measurement errors in caries diagnosis some further latent class models latent class models have been proposed for assessing relative errors in discrete measurements arising for example in caries diagnosis those models however that turned out to fit empirical data n 3 869 teeth 5 dentists to a sufficient degree needed the inclusion of interaction terms for pairs of raters at the latent levels in order to describe the observed interrelations of the judgments now it is shown that instead of giving up the concept of local stochastic independence increasing the number of classes while possibly restricting their parameters in the end has the same effect both the unrestricted three class model which can be interpreted to be the generalization of the carlos senning assumptions and a restricted four class model which resembles the latent distance model well known from psychometrics give good and excellent fit respectively to the caries data for the case of the four class model a second solution exists that exhibits exactly the same fit giving rise to warnings against the possibility of multiple solutions to the likelihood equations

an efficient robust adaptive filtering algorithm based on parallel subgradient projection techniques this paper presents a novel robust adaptive filtering scheme based on the interactive use of statistical noise information and the ideas developed originally for efficient algorithmic solutions to the convex feasibility problems the statistical noise information is quantitatively formulated as stochastic property closed convex sets by the simple design formulae developed in this paper a simple set theoretic inspection also leads to an important statistical reason for the sensitivity to noise of the affine projection algorithm apa the proposed adaptive algorithm is computationally efficient and robust to noise because it requires only an iterative parallel projection onto a series of closed half spaces that are highly expected to contain the unknown system to be identified and is free from the computational load of solving a system of linear equations the numerical examples show that the proposed adaptive filtering scheme realizes dramatically fast and stable convergence for highly colored excited speech like input signals in severe noise situations

on projection algorithms for solving convex feasibility problems due to their extraordinary utility and broad applicability in many areas of classical mathematics and modern physical sciences most notably computerized tomography algorithms for solving convex feasibility problems continue to receive great attention to unify generalize and review some of these algorithms a very broad and flexible framework is investigated several crucial new concepts which allow a systematic discussion of questions on behaviour in general hilbert spaces and on the quality of convergence are brought out numerous examples are given

maass cusp forms abstract it is shown that under certain standard assumptions such as extended riemann hypotheses the scattering matrix s for generic sl 2 r is unexpectedly of order 2 this leads to the conjecture that the generic cofinite has very few maass cusp forms

spectral simplicity and asymptotic separation of variables we describe a method for comparing the spectra of two real analytic families at and qt of quadratic forms that both degenerate as a positive parameter t tends to zero we suppose that the family at is amenable to separation of variables and that each eigenspace of at is 1 dimensional for some t we show that if qt is asymptotic to at at first order as t 0 then the eigenspaces of qt are also 1 dimensional for all but countably many t as an application we prove that for the generic triangle simplex in euclidean space constant curvature space form each eigenspace of the laplacian acting on dirichlet functions is 1 dimensional

efficient dictionary refining kernel adaptive filter with fundamental insights first we study a basic kernel adaptive filtering algorithm based on stochastic restricted gradient which is a natural extension of the naive online regularized risk minimization algorithm norma our error surface analysis shows that the algorithm has a decorrelation property due to its explicit use of kernel matrix it turns out that its normalized version projects the current coefficient vector onto the same hyperplane but with a different metric as the kernel normalized least mean square knlms algorithm this gives us a fundamental insight bridging two classes of kernel adaptive filtering algorithms second we use this insight to derive an efficient forward backward splitting algorithm the same metric as used for the normalized algorithm is employed in the forward step whereas the ordinary euclidean metric is employed in the backward step leading to efficient adaptive refinements of the filter dictionary we show a monotone approximation property of the proposed algorithm with respect to some modified cost function under certain conditions numerical examples show the efficacy of the proposed algorithm

adaptive nonlinear estimation based on parallel projection along affine subspaces in reproducing kernel hilbert space we propose a novel algorithm using a reproducing kernel for adaptive nonlinear estimation the proposed algorithm is based on three ideas projection along subspace selective update and parallel projection the projection along subspace yields excellent performances with small dictionary sizes the selective update effectively reduces the complexity without any serious degradation of performance the parallel projection leads to fast convergence tracking accompanied by noise robustness a convergence analysis in the non selective update case is presented by using the adaptive projected subgradient method simulation results exemplify the benefits from the three ideas as well as showing the advantages over the state of the art algorithms the proposed algorithm bridges the quantized kernel least mean square algorithm of chen and the sparse sequential algorithm of dodd

disappearance of cusp forms in special families in his 1954 g6ttingen lectures atle selberg sb posed the question of the asymptotic density of the poles of the eisenstein series for r a cofinite non cocompact subgroup of psl 2 r the question is known to be equivalent to the asymptotic count of the number of eigenvalues for the laplacebeltrami operator d acting in l2 h r where h is the upper halfplane with hyperbolic metric in general the spectral decomposition of d consists of the continuous band 1 4 oo with multiplicity the number of cusps of h r and a discrete component possibly in 1 4 0o spanned by eigenfunctions w1i wp2 see hj1 kb lxp for the eigenvalues aj dpj ajpj o consider the spectral counting function n r ij v n 0 see dips ps2 cor 2 3 luo lu recently established the unconditional result his argument does not involve the lindel6f hypothesis deshouillers et

the biplot as a diagnostic tool of local dependence in latent class models a medical application latent class models lcms can be used to assess diagnostic test performance when no reference test a gold standard is available considering two latent classes representing disease or non disease status one of the basic assumptions in such models is that of local or conditional independence all indicator variables tests are statistically independent within each latent class however in practice this assumption is often violated hence the two lcm fits the data poorly in this paper we propose the use of biplot methods to identify the conditional dependence between pairs of manifest variables within each latent class additionally we propose incorporating such dependence in the corresponding latent class using the log linear formulation of the model

effects of dependent errors in the assessment of diagnostic test performance latent class models can be used to assess diagnostic test performance when there is no perfectly accurate gold standard test available for comparison these models usually assume independent errors between the tests conditional on the true disease state of the subject maximum likelihood estimates of the prevalence of the disease and the error rates of diagnostic tests are then obtained this paper examines the impact of error dependencies between binary diagnostic tests on the parameter estimates obtained from the latent class models the independence model often gives parameter estimates having relatively small bias but in some situations for example when disease prevalence is low and the tests have low specificity such as in population screening the bias may be more serious

a weak to strong convergence principle for feje monotone methods in hilbert spaces we consider a wide class of iterative methods arising in numerical mathematics and optimization that are known to converge only weakly exploiting an idea originally proposed by haugazeau we present a simple modification of these methods that makes them strongly convergent without additional assumptions several applications are discussed

online kernel based classification using adaptive projection algorithms the goal of this paper is to derive a novel online algorithm for classification in reproducing kernel hilbert spaces rkhs by exploiting projection based adaptive filtering tools the paper brings powerful convex analytic and set theoretic estimation arguments in machine learning by revisiting the standard kernel based classification as the problem of finding a point which belongs to a closed halfspace a special closed convex set in an rkhs in this way classification in an online setting where data arrive sequentially is viewed as the problem of finding a point classifier in the nonempty intersection of an infinite sequence of closed halfspaces in the rkhs convex analysis is also used to introduce sparsification arguments in the design by imposing an additional simple convex constraint on the norm of the classifier an algorithmic solution to the resulting optimization problem where new convex constraints are added every time instant is given by the recently introduced adaptive projected subgradient method apsm which generalizes a number of well known projection based adaptive filtering algorithms such as the classical normalized least mean squares nlms and the affine projection algorithm apa under mild conditions the generated sequence of estimates enjoys monotone approximation strong convergence asymptotic optimality and a characterization of the limit point further we show that the additional convex constraint on the norm of the classifier naturally leads to an online sparsification of the resulting kernel series expansion we validate the proposed design by considering the adaptive equalization problem of a nonlinear channel and by comparing it with classical as well as with recently developed stochastic gradient descent techniques

convergence behavior of affine projection algorithms a class of equivalent algorithms that accelerate the convergence of the normalized lms nlms algorithm especially for colored inputs has previously been discovered independently the affine projection algorithm apa is the earliest and most popular algorithm in this class that inherits its name the usual apa algorithms update weight estimates on the basis of multiple unit delayed input signal vectors we analyze the convergence behavior of the generalized apa class of algorithms allowing for arbitrary delay between input vectors using a simple model for the input signal vectors conditions for convergence of the apa class are derived it is shown that the convergence rate is exponential and that it improves as the number of input signal vectors used for adaptation is increased however the rate of improvement in performance time to steady state diminishes as the number of input signal vectors increases for a given convergence rate apa algorithms are shown to exhibit less misadjustment steady state error than nlms simulation results are provided to corroborate the analytical results

latent class model diagnosis summary in many areas of medical research such as psychiatry and gerontology latent class variables are used to classify individuals into disease categories often with the intention of hierarchical modeling problems arise when it is not clear how many disease classes are appropriate creating a need for model selection and diagnostic techniques previous work has shown that the pearson 2 statistic and the log likelihood ratio g2 statistic are not valid test statistics for evaluating latent class models other methods such as information criteria provide decision rules without providing explicit information about where discrepancies occur between a model and the data identifiability issues further complicate these problems this paper develops procedures for assessing markov chain monte carlo convergence and model diagnosis and for selecting the number of categories for the latent variable based on evidence in the data using markov chain monte carlo techniques simulations and a psychiatric example are presented to demonstrate the effective use of these methods

erratum to spectral simplicity and asymptotic separation of variables the statement of lemma a 3 in hlljdg11 is false 1 this lemma is used in the proof of lemma 8 2 which is also incorrect and is used in the proof of proposition 9 1 despite this gap proposition 9 1 is correct and in order to rectify the situation we provide here the correct estimates needed to derive proposition 9 1 as a consequence the statements of the main results of the article hlljdg11 are correct we would like to emphasize that the overall strategy of the proof of proposition 9 1 remains unchanged in particular proposition 9 1 is a statement about concentration properties of quasimodes for the quadratic form a t coming from separation of variables more precisely it relies on the fact that a quasimode of order t for a t at a non critical energy cannot concentrate on the turning point and thus must have some mass in the classically allowed region in the exposition given in hlljdg11 this non concentration was hidden behind lemmas 9 4 and 9 5 we will make it more transparent here by directly using the langer cherry transform and the following estimate for solutions to the semiclassical airy equation 2

h sup spl infin optimality of the lms algorithm we show that the celebrated least mean squares lms adaptive algorithm is h sup spl infin optimal the lms algorithm has been long regarded as an approximate solution to either a stochastic or a deterministic least squares problem and it essentially amounts to updating the weight vector estimates along the direction of the instantaneous gradient of a quadratic cost function we show that the lms can be regarded as the exact solution to a minimization problem in its own right namely we establish that it is a minimax filter it minimizes the maximum energy gain from the disturbances to the predicted errors whereas the closely related so called normalized lms algorithm minimizes the maximum energy gain from the disturbances to the filtered errors moreover since these algorithms are central h sup spl infin filters they minimize a certain exponential cost function and are thus also risk sensitive optimal we discuss the various implications of these results and show how they provide theoretical justification for the widely observed excellent robustness properties of the lms filter

gradient based variable forgetting factor rls algorithm in time varying environments in this paper a new control mechanism for the variable forgetting factor vff of the recursive least square rls adaptive algorithm is presented the control algorithm is basically a gradient based method of which the gradient is derived from an improved mean square error analysis of rls the new mean square error analysis exploits the correlation of the inverse of the correlation matrix with itself that yields improved theoretical results especially in the transient and steady state mean square error it is shown that the theoretical analysis is close to simulation results for different forgetting factors and different model orders the analysis yields a dynamic equation of mean square error that can be used to derive a dynamic equation of the gradient of mean square error to control the forgetting factor the dynamic equation can produce a positive gradient when the error is large and a negative gradient when the error is in the steady state compared with other variable forgetting factor algorithms the new control algorithm gives fast tracking and small mean square model error for different signal to noise ratios snrs

using latent class models to characterize and assess relative error in discrete measurements whenever a definitive standard is not available to mark accuracy in a classification process discrete measurement error can be discussed only in relative terms if strong assumptions concerning the underlying discrete processes can be made latent class models allow one to characterize patterns of agreement disagreement among raters while simultaneously producing consensus estimates of prevalence a hypothetical definitive standard serves as the latent factor the discrete data are treated as incomplete and log linear models can be used to parameterize latent class models and extensions of latent class models data from the radiographic diagnosis of dental caries by five dentists were explored to estimate prevalence assess relative error and examine the validity of several traditional assumptions concerning diagnostic reliability latent class analysis allowed a more detailed description of diagnostic error than provided by commonly used summary statistics

generalised bilinear regression summary this paper discusses the application of generalised linear methods to bilinear models by criss cross regression it proposes an extension to segmented bilinear models in which the expectation matrix is linked to a sum in which each segment has specified row and column covariance matrices as well as a coefficient parameter matrix that is specified only by its rank this extension includes a variety of biadditive models including the generalised tukey degree of freedom for non additivity model that consists of two bilinear segments one of which is constant the extension also covers a variety of other models for which least squares fits had not hitherto been available such as higher way layouts combined into the rows and columns of a matrix and a harmonic model which can be reparameterised so a lower rank fit is equivalent to a constant phase parameter a number of practical applications are provided including displaying fits by biplots and using them to diagnose models

asymptotics of dirichlet eigenvalues and eigenfunctions of the laplacian on thin domains in rd abstract we consider the laplace operator with dirichlet boundary conditions on a domain in r d and study the effect that performing a scaling in one direction has on the eigenvalues and corresponding eigenfunctions as a function of the scaling parameter around zero this generalizes our previous results in two dimensions and as in that case allows us to obtain an approximation for dirichlet eigenvalues for a large class of domains under very mild assumptions as an application we derive a three term asymptotic expansion for the first eigenvalue of d dimensional ellipsoids

deformation of compact clifford klein forms of indefinite riemannian homogeneous manifolds 1 1 let g be a lie group and h a closed subgroup of g if a discrete subgroup of g acts properly discontinuously and freely on g h then the double coset space g h carries naturally a manifold structure such that the quotient map g h g h is locally diffeomorphic the manifold g h is said to be a clifford klein form of g h if it is compact then is said to be a uniform lattice for g h a typical example is a compact riemann surface mg with genus g 2 which is biholomorphic to a compact clifford klein form of the poincare disk g h sl 2 r so 2 by the uniformization theorem it is important from geometric view point that a clifford klein form g h inherits any g invariant local geometric structure on g h such as indefinite riemannian metric complex structure symplectic structure causal structure and so on

fast newton transversal filters a new class of adaptive estimation algorithms a class of adaptive algorithms for the estimation of fir finite impulse response transversal filters is presented the main characteristic of this class is the fast computation of the gain vector needed for the adaptation of the transversal filters the method for deriving these algorithms is based on the assumption that the input signal is autoregressive of order m where m can be much smaller than the order of the filter to be estimated under this assumption the covariance matrix of the input signal is estimated by extending in a min max way the m order sample covariance matrix this estimate can be regarded as a generalization of the diagonal covariance matrix used in lms and leads to an efficient computation of the gain needed for the adaptation the new class of algorithms contains the lms and the fast versions of ls as special cases the complexity changes linearly with m starting from the complexity of the lms for m 0 and ending at the complexity of the fast versions of ls

multikernel adaptive filtering this paper exemplifies that the use of multiple kernels leads to efficient adaptive filtering for nonlinear systems two types of multikernel adaptive filtering algorithms are proposed one is a simple generalization of the kernel normalized least mean square knlms algorithm 2 adopting a coherence criterion for dictionary designing the other is derived by applying the adaptive proximal forward backward splitting method to a certain squared distance function plus a weighted block l1 norm penalty encouraging the sparsity of an adaptive filter at the block level for efficiency the proposed multikernel approach enjoys a higher degree of freedom than those approaches which design a kernel as a convex combination of multiple kernels numerical examples show that the proposed approach achieves significant gains particularly for nonstationary data as well as insensitivity to the choice of some design parameters

pairwise optimal weight realization acceleration technique for set theoretic adaptive parallel subgradient projection algorithm the adaptive parallel subgradient projection psp algorithm was proposed in 2002 as a set theoretic adaptive filtering algorithm providing fast and stable convergence robustness against noise and low computational complexity by using weighted parallel projections onto multiple time varying closed half spaces in this paper we present a novel weighting technique named pairwise optimal weight realization power for further acceleration of the adaptive psp algorithm a simple closed form formula is derived to compute the projection onto the intersection of two closed half spaces defined by a triplet of vectors using the formula inductively the proposed weighting technique realizes a good direction of update the resulting weights turn out to be pairwise optimal in a certain sense the proposed algorithm has the inherently parallel structure composed of q primitive functions hence its total computational complexity o qrn is reduced to o rn with q concurrent processors r a constant positive integer numerical examples demonstrate that the proposed technique for r 1 yields significantly faster convergence than not only adaptive psp with uniform weights affine projection algorithm and fast newton transversal filters but also the regularized recursive least squares algorithm

fast recursive least squares transversal filters for adaptive filtering fast transversal filter ftf implementations of recursive least squares rls adaptive filtering algorithms are presented in this paper substantial improvements in transient behavior in comparison to stochastic gradient or lms adaptive algorithms are efficiently achieved by the presented algorithms the true not approximate solution of the rls problem is always obtained by the ftf algorithms even during the critical initialization period first n iterations of the adaptive filter this true solution is recursively calculated at a relatively modest increase in computational requirements in comparison to stochastic gradient algorithms factor of 1 6 to 3 5 depending upon application additionally the fast transversal filter algorithms are shown to offer substantial reductions in computational requirements relative to existing fast rls algorithms such as the fast kalman algorithms of morf ljung and falconer 1976 and the fast ladder lattice algorithms of morf and lee 1977 1981 they are further shown to attain steady state unnormalized or improve upon first n initialization steps the very low computational requirements of the efficient rls solutions of carayannis manolakis and kalouptsidis 1983 finally several efficient procedures are presented by which to ensure the numerical stability of the transversal filter algorithms including the incorporation of soft constraints into the performance criteria internal bounding and rescuing procedures and dynamic range increasing square root normalized variations of the transversal filters

robust reduced rank adaptive algorithm based on parallel subgradient projection and krylov subspace in this paper we propose a novel reduced rank adaptive filtering algorithm exploiting the krylov subspace associated with estimates of certain statistics of input and output signals we point out that when the estimated statistics are erroneous e g due to sudden changes of environments the existing krylov subspace based reduced rank methods compute the point that minimizes a ldquowrongrdquo mean square error mse in the subspace the proposed algorithm exploits the set theoretic adaptive filtering framework for tracking efficiently the optimal point in the sense of minimizing the ldquotruerdquo mse in the subspace therefore compared with the existing methods the proposed algorithm is more suited to adaptive filtering applications a convergence analysis of the algorithm is performed by extending the adaptive projected subgradient method apsm numerical examples demonstrate that the proposed algorithm enjoys better tracking performance than the existing methods for system identification problems

using a combination of reference tests to assess the accuracy of a new diagnostic test often the accuracy of a new diagnostic test must be assessed when a perfect gold standard does not exist use of an imperfect reference test biases accuracy estimates of the new test this paper reviews existing approaches to this problem including discrepant resolution and latent class analysis deficiencies with these approaches are identified a new approach is proposed that combines the results of several imperfect reference tests to define a better reference standard we call this the composite reference standard crs using the crs accuracy can be assessed using multi stage sampling designs maximum likelihood estimates of accuracy and expressions for the variance of sensitivity and specificity are provided data from clinical literature on the detection of chlamydia trachomatis are used to illustrate and compare the different approaches advantages of the crs relative to other approaches include that the crs is explicitly defined does not depend on the results of the new test under investigation and is easy to interpret

adaptive tracking of linear time variant systems by extended rls algorithms we exploit the one to one correspondences between the recursive least squares rls and kalman variables to formulate extended forms of the rls algorithm two particular forms of the extended rls algorithm are considered one pertaining to a system identification problem and the other pertaining to the tracking of a chirped sinusoid in additive noise for both of these applications experiments are presented that demonstrate the tracking superiority of the extended rls algorithms compared with the standard rls and least mean squares lms algorithms

krylov proportionate adaptive filtering techniques not limited to sparse systems this paper proposes a novel adaptive filtering scheme named the krylov proportionate normalized least mean square kpnlms algorithm kpnlms exploits the benefits i e fast convergence for sparse unknown systems of the proportionate nlms algorithm but its applications are not limited to sparse unknown systems a set of orthonormal basis vectors is generated from a certain krylov sequence it is proven that the unknown system is sparse with respect to the basis vectors in case of fairly uncorrelated input data different adaptation gain is allocated to a coefficient of each basis vector and the gain is roughly proportional to the absolute value of the corresponding coefficient of the current estimate kpnlms enjoys i fast convergence ii linear complexity per iteration and iii no use of any a priori information numerical examples demonstrate significant advantages of the proposed scheme over the reduced rank method based on the multistage wiener filter mwf and the transform domain adaptive filter tdaf both in noisy and silent situations

a family of adaptive filter algorithms with decorrelating properties although the normalized least mean square nlms algorithm is robust it suffers from low convergence speed if driven by highly correlated input signals one method presented to overcome this problem is the ozeki umeda 1984 affine projection ap algorithm the algorithm applies update directions that are orthogonal to the last p input vectors and thus allows decorrelation of an ar p input process speeding up the convergence this article presents a simple approach to show this property which furthermore leads to the construction of new algorithms that can handle other kinds of correlations such as ma and arma processes a statistical analysis is presented for this family of algorithms similar to the ap algorithm these algorithms also suffer a possible increase in the noise energy caused by their pre whitening filters

on selberg s small eigenvalue conjecture and residual eigenvalues we show that selberg s eigenvalue conjecture concern ing small eigenvalues of the automorphic laplacian for congruence groups is equivalent to a conjecture about the non existence of residual eigenvalues for a perturbed system we prove this using a combination of methods from asymptotic perturbation theory and number theory

deformation of γ0 5 cusp forms we develop an algorithm for numerical computation of the eisenstein series on a riemann surface of constant negative curvature we focus in particular on the computation of the poles of the eisenst

stabilizing the fast kalman algorithms the fast kalman algorithms are stabilized by introducing a quantity that measures the accumulation of the roundoff errors this quantity is used to correct the variables of the algorithm at every time step the correction is defined as the solution of a specific minimization problem the resulting algorithm still has the nice complexity properties of the original algorithm linear in the number of parameters to be estimated but it has a much more stable behavior