generalizing the hough transform to detect arbitrary shapes abstract the hough transform is a method for detecting curves by exploiting the duality between points on a curve and parameters of that curve the initial work showed how to detect both analytic curves 1 2 and non analytic curves 3 but these methods were restricted to binary edge images this work was generalized to the detection of some analytic curves in grey level images specifically lines 4 circles 5 and parabolas 6 the line detection case is the best known of these and has been ingeniously exploited in several applications 7 8 9 we show how the boundaries of an arbitrary non analytic shape can be used to construct a mapping between image space and hough transform space such a mapping can be exploited to detect instances of that particular shape in an image furthermore variations in the shape such as rotations scale changes or figure ground reversals correspond to straightforward transformations of this mapping however the most remarkable property is that such mappings can be composed to build mappings for complex shapes from the mappings of simpler component shapes this makes the generalized hough transform a kind of universal transform which can be used to find arbitrarily complex shapes

m quantile models for small area estimation small area estimation techniques are employed when sample data are insufficient for acceptably precise direct estimation in domains of interest these techniques typically rely on regression models that use both covariates and random effects to explain variation between domains however such models also depend on strong distributional assumptions require a formal specification of the random part of the model and do not easily allow for outlier robust inference we describe a new approach to small area estimation that is based on modelling quantile like parameters of the conditional distribution of the target variable given the covariates this avoids the problems associated with specification of random effects allowing inter domain differences to be characterized by the variation of area specific m quantile coefficients the proposed approach is easily made robust against outlying data values and can be adapted for estimation of a wide range of area specific parameters including that of the quantiles of the distribution of the target variable in the different small areas results from two simulation studies comparing the performance of the m quantile modelling approach with more traditional mixed model approaches are also provided

free levy matrices and financial correlations abstract we consider a covariance matrix composed of asymmetric and free random levy matrices we use the results of free random variables to derive an algebraic equation for the resolvent and solve it to extract the spectral density for an appropriate choice of asymmetry and levy index 2 3 4 the free eigenvalue spectrum is in remarkable agreement with the one obtained from the covariance matrix of the sp500 financial market our results are of interest to a number of stochastic systems with power law noise

limit laws for random matrices and free products in earlier articles we studied a kind of probability theory in the framework of operator algebras with the tensor product replaced by the free product we prove here that free random variables naturally arise as limits of random matrices and that wigner s semicircle law is a consequence of the central limit theorem for free random variables in this way we obtain a non commutative limit distribution of a general gaussian random matrix as an operator in a certain operator algebra wigner s law being given by the trace of the spectral measure of the selfadjoint component of this operator

quantiles for counts this article studies the estimation of conditional quantiles of counts given the discreteness of the data some smoothness must be artificially imposed on the problem we show that it is possible to smooth the data in a way that allows inference to be performed using standard quantile regression techniques the performance and implementation of the estimators are illustrated by simulations and an application

overlaps between eigenvectors of correlated random matrices we obtain general exact formulas for the overlaps between the eigenvectors of large correlated random matrices with additive or multiplicative noise these results have potential applications in many different contexts from quantum thermalization to high dimensional statistics we find that the overlaps only depend on measurable quantities and do not require the knowledge of the underlying true noiseless matrices we apply our results to the case of empirical correlation matrices that allow us to estimate reliably the width of the spectrum of the true correlation matrix even when the latter is very close to the identity we illustrate our results on the example of stock returns correlations which clearly reveal a nontrivial structure for the bulk eigenvalues we also apply our results to the problem of matrix denoising in high dimensions

eigenvector dynamics general theory and some applications we propose a general framework to study the stability of the subspace spanned by p consecutive eigenvectors of a generic symmetric matrix h0 when a small perturbation is added this problem is relevant in various contexts including quantum dissipation h0 is then the hamiltonian and financial risk control in which case h0 is the assets return covariance matrix we argue that the problem can be formulated in terms of the singular values of an overlap matrix which allows one to define an overlap distance we specialize our results for the case of a gaussian orthogonal h0 for which the full spectrum of singular values can be explicitly computed we also consider the case when h0 is a covariance matrix and illustrate the usefulness of our results using financial data the special case where the top eigenvalue is much larger than all the other ones can be investigated in full detail in particular the dynamics of the angle made by the top eigenvector and its true direction defines an interesting class of random processes

bayesian semiparametric model with spatially temporally varying coefficients selection in spatiotemporal analysis the effect of a covariate on the outcome usually varies across areas and time the spatial configuration of the areas may potentially depend on not only the structured random intercept but also spatially varying coefficients of covariates in addition the normality assumption of the distribution of spatially varying coefficients could lead to potential biases of estimations in this article we proposed a bayesian semiparametric space time model where the spatially temporally varying coefficient is decomposed as fixed spatially varying and temporally varying coefficients we nonparametrically modeled the spatially varying coefficients of space time covariates by using the area specific dirichlet process prior with weights transformed via a generalized transformation we modeled the temporally varying coefficients of covariates through the dynamic model we also took into account the uncertainty of inclusion of the spatially temporally varying coefficients by variable selection procedure through determining the probabilities of different effects for each covariate the proposed semiparametric approach shows its improvement compared with the bayesian spatial temporal models with normality assumption on spatial random effects and the bayesian model with the dirichlet process prior on the random intercept we presented a simulation example to evaluate the performance of the proposed approach with the competing models we used an application to low birth weight data in south carolina as an illustration

spectral moments of correlated wishart matrices we present an analytic method to determine the spectral properties of the covariance matrices constructed of correlated wishart random matrices the method gives in the limit of large matrices exact analytic relations between the spectral moments and the eigenvalue densities of the covariance matrices and their estimators the results can be used in practice to extract the information about genuine correlations from the given experimental realization of random matrices

signal and noise in correlation matrix using random matrix technique we determine an exact relation between the eigenvalue spectrum of the covariance matrix and of its estimator this relation can be used in practice to compute eigenvalue invariants of the covariance correlation matrix results can be applied in various problems where one experimentally estimates correlations in a system with many degrees of freedom like for instance those in statistical physics lattice measurements of field theory genetics quantitative finance and other applications of multivariate statistics

eigenvectors of some large sample covariance matrix ensembles we consider sample covariance matrices s n frac 1 p sigma n 1 2 x nx n sigma n 1 2 where xn is a n p real or complex matrix with i i d entries with finite 12th moment and n is a n n positive definite matrix in addition we assume that the spectral measure of n almost surely converges to some limiting probability distribution as n and p n 0 we quantify the relationship between sample and population eigenvectors by studying the asymptotics of functionals of the type frac 1 n text tr g sigma n s n zi 1 where i is the identity matrix g is a bounded function and z is a complex number this is then used to compute the asymptotically optimal bias correction for sample eigenvalues paving the way for a new generation of improved estimators of the covariance matrix and its inverse

robust inference for generalized linear models by starting from a natural class of robust estimators for generalized linear models based on the notion of quasi likelihood we define robust deviances that can be used for stepwise model selection as in the classical framework we derive the asymptotic distribution of tests based on robust deviances and we investigate the stability of their asymptotic level under contamination the binomial and poisson models are treated in detail two applications to real data and a sensitivity analysis show that the inference obtained by means of the new techniques is more reliable than that obtained by classical estimation and testing procedures

fixed energy universality for generalized wigner matrices we prove the wigner dyson mehta conjecture at fixed energy in the bulk of the spectrum for generalized symmetric and hermitian wigner matrices previous results concerning the universality of random matrices either require an averaging in the energy parameter or they hold only for hermitian matrices if the energy parameter is fixed we develop a homogenization theory of the dyson brownian motion and show that microscopic universality follows from mesoscopic statistics 2015 wiley periodicals inc

a fast hough transform for segment detection the authors describe a new algorithm for the fast hough transform fht that satisfactorily solves the problems other fast algorithms propose in the literature erroneous solutions point redundance scaling and detection of straight lines of different sizes and needs less storage space by using the information generated by the algorithm for the detection of straight lines they manage to detect the segments of the image without appreciable computational overhead they also discuss the performance and the parallelization of the algorithm and show its efficiency with some examples

pseudo maximum likelihood methods applications to poisson models pseudo maximum likelihood techniques are applied to basic poisson models and to poisson models with specification errors in the latter case it is shown that consistent and asymptotically normal estimators can be obtained without specifying the p d f of the disturbances these estimators are compared both from the finite sample and the asymptotic point of view quasi generalized pml estimators which asymptotically dominate all pml estimators are also proposed finally bivariate and panel data poisson models are discussed the analysis of economic behavior often leads to the study of characteristics taking a small number of positive values the classical linear model is not adapted to explain how such discrete variables depend on other quantitative or qualitative variables the reasons are similar to those usually given in the case of an endogenous qualitative variable the shape of the observation set does not correspond to a linear model the assumption of normality of the disturbances cannot be made since the endogenous variables take a small number of values with strictly positive probabilities and the prediction formulae which are deduced from a linear model give impossible values in the models considered in the literature to describe discrete variables cox and lewis 2 el sayyad 3 frome kutner and beauchamp 4 gilbert 5 hausman hall and griliches 8 see also lancaster 12 the endogenous variable is assumed to have a poisson distribution conditional upon the exogenous variables the parameter of this distribution is a function of the values of the exogenous variables the choice of such a model is justified if the dependent variable counts the occurrence of a given event during a fixed period and if the usual assumptions of the poisson process are satisfied for instance the model is adapted to describe daily numbers of oil tankers arrivals in a port the number of accidents at work by factory or the number of patents applied for and received by firms hausman hall and griliches 8

approximate inference in generalized linear mixed models statistical approaches to overdispersion correlated errors shrinkage estimation and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model glmm given an unobserved vector of random effects observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function known prior weights and a scale factor the random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components for problems involving time series spatial aggregation and smoothing the dispersion may be specified in terms of a rank deficient inverse covariance matrix approximation of the marginal quasi likelihood using laplace s method leads eventually to estimating equations based on penalized quasilikelihood or pql for the mean parameters and pseudo likelihood for the variances im

poisson overdispersion estimates based on the method of asymmetric maximum likelihood abstract a common difficulty in regression problems with poisson or binomial or other exponential family response variables is over dispersion the scatter around the fitted regression is too large by the standards of poisson variability this article concerns the description estimation and testing of various patterns of overdispersion with particular emphasis on the poisson case asymmetric maximum likelihood aml is a method of fitting regressions for the conditional percentiles of the response variable as a function of the predictors e g the conditional 90th percentile of y given x distances between the various regression percentiles give a direct assessment of overdispersion the discussion is carried through in terms of an archaeological data set where we see that the counts are overdispersed by a factor of 1 35 in one part of the covariate space but not at all in another moreover the overdispersion is about 40 larger in the positive response direction than in the negative the aml es

top eigenpair statistics for weighted sparse graphs we develop a formalism to compute the statistics of the top eigenpair of weighted sparse graphs with finite mean connectivity and bounded maximal degree framing the problem in terms of optimisation of a quadratic form on the sphere and introducing a fictitious temperature we employ the cavity and replica methods to find the solution in terms of self consistent equations for auxiliary probability density functions which can be solved by population dynamics this derivation allows us to identify and unpack the individual contributions to the top eigenvector s components coming from nodes of degree k the analytical results are in perfect agreement with numerical diagonalisation of large weighted adjacency matrices and are further cross checked on the cases of random regular graphs and sparse markov transition matrices for unbiased random walks

disease mapping via negative binomial regression m quantiles we introduce a semi parametric approach to ecological regression for disease mapping based on modelling the regression m quantiles of a negative binomial variable the proposed method is robust to outliers in the model covariates including those due to measurement error and can account for both spatial heterogeneity and spatial clustering a simulation experiment based on the well known scottish lip cancer data set is used to compare the m quantile modelling approach with a disease mapping approach based on a random effects model this suggests that the m quantile approach leads to predicted relative risks with smaller root mean square error the paper concludes with an illustrative application of the m quantile approach mapping low birth weight incidence data for english local authority districts for the years 2005 2010 copyright 2014 john wiley sons ltd

a brownian motion model for the parameter dependence of matrix elements we introduce a brownian motion model for the parametric evolution of eigenstates of a complex quantum system modelled by a random matrix the model is analogous to dyson s model for the evolution of the eigenvalues we use this approach to analyse correlation functions describing the parameter dependence of diagonal and off diagonal matrix elements of a generic operator in the case of diagonal matrix elements we compare our results with a semiclassical approach which relates sums of matrix elements to periodic classical orbits for systems with a chaotic classical limit the semiclassical correlation function agrees exactly with the random matrix theory

rotational invariant estimator for general noisy matrices we investigate the problem of estimating a given real symmetric signal matrix c from a noisy observation matrix m in the limit of large dimension we consider the case where the noisy measurement m comes either from an arbitrary additive or multiplicative rotational invariant perturbation we establish using the replica method the asymptotic global law estimate for three general classes of noisy matrices significantly extending previously obtained results we give exact results concerning the asymptotic deviations called overlaps of the perturbed eigenvectors away from the true ones and we explain how to use these overlaps to clean the noisy eigenvalues of m we provide some numerical checks for the different estimators proposed in this paper and we also make the connection with some well known results of bayesian statistics

spectrum estimation for large dimensional covariance matrices using random matrix theory estimating the eigenvalues of a population covariance matrix from a sample covariance matrix is a problem of fundamental importance in multivariate statistics the eigenvalues of covariance matrices play a key role in many widely used techniques in particular in principal component analysis pca in many modern data analysis problems statisticians are faced with large datasets where the sample size n is of the same order of magnitude as the number of variables p random matrix theory predicts that in this context the eigenvalues of the sample covariance matrix are not good estimators of the eigenvalues of the population covariance we propose to use a fundamental result in random matrix theory the marcenko pastur equation to better estimate the eigenvalues of large dimensional covariance matrices the marcenko pastur equation holds in very wide generality and under weak assumptions the estimator we obtain can be thought of as shrinking in a nonlinear fashion the eigenvalues of the sample covariance matrix to estimate the population eigenvalues inspired by ideas of random matrix theory we also suggest a change of point of view when thinking about estimation of high dimensional vectors we do not try to estimate directly the vectors but rather a probability measure that describes them we think this is a theoretically more fruitful way to think about these problems our estimator gives fast and good or very good results in extended simulations our algorithmic approach is based on convex optimization we also show that the proposed estimator is consistent

on the principal components of sample covariance matrices we introduce a class of m times m sample covariance matrices mathcal q which subsumes and generalizes several previous models the associated population covariance matrix sigma mathbb e mathcal q is assumed to differ from the identity by a matrix of bounded rank all quantities except the rank of sigma i m may depend on m in an arbitrary fashion we investigate the principal components i e the top eigenvalues and eigenvectors of mathcal q we derive precise large deviation estimates on the generalized components langle mathbf w varvec xi i rangle of the outlier and non outlier eigenvectors varvec xi i our results also hold near the so called bbp transition where outliers are created or annihilated and for degenerate or near degenerate outliers we believe the obtained rates of convergence to be optimal in addition we derive the asymptotic distribution of the generalized components of the non outlier eigenvectors a novel observation arising from our results is that unlike the eigenvalues the eigenvectors of the principal components contain information about the subcritical spikes of sigma the proofs use several results on the eigenvalues and eigenvectors of the uncorrelated matrix mathcal q satisfying mathbb e mathcal q i m as input the isotropic local marchenko pastur law established in bloemendal et al electron j probab 19 1 53 2014 level repulsion and quantum unique ergodicity of the eigenvectors the latter is a special case of a new universality result for the joint eigenvalue eigenvector distribution

anisotropic local laws for random matrices we develop a new method for deriving local laws for a large class of random matrices it is applicable to many matrix models built from sums and products of deterministic or independent random matrices in particular it may be used to obtain local laws for matrix ensembles that are anisotropic in the sense that their resolvents are well approximated by deterministic matrices that are not multiples of the identity for definiteness we present the method for sample covariance matrices of the form open image in new window where t is deterministic and x is random with independent entries we prove that with high probability the resolvent of q is close to a deterministic matrix with an optimal error bound and down to optimal spectral scales as an application we prove the edge universality of q by establishing the tracy widom airy statistics of the eigenvalues of q near the soft edges this result applies in the single cut and multi cut cases further applications include the distribution of the eigenvectors and an analysis of the outliers and bbp type phase transitions in finite rank deformations they will appear elsewhere we also apply our method to wigner matrices whose entries have arbitrary expectation i e we consider w a where w is a wigner matrix and a a hermitian deterministic matrix we prove the anisotropic local law for w a and use it to establish edge universality

lane departure warning for mobile devices based on a fuzzy representation of images the use of driver assistance systems is a current trend in the car industry however most driver assistance systems require the use of multiple sensors increasing the cost of their implementation in cars and making them inaccessible to many users in this paper we present an efficient lane departure warning system for mobile devices which is real time accurate and accessible to most users on the one hand the accuracy of the system relies on line detection based on hough transforms a combination that has proven to be reliable for this goal in many approaches on the other hand the reduction of the computational time to achieve real time processing is due mainly to a proposed fuzzy representation of images finally we also present various tests that show that the system proposed runs at up to 20 fps on a mobile device with a dual core cpu at 1 0 ghz with a resolution of 320240px