assumption for the labeling so called covariate shift poses a challenge for many existing semi supervised or supervised learning techniques covariate shift models allow the marginal distributions of the labeled and unlabeled feature data to differ but the conditional distribution of the response given the feature data is the same an example of this occurs when a complete labeled data sample and then an unlabeled sample are obtained sequentially as it would likely follow that the distributions of the feature data are quite different between samples the value of using unlabeled data during training for the elastic net is justified geometrically in such practical covariate shift problems the approach works by obtaining adjusted coefficients for unlabeled prediction which recalibrate the supervised elastic net to compromise i maintaining elastic net predictions on the labeled data with ii shrinking unlabeled predictions to zero our approach is shown to dominate linear supervised alternatives on unlabeled response predictions when the unlabeled feature data are concentrated on a low dimensional manifold away from the labeled data and the true coefficient vector emphasizes directions away from this manifold large variance of the supervised predictions on the unlabeled set is reduced more than the increase in squared bias when the unlabeled responses are expected to be small so an improved compromise within the bias variance tradeoff is the rationale for this performance improvement performance is validated on simulated and real data

a least squares approach to direct importance estimation we address the problem of estimating the ratio of two probability density functions which is often referred to as the importance the importance values can be used for various succeeding tasks such as covariate shift adaptation or outlier detection in this paper we propose a new importance estimation method that has a closed form solution the leave one out cross validation score can also be computed analytically therefore the proposed method is computationally highly efficient and simple to implement we also elucidate theoretical properties of the proposed method such as the convergence rate and approximation error bounds numerical experiments show that the proposed method is comparable to the best existing method in accuracy while it is computationally more efficient than competing approaches

hierarchical x fem for n phase flow n 2 the extended finite element method x fem has been successfully used in two phase flow problems involving a moving interface in order to simulate problems involving more than two phases the x fem has to be further extended the proposed approach is presented in the case of a quasi static stokes n phase flow and it is based on using an ordered collection of level set functions to describe the location of the phases a level set hierarchy allows describing triple junctions avoiding overlapping or voids between materials moreover an enriched solution accounting for several simultaneous phases inside one element is proposed the interpolation functions corresponding to the enriched degrees of freedom require redefining the associated ridge function accounting for all the level sets the computational implementation of this scheme involves calculating integrals in elements having several materials inside an adaptive quadrature accounting for the interfaces locations is proposed to accurately compute these integrals examples of the hierarchical x fem approach are given for a n phase stokes problem in 2 and 3 dimensions

on the influence of the kernel on the consistency of support vector machines in this article we study the generalization abilities of several classifiers of support vector machine svm type using a certain class of kernels that we call universal it is shown that the soft margin algorithms with universal kernels are consistent for a large class of classification problems including some kind of noisy tasks provided that the regularization parameter is chosen well in particular we derive a simple sufficient condition for this parameter in the case of gaussian rbf kernels on the one hand our considerations are based on an investigation of an approximation property the so called universality of the used kernels that ensures that all continuous functions can be approximated by certain kernel expressions this approximation property also gives a new insight into the role of kernels in these and other algorithms on the other hand the results are achieved by a precise study of the underlying optimization problems of the classifiers furthermore we show consistency for the maximal margin classifier as well as for the soft margin svm s in the presence of large margins in this case it turns out that also constant regularization parameters ensure consistency for the soft margin svm s finally we prove that even for simple noise free classification problems svm s with polynomial kernels can behave arbitrarily badly

an adaptive variational procedure for the conservative and positivity preserving allen cahn phase field model abstract in this paper we present an adaptive variational procedure for unstructured meshes to capture fluid fluid interfaces in two phase flows the two phases are modeled by the phase field finite element formulation which involves the conservative allen cahn equation coupled with the incompressible navier stokes equations the positivity preserving variational formulation is designed to maintain the bounded and stable solution of the allen cahn equation for the adaptivity procedure we consider the residual based error estimates for the underlying differential equations of the two phase system in particular the adaptive refinement coarsening is carried out by the newest vertex bisection algorithm by evaluating the residual error indicators based on the error estimates of the allen cahn equation the coarsening algorithm avoids the storage of the tree data structures for the hierarchical mesh thus providing the ease of numerical implementation furthermore the proposed nonlinear adaptive partitioned procedure aims at reducing the amount of coarsening while maintaining the convergence properties of the underlying nonlinear coupled differential equations we investigate the adaptive phase field finite element scheme through the spinodal decomposition in a complex curved geometry and the volume conserved interface motion driven by the mean curvature flow for two circles in a square domain we then assess the accuracy and efficiency of the proposed procedure by modeling the free surface motion in a sloshing tank in contrast to the non adaptive eulerian grid counterpart we demonstrate that the mesh adaptivity remarkably reduces the degrees of freedom and the computational cost by nearly half for similar accuracy the mass loss in the allen cahn equation via adaptivity process is also reduced by nearly three times compared to the non adaptive mesh finally we apply the adaptive numerical framework to solve the application of a dam breaking problem with topological changes

a conformal decomposition finite element method for arbitrary discontinuities on moving interfaces summary interface capturing methods using enriched finite element formulations are well suited for solving multimaterial transport problems that contain weak or strong discontinuities the conformal decomposition fem decomposes multimaterial elements of a non conforming background mesh into sub elements that conform to material interfaces captured using a level set method as the interface evolves interfacial nodes move and background nodes may change material the present work describes approaches for handling moving interfaces in the context of the conformal decomposition fem for both weakly and strongly discontinuous fields dynamic discretization methods using extrapolation and moving mesh approaches are considered and developed with first order and second order time integration methods the moving mesh approach is demonstrated to be a stable method that preserves both weak and strong discontinuities on a variety of one dimensional and two dimensional test problems while achieving the expected second order error convergence rate in space and time copyright 2014 john wiley sons ltd

a finite element technique for multifluid incompressible flow using eulerian grids the paper presents a finite element method for 3d incompressible fluid flows with capillary free boundaries it uses a fixed eulerian grid of 10 nodes p2 p1 tetrahedra and tracks the free boundary using a six nodes p2 triangular surface grid in order to improve the mass conservation properties of the method a local enrichment of the finite element basis in the elements intersected by the free boundaries is employed in addition to the surface tracking it also advects a smooth indicator function for an easy identification of the fluid properties in the different parts of the domain the advective part of the navier stokes equations is split and integrated with a characteristic method the remaining generalized stokes problem is resolved by means of an inexact outer inner uzawa iteration with a properly chosen preconditioner the performance of this technique is evaluated on several problems involving droplets in viscous liquids

on the performance of high aspect ratio elements for incompressible flows a systematic study of the effect of high aspect ratio elements using equal order interpolation velocity pressure elements for computation of incompressible flows is conducted both quadrilateral and triangular elements utilizing bilinear q1q1 and linear p1p1 interpolation functions respectively are considered stabilized finite element formulations are employed to solve the incompressible navier stokes equations in the primitive variables the element length h plays an important role in the calculation of stabilizing coefficients in the formulation three definitions of h are utilized these are based on the maximum edge length minimum edge length of an element and the element length along the streamwise direction performance of the implementations is evaluated for both steady and unsteady flows numerical experiments are conducted for flow past a circular cylinder at reynolds numbers 10 and 100 while in the former case the flow is steady the latter one is associated with temporally periodic vortex shedding it is observed that for the re 10 flow all definitions of h produce acceptable solutions even with elements that have very high aspect ratios in the case of re 100 flow again all definitions of h work well for elements with reasonable low aspect ratios however for large aspect ratio elements it is only the definition based on the minimum edge length of an element that results in acceptable solution it is also observed that the effect of high aspect ratio is felt more by the p1p1 element as compared to the q1q1 element

stability of incompressible formulations enriched with x fem abstract the treatment of near incompressibility is a major concern for applications involving rubber like materials or when important plastic flows occurs as in forming processes the use of mixed finite element methods is known to prevent the locking of the finite element approximation in the incompressible limit however it also introduces a critical condition for the stability of the formulation called the inf sup or lbb condition recently the finite element method has evolved with the introduction of the partition of unity method the extended finite element method x fem uses the partition of unity method to remove the need to mesh physical surfaces or to re mesh them as they evolve the enrichment of the displacement field makes it possible to treat surfaces of discontinuity inside finite elements in this paper some strategies are proposed for the enrichment of low order mixed finite element approximations in the incompressible setting the case of holes material interfaces and cracks are considered numerical examples show that for well chosen enrichment strategies the finite element convergence rate is preserved and the inf sup condition is passed

least squares independent component analysis accurately evaluating statistical independence among random variables is a key element of independent component analysis ica in this letter we employ a squared loss variant of mutual information as an independence measure and give its estimation method our basic idea is to estimate the ratio of probability densities directly without going through density estimation thereby avoiding the difficult task of density estimation in this density ratio approach a natural cross validation procedure is available for hyperparameter selection thus all tuning parameters such as the kernel width or the regularization parameter can be objectively optimized this is an advantage over recently developed kernel based independence measures and is a highly useful property in unsupervised learning problems such as ica based on this novel independence measure we develop an ica algorithm named least squares independent component analysis

outlier detection and robust normal curvature estimation in mobile laser scanning 3d point cloud data this paper proposes two robust statistical techniques for outlier detection and robust saliency features such as surface normal and curvature estimation in laser scanning 3d point cloud data one is based on a robust z score and the other uses a mahalanobis type robust distance the methods couple the ideas of point to plane orthogonal distance and local surface point consistency to get maximum consistency with minimum distance mcmd the methods estimate the best fit plane based on most probable outlier free and most consistent points set in a local neighbourhood then the normal and curvature from the best fit plane will be highly robust to noise and outliers experiments are performed to show the performance of the algorithms compared to several existing well known methods from computer vision data mining machine learning and statistics using synthetic and real laser scanning datasets of complex planar and non planar objects results for plane fitting denoising sharp feature preserving and segmentation are significantly improved the algorithms are demonstrated to be significantly faster more accurate and robust quantitatively for a sample size of 50 with 20 outliers the proposed mcmd z is approximately 5 15 and 98 times faster than the existing methods ulsif ransac and rpca respectively the proposed mcmd md method can tolerate 75 clustered outliers whereas rpca and ransac can only tolerate 47 and 64 outliers respectively in terms of outlier detection for the same dataset mcmd z has an accuracy of 99 72 0 4 false positive rate and 0 false negative rate for rpca ransac and ulsif the accuracies are 97 05 47 06 and 94 54 respectively and they have misclassification rates higher than the proposed methods the new methods have potential for local surface reconstruction fitting and other point cloud processing tasks highlightstwo statistical techniques are proposed for outlier detection in point cloud data the proposed methods can fit robust plane in laser scanning data the proposed methods produce robust normal and curvature in point cloud processing they are faster and robust than ransac robust pca and other existing efficient methods they have potential for point cloud denoising segmentation and reconstruction

domain adaptation via transfer component analysis domain adaptation allows knowledge from a source domain to be transferred to a different but related target domain intuitively discovering a good feature representation across domains is crucial in this paper we first propose to find such a representation through a new learning method transfer component analysis tca for domain adaptation tca tries to learn some transfer components across domains in a reproducing kernel hilbert space using maximum mean miscrepancy in the subspace spanned by these transfer components data properties are preserved and data distributions in different domains are close to each other as a result with the new representations in this subspace we can apply standard machine learning methods to train classifiers or regression models in the source domain for use in the target domain furthermore in order to uncover the knowledge hidden in the relations between the data labels from the source and target domains we extend tca in a semisupervised learning setting which encodes label information into transfer components learning we call this extension semisupervised tca the main contribution of our work is that we propose a novel dimensionality reduction framework for reducing the distance between domains in a latent space for domain adaptation we propose both unsupervised and semisupervised feature extraction approaches which can dramatically reduce the distance between domain distributions by projecting data onto the learned transfer components finally our approach can handle large datasets and naturally lead to out of sample generalization the effectiveness and efficiency of our approach are verified by experiments on five toy datasets and two real world applications cross domain indoor wifi localization and cross domain text classification