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

a family of multi path congestion control algorithms with global stability and delay robustness the goal of traffic management is to efficiently allocate network resources via adjustment of source transmission rates and routes selection mathematically it aims to solve a traditional utility maximization problem in a fair and distributed manner in this paper we first develop a generalized multi path utility maximization problem which features a weighted average of the classical kelly s formulation and the voice s model next we design from this broader framework a family of multi path dual congestion control algorithms whose equilibrium point can both achieve a desired bandwidth utilization and preserve a notion of fairness among competing users global stability can be guaranteed for the proposed schemes in the absence of delays by use of a totally novel lyapunov function moreover when heterogeneous propagation delays are taken into account we establish decentralized and scalable sufficient conditions for robust global stability by constructing a reasonable lyapunov krasovskii functional candidate these conditions give estimates for the maximum admissible delays that the controller can tolerate without losing stability finally we verify the results through simulation

contour regression a general approach to dimension reduction we propose a novel approach to sufficient dimension reduction in regression based on estimating contour directions of small variation in the response these directions span the orthogonal complement of the minimal space relevant for the regression and can be extracted according to two measures of variation in the response leading to simple and general contour regression scr and gcr methodology in comparison with existing sufficient dimension reduction techniques this contour based methodology guarantees exhaustive estimation of the central subspace under ellipticity of the predictor distribution and mild additional assumptions while maintaining sqrt n consistency and computational ease moreover it proves robust to departures from ellipticity we establish population properties for both scr and gcr and asymptotic properties for scr simulations to compare performance with that of standard techniques such as ordinary least squares sliced inverse regression principal hessian directions and sliced average variance estimation confirm the advantages anticipated by the theoretical analyses we demonstrate the use of contour based methods on a data set concerning soil evaporation

on principal hessian directions for data visualization and dimension reduction another application of stein s lemma abstract modern graphical tools have enhanced our ability to learn many things from data directly with much user friendly graphical software available we are encouraged to plot a lot more often than before the benefits from direct interaction with graphics have been enormous but trailing behind these high tech advances is the issue of appropriate guidance on what to plot there are too many directions to project a high dimensional data set and unguided plotting can be time consuming and fruitless in a recent article li set up a statistical framework for study on this issue based on a notion of effective dimension reduction edr directions they are the directions to project a high dimensional input variable for the purpose of effectively viewing and studying its relationship with an output variable a methodology sliced inverse regression was introduced and shown to be useful in finding edr directions this article introduces another method for finding edr directions it begins with the observat

svm decision boundary based discriminative subspace induction we study the problem of linear dimension reduction for classification with a focus on sufficient dimension reduction i e finding subspaces without loss of discrimination power first we formulate the concept of sufficient subspace for classification in parallel terms as for regression then we present a new method to estimate the smallest sufficient subspace based on an improvement of decision boundary analysis dba the main idea is to combine dba with support vector machines svm to overcome the inherent difficulty of dba in small sample size situations while keeping dba s estimation simplicity the compact representation of svm boundary results in a significant gain in both speed and accuracy over previous dba implementations alternatively this technique can be viewed as a way to reduce the run time complexity of svm itself comparative experiments on one simulated and four real world benchmark datasets highlight the superior performance of the proposed approach

using the bootstrap to select one of a new class of dimension reduction methods dimension reduction in a regression analysis of response y given a p dimensional vector of predictors x reduces the dimension of x by replacing it with a lower dimensional linear combination x of the x s without specifying a parametric model and without loss of information about the conditional distribution of y given x we unify three existing methods sliced inverse regression sir sliced average variance estimate save and principal hessian directions phd into a larger class of methods each method estimates a particular candidate matrix essentially a matrix of parameters we introduce broad classes of dimension reduction candidate matrices and we distinguish estimators of the matrices from the matrices themselves given these classes of methods and several ways to estimate any matrix we now have the problem of selecting a particular matrix and estimation method we propose bootstrap methodology to select among candidate matrices estimators and dimension and in particular we investigate l

estimation of the mean of a multivariate normal distribution estimation of the means of independent normal random variables is considered using sum of squared errors as loss an unbiased estimate of risk is obtained for an arbitrary estimate and certain special classes of estimates are then discussed the results are applied to smoothing by use of moving averages and to trimmed analogs of the james stein estimate a suggestion is made for calculating approximate confidence sets for the mean vector centered at an arbitrary estimate

efficient and adaptive linear regression in semi supervised settings we consider the linear regression problem under semi supervised settings wherein the available data typically consists of i a small or moderate sized labeled data and ii a much larger sized unlabeled data such data arises naturally from settings where the outcome unlike the covariates is expensive to obtain a frequent scenario in modern studies involving large databases like electronic medical records emr supervised estimators like the ordinary least squares ols estimator utilize only the labeled data it is often of interest to investigate if and when the unlabeled data can be exploited to improve estimation of the regression parameter in the adopted linear model in this paper we propose a class of efficient and adaptive semi supervised estimators ease to improve estimation efficiency the ease are two step estimators adaptive to model mis specification leading to improved optimal in some cases efficiency under model mis specification and equal optimal efficiency under a linear model this adaptive property often unaddressed in the existing literature is crucial for advocating safe use of the unlabeled data the construction of ease primarily involves a flexible semi nonparametric imputation including a smoothing step that works well even when the number of covariates is not small and a follow up refitting step along with a cross validation cv strategy both of which have useful practical as well as theoretical implications towards addressing two important issues under smoothing and over fitting we establish asymptotic results including consistency asymptotic normality and the adaptive properties of ease we also provide influence function expansions and a double cv strategy for inference the results are further validated through extensive simulations followed by application to an emr study on auto immunity

testing predictor contributions in sufficient dimension reduction we develop tests of the hypothesis of no effect for selected predictors in regression without assuming a model for the conditional distribution of the response given the predictors predictor effects need not be limited to the mean function and smoothing is not required the general approach is based on sufficient dimension reduction the idea being to replace the predictor vector with a lower dimensional version without loss of information on the regression methodology using sliced inverse regression is developed in detail

a note on shrinkage sliced inverse regression summary we employ lasso shrinkage within the context of sufficient dimension reduction to obtain a shrinkage sliced inverse regression estimator which provides easier interpretations and better pre diction accuracy without assuming a parametric model the shrinkage sliced inverse regression approach can be employed for both single index and multiple index models simulation studies suggest that the new estimator performs well when its tuning parameter is selected by either the bayesian information criterion or the residual information criterion

reweighting to achieve elliptically contoured covariates in regression abstract we investigate a method of constructing weights to induce elliptically contoured covariates in regression analyses much recent work in regression has identified various data analytic and model robustness advantages associated with such covariates in particular new estimation methods like sir sirii save and phd have been built around the assumption of elliptically contoured covariates finite samples of regression covariates may deviate from this ideal in practice and the method developed here termed voronoi weighting can be used to induce elliptical symmetry in such samples in a number of examples we show that reweighting cases by the voronoi method can substantially enhance various procedures for covariates that deviate from elliptical symmetry we show that voronoi weighting in conjunction with some trimming via the minimum volume ellipsoid method can be effective

an interpretation of completeness and basu s theorem abstract in order to obtain a statistical interpretation of completeness of a sufficient statistic t an attempt is made to characterize this property as equivalent to the condition that all ancillary statistics are independent of t for technical reasons this characterization is not correct but two correct versions are obtained in section 3 by modifying either the definition of ancillarity or of completeness the light this throws on the meaning of completeness is discussed in section 4 finally section 5 reviews some of the difficulties encountered in models that lack completeness

on a projective resampling method for dimension reduction with multivariate responses consider the dimension reduction problem where both the response and the predictor are vectors existing estimators of this problem take one of the following routes 1 targeting the part of the dimension reduction space that is related to the conditional mean or moments of the response vector 2 pooling the estimates for the marginal dimension reduction spaces and 3 estimating the whole dimension reduction space directly by multivariate slicing however the first two approaches do not fully recover the dimension reduction space and the third is hampered by the fact that the accuracy of estimators based on multivariate slicing drops sharply as the dimension of response increases a phenomenon often called the curse of dimensionality we propose a new method that overcomes both difficulties in that it involves univariate slicing only and it is guaranteed to fully recover the dimension reduction space under reasonable conditions the method will be compared with the existing estimators by simula

dimension reduction for the conditional mean in regressions with categorical predictors consider the regression of a response y on a vector of quantitative predictors x and a categorical predictor w in this article we describe a first method for reducing the dimension of x without loss of information on the conditional mean mathrm e y x w and without requiring a prespecified parametric model the method which allows for but does not require parametric versions of the subpopulation mean functions mathrm e y x w w includes a procedure for inference about the dimension of x after reduction this work integrates previous studies on dimension reduction for the conditional mean mathrm e y x in the absence of categorical predictors and dimension reduction for the full conditional distribution of y x w the methodology we describe may be particularly useful for constructing low dimensional summary plots to aid in model building at the outset of an analysis our proposals provide an often parsimonious alternative to the standard technique of modeling with interaction terms to adapt a mean function for different subpopulations determined by the levels of w examples illustrating this and other aspects of the development are presented

identifying regression outliers and mixtures graphically regressions in practice can include outliers and other unknown subpopulation structures for example mixtures of regressions occur if there is an omitted categorical predictor like gender or location and different regressions occur within each category the theory of regression graphics based on central subspaces can be used to construct graphical solutions to long standing problems of this type it is argued that in practice the central subspace automatically expands to incorporate outliers and regression mixtures thus methods of estimating the central subspace can be used to identify these phenomena without specifying a model examples illustrating the power of the theory are presented

constrained inverse regression for incorporating prior information inverse regression methods facilitate dimension reduction analyses of high dimensional data by extracting a small number of factors that are linear combinations of the original predictor variables but the estimated factors may not lend themselves readily to interpretation consistent with prior information our approach to solving this problem is to first incorporate prior information via theory or data driven constraints on model parameters and then apply the proposed method constrained inverse regression cir to extract factors that satisfy the constraints we provide chi squared and t tests to assess the significance of each factor and its estimated coefficients and we also generalize cir to other inverse regression methods in situations where both dimension reduction and factor interpretation are important finally we investigate cir s small sample performance test data driven constraints and present a marketing example to illustrate its use in discovering meaningful factors that influence th

a general theory for nonlinear sufficient dimension reduction formulation and estimation in this paper we introduce a general theory for nonlinear sufficient dimension reduction and explore its ramifications and scope this theory subsumes recent work employing reproducing kernel hilbert spaces and reveals many parallels between linear and nonlinear sufficient dimension reduction using these parallels we analyze the properties of existing methods and develop new ones we begin by characterizing dimension reduction at the general level of sigma fields and proceed to that of classes of functions leading to the notions of sufficient complete and central dimension reduction classes we show that when it exists the complete and sufficient class coincides with the central class and can be unbiasedly and exhaustively estimated by a generalized sliced inverse regression estimator gsir when completeness does not hold this estimator captures only part of the central class however in these cases we show that a generalized sliced average variance estimator gsave can capture a larger portion of the class both estimators require no numerical optimization because they can be computed by spectral decomposition of linear operators finally we compare our estimators with existing methods by simulation and on actual data sets

estimating central subspaces via inverse third moments summary modern graphical tools have enhanced our ability to learn many things from data directly in recent years dimension reduction has proven to be an effective tool for generating low dimensional summary plots without appreciable loss of information some well known inverse regression methods for dimension reduction such as sliced inverse regression li 1991 and sliced average variance estimation cook weisberg 1991 have been developed to estimate summary plots for regression and discriminant analysis in this paper we suggest a new method that makes use of inverse third moments this method can find structure beyond that found by sliced inverse regression and sliced average variance estimation particularly regression mixtures illustrative examples are presented

on wielandt s inequality and its application to the asymptotic distribution of the eigenvalues of a random symmetric matrix a relatively obscure eigenvalue inequality due to wielandt is used to give a simple derivation of the asymptotic distribution of the eigenvalues of a random symmetric matrix the asymptotic distributions are obtained under a fairly general setting an application of the general theory to the bootstrap distribution of the eigenvalues of the sample covariance matrix is given 1 introduction and summary the derivation of the asymptotic distribution of the eigenvalues of a random symmetric matrix arises in many papers in multivariate analysis although the main idea behind most of the derivations is quite basic i e the expansion of the sample roots about the population roots the derivations themselves are often quite involved these complications are primarily due to the mathematical rather than statistical nature of the eigenvalue problem one of the main objectives of this paper is to introduce a simple method for obtaining the asymptotic distribution of the eigenvalue of random symmetric matrices the method is based upon a relatively obscure eigenvalue inequality

broue s conjecture holds for principal 3 blocks with elementary abelian defect group of order 9 abstract in representation theory of finite groups there is a well known and important conjecture due to m broue he conjectures that for any prime p if a finite group g has an abelian sylow p subgroup p then the derived categories of the principal p blocks of g and of the normalizer ng p of p in g are equivalent we prove in this paper that broue inage kus conjecture holds for the principal 3 block of an arbitrary finite group g with an elementary abelian sylow 3 subgroup p of order 9 by using initiated works for the case where g is simple which are due to puig okuyama waki miyachi and the authors the result depends on the classification of finite simple groups

principal hessian directions for regression with measurement error summary we consider a nonlinear regression problem with predictors with measurement error we assume that the response is related to unknown linear combinations of a p dimensional predictor vector through an unknown link function instead of observing the predictors we observe a surrogate vector with the property that its expectation is linearly related to the predictor vector with constant variance we use an important linear transformation of the surrogates based on the transformed variables we develop the modified principal hessian directions method for estimating the subspace of the effective dimension reduction space we derive the asymptotic variances of the modified principal hessian directions estimators several examples are reported and comparisons are made with the sliced inverse regression method of carroll li 1992

interactive tree structured regression via principal hessian directions abstract an interactive approach to tree structured regression is introduced unlike other procedures driven by cost optimization this approach focuses on the exploration of geometric information in the data the procedure begins with finding a direction along which the regression surface bends the most this direction is used for splitting the data into two regions within each region another direction is found and the partition is made in the same manner the process continues recursively until the entire regressor domain is decomposed into regions wherein the surface no longer bends significantly and linear regression fit becomes appropriate for implementing the direction search the method of principal hessian directions is applied several simulation and empirical results are reported comparison with three methods cart support and mars is made the benefit of using geometric information is highlighted

sliced inverse regression for dimension reduction abstract modern advances in computing power have greatly widened scientists scope in gathering and investigating information from many variables information which might have been ignored in the past yet to effectively scan a large pool of variables is not an easy task although our ability to interact with data has been much enhanced by recent innovations in dynamic graphics in this article we propose a novel data analytic tool sliced inverse regression sir for reducing the dimension of the input variable x without going through any parametric or nonparametric model fitting process this method explores the simplicity of the inverse view of regression that is instead of regressing the univariate output variable y against the multivariate x we regress x against y forward regression and inverse regression are connected by a theorem that motivates this method the theoretical properties of sir are investigated under a model of the form y f 1 x k x e where the k s are the unknown

principal weighted support vector machines for sufficient dimension reduction in binary classification sufficient dimension reduction is popular for reducing data dimensionality without stringent model assumptions however most existing methods may work poorly for binary classification for example sliced inverse regression li 1991 can estimate at most one direction if the response is binary in this paper we propose principal weighted support vector machines a unified framework for linear and nonlinear sufficient dimension reduction in binary classification its asymptotic properties are studied and an efficient computing algorithm is proposed numerical examples demonstrate its performance in binary classification

combining eigenvalues and variation of eigenvectors for order determination in applying statistical methods such as principal component analysis canonical correlation analysis and sufficient dimension reduction we need to determine how many eigenvectors of a random matrix are important for estimation this problem is known as order determination and amounts to estimating the rank of a matrix previous order determination procedures rely either on the decreasing pattern or elbow of the eigenvalues or on the increasing pattern of the variability in the directions of the eigenvectors in this paper we propose a new order determination procedure by exploiting both patterns when the eigenvalues of a random matrix are close together their eigenvectors tend to vary greatly when the eigenvalues are far apart their variability tends to be small the combination of both helps to pinpoint the rank of a matrix more precisely than the previous methods we establish the consistency of the new order determination procedure and compare it with other such procedures by simulation and in an applied setting

dimension reduction in binary response regression abstract the idea of dimension reduction without loss of information can be quite helpful for guiding the construction of summary plots in regression without requiring a prespecified model focusing on the central subspace we investigate such sufficient dimension reduction in regressions with a binary response three existing methods sliced inverse regression principal hessian direction and sliced average variance estimation and one new method difference of covariances are studied for their ability to estimate the central subspace and produce sufficient summary plots combining these numerical methods with the graphical methods proposed earlier by cook leads to a novel paradigm for the analysis of binary response regressions

on an additive partial correlation operator and nonparametric estimation of graphical models we introduce an additive partial correlation operator as an extension of partial correlation to the nonlinear setting and use it to develop a new estimator for nonparametric graphical models our graphical models are based on additive conditional independence a statistical relation that captures the spirit of conditional independence without having to resort to high dimensional kernels for its estimation the additive partial correlation operator completely characterizes additive conditional independence and has the additional advantage of putting marginal variation on appropriate scales when evaluating interdependence which leads to more accurate statistical inference we establish the consistency of the proposed estimator through simulation experiments and analysis of the dream4 challenge dataset we demonstrate that our method performs better than existing methods in cases where the gaussian or copula gaussian assumption does not hold and that a more appropriate scaling for our method further enhances its performance

sufficient reductions in regressions with elliptically contoured inverse predictors there are two general approaches based on inverse regression for estimating the linear sufficient reductions for the regression of y on x the moment based approach such as sir pir save and dr and the likelihood based approach such as principal fitted components pfc and likelihood acquired directions lad when the inverse predictors x y are normal by construction these methods extract information from the first two conditional moments of x y they can only estimate linear reductions and thus form the linear sufficient dimension reduction sdr methodology when var x y is constant e x y contains the reduction and it can be estimated using pfc when var x y is nonconstant pfc misses the information in the variance and second moment based methods save dr lad are used instead resulting in efficiency loss in the estimation of the mean based reduction in this article we prove that a if x y is elliptically contoured with parameters y and density gy there is no linear nontrivial suf

consensus in multi agent systems with coupling delays and switching topology the robustness of consensus in single integrator multi agent systems mas to coupling delays and switching topologies is investigated it is shown that consensus is reached for arbitrarily large constant time varying or distributed delays if consensus is reached without delays this delay robustness holds under the weakest possible connectivity assumptions on the underlying graph i e as long as the graph is uniformly quasi strongly connected and switches with a dwell time the proof is based on a contraction argument and allows to remove technical assumptions that were used in previous publications moreover the result also applies to non scalar single integrators an important extension toward consensus and rendezvous in higher dimensions

an rkhs formulation of the inverse regression dimension reduction problem suppose that y is a scalar and x is a second order stochastic process where y and x are conditionally independent given the random variables 1 p which belong to the closed span l2 of x this paper investigates a unified framework for the inverse regression dimension reduction problem it is found that the identification of l2 with the reproducing kernel hilbert space of x provides a platform for a seamless extension from the finite to infinite dimensional settings it also facilitates convenient computational algorithms that can be applied to a variety of models

on the interpretation of regression plots abstract a framework is developed for the interpretation of regression plots including plots of the response against selected covariates residual plots added variable plots and detrended added variable plots it is shown that many of the common interpretations associated with these plots can be misleading the framework also allows for the generalization of standard plots and the development of new plotting paradigms a paradigm for graphical exploration of regression problems is sketched

on almost linearity of low dimensional projections from high dimensional data this paper studies the shapes of low dimensional projections from high dimensional data after standardization let mathbf x be a p dimensional random variable with mean zero and identity covariance for a projection beta mathbf x beta 1 find another direction b so that the regression curve of b mathbf x against beta mathbf x is as nonlinear as possible we show that when the dimension of mathbf x is large for most directions beta even the most nonlinear regression is still nearly linear our method depends on the construction of a pair of p dimensional random variables mathbf w 1 mathbf w 2 called the rotational twin and its density function with respect to the standard normal density with this we are able to obtain closed form expressions for measuring deviation from normality and deviation from linearity in a suitable sense of average as an interesting by product from a given set of data we can find simple unbiased estimates of e f beta mathbf x t phi 1 t 1 2 and e lbrack e mathbf x mid beta beta mathbf x t 2 t 2 f 2 beta mathbf x t phi 2 1 t rbrack where phi 1 is the standard normal density f beta mathbf x is the density for beta mathbf x and the e is taken with respect to the uniformly distributed beta this is achieved without any smoothing and without resorting to any laborious projection procedures such as grand tours our result is related to the work of diaconis and freedman the impact of our result on several fronts of data analysis is discussed for example it helps establish the validity of regression analysis when the link function of the regression model may be grossly wrong a further generalization which replaces beta mathbf x by b mathbf x with b beta 1 ldots beta k for k randomly selected orthonormal vectors beta i i 1 ldots k helps broaden the scope of application of sliced inverse regression sir

principal hessian directions revisited abstract li has suggested the method of principal hessian directions for estimating plotting directions that capture curvature in regression functions this article revisits li s proposal offering a number of suggestions for improved application

inverse regression based uncertainty quantification algorithms for high dimensional models many uncertainty quantification uq approaches suffer from the curse of dimensionality that is their computational costs become intractable for problems involving a large number of uncertainty parameters in these situations the classic monte carlo often remains the preferred method of choice because its convergence rate o n 1 2 where n is the required number of model simulations does not depend on the dimension of the problem however many high dimensional uq problems are intrinsically low dimensional because the variation of the quantity of interest qoi is often caused by only a few latent parameters varying within a low dimensional subspace known as the sufficient dimension reduction sdr subspace in the statistics literature motivated by this observation we propose two inverse regression based uq algorithms iruq for high dimensional problems both algorithms use inverse regression to convert the original high dimensional problem to a low dimensional one which is then efficiently solved by building a response surface for the reduced model for example via the polynomial chaos expansion the first algorithm which is for the situations where an exact sdr subspace exists is proved to converge at rate o n 1 hence much faster than mc the second algorithm which doesn t require an exact sdr employs the reduced model as a control variate to reduce the error of the mc estimate the accuracy gain could still be significant depending on how well the reduced model approximates the original high dimensional one iruq also provides several additional practical advantages it is non intrusive it does not require computing the high dimensional gradient of the qoi and it reports an error bar so the user knows how reliable the result is

dimension reduction for conditional mean in regression in many situations regression analysis is mostly concerned with inferring about the conditional mean of the response given the predictors and less concerned with the other aspects of the conditional distribution in this paper we develop dimension reduction methods that incorporate this consideration we introduce the notion of the central mean subspace cms a natural inferential object for dimension reduction when the mean function is of interest we study properties of the cms and develop methods to estimate it these methods include a new class of estimators which requires fewer conditions than phd and which displays a clear advantage when one of the conditions for phd is violated cms also reveals a transparent distinction among the existing methods for dimension reduction ols phd sir and save we apply the new methods to a data set involving recumbent cows

kernel independent component analysis we present a class of algorithms for independent component analysis ica which use contrast functions based on canonical correlations in a reproducing kernel hilbert space on the one hand we show that our contrast functions are related to mutual information and have desirable mathematical properties as measures of statistical dependence on the other hand building on recent developments in kernel methods we show that these criteria and their derivatives can be computed efficiently minimizing these criteria leads to flexible and robust algorithms for ica we illustrate with simulations involving a wide variety of source distributions showing that our algorithms outperform many of the presently known algorithms

sparse estimation of conditional graphical models with application to gene networks in many applications the graph structure in a network arises from two sources intrinsic connections and connections due to external effects we introduce a sparse estimation procedure for graphical models that is capable of isolating the intrinsic connections by removing the external effects technically this is formulated as a conditional graphical model in which the external effects are modeled as predictors and the graph is determined by the conditional precision matrix we introduce two sparse estimators of this matrix using the reproduced kernel hilbert space combined with lasso and adaptive lasso we establish the sparsity variable selection consistency oracle property and the asymptotic distributions of the proposed estimators we also develop their convergence rate when the dimension of the conditional precision matrix goes to infinity the methods are compared with sparse estimators for unconditional graphical models and with the constrained maximum likelihood estimate that assumes a know

construction of lyapunov krasovskii functionals for networks of iiss retarded systems in small gain formulation this paper tackles a problem of verifying stability of retarded dynamical networks in a dissipative formulation subsystems are assumed to be integral input to state stable iiss time delays are allowed to reside in both subsystems and interconnection channels and may be both discrete and distributed no assumption is made on the interconnection topology a small gain methodology is developed for constructing a lyapunov krasovskii functional to establish iiss of such a network

variable selection via additive conditional independence summary we propose a non parametric variable selection method which does not rely on any regression model or predictor distribution the method is based on a new statistical relationship called additive conditional independence that has been introduced recently for graphical models unlike most existing variable selection methods which target the mean of the response the method proposed targets a set of attributes of the response such as its mean variance or entire distribution in addition the additive nature of this approach offers non parametric flexibility without employing multi dimensional kernels as a result it retains high accuracy for high dimensional predictors we establish estimation consistency convergence rate and variable selection consistency of the method proposed through simulation comparisons we demonstrate that the method proposed performs better than existing methods when the predictor affects several attributes of the response and it performs competently in the classical setting where the predictors affect the mean only we apply the new method to a data set concerning how gene expression levels affect the weight of mice

sliced regression for dimension reduction a new dimension reduction method involving slicing the region of the response and applying local kernel regression to each slice is proposed compared with the traditional inverse regression methods e g sliced inverse regression sir the new method is free of the linearity condition and has much better estimation accuracy compared with the direct estimation methods e g mave the new method is much more robust against extreme values and can capture the entire central subspace cs exhaustively to determine the cs dimension a consistent cross validation criterion is developed extensive numerical studies including a real example confirm our theoretical findings

splendid equivalences derived categories and permutation modules we introduce the notion of a splendid equivalence between blocks of finite groups which is a strengthening of the notion of an equivalence of derived categories such an equivalence is always induced by a two sided tilting complex whose terms are summands of permutation modules a feature that is compatible with the belief that these complexes should be related to the adic cohomology of deligne lusztig varities in the case of reductive groups over finite fields we show that a splendid equivalence has good consequences over and above those that follow from a derived equivalence in particular it gives for principal blocks a structural explanation of brou s concept of an isotypy a compatible family of perfect isometries we give several examples including examples of morita equivalences that are splendid in an unexpectedly non trivial way

dimension reduction for non elliptically distributed predictors second order methods summary many classical dimension reduction methods especially those based on inverse conditional moments require the predictors to have elliptical distributions or at least to satisfy a linearity condition such conditions however are too strong for some applications li and dong 2009 introduced the notion of the central solution space and used it to modify first order methods such as sliced inverse regression so that they no longer rely on these conditions in this paper we generalize this idea to second order methods such as sliced average variance estimation and directional regression in doing so we demonstrate that the central solution space is a versatile framework we can use it to modify essentially all inverse conditional moment based methods to relax the distributional assumption on the predictors simulation studies and an application show a substantial improvement of the modified methods over their classical counterparts

delay robustness of nonlinear internet congestion control schemes several nonlinear internet congestion control schemes have been proposed in the previous years based on primal and dual decompositions of convex yet centralized optimization problems that describe the bandwidth allocation problem this design methodology uses sub gradient methods for the design of node link dynamics and guarantees nominal functionality for arbitrary system sizes in this technical note we analyze the robustness of such nonlinear schemes to the presence of multiple non commensurate heterogeneous communication delays

global stability of congestion controllers for the internet we consider a single link accessed by a single source which responds to congestion signals from the network the design of controllers for such sources in the presence of feedback delay has received much attention recently here we present conditions for the global asymptotic stability and semiglobal exponential stability of congestion controllers these conditions are natural extensions of conditions obtained through linearized analysis of such systems our result on exponential stability provides the missing link in the proof of how one obtains a single deterministic congestion control equation from a system with many congestion controlled sources and random disturbances using numerical examples we compare the conditions on the congestion control parameters obtained using local and global stability analysis

the derived categories of some blocks of symmetric groups and a conjecture of broue abstract a well known conjecture of broue in the representation theory of finite groups involves equivalences of derived categories of blocks the aim of this paper is to verify this conjecture for defect 2 blocks of symmetric groups actually we prove for these blocks a refinement of broue s conjecture due to rickard

cooperative enclosing control for multiple moving targets by a group of agents in this paper the enclosing control problem of second order multi agent systems is considered where the targets can be either stationary or moving the objective is to achieve an equidistant circular formation for a group of agents to enclose a team of targets in order to do so we first introduce a formal definition explaining certain basic properties of the exploring relation between the agents and the targets we then construct the estimator of the centre of the targets which is used to build the control protocol to achieve equidistant circular enclosing using a lyapunov function and lasalle s invariance principle the convergency of the estimator and control protocol are respectively established we then construct a smooth function to approximate the discontinuous term in the estimator finally the simulations for stationary targets and moving targets are given to verify the validity of the results obtained

sufficient dimension reduction via inverse regression a family of dimension reduction methods the inverse regression ir family is developed by minimizing a quadratic objective function an optimal member of this family the inverse regression estimator ire is proposed along with inference methods and a computational algorithm the ire has at least three desirable properties 1 its estimated basis of the central dimension reduction subspace is asymptotically efficient 2 its test statistic for dimension has an asymptotic chi squared distribution and 3 it provides a chi squared test of the conditional independence hypothesis that the response is independent of a selected subset of predictors given the remaining predictors current methods like sliced inverse regression belong to a suboptimal class of the ir family comparisons of these methods are reported through simulation studies the approach developed here also allows a relatively straightforward derivation of the asymptotic null distribution of the test statistic for dimension used in slic

graphics for regressions with a binary response abstract central dimension reduction subspaces which characterize the dependence of a response variable on one or more predictors are developed and then used to guide the construction and interpretation of graphics for regression problems with a binary response variable graphical methods requiring neither a link function nor residuals are suggested for both development and criticism of model components implied by the central dimension reduction subspace

a nonparametric graphical model for functional data with application to brain networks based on fmri abstractwe introduce a nonparametric graphical model whose observations on vertices are functions many modern applications such as electroencephalogram and functional magnetic resonance imaging fmri produce data are of this type the model is based on additive conditional independence aci a statistical relation that captures the spirit of conditional independence without resorting to multi dimensional kernels the random functions are assumed to reside in a hilbert space no distributional assumption is imposed on the random functions instead their statistical relations are characterized nonparametrically by a second hilbert space which is a reproducing kernel hilbert space whose kernel is determined by the inner product of the first hilbert space a precision operator is then constructed based on the second space which characterizes aci and hence also the graph the resulting estimator is relatively easy to compute requiring no iterative optimization or inversion of large matrices we estab

on an additive semigraphoid model for statistical networks with application to pathway analysis we introduce a nonparametric method for estimating non gaussian graphical models based on a new statistical relation called additive conditional independence which is a three way relation among random vectors that resembles the logical structure of conditional independence additive conditional independence allows us to use one dimensional kernel regardless of the dimension of the graph which not only avoids the curse of dimensionality but also simplifies computation it also gives rise to a parallel structure to the gaussian graphical model that replaces the precision matrix by an additive precision operator the estimators derived from additive conditional independence cover the recently introduced nonparanormal graphical model as a special case but outperform it when the gaussian copula assumption is violated we compare the new method with existing ones by simulations and in genetic pathway analysis supplementary materials for this article are available online

an estimating equation approach to dimension reduction for longitudinal data sufficient dimension reduction has been extensively explored in the context of independent and identically distributed data in this article we generalize sufficient dimension reduction to longitudinal data and propose an estimating equation approach to estimating the central mean subspace the proposed method accounts for the covariance structure within each subject and improves estimation efficiency when the covariance structure is correctly specified even if the covariance structure is misspecified our estimator remains consistent in addition our method relaxes distributional assumptions on the covariates and is doubly robust to determine the structural dimension of the central mean subspace we propose a bayesian type information criterion we show that the estimated structural dimension is consistent and that the estimated basis directions are root formula see text consistent asymptotically normal and locally efficient simulations and an analysis of the framingham heart study data confirm the effectiveness of our approach

robust global stability to delays of a multi path dual congestion control algorithm abstract global stability has been shown for network congestion control algorithms in the absence of propagation delays by use of the conventional lyapunov function method when heterogeneous delays are taken into account this problem becomes harder and is partly answered until the latest work of papachristodoulou et al where a lyapunov krasovskii functional argument is used to analyze global stability of nonlinear congestion control algorithms but only applicable to the single path case in this paper we develop a new multi path extension to the dual algorithm in the presence of delays by finding a reasonable lyapunov krasovskii functional candidate usually difficult to do in a constructive way we establish a new sufficient condition for robust global stability to delays which includes papachristodoulou s as a special case finally we verify the results through simulations

extending sliced inverse regression sliced inverse regression sir and an associated chi squared test for dimension have been introduced as a method for reducing the dimension of regression problems whose predictor variables are normal in this article the assumptions on the predictor distribution under which the chi squared test was proved to apply are relaxed and the result is extended a general weighted chi squared test that does not require normal regressors for the dimension of a regression is given simulations show that the weighted chi squared test is more reliable than the chi squared test when the regressor distribution digresses from normality significantly and that it compares well with the chi squared test when the regressors are normal

structure adaptive approach for dimension reduction we propose a new method of effective dimension reduction for a multiindex model which is based on iterative improvement of the family of average derivative estimates the procedure is computationally straightforward and does not require any prior information about the structure of the underlying model we show that in the case when the effective dimension m of the index space does not exceed 3 this space can be estimated with the rate n 1 2 under rather mild assumptions on the model

sparse non gaussian component analysis non gaussian component analysis ngca introduced in offered a method for high dimensional data analysis allowing for identifying a low dimensional non gaussian component of the whole distribution in an iterative and structure adaptive way an important step of the ngca procedure is identification of the non gaussian subspace using principle component analysis pca method this article proposes a new approach to ngca called sparse ngca which replaces the pca based procedure with a new the algorithm we refer to as convex projection