on multivariate ridge regression summary a multivariate linear regression model with q responses as a linear function of p independent variables is considered with a p x q parameter matrix b the least squares or normal theory maximum likelihood estimate of b is deficient in that it takes no account of the across regression correlations and ignores the stein effect a remedy was offered by brown zidek 1980 in the form of a multivariate ridge estimator a richer class of estimators is obtained here by casting the model in a linear hierarchical framework obtaining the brown zidek multivariate ridge estimates efron morris s estimates of several normal mean vectors and fearn s bayesian estimates of growth curves as special cases the unknown covariance case results in an identifiability problem which can be overcome by a bayesian approach using conjugate priors for the unidentified covariance matrices

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

nonparametric modeling of longitudinal covariance structure in functional mapping of quantitative trait loci estimation of the covariance structure of longitudinal processes is a fundamental prerequisite for the practical deployment of functional mapping designed to study the genetic regulation and network of quantitative variation in dynamic complex traits we present a nonparametric approach for estimating the covariance structure of a quantitative trait measured repeatedly at a series of time points specifically we adopt huang et al s 2006 biometrika 93 85 98 approach of invoking the modified cholesky decomposition and converting the problem into modeling a sequence of regressions of responses a regularized covariance estimator is obtained using a normal penalized likelihood with an l 2 penalty this approach embedded within a mixture likelihood framework leads to enhanced accuracy precision and flexibility of functional mapping while preserving its biological relevance simulation studies are performed to reveal the statistical properties and advantages of the proposed method a real example from a mouse genome project is analyzed to illustrate the utilization of the methodology the new method will provide a useful tool for genome wide scanning for the existence and distribution of quantitative trait loci underlying a dynamic trait important to agriculture biology and health sciences

penalized estimating equations les modeles avec penalisation comme l estimateur ridge l estimateur de stein l estimateur en pont et le lasso ont ete proposes pour prendre en compte la collineariteen regression le lasso a ete applique au modele lineaire a la regression logistique au modele des hasards proportionnels de cox et aux reseaux de neurones cet article etudie le modele avec penalisation en pont pour une penalite j j applique aux equations d estimation et applique ce modele avec penalisation aux equations d estimation generalisees gee dans des etudes longitudinales le defaut de vraisemblance jointe dans les gee est surmonte par les equations d estimation penalisees pour lesquelles aucune vraisemblance jointe n est requise on donne les resultats asymptotiques pour l estimateur sons penalite on montre par des simulations et une application que les cee avec penalisation ameliorent potentiellement les resultats de l estimateur gee et presentent les memes proprietes que les modeles lineaires penalises

fuzzy dea a perceptual evalution method abstract dea data envelopment analysis is a non parametric technique for measuring and evaluating the relative efficiencies of a set of entities with common crisp inputs and outputs in fact in a real evaluation problem input and output data of entities evaluated often fluctuate these fluctuating data can be represented as linguistic variables characterized by fuzzy numbers for reflecting a kind of general feeling or experience of experts based on the fundamental ccr model a fuzzy dea model is proposed to deal with the efficiency evaluation problem with the given fuzzy input and output data furthermore an extension of the fuzzy dea model to a more general form is also proposed with considering the relationship between dea and ra regression analysis using the proposed fuzzy dea models the crisp efficiency in ccr model is extended to be a fuzzy number to reflect the inherent uncertainty in real evaluation problems

kernel methods in machine learning we review machine learning methods employing positive definite kernels these methods formulate learning and estimation problems in a reproducing kernel hilbert space rkhs of functions defined on the data domain expanded in terms of a kernel working in linear spaces of function has the benefit of facilitating the construction and analysis of learning algorithms while at the same time allowing large classes of functions the latter include nonlinear functions as well as functions defined on nonvectorial data we cover a wide range of methods ranging from binary classifiers to sophisticated methods for estimation with structured data

sparse kernel regression modeling using combined locally regularized orthogonal least squares and d optimality experimental design the note proposes an efficient nonlinear identification algorithm by combining a locally regularized orthogonal least squares lrols model selection with a d optimality experimental design the proposed algorithm aims to achieve maximized model robustness and sparsity via two effective and complementary approaches the lrols method alone is capable of producing a very parsimonious model with excellent generalization performance the d optimality design criterion further enhances the model efficiency and robustness an added advantage is that the user only needs to specify a weighting for the d optimality cost in the combined model selecting criterion and the entire model construction procedure becomes automatic the value of this weighting does not influence the model selection procedure critically and it can be chosen with ease from a wide range of values

maximum set estimators with bounded estimation error we consider the linear regression problem of estimating a deterministic parameter vector x from observations y hx w where h is known and w is additive noise we seek an estimator whose estimation error does not exceed a given maximum error for as wide a range of conditions as possible the maximum error is a design choice and is generally lower than the error provided by the well known least squares ls estimator we develop estimators guaranteeing the required error for as large a parameter set as possible and for as large a noise level as possible we discuss methods for finding these estimators and demonstrate that in many cases the proposed estimators outperform the ls estimator

on some bayesian regularization methods for image restoration methods are reviewed for choosing regularized restorations in image processing in particular a method developed by galatsanos and katsaggelos see ibid vol 1 p 322 336 1992 is given a bayesian interpretation and is compared with other bayesian and non bayesian alternatives a small illustrative example is provided and a complement is provided for the discussion of noise variance estimation of galatsanos et al

a statistical framework to infer delay and direction of information flow from measurements of complex systems in neuroscience data are typically generated from neural network activity the resulting time series represent measurements from spatially distributed subsystems with complex interactions weakly coupled to a high dimensional global system we present a statistical framework to estimate the direction of information flow and its delay in measurements from systems of this type informed by differential topology gaussian process regression is employed to reconstruct measurements of putative driving systems from measurements of the driven systems these reconstructions serve to estimate the delay of the interaction by means of an analytical criterion developed for this purpose the model accounts for a range of possible sources of uncertainty including temporally evolving intrinsic noise while assuming complex nonlinear dependencies furthermore we show that if information flow is delayed this approach also allows for inference in strong coupling scenarios of systems exhibiting synchronization phenomena the validity of the method is demonstrated with a variety of delay coupled chaotic oscillators in addition we show that these results seamlessly transfer to local field potentials in cat visual cortex

multiclass classifiers based on dimension reduction with generalized lda linear discriminant analysis lda has been widely used for dimension reduction of data sets with multiple classes the lda has been recently extended to various generalized lda methods that are applicable regardless of the relative sizes between the data dimension and the number of data items in this paper we propose several multiclass classifiers based on generalized lda glda algorithms taking advantage of the dimension reducing transformation matrix without requiring additional training or parameter optimization a marginal linear discriminant classifier mldc a bayesian linear discriminant classifier bldc and a one dimensional bldc are introduced for multiclass classification our experimental results illustrate that these classifiers produce higher ten fold cross validation accuracy than knn and centroid based classifiers in the reduced dimensional space obtained from glda

eine arithmetische eigenschaft automorpher formen zu gewissen nicht arithmetischen gruppen let sl2 open image in new window denote a fuchsian triangle group anda an elliptic fixed point of for any weightk and any multiplier systemv whose values are roots of unity there is a basis of automorphic forms with expansions f left z right left z bar a right k sum limits n 0 infty r n b n left frac z a z a right n

upper and lower approximation models in interval regression using regression quantile techniques in this paper we propose new interval regression analysis based on the regression quantile techniques to analyze a phenomenon in a fuzzy environment we propose two interval approximation models without using all data we first identify the main trend from the designated proportion of the given data to select the main part of data to be analyzed we introduce the regression quantile techniques the obtained model is not influenced by extreme points since it is formulated from the center located main proportion of the given data after that the interval regression model including all data can be identified based on the acquired main trend the obtained interval regression model by the main proportion of the given data is called the lower approximation model while interval regression model by all data is called the upper approximation model for the given phenomenon also it is shown that from the lower approximation model main trend and the upper approximation model we can construct a trapezoidal fuzzy model the membership function of this fuzzy model is useful to obtain the locational information for each observation the characteristic of our approach can be described as obtaining the upper and lower approximation models and combining them to be a fuzzy model for representing the given phenomenon in a fuzzy environment

origins and uses of linear programming methods for treating l1 and l regressions corrections and comments on abstract this note comments on and corrects some of the referrals and comments of castillo et al castillo e minguez r castillo c confino a s 2008 dealing with the multiplicity of solutions of the l 1 and l regression models european journal of operational research 188 460 484 concerning the origins and uses of linear programming to estimate l 1 and l statistical regressions

constrained regression median for measuring possible salary discrimination abstract this study proposes a new analytical method for empirically examining possible salary discrimination against a protected e g female or minority group the proposed approach is referred to as constrained regression median crm the method can be used for regressing salary with job qualifications as dependent variables the result of crm is transformed into a 2 2 contingency table and the degree of salary discrimination is determined by the result of the contingency table the approach can be easily explained to and understood by lawyers judges and other individuals involved in a discrimination case the crm method is particularly useful and practical when a data set maintains the problems of outlier and or multicollinearity between job qualifications and gender or race

exceptional polynomials of affine type abstract let k be a finite field of characteristic p a polynomial f with coefficients in k is said to be exceptional if it induces a permutation on infinitely many finite extensions of k let t be a transcendental and k be an algebraic closure of k the exceptional polynomials known to date are constructed from certain twists of polynomials g such that the splitting field of g x t over k is rational on the other hand we know that except for p 2 or 3 either the degree of an exceptional polynomial f is a power of the characteristic p or f is a dickson polynomial the case deg f p has been settled completely we give a new series of exceptional polynomials of degree p m with m even which does not follow the above mentioned construction principle we show under certain additional hypotheses that the associated monodromy groups of exceptional polynomials will be severely restricted in particular we determine precisely what the geometric monodromy groups of exceptional polynomials of degree p 2 will be

bayes model averaging with selection of regressors when a number of distinct models contend for use in prediction the choice of a single model can offer rather unstable predictions in regression stochastic search variable selection with bayesian model averaging offers a cure for this robustness issue but at the expense of requiring very many predictors here we look at bayes model averaging incorporating variable selection for prediction this offers similar mean square errors of prediction but with a vastly reduced predictor space this can greatly aid the interpretation of the model it also reduces the cost if measured variables have costs the development here uses decision theory in the context of the multivariate general linear model in passing this reduced predictor space bayes model averaging is contrasted with single model approximations a fast algorithm for updating regressions in the markov chain monte carlo searches for posterior inference is developed allowing many more variables than observations to be contemplated we discuss the merits of absolute rather than proportionate shrinkage in regression especially when there are more variables than observations the methodology is illustrated on a set of spectroscopic data used for measuring the amounts of different sugars in an aqueous solution

a class of exceptional polynomials we present a class of indecomposable polynomials of non primepower degree over the finite field of two elements which are permutation polynomials on infinitely many finite extensions of the field the associated geometric monodromy groups are the simple groups where k 3 and odd the first member of this class was previously found by p muller 17 this realises one of only two possibilities for such a class which remain following deep work of fried guralnick and saxl 7 the other is associated with psl 3 k 3 and odd in fields of characteristic 3

model sparsity and brain pattern interpretation of classification models in neuroimaging interest is increasing in applying discriminative multivariate analysis techniques to the analysis of functional neuroimaging data model interpretation is of great importance in the neuroimaging context and is conventionally based on a brain map derived from the classification model in this study we focus on the relative influence of model regularization parameter choices on both the model generalization the reliability of the spatial patterns extracted from the classification model and the ability of the resulting model to identify relevant brain networks defining the underlying neural encoding of the experiment for a support vector machine logistic regression and fisher s discriminant analysis we demonstrate that selection of model regularization parameters has a strong but consistent impact on the generalizability and both the reproducibility and interpretable sparsity of the models for both 2 and 1 regularization importantly we illustrate a trade off between model spatial reproducibility and prediction accuracy we show that known parts of brain networks can be overlooked in pursuing maximization of classification accuracy alone with either 2 and or 1 regularization this supports the view that the quality of spatial patterns extracted from models cannot be assessed purely by focusing on prediction accuracy our results instead suggest that model regularization parameters must be carefully selected so that the model and its visualization enhance our ability to interpret the brain

forecasting using random subspace methods textabstractrandom subspace methods are a novel approach to obtain accurate forecasts in high dimensional regression settings we provide a theoretical justification of the use of random subspace methods and show their usefulness when forecasting monthly macroeconomic variables we focus on two approaches the first is random subset regression where random subsets of predictors are used to construct a forecast second we discuss random projection regression where artificial predictors are formed by randomly weighting the original predictors using recent results from random matrix theory we obtain a tight bound on the mean squared forecast error for both randomized methods we identify settings in which one randomized method results in more precise forecasts than the other and than alternative regularization strategies such as principal component regression partial least squares lasso and ridge regression the predictive accuracy on the high dimensional macroeconomic fred md data set increases substantially when using the randomized methods with random subset regression outperforming any one of the above mentioned competing methods for at least 66 of the series

translating solitons of mean curvature flow of noncompact spacelike hypersurfaces in minkowski space abstract in this paper we study the existence uniqueness and asymptotic behavior of rotationally symmetric translating solitons of the mean curvature flow in minkowski space we also study the asymptotic behavior and the strict convexity of general solitons of such flows

outlier induced collinearities when an observation in a regression analysis has very large values on two or more predictor variables artificial collinearities can be induced the effects of such collinearities on a regression analysis are not well documented although they can be shown to be similar in many respects to those resulting from approximate linear dependencies among the columns of predictor variable values the purpose of this article is to explore the effects of outlier induced collinearities on the estimation of regression coefficients

the dirichlet problem for monge ampere equations in non convex domains and spacelike hypersurfaces of constant gauss curvature in this paper we extend the well known results on the existence and regularity of solutions of the dirichlet problem for monge ampere equations in a strictly convex domain to an arbitrary smooth bounded domain in r as well as in a general riemannian manifold we prove for the nondegenerate case that a sufficient and necessary condition for the classical solvability is the existence of a subsolution for the totally degenerate case we show that the solution is in c11 q if the given boundary data extends to a locally strictly convex c2 function ori q as an application we prove some existence results for spacelike hypersurfaces of constant gauss kronecker curvature in minkowski space spanning a prescribed boundary

stability of mean convex cones under mean curvature flow we consider graphical solutions to mean curvature flow and obtain a stability result for homothetically expanding solutions coming out of cones of positive mean curvature if another solution is initially close to the cone at infinity then the difference to the homothetically expanding solution becomes small for large times the proof involves the construction of appropriate barriers

polynomials with psl 2 monodromy let k be a field of characteristic p 0 let q be a power of p and let u be transcendental over k we determine all polynomials f k x k x p of degree q q 1 2 for which the galois group of f x u over k u has a transitive normal subgroup isomorphic to psl 2 q subject to a certain ramification hypothesis as a consequence we describe all polynomials f k x such that deg f is not a power of p and f is functionally indecomposable over k but f decomposes over an extension of k moreover except for one ramification configuration which is handled in a companion paper with rosenberg we describe all indecomposable polynomials f k x such that deg f is not a power of p and f is exceptional in the sense that x y is the only absolutely irreducible factor of f x f y which lies in k x y it is known that when k is finite a polynomial f is exceptional if and only if it induces a bijection on infinitely many finite extensions of k

principal component estimation for generalized linear regression summary the generalized linear model nelder wedderburn 1972 has become an elegant and practical option to classical least squares linear model building we consider the specific problem of generalized linear regression utilizing a set of continuous explanatory variables to model an exponential family response it is the objective of this paper to develop and present an asymptotically biased principal component parameter estimation technique as an option to traditional maximum likelihood estimation for generalized linear regression both iterative and one step principal component estimators are developed directly compared and can be particularly useful with the presence of an ill conditioned information matrix the bias variance and mean squared error of principal component estimation will be quantified generalizations for rules of deletion of components will be examined lastly an example employs principal component estimation for poisson response data

the best parameter subset using the chebychev curve fitting criterion the chebychev also minimax andl norm criterion has been widely studied as a method for curve fitting published computer codes are available to obtain the optimal parameter estimates to fit a linear function to a set of given points under the chebychev criterion the purpose of this paper is to study procedures for obtaining the best subset ofq parameters from a given set ofm parameters whereq is less than or equal tom

entire spacelike hypersurfaces of constant gaus curvature in minkowski space we prove existence and stability of smooth entire strictly convex spacelike hypersurfaces of prescribed gaus curvature in minkowski space the proof is based on barrier constructions and local a priori estimates

risk reducing shrinkage estimation for generalized linear models to generalized linear models in a manner retaining the original spirit of shrinkage estimation which is to reduce risk the investigation identifies two classes of simple all purpose prior distributions which supplement such non informative priors as jeffreys s prior with mechanisms for risk reduction one new class of priors is motivated as optimizers of a core component of asymptotic risk the methodology is evaluated in a numerical exploration and application to an existing data set

algebraic relationships between classical regression and total least squares estimation abstract the total least squares tls technique which is well known in numerical linear algebra and able to compute strongly consistent estimators of the parameters in a linear errors in variables model is compared algebraically with the classical regression estimators using the singular value decomposition and geometric concepts algebraic equivalences and important relationships between the classical regression techniques and tls estimation are established with special reference to problems of collinearity the equivalence between principal component and latent root regression in collinearity problems is proven and the difference between latent root regression and tls estimation is clarified

an investigation of the use of goal programming to fit response surfaces abstract this paper deals with the development and implementation of goal programming models for fitting response surfaces where the observed data are characterized by certain peculiarities such as the existence of outliers a factorial statistical experiment is designed to compare through multivariate anova various forms of the goal programming algorithm with the traditional ordinary least squares method the comparison is based on both the speed of convergence of the proposed algorithms and the accuracy of the estimated optimum solution relative to the true optimum of a pre specified theoretical response surface results indicate that two different goal programming methods each involving two secondary criteria achieved a more accurate estimated solution than did the ordinary least squares method this advantage is realized at the expense of slower convergence speed however

least squares ridge regression and goal programming constrained regression alternatives abstract ridge regression has been extensively reviewed in the literature of applied statistics as a method for dealing with problems of collinearity in least squares regressions in this paper ordinary least squares and least squares combined with ridge regressions are examined and compared with ordinary goal programming and goal programming combined with constraints on regressand values that admissible statistical estimates must satisfy the comparisons are effected by means of an example in chemical processing that has been extensively treated in the ridge regression literature

active learning and basis selection for kernel based linear models a bayesian perspective we develop an active learning algorithm for kernel based linear regression and classification the proposed greedy algorithm employs a minimum entropy criterion derived using a bayesian interpretation of ridge regression we assume access to a matrix bbrn n for which the i j th element is defined by the kernel function k i j bbr with the observed data i bbrd we seek a model m i yi where yi is a real valued response or integer valued label which we do not have access to a priori to achieve this goal a submatrix il ib bbrn m is sought that corresponds to the intersection of n rows and m columns of indexed by the sets il and ib respectively typically m n and n n we have two objectives i determine the m columns of indexed by the set ib that are the most informative for building a linear model m 1 i ib t yi without any knowledge of yi i 1n and ii using active learning sequentially determine which subset of n elements of yi i 1n should be acquired both stopping values ib m and il n are also to be inferred from the data these steps are taken with the goal of minimizing the uncertainty of the model parameters x as measured by the differential entropy of its posterior distribution the parameter vector x bbrm as well as the model bias bbr is then learned from the resulting problem yil il ibx 1 the remaining n n responses labels not included in yil can be inferred by applying x to the remaining n n rows of ib we show experimental results for several regression and classification problems and compare to other active learning methods

a new family of exceptional polynomials in characteristic two we produce a new family of polynomials f x over fields k of characteristic 2 which are exceptional in the sense that f x f y has no absolutely irreducible factors in k x y except for scalar multiples of x y when k is finite this condition is equivalent to saying that the map f induces a bijection on an infinite algebraic extension of k our polynomials have degree 2 e 1 2 e 1 where e 1 is odd we also prove that this completes the classification of indecomposable exceptional polynomials of degree not a power of the characteristic

two nonparametric methods for identifying the impulse response of linear systems this paper addresses the problem of impulse response identification using nonparametric methods although the techniques developed herein apply to the truncated untruncated and circulant models we focus on the truncated model which is useful in certain applications two methods of impulse response identification will be presented the first is based on the minimization of the c l statistic which is an estimate of the mean square prediction error the second is a bayesian approach for both of these methods we consider the effects of using both the identity matrix and the laplacian matrix as weights on the energy in the impulse response in addition we present a method for estimating the effective length of the impulse response estimating the length is particularly important in the truncated case finally we develop a method for estimating the noise variance at the output which is needed in the approach involving the c l statistic often prior information on the noise variance is not available and a good estimate is crucial to the success of estimating the impulse response with a nonparametric technique

serial correlation estimation through the imprecise goal programming model abstract the goal programming gp model was used as a time series analysis tool that incorporates a serial correlation where the dependent variable is considered as precise this formulation does not take into consideration the decision maker s preferences however the dependent variable can be imprecise and its value can be expressed through an interval the aim of this paper is to develop a new formulation of the gp model for regression with serial correlation where the dependent variable is imprecise the proposed model will also integrate explicitly the decision maker s preferences a numerical example was used to illustrate our model

variable selection in a log linear birnbaum saunders regression model for high dimensional survival data via the elastic net and stochastic em the birnbaum saunders bs distribution is broadly used to model failure times in reliability and survival analysis in this article we propose a simultaneous parameter estimation and variable selection procedure in a log linear bs regression model for high dimensional survival data to deal with censored survival data we iteratively run a combination of the stochastic em algorithm sem and variable selection procedure to generate pseudo complete data and select variables until convergence treating pseudo complete data as uncensored data via sem makes it possible to incorporate iterative penalized least squares and simplify computation we demonstrate the efficacy of our method using simulated and real datasets

orthogonalizing em a design based least squares algorithm we introduce an efficient iterative algorithm intended for various least squares problems based on a design of experiments perspective the algorithm called orthogonalizing em oem works for ordinary least squares ols and can be easily extended to penalized least squares the main idea of the procedure is to orthogonalize a design matrix by adding new rows and then solve the original problem by embedding the augmented design in a missing data framework we establish several attractive theoretical properties concerning oem for the ols with a singular regression matrix an oem sequence converges to the moore penrose generalized inverse based least squares estimator for ordinary and penalized least squares with various penalties it converges to a point having grouping coherence for fully aliased regression matrices convergence and the convergence rate of the algorithm are examined finally we demonstrate that oem is highly efficient for large scale least squares and penalized least squares proble

piecewise linear regularized solution paths we consider the generic regularized optimization problem argmin l y x j efron hastie johnstone and tibshirani ann statist 32 2004 407 499 have shown that for the lasso that is if l is squared error loss and j 1 is the l 1 norm of the optimal coefficient path is piecewise linear that is is piecewise constant we derive a general characterization of the properties of loss l penalty j pairs which give piecewise linear coefficient paths such pairs allow for efficient generation of the full regularized coefficient paths we investigate the nature of efficient path following algorithms which arise we use our results to suggest robust versions of the lasso for regression and classification and to develop new efficient algorithms for existing problems in the literature including mammen and van de geer s locally adaptive regression splines

s values conventional context minimal measures of the sturdiness of regression coefficients this paper proposes a context minimal range of alternative regression models that is used to generate a range of alternative estimates a prior distribution is assumed with a zero mean but an ambiguous covariance matrix the choice of the prior covariance matrix is facilitated by transformation to standardized variables which makes the prior expected r2 equal to the sum of the prior variances three different ranges of the prior expected r2 are used to define three different intervals of prior covariance matrices which are used to produce three different sets of s values

grafting fast incremental feature selection by gradient descent in function space we present a novel and flexible approach to the problem of feature selection called grafting rather than considering feature selection as separate from learning grafting treats the selection of suitable features as an integral part of learning a predictor in a regularized learning framework to make this regularized learning process sufficiently fast for large scale problems grafting operates in an incremental iterative fashion gradually building up a feature set while training a predictor model using gradient descent at each iteration a fast gradient based heuristic is used to quickly assess which feature is most likely to improve the existing model that feature is then added to the model and the model is incrementally optimized using gradient descent the algorithm scales linearly with the number of data points and at most quadratically with the number of features grafting can be used with a variety of predictor model classes both linear and non linear and can be used for both classification and regression experiments are reported here on a variant of grafting for classification using both linear and non linear models and using a logistic regression inspired loss function results on a variety of synthetic and real world data sets are presented finally the relationship between grafting stagewise additive modelling and boosting is explored

bivariate factorizations via galois theory with application to exceptional polynomials abstract we present a method for factoring polynomials of the shape f x f y where f is a univariate polynomial over a field k we then apply this method in the case when f is a member of the infinite family of exceptional polynomials we discovered jointly with h lenstra in 1995 factoring f x f y in this case was posed as a problem by s cohen shortly after the discovery of these polynomials

closed weingarten hypersurfaces in semi riemannian manifolds the existence of closed hypersurfaces of prescribed curvature in semi riemannian manifolds is proved provided there are barriers

covariance regularized regression and classification for high dimensional problems in recent years many methods have been developed for regression in high dimensional settings we propose covariance regularized regression a family of methods that use a shrunken estimate of the inverse covariance matrix of the features in order to achieve superior prediction an estimate of the inverse covariance matrix is obtained by maximizing its log likelihood under a multivariate normal model subject to a constraint on its elements this estimate is then used to estimate coefficients for the regression of the response onto the features we show that ridge regression the lasso and the elastic net are special cases of covariance regularized regression and we demonstrate that certain previously unexplored forms of covariance regularized regression can outperform existing methods in a range of situations the covariance regularized regression framework is extended to generalized linear models and linear discriminant analysis and is used to analyze gene expression data sets with multiple class and survival outcomes

a group bridge approach for variable selection in multiple regression problems when covariates can be naturally grouped it is important to carry out feature selection at the group and within group individual variable levels simultaneously the existing methods including the lasso and group lasso are designed for either variable selection or group selection but not for both we propose a group bridge approach that is capable of simultaneous selection at both the group and within group individual variable levels the proposed approach is a penalized regularization method that uses a specially designed group bridge penalty it has the oracle group selection property in that it can correctly select important groups with probability converging to one in contrast the group lasso and group least angle regression methods in general do not possess such an oracle property in group selection simulation studies indicate that the group bridge has superior performance in group and individual variable selection relative to several existing methods

functional multiple set canonical correlation analysis we propose functional multiple set canonical correlation analysis for exploring associations among multiple sets of functions the proposed method includes functional canonical correlation analysis as a special case when only two sets of functions are considered as in classical multiple set canonical correlation analysis computationally the method solves a matrix eigen analysis problem through the adoption of a basis expansion approach to approximating data and weight functions we apply the proposed method to functional magnetic resonance imaging fmri data to identify networks of neural activity that are commonly activated across subjects while carrying out a working memory task

optimal weighting of a priori statistics in linear estimation theory abstract many scientific and engineering applications require the determination of the state of a dynamical system at some reference time a common solution technique is to perform a taylor series expansion about a nominal solution and compute linear corrections to this nominal by the use of a set of discrete observations of the dynamical system in cases where the observational data set is ill conditioned statistical information on the nominal solution is commonly incorporated into the solution process in order to provide stability in the computation of the linear corrections this statistical information is generally the uncertainty in the nominal solution known as the a priori covariance this a priori information is typically weighted equally with the observational data in conventional minimum variance or maximum likelihood solution methods often the a priori information available for certain types of dynamical systems is inaccurate or generated by inadequate means it has been shown that the accuracy of the estimates is highly dependent on the choice of the a priori covariance inaccurate a priori information can contribute to large errors in the estimates in ill conditioned problems methods developed herein provide for the optimal weighting of the a priori covariance used in the solution of the linear correction to the nominal solution these methods are demonstrated by their application to a space mechanics simulation in which a satellite s orbit must be precisely determined results are compared to those obtained by conventional minimum variance solution techniques in order to demonstrate the possible improvement in the estimate accuracy achievable by the use of such optimal weighting techniques

simultaneous regression shrinkage variable selection and supervised clustering of predictors with oscar variable selection can be challenging particularly in situations with a large number of predictors with possibly high correlations such as gene expression data in this article a new method called the oscar octagonal shrinkage and clustering algorithm for regression is proposed to simultaneously select variables while grouping them into predictive clusters in addition to improving prediction accuracy and interpretation these resulting groups can then be investigated further to discover what contributes to the group having a similar behavior the technique is based on penalized least squares with a geometrically intuitive penalty function that shrinks some coefficients to exactly zero additionally this penalty yields exact equality of some coefficients encouraging correlated predictors that have a similar effect on the response to form predictive clusters represented by a single coefficient the proposed procedure is shown to compare favorably to the existing shrinkage and variable selection techniques in terms of both prediction error and model complexity while yielding the additional grouping information

on a relationship between minimax linear and admissible estimators in linear regression minimax linear estimation with respect to the quadratic risk is considered among the class of linear estimators of under the linear regression model m y x 2i new classes of minimax linear estimators of are derived among certain subsets of linear estimators which are simple from the point of view of minimax estimation the admissible linear estimators of under m are then characterized via these classes of minimax linear estimators and the relationship between the minimax linear and admissible estimators of is examined various properties of linear admissible estimators follow readily from this new characterization

spacelike hypersurfaces with prescribed boundary values and mean curvature we consider the boundary value problem for the mean curvature operator in minkowski space and give necessary and sufficient conditions for the existence of smooth strictly spacelike solutions our main results hold for non constant mean curvature and make no assumptions about the smoothness of the boundary or boundary data

correlation weights in multiple regression a general theory on the use of correlation weights in linear prediction has yet to be proposed in this paper we take initial steps in developing such a theory by describing the conditions under which correlation weights perform well in population regression models using ols weights as a comparison we define cases in which the two weighting systems yield maximally correlated composites and when they yield minimally similar weights we then derive the least squares weights for any set of predictors that yield the largest drop in r 2 the coefficient of determination when switching to correlation weights our findings suggest that two characteristics of a model data combination are especially important in determining the effectiveness of correlation weights 1 the condition number of the predictor correlation matrix r xx and 2 the orientation of the correlation weights to the latent vectors of r xx

on isometric immersions of the hyperbolic plane into the lorentz minkowski space and the monge ampere equation of a certain type

bayesian sparse polynomial chaos expansion for global sensitivity analysis polynomial chaos expansions are frequently used by engineers and modellers for uncertainty and sensitivity analyses of computer models they allow representing the input output relations of computer models usually only a few terms are really relevant in such a representation it is a challenge to infer the best sparse polynomial chaos expansion of a given model input output data set in the present article sparse polynomial chaos expansions are investigated for global sensitivity analysis of computer model responses a new bayesian approach is proposed to perform this task based on the kashyap information criterion for model selection the efficiency of the proposed algorithm is assessed on several benchmarks before applying the algorithm to identify the most relevant inputs of a double diffusive convection model

penalized likelihood in cox regression in a cox regression model instability of the estimated regression coefficients can be reduced by maximizing a penalized partial log likelihood where a penalty function of the regression coefficients is substracted from the partial log likelihood in this paper we choose the optimal weight of the penalty function by maximizing the predictive value of the model as measured by the crossvalidated partial log likelihood our methods are illustrated by a study of ovarian cancer survival and by a study of centre effects in kidney graft survival

a penalized method for multivariate concave least squares with application to productivity analysis abstract we propose a penalized method for the least squares estimator of a multivariate concave regression function this estimator is formulated as a quadratic programing qp problem with o n2 constraints where n is the number of observations computing such an estimator is a very time consuming task and the computational burden rises dramatically as the number of observations increases by introducing a quadratic penalty function we reformulate the concave least squares estimator as a qp with only non negativity constraints this reformulation can be adapted for estimating variants of shape restricted least squares i e the monotonic concave convex least squares the experimental results and an empirical study show that the reformulated problem and its dual are solved significantly faster than the original problem the matlab and r codes for implementing the penalized problems are provided in the paper

the regularized iteratively reweighted mad method for change detection in multi and hyperspectral data this paper describes new extensions to the previously published multivariate alteration detection mad method for change detection in bi temporal multi and hypervariate data such as remote sensing imagery much like boosting methods often applied in data mining work the iteratively reweighted ir mad method in a series of iterations places increasing focus on difficult observations here observations whose change status over time is uncertain the mad method is based on the established technique of canonical correlation analysis for the multivariate data acquired at two points in time and covering the same geographical region we calculate the canonical variates and subtract them from each other these orthogonal differences contain maximum information on joint change in all variables spectral bands the change detected in this fashion is invariant to separate linear affine transformations in the originally measured variables at the two points in time such as 1 changes in gain and offset in the measuring device used to acquire the data 2 data normalization or calibration schemes that are linear affine in the gray values of the original variables or 3 orthogonal or other affine transformations such as principal component pc or maximum autocorrelation factor maf transformations the ir mad method first calculates ordinary canonical and original mad variates in the following iterations we apply different weights to the observations large weights being assigned to observations that show little change i e for which the sum of squared standardized mad variates is small and small weights being assigned to observations for which the sum is large like the original mad method the iterative extension is invariant to linear affine transformations of the original variables to stabilize solutions to the ir mad problem some form of regularization may be needed this is especially useful for work on hyperspectral data this paper describes ordinary two set canonical correlation analysis the mad transformation the iterative extension and three regularization schemes a simple case with real landsat thematic mapper tm data at one point in time and partly constructed data at the other point in time that demonstrates the superiority of the iterative scheme over the original mad method is shown also examples with spot high resolution visible data from an agricultural region in kenya and hyperspectral airborne hymap data from a small rural area in southeastern germany are given the latter case demonstrates the need for regularization

prediction by supervised principal components in regression problems where the number of predictors greatly exceeds the number of observations conventional regression techniques may produce unsatisfactory results we describe a technique called supervised principal components that can be applied to this type of problem supervised principal components is similar to conventional principal components analysis except that it uses a subset of the predictors selected based on their association with the outcome supervised principal components can be applied to regression and generalized regression problems such as survival analysis it compares favorably to other techniques for this type of problem and can also account for the effects of other covariates and help identify which predictor variables are most important we also provide asymptotic consistency results to help support our empirical findings these methods could become important tools for dna microarray data where they may be used to more accurately diagnose and treat cancer

deforming the metric on complete riemannian manifolds soit m g ij x une variete de riemann a n dimensions complete non compacte de tenseur de complexe riemannien r ijkl satisfaisant r ijkl 2 k 0 sur m ou 0 0 dependant seulement de n et de k 0 telle que l equation d evolution g ij x t t 2r ij x t sur m g ij x o g ij x x m ait une solution lisse g ij x t 0 pour un temps court 0 t t u k 0 et satisfait l estimation suivante pour un entier m 0 il existe des constantes c m 0 dependant seulement de n m et k 0 telles que sup x m v m r ijkl x t 2 c m t m 0 t t u k 0

universal weighted mse improvement of the least squares estimator since the seminal work of stein in the 1950s there has been continuing research devoted to improving the total mean squared error mse of the least squares ls estimator in the linear regression model however a drawback of these methods is that although they improve the total mse they do so at the expense of increasing the mse of some of the individual signal components here we consider a framework for developing linear estimators that outperform the ls strategy over bounded norm signals under all weighted mse measures this guarantees for example that both the total mse and the mse of each of the elements will be smaller than that resulting from the ls approach we begin by deriving an easily verifiable condition on a linear method that ensures ls domination for every weighted mse we then suggest a minimax estimator that minimizes the worst case mse over all weighting matrices and bounded norm signals subject to the universal weighted mse domination constraint

maximin effects in inhomogeneous large scale data large scale data are often characterized by some degree of inhomogeneity as data are either recorded in different time regimes or taken from multiple sources we look at regression models and the effect of randomly changing coefficients where the change is either smoothly in time or some other dimension or even without any such structure fitting varying coefficient models or mixture models can be appropriate solutions but are computationally very demanding and often return more information than necessary if we just ask for a model estimator that shows good predictive properties for all regimes of the data then we are aiming for a simple linear model that is reliable for all possible subsets of the data we propose the concept of maximin effects and a suitable estimator and look at its prediction accuracy from a theoretical point of view in a mixture model with known or unknown group structure under certain circumstances the estimator can be computed orders of magnitudes faster than standard penalized regression estimators making computations on large scale data feasible empirical examples complement the novel methodology and theory

small sample properties of ml cols and dea estimators of frontier models in the presence of heteroscedasticity by a n bojanic s b caudill and j m ford european journal of operational research 108 1998 140 148 a comment

penalized partial likelihood regression for right censored data with bootstrap selection of the penalty parameter le modele de cox a risque proportionnel est souvent utilise pour estimer l association entre des covariables et un delai de survenue d un evenement qui peut etre censure les estimateurs bases sur la vraisemblance partielle sont utilises pour l estimation et la prediction du risque relatif de l evenement cependant ces estimateurs sont instables et ont une grande variance en cas de colinearite entre les covariables ou quand le nombre d evenements n est pas nettement plus grand que le nombre de covariables une vraisemblance partielle penalisee est proposee pour donner des estimateurs du risque relatif plus precis nous montrons qu asymptotiquement il existe toujours un parametre de penalite pour la vraisemblance partielle penalisee qui reduit le carre moyen de l erreur d estimation du logarithme du risque relatif nous proposons une methode de reechantillonnage pour choisir le parametre de penalite des simulations et un exemple montrent que des estimateurs bases sur la vraisemblance partielle penalisee et la methode du bootstrap peuvent dans certaines circonstances avoir un biais plus petit que celui des estimateurs bases sur la vraisemblance partielle ainsi qu un carre moyeu plus petit de l erreur d estimation et de prediction du logarithme du risque relatif nous illustrons ces methodes avec des donnees d une etude sur le myelome multiple du eastern cooperative oncology group ecog