automatic bandwidth choice and confidence intervals in nonparametric regression in the present paper we combine the issues of bandwidth choice and construction of confidence intervals in nonparametric regression main emphasis is put on fully data driven methods we modify the n consistent bandwidth selector of hahrdle hall and marron such that it is appropriate for heteroscedastic data and we show how one can optimally choose the bandwidth g of the pilot estimator m g then we consider classical confidence intervals based on kernel estimators with data driven bandwidths and compare their coverage accuracy we propose a method to put undersmoothing with a data driven bandwidth into practice and show that this procedure outperforms explicit bias correction

time varying coefficients models for recurrent event data when different varying coefficients admit different degrees of smoothness application to heart disease modeling we consider a class of semiparametric marginal rate models for analyzing recurrent event data in these models both time varying and time free effects are present and the estimation of time varying effects may result in non smooth regression functions a typical approach for avoiding this problem and producing smooth functions is based on kernel methods the traditional kernel based approach however assumes a common degree of smoothness for all time varying regression functions which may result in suboptimal estimators if the functions have different levels of smoothness in this paper we extend the traditional approach by introducing different bandwidths for different regression functions first we establish the asymptotic properties of the suggested estimators next we demonstrate the superiority of our proposed method using two finite sample simulation studies finally we illustrate our methodology by analyzing a real world heart disease dataset copyright 2016 john wiley sons ltd

simultaneous inferences on the contrast of two hazard functions with censored observations in survival analysis often times the pattern of instantaneous risk over time is more interesting than that of the cumulative risk for this case a nonparametric hazard function estimate is more appropriate for summarizing the risk experience of a group of patients than the corresponding kaplan meier estimate in comparing a new treatment with a standard therapy it is important to know if the treatment loses it potency during the follow up period and if it does one would like to know when it becomes ineffective unfortunately with a plot of the differences of two kaplan meier curves it is rather difficult to capture such temporal trends in this article we propose simple procedures for constructing confidence bands for the contrast of two hazard functions with censored data the simultaneous interval estimates are quite useful for identifying possible values of the contrast over time with a certain degree of confidence the new proposals are illustrated with an example and a small simulation study

regression discontinuity design with many thresholds abstract numerous empirical studies employ regression discontinuity designs with multiple cutoffs and heterogeneous treatments a common practice is to normalize all the cutoffs to zero and estimate one effect this procedure identifies the average treatment effect ate on the observed distribution of individuals local to existing cutoffs however researchers often want to make inferences on more meaningful ates computed over general counterfactual distributions of individuals rather than simply the observed distribution of individuals local to existing cutoffs this paper proposes a consistent and asymptotically normal estimator for such ates when heterogeneity follows a non parametric function of cutoff characteristics in the sharp case the proposed estimator converges at the minimax optimal rate of root n for a specific choice of tuning parameters identification in the fuzzy case with multiple cutoffs is impossible unless heterogeneity follows a finite dimensional function of cutoff characteristics under parametric heterogeneity this paper proposes an ate estimator for the fuzzy case that optimally combines observations to maximize its precision

distributed source modeling and direction of arrival estimation techniques in direction of arrival doa estimation the direction of a signal is usually assumed to be a point if the direction of a signal is distributed due to some environmental phenomenon however doa estimation methods based on the point source assumption may result in poor performance we consider doa estimation when the signal sources are distributed parametric and nonparametric models are proposed and estimation methods are considered under these models in addition the asymptotic distribution of estimation errors is obtained to show the models statistical properties

bootstrap confidence regions for the intensity of a poisson point process abstract bootstrap methods are developed for constructing confidence regions for the intensity function of a nonstationary poisson process several different resampling algorithms are suggested ranging from resampling a poisson process with intensity equal to that estimated nonparametrically from the data to resampling the data points themselves in the same manner that the bootstrap is used in problems involving independent and identically distributed observations for each different bootstrap method various percentile t ways of constructing confidence bands are described the effectiveness of these different approaches is demonstrated both theoretically and numerically for real and simulated data issues such as bias correction are addressed

inherent limitations in the localization of a coherently scattered source this paper addresses the problem of localizing a single coherently scattered far field narrowband source emitting a gaussian signal and observed in additive gaussian noise an explicit expression for the cramer rao bound crb of the unknown spatial and spectral i e source and noise power level parameters of the source is presented for arbitrary array geometry the crb is used to study the inherent limitations in the estimation of the mean angle of a scattered source in comparison to the case of a point source at the same mean angle

a k nearest neighbor simulator for daily precipitation and other weather variables a multivariate nonparametric time series simulation method is provided to generate random sequences of daily weather variables that honor the statistical properties of the historical data of the same weather variables at the site a vector of weather variables solar radiation maximum temperature minimum temperature average dew point temperature average wind speed and precipitation on a day of interest is resampled from the historical data by conditioning on the vector of the same variables feature vector on the preceding day the resampling is done from the k nearest neighbors in state space of the feature vector using a weight function this approach is equivalent to a nonparametric approximation of a multivariate lag 1 markov process it does not require prior assumptions as to the form of the joint probability density function of the variables an application of the resampling scheme with 30 years of daily weather data at salt lake city utah is provided results are compared with those from the application of a multivariate autoregressive model similar to that of richardson 1981

local likelihood smoothing of sample extremes trends in sample extremes are of interest in many contexts an example being environmental statistics parametric models are often used to model trends in such data but they may not be suitable for exploratory data analysis this paper outlines a semiparametric approach to smoothing sample extremes based on local polynomial fitting of the generalized extreme value distribution and related models the uncertainty of fits is assessed by using resampling methods the methods are applied to data on extreme temperatures and on record times for the women s 3000 m race

nonparametric regression optimal local bandwidth choice summary kernel estimators of a regression function are investigated the bandwidths are locally chosen by a data driven method based on the minimization of a local cross validation criterion this method is shown to be asymptotically optimal with respect to local quadratic measures of errors monte carlo experiments are presented and finally the method is applied to some data of medical interest

stochastic variational inference we develop stochastic variational inference a scalable algorithm for approximating posterior distributions we develop this technique for a large class of probabilistic models and we demonstrate it with two probabilistic topic models latent dirichlet allocation and the hierarchical dirichlet process topic model using stochastic variational inference we analyze several large collections of documents 300k articles from nature 1 8m articles from the new york times and 3 8m articles from wikipedia stochastic inference can easily handle data sets of this size and outperforms traditional variational inference which can only handle a smaller subset we also show that the bayesian nonparametric topic model outperforms its parametric counterpart stochastic variational inference lets us apply complex bayesian models to massive data sets

some asymptotic theory for the bootstrap efron s bootstrap method of distribution approximation is shown to be asymptotically valid in a large number of situations including t statistics the empirical and quantile processes and von mises functionals some counter examples are also given to show that the approximation does not always succeed

on edgeworth expansion and bootstrap confidence bands in nonparametric curve estimation summary the notion of pivoting and techniques of edgeworth expansion have become basic tools for using and understanding bootstrap methods in finite parameter problems this paper shows that these ideas have important contributions to make to infinite parameter problems e g in the construction of simultaneous confidence bands for nonparametric density estimators we propose a bootstrap method for confidence band construction based on a pivotal function estimator and illustrate its use we give an edgeworth expansion argument which demonstrates the efficacy of the technique the expansion is a power series in nh log h 1 3 1 2 where n is the sample size and h denotes the bandwidth this should be compared with a power series in n 1 2 in more conventional finite dimensional problems

nonparametric confidence intervals for receiver operating characteristic curves summary we study methods for constructing confidence intervals and confidence bands for estimators of receiver operating characteristics particular emphasis is placed on the way in which smoothing should be implemented when estimating either the characteristic itself or its variance we show that substantial undersmoothing is necessary if coverage properties are not to be impaired a theoretical analysis of the problem suggests an empirical plug in rule for bandwidth choice optimising the coverage accuracy of interval estimators the performance of this approach is explored our preferred technique is based on asymptotic approximation rather than a more sophisticated approach using the bootstrap since the latter requires a multiplicity of smoothing parameters all of which must be chosen in nonstandard ways it is shown that the asymptotic method can give very good performance

streamflow simulation a nonparametric approach in this paper kernel estimates of the joint and conditional probability density functions are used to generate synthetic streamflow sequences streamflow is assumed to be a markov process with time dependence characterized by a multivariate probability density function kernel methods are used to estimate this multivariate density function simulation proceeds by sequentially resampling from the conditional density function derived from the kernel estimate of the underlying multivariate probability density function this is a nonparametric method for the synthesis of streamflow that is data driven and avoids prior assumptions as to the form of dependence e g linear or nonlinear and the form of the probability density functions e g gaussian we show using synthetic examples with known underlying models that the nonparametric method presented is more flexible than the conventional models used in stochastic hydrology and is capable of reproducing both linear and nonlinear dependence the effectiveness of this model is illustrated through its application to simulation of monthly streamflow from the beaver river in utah

development of an energy boundary element formulation for computing high frequency sound radiation from incoherent intensity boundary conditions an energy boundary element analysis ebea formulation is presented for calculating sound radiation at high frequency from a radiator with arbitrary shape the ebea development presented in this paper compliments previous energy finite element analysis efea developments for computing high frequency vibration of structures immersed in an acoustic medium from the efea solution the structural vibrational energy throughout the structure and the acoustic power radiated from each surface element in contact with the surrounding fluid are computed the ebea utilizes the information for the acoustic power radiated from each element of the outer surface of the structure as a boundary condition in order to compute the acoustic field in an unbound medium with no damping that surrounds the radiating structure since the structural vibration between different elements is considered as incoherent in the efea the acoustic intensity associated with each surface element that radiates in the surrounding medium is also considered as incoherent between different elements in the ebea formulation the governing integral equation of ebea is established and a numerical solution is presented the present method is validated by comparing ebea results to analytical solutions and to numerical results from an axi symmetric hp finite element code with infinite acoustic elements suitable for structural acoustic computations good correlation is demonstrated for all the analyses

mixture of regression models with varying mixing proportions a semiparametric approach in this article we study a class of semiparametric mixtures of regression models in which the regression functions are linear functions of the predictors but the mixing proportions are smoothing functions of a covariate we propose a one step backfitting estimation procedure to achieve the optimal convergence rates for both regression parameters and the nonparametric functions of mixing proportions we derive the asymptotic bias and variance of the one step estimate and further establish its asymptotic normality a modified expectation maximization type em type estimation procedure is investigated we show that the modified em algorithms preserve the asymptotic ascent property numerical simulations are conducted to examine the finite sample performance of the estimation procedures the proposed methodology is further illustrated via an analysis of a real dataset

confidence bands for regression functions abstract a method for obtaining conservative confidence bands for regression functions in low dimensions is given of particular importance is the applicability of the method to nonparametric regression computations examples and comparisons indicate the effectiveness of the method

variational bayesian approach to canonical correlation analysis as a dimension reduction algorithm canonical correlation analysis cca encounters the issue of selecting the number of canonical correlations in this letter we present a bayesian model selection algorithm for cca based on a probabilistic interpretation a hierarchical bayesian model is applied to probabilistic cca and learned by variational approximation this method not only estimates the model parameters but also automatically determines the number of canonical correlations and avoids overfitting experiments show that it performs better compared with maximum likelihood and some other model selection methods

confidence bands in nonparametric regression abstract new bias corrected confidence bands are proposed for nonparametric kernal regression these bands are constructed using only a kernel estimator of the regression curve and its data selected bandwidth they are shown to have asymptotically correct coverage properties and to behave well in a small sample study one consequence of the large sample developments is that bonferroni type bands for the regression curve at the design points also have conservative asymptotic coverage behavior with no bias correction

a nearest neighbor bootstrap for resampling hydrologic time series a nonparametric method for resampling scalar or vector valued time series is introduced multivariate nearest neighbor probability density estimation provides the basis for the resampling scheme developed the motivation for this work comes from a desire to preserve the dependence structure of the time series while bootstrapping resampling it with replacement the method is data driven and is preferred where the investigator is uncomfortable with prior assumptions as to the form e g linear or nonlinear of dependence and the form of the probability density function e g gaussian such prior assumptions are often made in an ad hoc manner for analyzing hydrologic data connections of the nearest neighbor bootstrap to markov processes as well as its utility in a general monte carlo setting are discussed applications to resampling monthly streamflow and some synthetic data are presented the method is shown to be effective with time series generated by linear and nonlinear autoregressive models the utility of the method for resampling monthly streamflow sequences with asymmetric and bimodal marginal probability densities is also demonstrated

a practical bayesian framework for backpropagation networks a quantitative and practical bayesian framework is described for learning of mappings in feedforward networks the framework makes possible 1 objective comparisons between solutions using alternative network architectures 2 objective stopping rules for network pruning or growing procedures 3 objective choice of magnitude and type of weight decay terms or additive regularizers for penalizing large weights etc 4 a measure of the effective number of well determined parameters in a model 5 quantified estimates of the error bars on network parameters and on network output and 6 objective comparisons with alternative learning and interpolation models such as splines and radial basis functions the bayesian evidence automatically embodies occam s razor penalizing overflexible and overcomplex models the bayesian approach helps detect poor underlying assumptions in learning models for learning models well matched to a problem a good correlation between generalization ability and the bayesian evidence is obtained

effect of bias estimation on coverage accuracy of bootstrap confidence intervals for a probability density tion and so bias must be corrected by other means when the bootstrap is used to construct confidence intervals for a probability density bias may either be estimated explicitly or allowed for by undersmoothing the curve estimator which of these two approaches is to be preferred in the present paper we address this question from the viewpoint of coverage accuracy assuming a given number of derivatives of the unknown density we conclude that the simpler undersmoothing method is more efficacious undersmoothing also has advantages from the standpoint of minimizing interval width we derive formulae for bandwidths which are optimal in terms of coverage accuracy and also give formulae for the coverage error which results from using those bandwidths 1 introduction the bootstrap can be a notoriously poor estimator of bias in problems of nonparametric curve estimation e g 5 and this fact should be taken into account when using bootstrap methods to construct confidence intervals bias is usually significant when a curve estimator is constructed so as to minimize mean squared error but decreases as the amount of statistical smoothing is reduced therefore one way of alleviating bias is to smooth the curve estimator less than would be appropriate for point estimation as opposed to interval estimation a statistician must either estimate bias explicitly or allow for bias by undersmoothing the curve estimator which of these two methods is to be preferred in this paper we address this problem in the case of nonparametric density estimation and from the viewpoint of coverage error we use the percentile t approach to confidence interval construction and show that in a sense which we shall make precise two paragraphs below the undersmoothing method produces confidence intervals with greater coverage accuracy than those obtained by explicit bias correction l l f x nh h for the density estimator based on kernel k and bandwidth h let b and o2

bootstrap of residual processes in regression to smooth or not to smooth summaryin this paper we consider regression models with centred errors independent of the covariates given independent and identically distributed data and given an estimator of the regression function which can be parametric or nonparametric in nature we estimate the distribution of the error term by the empirical distribution of estimated residuals to approximate the distribution of this estimator koul lahiri 1994 and neumeyer 2009 proposed bootstrap procedures based on smoothing the residuals before drawing bootstrap samples so far it has been an open question as to whether a classical nonsmooth residual bootstrap is asymptotically valid in this context here we solve this open problem and show that the nonsmooth residual bootstrap is consistent we illustrate the theoretical result by means of simulations which demonstrate the accuracy of this bootstrap procedure for various models testing procedures and sample sizes

variational learning for switching state space models we introduce a new statistical model for time series that iteratively segments data into regimes with approximately linear dynamics and learns the parameters of each of these linear regimes this model combines and generalizes two of the most widely used stochastic time series models hidden markov models and linear dynamical systems and is closely related to models that are widely used in the control and econometrics literatures it can also be derived by extending the mixture of experts neural network jacobs jordan nowlan hinton 1991 to its fully dynamical version in which both expert and gating networks are recurrent inferring the posterior probabilities of the hidden states of this model is computationally intractable and therefore the exact expectation maximization em algorithm cannot be applied however we present a variational approximation that maximizes a lower bound on the log likelihood and makes use of both the forward and backward recursions for hidden markov models and the kalman filter recursions for linear dynamical systems we tested the algorithm on artificial data sets and a natural data set of respiration force from a patient with sleep apnea the results suggest that variational approximations are a viable method for inference and learning in switching state space models

residual variance and residual pattern in nonlinear regression summary a nonparametric estimator of residual variance in nonlinear regression is proposed it is based on local linear fitting asymptotically the estimator has a small bias but a larger variance compared with the parametric estimator in linear regression finite sample properties are investigated in a simulation study including a comparison with other nonparametric estimators the method is also useful for spotting heteroscedasticity and outliers in the residuals at an early stage of the data analysis a further application is checking the fit of parametric models this is illustrated for longitudinal growth data

optimal bandwidth selection in nonparametric regression function estimation kernel estimators of an unknown multivariate regression function are investigated a bandwidth selection rule is considered which can be formulated in terms of cross validation under mild assumptions on the kernel and the unknown regression function it is seen that this rule is asymptotically optimal

bandwidth choice for nonparametric regression this paper is concerned with the problem of choosing a bandwidth parameter for nonparametric regression we analyze a tapered fourier series estimate and discuss the relationship of this estimate to a kernel estimate we first consider a method based on an unbiased estimate of mean square error and show that the bandwidth thus chosen is asymptotically optimal other methods are examined as well and are shown to be asymptotically equivalent a small simulation shows however that for small or moderate sample size the methods perform quite differently

adaptive confidence interval for pointwise curve estimation we present a procedure associated with nonlinear wavelet methods that provides adaptive confidence intervals around f x 0 in either a white noise model or a regression setting a suitable modification in the truncation rule for wavelets allows construction of confidence intervals that achieve optimal coverage accuracy up to a logarithmic factor the procedure does not require knowledge of the regularity of the unknown function f it is also efficient for functions with a low degree of regularity

bootstrapping neural networks knowledge about the distribution of a statistical estimator is important for various purposes such as the construction of confidence intervals for model parameters or the determination of critical values of tests a widely used method to estimate this distribution is the so called boot strap which is based on an imitation of the probabilistic structure of the data generating process on the basis of the information provided by a given set of random observations in this article we investigate this classical method in the context of artificial neural networks used for estimating a mapping from input to output space we establish consistency results for bootstrap estimates of the distribution of parameter estimates

confidence bands for hazard rates under random censorship summary we suggest a completely empirical approach to the construction of confidence bands for hazard functions based on smoothing the nelsen aalen estimator in particular we introduce a local bandwidth choice method our approach uses empirical information about both the survival rate and the censoring rate and employs undersmoothing to alleviate difficulties caused by bias we use both edgeworth expansion and numerical simulation the former to develop a basic formula and the latter to modify it for general use

a bayesian approach to bandwidth selection for multivariate kernel regression with an application to state price density estimation abstract this paper presents a bayesian approach to bandwidth selection for multivariate kernel regression a monte carlo study shows that under the average squared error criterion the bayesian bandwidth selector is comparable to the cross validation method and clearly outperforms the bootstrapping and rule of thumb bandwidth selectors the bayesian bandwidth selector is applied to a multivariate kernel regression model that is often used to estimate the state price density of arrow debreu securities with the s p 500 index options data and the dax index options data the proposed bayesian bandwidth selector represents a data driven solution to the problem of choosing bandwidths for the multivariate kernel regression involved in the nonparametric estimation of the state price density pioneered by ait sahalia and lo ait sahalia y lo a w 1998 nonparametric estimation of state price densities implicit in financial asset prices the journal of finance 53 499 547

a simple bootstrap method for constructing nonparametric confidence bands for functions standard approaches to constructing nonparametric confidence bands for functions are frustrated by the impact of bias which generally is not estimated consistently when using the bootstrap and conventionally smoothed function estimators to overcome this problem it is common practice to either undersmooth so as to reduce the impact of bias or oversmooth and thereby introduce an explicit or implicit bias estimator however these approaches and others based on nonstandard smoothing methods complicate the process of inference for example by requiring the choice of new unconventional smoothing parameters and in the case of undersmoothing producing relatively wide bands in this paper we suggest a new approach which exploits to our advantage one of the difficulties that in the past has prevented an attractive solution to the problem the fact that the standard bootstrap bias estimator suffers from relatively high frequency stochastic error the high frequency together with a technique based on quantiles can be exploited to dampen down the stochastic error term leading to relatively narrow simple to construct confidence bands

transformations in stochastic dea models abstract a set of transformations based on the lp norm are used to generate alternative parametric and nonparametric formulations of production frontiers particular attention is paid to the cases p 1 least absolute value estimation and p chebyshev estimation a class of generalized transformations of inputs and outputs by using the box cox transformations is also explored and illustrated

adaptive bandwidth choice for kernel regression abstract a data based procedure is introduced for local bandwidth selection for kernel estimation of a regression function at a point the estimated bandwidth is shown to be consistent and asymptotically normal as an estimator of the asymptotic optimal value for minimum mean square estimation simulation studies indicate satisfactory behavior of the new bandwidth estimator in finite samples the findings are improvements over a global bandwidth estimator the same methodology works for local linear regression and extends easily to weighted local polynomial fits

bootstrap technology and applications bootstrap resampling methods have emerged as powerful tools for constructing inferential procedures in modern statistical data analysis although these methods depend on the availability of fast inexpensive computing they offer the potential for highly accurate methods of inference moreover they can even eliminate the need to impose a convenient statistical model that does not have a strong scientific basis in this article we review some bootstrap methods emphasizing applications through illustrations with some real data special attention is given to regression problems with dependent data and choosing tuning parameters for optimal performance

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bayesian canonical correlation analysis canonical correlation analysis cca is a classical method for seeking correlations between two multivariate data sets during the last ten years it has received more and more attention in the machine learning community in the form of novel computational formulations and a plethora of applications we review recent developments in bayesian models and inference methods for cca which are attractive for their potential in hierarchical extensions and for coping with the combination of large dimensionalities and small sample sizes the existing methods have not been particularly successful in fulfilling the promise yet we introduce a novel efficient solution that imposes group wise sparsity to estimate the posterior of an extended model which not only extracts the statistical dependencies correlations between data sets but also decomposes the data into shared and data set specific components in statistics literature the model is known as inter battery factor analysis ibfa for which we now provide a bayesian treatment

bayesian confidence intervals for smoothing splines abstract the frequency properties of wahba s bayesian confidence intervals for smoothing splines are investigated by a large sample approximation and by a simulation study when the coverage probabilities for these pointwise confidence intervals are averaged across the observation points the average coverage probability acp should be close to the nominal level from a frequency point of view this agreement occurs because the average posterior variance for the spline is similar to a consistent estimate of the average squared error and because the average squared bias is a modest fraction of the total average squared error these properties are independent of the bayesian assumptions used to derive this confidence procedure and they explain why the acp is accurate for functions that are much smoother than the sample paths prescribed by the prior this analysis accounts for the choice of the smoothing parameter bandwidth using cross validation in the case of natural splines an adaptive method for avo

bootstrapping in nonparametric regression local adaptive smoothing and confidence bands abstract the operation of the bootstrap in the context of nonparametric regression is considered bootstrap samples are taken from estimated residuals to study the distribution of a suitably recentered kernel estimator the application of this principle to the problem of local adaptive choice of bandwidth and to the construction of confidence bands is investigated and compared with a direct method based on asymptotic means and variances the technique of the bootstrap is to replace any occurrence of the unknown distribution in the definition of the statistical function of interest by the empirical distribution function of the observed errors in a regression context these errors are not directly observed although their role can be played by the residuals from the fitted model in this article the fitted model is a kernel nonparametric regression estimator since nonparametric smoothing is involved an additional difficulty is created by the bias incurred in smoothing this bias however can be estimated

adaptive confidence bands we show that there do not exist adaptive confidence bands for curve estimation except under very restrictive assumptions we propose instead to construct adaptive bands that cover a surrogate function f which is close to but simpler than f the surrogate captures the significant features in f we establish lower bounds on the width for any confidence band for f and construct a procedure that comes within a small constant factor of attaining the lower bound for finite samples

generalized discriminant analysis using a kernel approach we present a new method that we call generalized discriminant analysis gda to deal with nonlinear discriminant analysis using kernel function operator the underlying theory is close to the support vector machines svm insofar as the gda method provides a mapping of the input vectors into high dimensional feature space in the transformed space linear properties make it easy to extend and generalize the classical linear discriminant analysis lda to nonlinear discriminant analysis the formulation is expressed as an eigenvalue problem resolution using a different kernel one can cover a wide class of nonlinearities for both simulated data and alternate kernels we give classification results as well as the shape of the decision function the results are confirmed using real data to perform seed classification

bayesian sparse partial least squares partial least squares pls is a class of methods that makes use of a set of latent or unobserved variables to model the relation between typically two sets of input and output variables respectively several flavors depending on how the latent variables or components are computed have been developed over the last years in this letter we propose a bayesian formulation of pls along with some extensions in a nutshell we provide sparsity at the input space level and an automatic estimation of the optimal number of latent components we follow the variational approach to infer the parameter distributions we have successfully tested the proposed methods on a synthetic data benchmark and on electrocorticogram data associated with several motor outputs in monkeys

automatic classification of single facial images we propose a method for automatically classifying facial images based on labeled elastic graph matching a 2d gabor wavelet representation and linear discriminant analysis results of tests with three image sets are presented for the classification of sex race and expression a visual interpretation of the discriminant vectors is provided

spline estimation of paths using bearings only tracking data abstract in many applications bearings are measured to a moving object with the goal of estimating the object s course of movement if movement is appropriately modeled as a smooth deterministic curve in the plane then a cubic spline is a reasonable representation of the curve maximum likelihood estimators are presented for parameters of regression splines assuming that observation errors follow a von mises distribution location estimates are obtainable even when data are sparse path estimation error number and placement of knots and outlier detection are discussed examples including both simulated paths and observations from a wildlife radio tracking study are presented

reversible jump markov chain monte carlo computation and bayesian model determination markov chain monte carlo methods for bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some fixed standard underlying measure they have therefore not been available for application to bayesian model determination where the dimensionality of the parameter vector is typically not fixed this paper proposes a new framework for the construction of reversible markov chain samplers that jump between parameter subspaces of differing dimensionality which is flexible and entirely constructive it should therefore have wide applicability in model determination problems the methodology is illustrated with applications to multiple change point analysis in one and two dimensions and to a bayesian comparison of binomial experiments

a broadband maximum likelihood imager for a class of extended space time separable sources an algorithm is presented that reconstructs the shape of an extended incoherent source using only the broadband signals radiated from the source to a sparse array the source is modeled with a small set of parameters for the specific class of space time separable sources which have similar spatial structure at multiple frequencies the information radiated at each frequency is recombined into a broadband likelihood function in order to improve the estimation of the source parameters expressions for the cramer rao bounds crbs are provided and the performance of the algorithm is demonstrated for a gaussian lump shaped source

variational gaussian process classifiers gaussian processes are a promising nonlinear regression tool but it is not straightforward to solve classification problems with them in the paper the variational methods of jaakkola and jordan 2000 are applied to gaussian processes to produce an efficient bayesian binary classifier

choosing a range for the amount of smoothing in nonparametric regression abstract most nonparametric regression estimates smooth the observed data in the process of generating a suitable estimate the resulting curve estimate is sensitive to the amount of smoothing introduced and it is important to examine the estimate over a range of smoothing choices an objective way to specify such a range is to estimate the optimal value of the smoothing parameter bandwidth with respect to some loss function and then report a confidence interval for this parameter estimate this interval suggests examining three regression estimates an undersmoothed curve evaluated at the lower endpoint of the confidence interval an oversmoothed curve evaluated at the upper endpoint and also an optimal curve chosen by the data based method this article describes two strategies for constructing such confidence intervals using asymptotic approximations and simulation techniques suppose that data are observed from the model yk f tk ek 1 k n where f is a function that is twice differentia

on bootstrap confidence intervals in nonparametric regression priate in this paper we point out some of the theoretical advantages of pivoting they include a reduction in the error of the bootstrap distribution function estimate from n 1 2 to n lh 1 2 where h denotes bandwidth and a reduction in coverage error of confidence intervals from either n l 1 2h 1 2 or n 1 2h1 2 depending on which nonpivotal method is used to n 1 several comparisons are drawn with the case of nonparametric density estimation where a pivotal approach also reduces errors associated with confidence intervals but where the orders of magnitude of the respective errors are quite different from their counterparts for nonparametric regression

parametric localization of distributed sources most array processing algorithms are based on the assumption that the signals are generated by point sources this is a mathematical constraint that is not satisfied in many applications in this paper we consider situations where the sources are distributed in space with a parametric angular cross correlation kernel we propose an algorithm that estimates the parameters of this model using a generalization of the music algorithm the method involves maximizing a cost function that depends on a matrix array manifold and the noise eigenvectors we study two particular cases coherent and incoherent spatial source distributions the spatial correlation function for a uniformly distributed signal is derived from this we find the array gain and show that in contrast to point sources it does not increase linearly with the number of sources we compare our method to the conventional point source music algorithm the simulation studies show that the new method outperforms the music algorithm by reducing the estimation bias and the standard deviation for scenarios with distributed sources it is also shown that the threshold signal to noise ratio required for resolving two closely spaced distributed sources is considerably smaller for the new method

confidence bands in non parametric errors in variables regression summary errors in variables regression is important in many areas of science and social science e g in economics where it is often a feature of hedonic models in environmental science where air quality indices are measured with error in biology where the vegetative mass of plants is frequently obscured by mismeasurement and in nutrition where reported fat intake is typically subject to substantial error to date in non parametric contexts the great majority of work has focused on methods for estimating the mean as a function with relatively little attention being paid to techniques for empirical assessment of the accuracy of the estimator we develop methodologies for constructing confidence bands our contributions include techniques for tuning parameter choice aimed at minimizing the coverage error of confidence bands

facial expression recognition using kernel canonical correlation analysis kcca in this correspondence we address the facial expression recognition problem using kernel canonical correlation analysis kcca following the method proposed by lyons et al and zhang et al we manually locate 34 landmark points from each facial image and then convert these geometric points into a labeled graph lg vector using the gabor wavelet transformation method to represent the facial features on the other hand for each training facial image the semantic ratings describing the basic expressions are combined into a six dimensional semantic expression vector learning the correlation between the lg vector and the semantic expression vector is performed by kcca according to this correlation we estimate the associated semantic expression vector of a given test image and then perform the expression classification according to this estimated semantic expression vector moreover we also propose an improved kcca algorithm to tackle the singularity problem of the gram matrix the experimental results on the japanese female facial expression database and the ekman s pictures of facial affect database illustrate the effectiveness of the proposed method