on the gaussian approximation of convolutions under multidimensional analogues of s n bernstein s inequality conditions on etudie le taux d approximation de distribution de sommes de vecteurs aleatoires independants par des distributions gaussiennes correspondantes

covariance regularization by thresholding this paper considers regularizing a covariance matrix of p variables estimated from n observations by hard thresholding we show that the thresholded estimate is consistent in the operator norm as long as the true covariance matrix is sparse in a suitable sense the variables are gaussian or sub gaussian and log p n 0 and obtain explicit rates the results are uniform over families of covariance matrices which satisfy a fairly natural notion of sparsity we discuss an intuitive resampling scheme for threshold selection and prove a general cross validation result that justifies this approach we also compare thresholding to other covariance estimators in simulations and on an example from climate data 1 introduction estimation of covariance matrices is important in a number of areas of statistical analysis including dimension reduction by principal component analysis pca classification by linear or quadratic discriminant analysis lda and qda establishing independence and conditional independence relations in the context of graphical models and setting confidence intervals on linear functions of the means of the components in recent years many application areas where these tools are used have been dealing with very high dimensional datasets and sample sizes can be very small relative to dimension examples include genetic data brain imaging spectroscopic imaging climate data and many others it is well known by now that the empirical covariance matrix for samples of size n from a p variate gaussian distribution np p is not a good estimator of the population covariance if p is large many results in random matrix theory illustrate this from the classical mary law 29 to the more recent work of johnstone and his students on the theory of the largest eigenvalues 12 23 30 and associated eigenvectors 24 however with the exception of a method for estimating the covariance spectrum 11 these probabilistic results do not offer alternatives to the sample covariance matrix alternative estimators for large covariance matrices have therefore attracted a lot of attention recently two broad classes of covariance estimators have emerged those that rely on a natural ordering among variables and assume that variables

fuzzy impulsive control for uncertain nonlinear systems with guaranteed cost in this paper a guaranteed cost fuzzy impulsive control gcfic problem is addressed for uncertain continuous time nonlinear systems which can be represented by the takagi sugeno t s fuzzy model with parametric uncertainties based on the t s fuzzy model a novel time varying lyapunov function is initially constructed to derive the existence condition of guaranteed cost fuzzy impulsive controllers which cannot only exponentially stabilize the uncertain fuzzy system but also provide an upper bound on the quadratic cost function then two procedures for designing suboptimal guaranteed cost fuzzy impulsive controllers are given in the sense of minimizing an upper bound of the cost function one casts the controller design into a parameter dependent linear matrix inequality lmi optimization problem and the other casts the controller design into a sequential minimization problem subject to lmi constraints by using the cone complementary linearization ccl algorithm finally an example is presented to illustrate the effectiveness of the proposed method

tests for high dimensional covariance matrices we propose tests for sphericity and identity of high dimensional covariance matrices the tests are nonparametric without assuming a specific parametric distribution for the data they can accommodate situations where the data dimension is much larger than the sample size namely the large p small n situations we demonstrate by both theoretical and empirical studies that the tests have good properties for a wide range of dimensions and sample sizes we applied the proposed test on a microarray dataset on yorkshire gilts and tested for the covariance structure for the expression levels for sets of genes

brief delay dependent robust h control of uncertain linear state delayed systems this paper examines the problems of robust stabilization and robust h control for linear systems with a constant time delay in the state and subject to parameter uncertainty systems with norm bounded parameter uncertainty will be considered and attention is focused on the design of linear memoryless state feedback controllers we develop methods of robust stabilization and robust h control which are dependent on the size of the delay and are based on the solution of linear matrix inequalities the proposed methods can be easily extended to uncertain linear polytopic systems as well as to the case of multiple time delays

to how many simultaneous hypothesis tests can normal student s t or bootstrap calibration be applied in the analysis of microarray data and in some other contemporary statistical problems it is not uncommon to apply hypothesis tests in a highly simultaneous way the number n say of tests used can be much larger than the sample sizes n to which the tests are applied yet we wish to calibrate the tests so that the overall level of the simultaneous test is accurate often the sampling distribution is quite different for each test so there may not be an opportunity to combine data across samples in this setting how large can n be as a function of n before level accuracy becomes poor here we answer this question in cases where the statistic under test is of student s t type we show that if either the normal or student t distribution is used for calibration then the level of the simultaneous test is accurate provided that log n increases at a strictly slower rate than n 1 3 as n diverges on the other hand if bootstrap methods are used for calibration then we may choose log n almost as large as

doubly functional graphical models in high dimensions we consider estimating a functional graphical model from multivariate functional observations in functional data analysis the classical assumption is that each function has been measured over a densely sampled grid however in practice the functions have often been observed with measurement error at a relatively small number of points we propose a class of doubly functional graphical models to capture the evolving conditional dependence relationship among a large number of sparsely or densely sampled functions our approach first implements a nonparametric smoother to perform functional principal components analysis for each curve then estimates a functional covariance matrix and finally computes sparse precision matrices which in turn provide the doubly functional graphical model we derive some novel concentration bounds uniform convergence rates and model selection properties of our estimator for both sparsely and densely sampled functional data in the high dimensional large p small n regime we demonstrate via simulations that the proposed method significantly outperforms possible competitors our proposed method is applied to a brain imaging dataset

enhancing multiple point geostatistical modeling 1 graph theory and pattern adjustment in recent years higher order geostatistical methods have been used for modeling of a wide variety of large scale porous media such as groundwater aquifers and oil reservoirs their popularity stems from their ability to account for qualitative data and the great flexibility that they offer for conditioning the models to hard quantitative data which endow them with the capability for generating realistic realizations of porous formations with very complex channels as well as features that are mainly a barrier to fluid flow one group of such models consists of pattern based methods that use a set of data points for generating stochastic realizations by which the large scale structure and highly connected features are reproduced accurately the cross correlation based simulation ccsim algorithm proposed previously by the authors is a member of this group that has been shown to be capable of simulating multimillion cell models in a matter of a few cpu seconds the method is however sensitive to pattern s specifications such as boundaries and the number of replicates in this paper the original ccsim algorithm is reconsidered and two significant improvements are proposed for accurately reproducing large scale patterns of heterogeneities in porous media first an effective boundary correction method based on the graph theory is presented by which one identifies the optimal cutting path surface for removing the patchiness and discontinuities in the realization of a porous medium next a new pattern adjustment method is proposed that automatically transfers the features in a pattern to one that seamlessly matches the surrounding patterns the original ccsim algorithm is then combined with the two methods and is tested using various complex two and three dimensional examples it should however be emphasized that the methods that we propose in this paper are applicable to other pattern based geostatistical simulation methods

estimating high dimensional directed acyclic graphs with the pc algorithm we consider the pc algorithm spirtes et al 2000 for estimating the skeleton and equivalence class of a very high dimensional directed acyclic graph dag with corresponding gaussian distribution the pc algorithm is computationally feasible and often very fast for sparse problems with many nodes variables and it has the attractive property to automatically achieve high computational efficiency as a function of sparseness of the true underlying dag we prove uniform consistency of the algorithm for very high dimensional sparse dags where the number of nodes is allowed to quickly grow with sample size n as fast as o na for any 0 a the sparseness assumption is rather minimal requiring only that the neighborhoods in the dag are of lower order than sample size n we also demonstrate the pc algorithm for simulated data

lmi characterization of structural and robust stability abstract this paper introduces several stability conditions for a given class of matrices expressed in terms of linear matrix inequalities lmi being thus simply and efficiently computable diagonal and simultaneous stability both characterized by polytopes of matrices are addressed using this approach a method particularly attractive to test a given matrix for d stability is proposed lyapunov parameter dependent functions are built in order to reduce conservativeness of the stability conditions the key idea is to relate hurwitz stability with a positive realness condition

testing a single regression coefficient in high dimensional linear models abstract in linear regression models with high dimensional data the classical z test or t test for testing the significance of each single regression coefficient is no longer applicable this is mainly because the number of covariates exceeds the sample size in this paper we propose a simple and novel alternative by introducing the correlated predictors screening cps method to control for predictors that are highly correlated with the target covariate accordingly the classical ordinary least squares approach can be employed to estimate the regression coefficient associated with the target covariate in addition we demonstrate that the resulting estimator is consistent and asymptotically normal even if the random errors are heteroscedastic this enables us to apply the z test to assess the significance of each covariate based on the p value obtained from testing the significance of each covariate we further conduct multiple hypothesis testing by controlling the false discovery rate at the nominal level then we show that the multiple hypothesis testing achieves consistent model selection simulation studies and empirical examples are presented to illustrate the finite sample performance and the usefulness of the proposed method respectively

type i error robustness of anova and anova on ranks when the number of treatments is large summary agricultural screening trials often involve a large number t of treatments in a complete block design with limited replication b 3 or 4 blocks the null hypothesis of interest is that of no differences between treatments for the commonly used analysis of variance anova procedure most texts do not discuss agreement between actual and nominal type i error rates in the presence of nonnormality in this small b large t situation similarly for the friedman and the increasingly popular anova on ranks procedures it is not easy to find results concerning null performance given b small and t large in this article we therefore present results from two different bodies of theory that provide useful insight concerning null performance of these anova and rank procedures when t is large the two types of theory are i the classical approach based on moment approximations to the permutation distribution and ii central limit theory based asymptotics in the nonstandard t x situation both approaches demonstrate the validity of standard anova and of anova on within block ranks under nonnormality when t is large choice of the procedure to be used on a given data set should therefore be based on consideration of power properties in general anova on ranks will be superior to standard anova for data with frequent extreme values

partition based ultrahigh dimensional variable screening traditional variable selection methods are compromised by overlooking useful information on covariates with similar functionality or spatial proximity and by treating each covariate independently leveraging prior grouping information on covariates we propose partition based screening methods for ultrahigh dimensional variables in the framework of generalized linear models we show that partition based screening exhibits the sure screening property with a vanishing false selection rate and we propose a data driven partition screening framework with unavailable or unreliable prior knowledge on covariate grouping and investigate its theoretical properties we consider two special cases correlation guided partitioning and spatial location guided partitioning in the absence of a single partition we propose a theoretically justified strategy for combining statistics from various partitioning methods the utility of the proposed methods is demonstrated via simulation and analysis of functional neuroimaging data

lmi characterization of structural and robust stability the discrete time case abstract this paper extends to the discrete time case some robust stability conditions recently obtained for continuous time systems those conditions are expressed in terms of linear matrix inequalities lmi being thus simply and efficiently computable as in the continuous time case parameter dependent lyapunov functions can be constructed and consequently the new approach can yield much sharper and less conservative results than the simultaneous stability approach in particular well known stability problems namely d stability and robust stability in the presence of diagonally structured uncertainty can be more efficiently addressed numerical examples are included to illustrate the advantages of the new stability conditions

on delay dependent stability under model transformations of some neutral linear systems this paper focuses on the stability analysis of a class of neutral linear systems some sufficient delay dependent stability conditions are derived in terms of an appropriate model transformation of the original system transformation similar to the one used in the retarded case the analysis makes use of an appropriate construction of a degenerate lyapunov krasovskii functional several computational schemes and frequency domain interpretations as well as an example are also presented

quadratic stabilization of continuous time systems with state delay and norm bounded time varying uncertainties this paper develops a method for designing a feedback control law to stabilize a class of uncertain linear systems the class of systems under consideration is described by a continuous time model with variable state delay and depends on time varying unknown but bounded uncertain parameters it is shown that the construction of the stabilizing controller involves solving a certain algebraic riccati equation several previous results are derived as interesting special cases finally a simulation example is presented to illustrate the analytical developments

strong control conservative point estimation and simultaneous conservative consistency of false discovery rates a unified approach summary the false discovery rate fdr is a multiple hypothesis testing quantity that describes the expected proportion of false positive results among all rejected null hypotheses benjamini and hochberg introduced this quantity and proved that a particular step up p value method controls the fdr storey introduced a point estimate of the fdr for fixed significance regions the former approach conservatively controls the fdr at a fixed predetermined level and the latter provides a conservatively biased estimate of the fdr for a fixed predetermined significance region in this work we show in both finite sample and asymptotic settings that the goals of the two approaches are essentially equivalent in particular the fdr point estimates can be used to define valid fdr controlling procedures in the asymptotic setting we also show that the point estimates can be used to estimate the fdr conservatively over all significance regions simultaneously which is equivalent to controlling the fdr at all levels simultaneously the main tool that we use is to translate existing fdr methods into procedures involving empirical processes this simplifies finite sample proofs provides a framework for asymptotic results and proves that these procedures are valid even under certain forms of dependence

operator norm consistent estimation of large dimensional sparse covariance matrices estimating covariance matrices is a problem of fundamental importance in multivariate statistics in practice it is increasingly frequent to work with data matrices x of dimension n x p where p and n are both large results from random matrix theory show very clearly that in this setting standard estimators like the sample covariance matrix perform in general very poorly in this large n large p setting it is sometimes the case that practitioners are willing to assume that many elements of the population covariance matrix are equal to 0 and hence this matrix is sparse we develop an estimator to handle this situation the estimator is shown to be consistent in operator norm when for instance we have p n as n oo in other words the largest singular value of the difference between the estimator and the population covariance matrix goes to zero this implies consistency of all the eigenvalues and consistency of eigenspaces associated to isolated eigenvalues we also propose a notion of sparsity for matrices that is compatible with spectral analysis and is independent of the ordering of the variables

joint testing and false discovery rate control in high dimensional multivariate regression multivariate regression with high dimensional covariates has many applications in genomic and genetic research in which some covariates are expected to be associated with multiple responses this paper considers joint testing for regression coefficients over multiple responses and develops simultaneous testing methods with false discovery rate control the test statistic is based on inverse regression and bias corrected group lasso estimates of the regression coefficients and is shown to have an asymptotic chi squared null distribution a row wise multiple testing procedure is developed to identify the covariates associated with the responses the procedure is shown to control the false discovery proportion and false discovery rate at a prespecified level asymptotically simulations demonstrate the gain in power relative to entrywise testing in detecting the covariates associated with the responses the test is applied to an ovarian cancer dataset to identify the microrna regulators that regulate protein expression

testing differential networks with applications to the detection of gene gene interactions model organisms and human studies have led to increasing empirical evidence that interactions among genes contribute broadly to genetic variation of complex traits in the presence of gene by gene interactions the dimensionality of the feature space becomes extremely high relative to the sample size this imposes a significant methodological challenge in identifying gene by gene interactions in the present paper through a gaussian graphical model framework we translate the problem of identifying gene by gene interactions associated with a binary trait d into an inference problem on the difference of two high dimensional precision matrices which summarize the conditional dependence network structures of the genes we propose a procedure for testing the differential network globally that is particularly powerful against sparse alternatives in addition a multiple testing procedure with false discovery rate control is developed to infer the specific structure of the differential network theoretical justification is provided to ensure the validity of the proposed tests and optimality results are derived under sparsity assumptions a simulation study demonstrates that the proposed tests maintain the desired error rates under the null and have good power under the alternative the methods are applied to a breast cancer gene expression study

regularized estimation of large covariance matrices this paper considers estimating a covariance matrix of p variables from n observations by either banding the sample covariance matrix or estimating a banded version of the inverse of the covariance we show that these estimates are consistent in the operator norm as long as logp 2 n 0 and obtain explicit rates the results are uniform over some fairly natural well conditioned families of covariance matrices we also introduce an analogue of the gaussian white noise model and show that if the population covariance is embeddable in that model and well conditioned then the banded approximations produce consistent estimates of the eigenvalues and associated eigenvectors of the covariance matrix the results can be extended to smooth versions of banding and to non gaussian distributions with su ciently short tails a resampling approach is proposed for choosing the banding parameter in practice this approach is illustrated numerically on both simulated and real data

generalized fiducial inference for ultrahigh dimensional regression in recent years the ultrahigh dimensional linear regression problem has attracted enormous attention from the research community under the sparsity assumption most of the published work is devoted to the selection and estimation of the predictor variables with nonzero coefficients this article studies a different but fundamentally important aspect of this problem uncertainty quantification for parameter estimates and model choices to be more specific this article proposes methods for deriving a probability density function on the set of all possible models and also for constructing confidence intervals for the corresponding parameters these proposed methods are developed using the generalized fiducial methodology which is a variant of fisher s controversial fiducial idea theoretical properties of the proposed methods are studied and in particular it is shown that statistical inference based on the proposed methods will have correct asymptotic frequentist property in terms of empirical perform

extended bayesian information criteria for model selection with large model spaces summary the ordinary bayesian information criterion is too liberal for model selection when the model space is large in this paper we re examine the bayesian paradigm for model selection and propose an extended family of bayesian information criteria which take into account both the number of unknown parameters and the complexity of the model space their consistency is established in particular allowing the number of covariates to increase to infinity with the sample size their performance in various situations is evaluated by simulation studies it is demonstrated that the extended bayesian information criteria incur a small loss in the positive selection rate but tightly control the false discovery rate a desirable property in many applications the extended bayesian information criteria are extremely useful for variable selection in problems with a moderate sample size but with a huge number of covariates especially in genome wide association studies which are now an active area in genetics research

confidence regions for entries of a large precision matrix we consider the statistical inference for high dimensional precision matrices specifically we propose a data driven procedure for constructing a class of simultaneous confidence regions for a subset of the entries of a large precision matrix the confidence regions can be applied to test for specific structures of a precision matrix and to recover its nonzero components we first construct an estimator for the precision matrix via penalized node wise regression we then develop the gaussian approximation to approximate the distribution of the maximum difference between the estimated and the true precision coefficients a computationally feasible parametric bootstrap algorithm is developed to implement the proposed procedure the theoretical justification is established under the setting which allows temporal dependence among observations therefore the proposed procedure is applicable to both independent and identically distributed data and time series data numerical results with both simulated and real data confirm the good performance of the proposed method

marginal asymptotics for the large p small n paradigm with applications to microarray data the large p small n paradigm arises in microarray studies image analysis high throughput molecular screening astronomy and in many other high dimensional applications false discovery rate fdr methods are useful for resolving the accompanying multiple testing problems in cdna microarray studies for example p values may be computed for each of p genes using data from n arrays where typically p is in the thousands and n is less than 30 for fdr methods to be valid in identifying differentially expressed genes the p values for the nondifferentially expressed genes must simultaneously have uniform distributions marginally while feasible for permutation p values this uniformity is problematic for asymptotic based p values since the number of p values involved goes to infinity and intuition suggests that at least some of the p values should behave erratically we examine this neglected issue when n is moderately large but p is almost exponentially large relative to n we show the somewhat surprising result that under very general dependence structures and for both mean and median tests the p values are simultaneously valid a small simulation study and data analysis are used for illustration

high dimensional variable selection via tilting the paper considers variable selection in linear regression models where the number of covariates is possibly much larger than the number of observations high dimensionality of the data brings in many complications such as possibly spurious high correlations between the variables which result in marginal correlation being unreliable as a measure of association between the variables and the response we propose a new way of measuring the contribution of each variable to the response which takes into account high correlations between the variables in a data driven way the proposed tilting procedure provides an adaptive choice between the use of marginal correlation and tilted correlation for each variable where the choice is made depending on the values of the hard thresholded sample correlation of the design matrix we study the conditions under which this measure can successfully discriminate between the relevant and the irrelevant variables and thus be used as a tool for variable selection finally an iterative variable screening algorithm is constructed to exploit the theoretical properties of tilted correlation and its good practical performance is demonstrated in a comparative simulation study

tests for high dimensional regression coefficients with factorial designs we propose simultaneous tests for coefficients in high dimensional linear regression models with factorial designs the proposed tests are designed for the large p small n situations where the conventional f test is no longer applicable we derive the asymptotic distribution of the proposed test statistic under the high dimensional null hypothesis and various scenarios of the alternatives which allow power evaluations we also evaluate the power of the f test for models of moderate dimension the proposed tests are employed to analyze a microarray data on yorkshire gilts to find significant gene ontology terms which are significantly associated with the thyroid hormone after accounting for the designs of the experiment

super resolution reconstruction of μ ct image of rock sample using neighbour embedding algorithm abstract x ray computed tomography ct is considered to be the most effective way to obtain the inner structure of rock sample without destructions however its limited resolution hampers its ability to probe sub micro structures which is critical for flow transportation of rock sample in this study we propose an innovative methodology to improve the resolution of ct image using neighbour embedding algorithm where low frequency information is provided by ct image itself while high frequency information is supplemented by high resolution scanning electron microscopy sem image in order to obtain prior for reconstruction a large number of image patch pairs contain high and low image patches are extracted from the gaussian image pyramid generated by sem image these image patch pairs contain abundant information about tomographic evolution of local porous structures under different resolution spaces relying on the assumption of self similarity of porous structure this prior information can be used to supervise the reconstruction of high resolution ct image effectively the experimental results show that the proposed method is able to achieve the state of the art performance

asymptotics for analysis of variance when the number of levels is large abstract we study asymptotic results for f tests in analysis of variance models as the number of factor levels goes to but the number of observations for each factor combination is fixed asymptotic derivations of the type discussed in this article would be relevant whenever both the numerator and denominator degrees of freedom go to at the same rate we consider null and alternative distributions of f the usual f statistic for fixed effects and random effects balanced and unbalanced one way and two way and normal and nonnormal analysis of variance anova models the results may be most relevant for random effects and mixed models for example we may have an agricultural experiment in which the number of cows is quite large but the number of measurements on each cow is small the results would also be relevant for fixed effects models in which there are many factor levels but not many observations for each factor level

testing independence with high dimensional correlated samples testing independence among a number of ultra high dimensional random samples is a fundamental and challenging problem by arranging n identically distributed p dimensional random vectors into a p times n data matrix we investigate the problem of testing independence among columns under the matrix variate normal modeling of data we propose a computationally simple and tuning free test statistic characterize its limiting null distribution analyze the statistical power and prove its minimax optimality as an important by product of the test statistic a ratio consistent estimator for the quadratic functional of a covariance matrix from correlated samples is developed we further study the effect of correlation among samples to an important high dimensional inference problem large scale multiple testing of pearson s correlation coefficients indeed blindly using classical inference results based on the assumed independence of samples will lead to many false discoveries which suggests the need for conducting independence testing before applying existing methods to address the challenge arising from correlation among samples we propose a sandwich estimator of pearson s correlation coefficient by de correlating the samples based on this approach the resulting multiple testing procedure asymptotically controls the overall false discovery rate at the nominal level while maintaining good statistical power both simulated and real data experiments are carried out to demonstrate the advantages of the proposed methods

robust estimation for neural networks with randomly occurring distributed delays and markovian jump coupling this paper studies the issue of robust state estimation for coupled neural networks with parameter uncertainty and randomly occurring distributed delays where the polytopic model is employed to describe the parameter uncertainty a set of bernoulli processes with different stochastic properties are introduced to model the randomly occurrences of the distributed delays novel state estimators based on the local coupling structure are proposed to make full use of the coupling information the augmented estimation error system is obtained based on the kronecker product a new lyapunov function which depends both on the polytopic uncertainty and the coupling information is introduced to reduce the conservatism sufficient conditions which guarantee the stochastic stability and the l 2 l infty performance of the augmented estimation error system are established then the estimator gains are further obtained on the basis of these conditions finally a numerical example is used to prove the effectiveness of the results

high dimensional ordinary least squares projection for screening variables variable selection is a challenging issue in statistical applications when the number of predictors p far exceeds the number of observations n in this ultra high dimensional setting the sure independence screening sis procedure was introduced to significantly reduce the dimensionality by preserving the true model with overwhelming probability before a refined second stage analysis however the aforementioned sure screening property strongly relies on the assumption that the important variables in the model have large marginal correlations with the response which rarely holds in reality to overcome this we propose a novel and simple screening technique called the high dimensional ordinary least squares projection holp we show that holp possesses the sure screening property and gives consistent variable selection without the strong correlation assumption and has a low computational complexity a ridge type holp procedure is also discussed simulation study shows that holp performs competitively compared to many other marginal correlation based methods an application to a mammalian eye disease data illustrates the attractiveness of holp

blessing of massive scale spatial graphical model estimation with a total cardinality constraint approach we consider the problem of estimating high dimensional spatial graphical models with a total cardinality constraint i e the ell 0 constraint though this problem is highly nonconvex we show that its primal dual gap diminishes linearly with the dimensionality and provide a convex geometry justification of this blessing of massive scale phenomenon motivated by this result we propose an efficient algorithm to solve the dual problem which is concave and prove that the solution achieves optimal statistical properties extensive numerical results are also provided

innovated scalable efficient estimation in ultra large gaussian graphical models large scale precision matrix estimation is of fundamental importance yet challenging in many contemporary applications for recovering gaussian graphical models in this paper we suggest a new approach of innovated scalable efficient estimation isee for estimating large precision matrix motivated by the innovated transformation we convert the original problem into that of large covariance matrix estimation the suggested method combines the strengths of recent advances in high dimensional sparse modeling and large covariance matrix estimation compared to existing approaches our method is scalable and can deal with much larger precision matrices with simple tuning under mild regularity conditions we establish that this procedure can recover the underlying graphical structure with significant probability and provide efficient estimation of link strengths both computational and theoretical advantages of the procedure are evidenced through simulation and real data examples

systematic sampling with errors in sample locations systematic sampling of points in continuous space is widely used in microscopy and spatial surveys classical theory provides asymptotic expressions for the variance of estimators based on systematic sampling as the grid spacing decreases however the classical theory assumes that the sample grid is exactly periodic real physical sampling procedures may introduce errors in the placement of the sample points this paper studies the effect of errors in sample positioning on the variance of estimators in the case of one dimensional systematic sampling first we sketch a general approach to variance analysis using point process methods we then analyze three different models for the error process calculate exact expressions for the variances and derive asymptotic variances errors in the placement of sample points can lead to substantial inflation of the variance dampening of zitterbewegung that is fluctuation effects and a slower order of convergence this suggests that the current practice in some areas of microscopy may be based on over optimistic predictions of estimator accuracy

high dimensional semiparametric gaussian copula graphical models ing the spearman s rho and kendall s tau we prove that the nonparanormal skeptic achieves the optimal parametric rates of convergence for both graph recovery and parameter estimation this result suggests that the nonparanormal graphical models can be used as a safe replacement of the popular gaussian graphical models even when the data are truly gaussian besides theoretical analysis we also conduct thorough numerical simulations to compare the graph recovery performance of dierent estimators under both ideal and noisy settings the proposed methods are then applied on a largescale genomic dataset to illustrate their empirical usefulness the r package huge implementing the proposed methods is available on the comprehensive r archive network http cran r project org

a high dimensional nonparametric multivariate test for mean vector this work is concerned with testing the population mean vector of nonnormal high dimensional multivariate data several tests for high dimensional mean vector based on modifying the classical hotelling t2 test have been proposed in the literature despite their usefulness they tend to have unsatisfactory power performance for heavy tailed multivariate data which frequently arise in genomics and quantitative finance this article proposes a novel high dimensional nonparametric test for the population mean vector for a general class of multivariate distributions with the aid of new tools in modern probability theory we proved that the limiting null distribution of the proposed test is normal under mild conditions when p is substantially larger than n we further study the local power of the proposed test and compare its relative efficiency with a modified hotelling t2 test for high dimensional data an interesting finding is that the newly proposed test can have even more substantial power gain with l

robust controller design for uncertain systems with time delays lmi approach we present a robust output feedback controller design method for linear systems with norm bounded time varying parameter uncertainties and time varying delays in both states and controls and sufficient conditions for the existence of the robust output feedback controller of any order are given in terms of three linear matrix inequalities lmis furthermore we provide a parameterization of all robust controllers from the positive definite solutions of the lmis

factor profiled sure independence screening we propose a method of factor profiled sure independence screening for ultrahigh dimensional variable selection the objective of this method is to identify nonzero components consistently from a sparse coefficient vector the new method assumes that the correlation structure of the high dimensional data can be well represented by a set of low dimensional latent factors which can be estimated consistently by eigenvalue eigenvector decomposition the estimated latent factors should then be profiled out from both the response and the predictors such an operation referred to as factor profiling produces uncorrelated predictors therefore sure independence screening can be applied subsequently and the resulting screening result is consistent for model selection a major advantage that standard sure independence screening does not share we refer to the new method as factor profiled sure independence screening numerical studies confirm its outstanding performance copyright 2012 oxford university press

tests alternative to higher criticism for high dimensional means under sparsity and column wise dependence we consider two alternative tests to the higher criticism test of donoho and jin ann statist 32 2004 962 994 for high dimensional means under the sparsity of the nonzero means for sub gaussian distributed data with unknown column wise dependence the two alternative test statistics are constructed by first thresholding l 1 and l 2 statistics based on the sample means respectively followed by maximizing over a range of thresholding levels to make the tests adaptive to the unknown signal strength and sparsity the two alternative tests can attain the same detection boundary of the higher criticism test in ann statist 32 2004 962 994 which was established for uncorrelated gaussian data it is demonstrated that the maximal l 2 thresholding test is at least as powerful as the maximal l 1 thresholding test and both the maximal l 2 and l 1 thresholding tests are at least as powerful as the higher criticism test

improved lmi representations for the analysis and the design of continuous time systems with polytopic type uncertainty simple modifications to the representation of the bounded real lemma brl in the linear continuous time invariant case are introduced these modifications reduce the overdesign that occurs in the analysis and the design of systems with polytopic type uncertainties a different lyapunov function accompanies each of the vertices of the uncertainty polytope thus eliminating the need for quadratic stability or stabilizability the advantages of these new representations are demonstrated by way of two examples

variable screening via quantile partial correlation abstractin quantile linear regression with ultrahigh dimensional data we propose an algorithm for screening all candidate variables and subsequently selecting relevant predictors specifically we first employ quantile partial correlation for screening and then we apply the extended bayesian information criterion ebic for best subset selection our proposed method can successfully select predictors when the variables are highly correlated and it can also identify variables that make a contribution to the conditional quantiles but are marginally uncorrelated or weakly correlated with the response theoretical results show that the proposed algorithm can yield the sure screening set by controlling the false selection rate model selection consistency can be achieved theoretically in practice we proposed using ebic for best subset selection so that the resulting model is screening consistent simulation studies demonstrate that the proposed algorithm performs well and an empirical example is present

rocket robust confidence intervals via kendall s tau for transelliptical graphical models understanding complex relationships between random variables is of fundamental importance in high dimensional statistics with numerous applications in biological and social sciences undirected graphical models are often used to represent dependencies between random variables where an edge between two random variables is drawn if they are conditionally dependent given all the other measured variables a large body of literature exists on methods that estimate the structure of an undirected graphical model however little is known about the distributional properties of the estimators beyond the gaussian setting in this paper we focus on inference for edge parameters in a high dimensional transelliptical model which generalizes gaussian and nonparanormal graphical models we propose rocket a novel procedure for estimating parameters in the latent inverse covariance matrix we establish asymptotic normality of rocket in an ultra high dimensional setting under mild assumptions without relying on oracle model selection results rocket requires the same number of samples that are known to be necessary for obtaining a sqrt n consistent estimator of an element in the precision matrix under a gaussian model hence it is an optimal estimator under a much larger family of distributions the result hinges on a tight control of the sparse spectral norm of the nonparametric kendall s tau estimator of the correlation matrix which is of independent interest empirically rocket outperforms the nonparanormal and gaussian models in terms of achieving accurate inference on simulated data we also compare the three methods on real data daily stock returns and find that the rocket estimator is the only method whose behavior across subsamples agrees with the distribution predicted by the theory

structural similarity and difference testing on multiple sparse gaussian graphical models we present a new framework on inferring structural similarities and differences among multiple high dimensional gaussian graphical models ggms corresponding to the same set of variables under distinct experimental conditions the new framework adopts the partial correlation coefficients to characterize the potential changes of dependency strengths between two variables a hierarchical method has been further developed to recover edges with different or similar dependency strengths across multiple ggms in particular we first construct two sample test statistics for testing the equality of partial correlation coefficients and conduct large scale multiple tests to estimate the substructure of differential dependencies after removing differential substructure from original ggms a follow up multiple testing procedure is used to detect the substructure of similar dependencies among ggms in each step false discovery rate is controlled asymptotically at a desired level power results are proved which demonstrate that our method is more powerful on finding common edges than the common approach that separately estimates ggms the performance of the proposed hierarchical method is illustrated on simulated datasets

multiple testing of submatrices of a precision matrix with applications to identification of between pathway interactions abstractmaking accurate inference for gene regulatory networks including inferring about pathway by pathway interactions is an important and difficult task motivated by such genomic applications we consider multiple testing for conditional dependence between subgroups of variables under a gaussian graphical model framework the problem is translated into simultaneous testing for a collection of submatrices of a high dimensional precision matrix with each submatrix summarizing the dependence structure between two subgroups of variables a novel multiple testing procedure is proposed and both theoretical and numerical properties of the procedure are investigated asymptotic null distribution of the test statistic for an individual hypothesis is established and the proposed multiple testing procedure is shown to asymptotically control the false discovery rate fdr and false discovery proportion fdp at the prespecified level under regularity conditions simulations show that the procedure works well in

a two way semilinear model for normalization and analysis of cdna microarray data a basic question in analyzing cdna microarray data is normalization the purpose of which is to remove systematic bias in the observed expression values by establishing a normalization curve across the whole dynamic range a proper normalization procedure ensures that the normalized intensity ratios provide meaningful measures of relative expression levels we propose a two way semilinear model tw slm for normalization and analysis of microarray data this method does not make the usual assumptions underlying some of the existing methods for example it does not assume that the percentage of differentially expressed genes is small or that there is symmetry in the expression levels of up regulated and down regulated genes as required in the lowess normalization method the tw slm also naturally incorporates uncertainty due to normalization into significance analysis of microarrays we use a semiparametric approach based on polynomial splines in the tw slm to estimate the normalization curves and the no

one step sparse estimates in nonconcave penalized likelihood models fan and li propose a family of variable selection methods via penalized likelihood using concave penalty functions the nonconcave penalized likelihood estimators enjoy the oracle properties but maximizing the penalized likelihood function is computationally challenging because the objective function is nondifferentiable and nonconcave in this article we propose a new unified algorithm based on the local linear approximation lla for maximizing the penalized likelihood for a broad class of concave penalty functions convergence and other theoretical properties of the lla algorithm are established a distinguished feature of the lla algorithm is that at each lla step the lla estimator can naturally adopt a sparse representation thus we suggest using the one step lla estimator from the lla algorithm as the final estimates statistically we show that if the regularization parameter is appropriately chosen the one step lla estimates enjoy the oracle properties with good initial estimators computationally the one step lla estimation methods dramatically reduce the computational cost in maximizing the nonconcave penalized likelihood we conduct some monte carlo simulation to assess the finite sample performance of the one step sparse estimation methods the results are very encouraging

on designing of sliding mode control for stochastic jump systems in this note we consider the problems of stochastic stability and sliding mode control for a class of linear continuous time systems with stochastic jumps in which the jumping parameters are modeled as a continuous time discrete state homogeneous markov process with right continuous trajectories taking values in a finite set by using linear matrix inequalities lmis approach sufficient conditions are proposed to guarantee the stochastic stability of the underlying system then a reaching motion controller is designed such that the resulting closed loop system can be driven onto the desired sliding surface in a limited time it has been shown that the sliding mode control problem for the markovian jump systems is solvable if a set of coupled lmis have solutions a numerical example is given to show the potential of the proposed techniques

chord distribution functions of three dimensional random media approximate first passage times of gaussian processes the main result of this paper is a semianalytic approximation for the chord distribution functions of three dimensional models of microstructure derived from gaussian random fields in the simplest case the chord functions are equivalent to a standard first passage time problem i e the probability density governing the time taken by a gaussian random process to first exceed a threshold we obtain an approximation based on the assumption that successive chords are independent the result is a generalization of the independent interval approximation recently used to determine the exponent of persistence time decay in coarsening the approximation is easily extended to more general models based on the intersection and union sets of models generated from the isosurfaces of random fields the chord distribution functions play an important role in the characterization of random composite and porous materials our results are compared with experimental data obtained from a three dimensional image of a porous fontainebleau sandstone and a two dimensional image of a tungsten silver composite alloy

asymptotic behavior of m estimators of p regression parameters when p 2 n is large ii normal approximation in a general linear model y x beta r with y and r n dimensional x a n times p matrix and beta p dimensional let hat beta be an m estimator of beta satisfying 0 sum x i psi y i x i beta let p rightarrow infty such that p log n 3 2 n rightarrow 0 then max i x i hat beta beta rightarrow p 0 and it is possible to find a uniform normal approximation for the distribution of hat beta under which arbitrary linear combinations a n hat beta beta are asymptotically normal when appropriately normalized and hat beta beta x x hat beta beta is approximately chi 2 p

forward regression for ultra high dimensional variable screening motivated by the seminal theory of sure independence screening fan and lv 2008 sis we investigate here another popular and classical variable screening method namely forward regression fr our theoretical analysis reveals that fr can identify all relevant predictors consistently even if the predictor dimension is substantially larger than the sample size in particular if the dimension of the true model is finite fr can discover all relevant predictors within a finite number of steps to practically select the best candidate from the models generated by fr the recently proposed bic criterion of chen and chen 2008 can be used the resulting model can then serve as an excellent starting point from where many existing variable selection methods e g scad and adaptive lasso can be applied directly fr s outstanding finite sample performances are confirmed by extensive numerical studies

robust control of state delayed systems with polytopic type uncertainties via parameter dependent lyapunov functionals abstract this paper considers the problem of robust stability and robust stabilization for linear systems with a constant time delay in the state and subject to real convex polytopic uncertainty first of all for robust stability problem we exploit new matrix inequalities characterization of delay dependent quadratic stability results demonstrate that it allows the use of parameter dependent lyapunov functionals and develop control design methods based on linear matrix inequalities lmis for solving the robust control problem next the problem of determining the maximum time delay under which the system remains stable is cast into a generalized eigenvalue problem and thus solved by lmi techniques finally illustrative examples are given to demonstrate the advantage of these new representations

a constrained l1 minimization approach to sparse precision matrix estimation this article proposes a constrained l1 minimization method for estimating a sparse inverse covariance matrix based on a sample of n iid p variate random variables the resulting estimator is shown to have a number of desirable properties in particular the rate of convergence between the estimator and the true s sparse precision matrix under the spectral norm is when the population distribution has either exponential type tails or polynomial type tails we present convergence rates under the elementwise l norm and frobenius norm in addition we consider graphical model selection the procedure is easily implemented by linear programming numerical performance of the estimator is investigated using both simulated and real data in particular the procedure is applied to analyze a breast cancer dataset and is found to perform favorably compared with existing methods

pore space reconstruction of vuggy carbonates using microtomography and multiple point statistics 1 to reconstruct complex porous media such as carbonates we propose a two step approach to combine different types of images microtomography at the resolution of a few microns to resolve large pores and vugs with statistically reconstructed high resolution images for smaller features two dimensional 2 d thin sections provide multiple point statistics which describe the statistical relation between multiple spatial locations that can be used to generate 3 d images with accurate connectivity these statistical reconstructions are combined with images directly measured by microtomography the integrated method is tested on carbonates for which 3 d images of disconnected vugs are captured while 2 d thin sections characterize the small scale structure the integrated images have permeabilities computed using the lattice boltzmann method that are similar to laboratory measured values

box type approximations in nonparametric factorial designs abstract linear rank statistics in nonparametric factorial designs are asymptotically normal and in general heteroscedastic in a comprehensive simulation study the asymptotic chi squared law of the corresponding quadratic forms is shown to be a rather poor approximation of the finite sample distribution motivated by this problem we propose simple finite sample size approximations for the distribution of quadratic forms in factorial designs under a normal heteroscedastic error structure these approximations are based on an f distribution with estimated degrees of freedom that generalizes ideas of patnaik and box simulation studies show that the nominal level is maintained with high accuracy and in most cases the power is comparable to the asymptotic maximin wald test data driven guidelines are given to select the most appropriate test procedure these ideas are finally transferred to nonparametric factorial designs where the same quadratic forms as in the parametric case are applied to the vector

feature screening via distance correlation learning this article is concerned with screening features in ultrahigh dimensional data analysis which has become increasingly important in diverse scientific fields we develop a sure independence screening procedure based on the distance correlation dc sis the dc sis can be implemented as easily as the sure independence screening sis procedure based on the pearson correlation proposed by fan and lv however the dc sis can significantly improve the sis fan and lv established the sure screening property for the sis based on linear models but the sure screening property is valid for the dc sis under more general settings including linear models furthermore the implementation of the dc sis does not require model specification e g linear model or generalized linear model for responses or predictors this is a very appealing property in ultrahigh dimensional data analysis moreover the dc sis can be used directly to screen grouped predictor variables and multivariate response variables we establish

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 new robust d stability condition for real convex polytopic uncertainty abstract the problem of robust d stability analysis with respect to real convex polytopic uncertainties is tackled a new lmi based sufficient condition for the existence of parameter dependent lyapunov functions is proposed this condition generalises previously published conditions numerical comparisons with quadratic stability results as well as previous results based on parameter dependent lyapunov functions illustrate the relevance of this new condition finally this result appears to be promising for robust multi objective performance analysis and control synthesis purposes

prediction of permeability for porous media reconstructed using multiple point statistics to predict multiphase flow through geologically realistic porous media it is necessary to have a three dimensional 3d representation of the pore space we use multiple point statistics based on two dimensional 2d thin sections as training images to generate geologically realistic 3d pore space representations thin section images can provide multiple point statistics which describe the statistical relation between multiple spatial locations and use the probability of occurrence of particular patterns assuming that the medium is isotropic a 3d image can be generated that preserves typical patterns of the void space seen in the thin sections the method is tested on berea sandstone for which a 3d image from micro ct computerized tomography scanning is available and shows that the use of multiple point statistics allows the long range connectivity of the structure to be preserved in contrast to two point statistics methods that tend to underestimate the connectivity furthermore a high resolution 2d thin section image of a carbonate reservoir rock is used to reconstruct 3d structures by the proposed method the permeabilities of the statistical images are computed using the lattice boltzmann method lbm the results are similar to the measured values to the permeability directly computed on the micro ct image for berea and to predictions using analysis of the 2d images and the effective medium approximation

a direct approach to false discovery rates summary multiple hypothesis testing involves guarding against much more complicated errors than single hypothesis testing whereas we typically control the type i error rate for a single hypothesis test a compound error rate is controlled for multiple hypothesis tests for example controlling the false discovery rate fdr traditionally involves intricate sequential p value rejection methods based on the observed data whereas a sequential p value method fixes the error rate and estimates its corresponding rejection region we propose the opposite approach we fix the rejection region and then estimate its corresponding error rate this new approach offers increased applicability accuracy and power we apply the methodology to both the positive false discovery rate pfdr and fdr and provide evidence for its benefits it is shown that pfdr is probably the quantity of interest over fdr also discussed is the calculation of the q value the pfdr analogue of the p value which eliminates the need to set the error rate beforehand as is traditionally done some simple numerical examples are presented that show that this new approach can yield an increase of over eight times in power compared with the benjamini hochberg fdr method

a new discrete time robust stability condition a new robust stability condition for uncertain discrete time systems with convex polytopic uncertainty is given it enables to check stability using parameter dependent lyapunov functions which are derived from lmi conditions it is shown that this new condition provides better results than the classical quadratic stability besides the use of a parameter dependent lyapunov function this condition exhibits a kind of decoupling between the lyapunov and the system matrices which may be explored for control synthesis purposes a numerical example illustrates the results

synchronization of fuzzy bidirectional associative memory neural networks with various time delays the problem of synchronization for fuzzy bidirectional associative memory bam neural networks nns with various time delays is formulated and investigated the various delays consist of discrete delays unbounded distributed delays and constant delay in the leakage term i e leakage delay are considered then some sufficient conditions are presented to guarantee the global asymptotic stability of the error dynamical system by using lyapunov krasovskii functional and linear matrix inequality lmi method as a result we achieved synchronization of master slave drive response fuzzy bam nns systems even if there is no leakage delay the obtained results are less restrictive to some known sufficient conditions moreover the proposed results do not require the boundedness differentiability and monotonicity of the activation functions which can also be easily checked via the lmi solver in robust control toolbox in matlab furthermore using a parameter dependent lyapunov function approach the synchronization problem for polytopic uncertain fuzzy bam nns with various time delays is considered the parameter uncertainties under consideration are assumed to belong to a fixed convex polytope finally two numerical examples and simulations are given to illustrate the effectiveness of the derived theoretical results

testing against a high dimensional alternative summary as the dimensionality of the alternative hypothesis increases the power of classical tests tends to diminish quite rapidly this is especially true for high dimensional data in which there are more parameters than observations we discuss a score test on a hyperparameter in an empirical bayesian model as an alternative to classical tests it gives a general test statistic which can be used to test a point null hypothesis against a high dimensional alternative even when the number of parameters exceeds the number of samples this test will be shown to have optimal power on average in a neighbourhood of the null hypothesis which makes it a proper generalization of the locally most powerful test to multiple dimensions to illustrate this new locally most powerful test we investigate the case of testing the global null hypothesis in a linear regression model in more detail the score test is shown to have significantly more power than the f test whenever under the alternative the large variance principal components of the design matrix explain substantially more of the variance of the outcome than do the small variance principal components the score test is also useful for detecting sparse alternatives in truly high dimensional data where its power is comparable with the test based on the maximum absolute t statistic

testing against a high dimensional alternative in the generalized linear model asymptotic type i error control summary testing a low dimensional null hypothesis against a high dimensional alternative in a generalized linear model may lead to a test statistic that is a quadratic form in the residuals under the null model using asymptotic arguments we show that the distribution of such a test statistic can be approximated by a ratio of quadratic forms in normal variables for which algorithms are readily available for generalized linear models the asymptotic distribution shows good control of type i error for moderate to small samples even when the number of covariates in the model far exceeds the sample size

large scale multiple testing of correlations multiple testing of correlations arises in many applications including gene coexpression network analysis and brain connectivity analysis in this article we consider large scale simultaneous testing for correlations in both the one sample and two sample settings new multiple testing procedures are proposed and a bootstrap method is introduced for estimating the proportion of the nulls falsely rejected among all the true nulls we investigate the properties of the proposed procedures both theoretically and numerically it is shown that the procedures asymptotically control the overall false discovery rate and false discovery proportion at the nominal level simulation results show that the methods perform well numerically in terms of both the size and power of the test and it significantly outperforms two alternative methods the two sample procedure is also illustrated by an analysis of a prostate cancer dataset for the detection of changes in coexpression patterns between gene expression levels suppl

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples

high dimensional variable selection this paper explores the following question what kind of statistical guarantees can be given when doing variable selection in high dimensional models in particular we look at the error rates and power of some multi stage regression methods in the first stage we fit a set of candidate models in the second stage we select one model by cross validation in the third stage we use hypothesis testing to eliminate some variables we refer to the first two stages as screening and the last stage as cleaning we consider three screening methods the lasso marginal regression and forward stepwise regression our method gives consistent variable selection under certain conditions

debiased inference on treatment effect in a high dimensional model this article concerns the potential bias in statistical inference on treatment effects when a large number of covariates are present in a linear or partially linear model while the estimation bias

a two sample test for high dimensional data with applications to gene set testing we proposed a two sample test for means of high dimensional data when the data dimension is much larger than the sample size the classical hotelling s t 2 test does not work for this large p small n situation the proposed test does not require explicit conditions on the relationship between the data dimension and sample size this offers much flexibility in analyzing high dimensional data an application of the proposed test is in testing significance for sets of genes which we demonstrate in an empirical study on a leukemia data set

brief paper parameter dependent robust h filtering for uncertain discrete time systems this paper is concerned with the problem of parameter dependent h filtering for discrete time systems with polytopic uncertainties the uncertain parameters are supposed to reside in a polytope being different from previous results in the quadratic framework the parameter dependent lyapunov function is used in this paper both full and reduced order filters are designed which guarantee the asymptotic stability and a prescribed h performance level the filter parameters can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities which can be solved via efficient interior point algorithms numerical examples are presented to illustrate the feasibility and less conservativeness of the proposed method

robust h sub spl infin compensator design for time delay systems with norm bounded time varying uncertainties considers robust h sub spl infin compensator design for linear systems that involve unknown time delays both in states and controls and time varying norm bounded parameter uncertainties sufficient conditions for designing robust compensators are obtained in terms of two riccati inequalities which are not mutually coupled through which a full order robust h sub spl infin compensator can be obtained finally a small example is given to show the applicability of the proposed approach

image super resolution via sparse representation this paper presents a new approach to single image superresolution based upon sparse signal representation research on image statistics suggests that image patches can be well represented as a sparse linear combination of elements from an appropriately chosen over complete dictionary inspired by this observation we seek a sparse representation for each patch of the low resolution input and then use the coefficients of this representation to generate the high resolution output theoretical results from compressed sensing suggest that under mild conditions the sparse representation can be correctly recovered from the downsampled signals by jointly training two dictionaries for the low and high resolution image patches we can enforce the similarity of sparse representations between the low resolution and high resolution image patch pair with respect to their own dictionaries therefore the sparse representation of a low resolution image patch can be applied with the high resolution image patch dictionary to generate a high resolution image patch the learned dictionary pair is a more compact representation of the patch pairs compared to previous approaches which simply sample a large amount of image patch pairs reducing the computational cost substantially the effectiveness of such a sparsity prior is demonstrated for both general image super resolution sr and the special case of face hallucination in both cases our algorithm generates high resolution images that are competitive or even superior in quality to images produced by other similar sr methods in addition the local sparse modeling of our approach is naturally robust to noise and therefore the proposed algorithm can handle sr with noisy inputs in a more unified framework

gaussian graphical model estimation with false discovery rate control this paper studies the estimation of a high dimensional gaussian graphical model ggm typically the existing methods depend on regularization techniques as a result it is necessary to choose the regularized parameter however the precise relationship between the regularized parameter and the number of false edges in ggm estimation is unclear in this paper we propose an alternative method by a multiple testing procedure based on our new test statistics for conditional dependence we propose a simultaneous testing procedure for conditional dependence in ggm our method can control the false discovery rate fdr asymptotically the numerical performance of the proposed method shows that our method works quite well