geodesic convexity and covariance estimation geodesic convexity is a generalization of classical convexity which guarantees that all local minima of g convex functions are globally optimal we consider g convex functions with positive definite matrix variables and prove that kronecker products and logarithms of determinants are g convex we apply these results to two modern covariance estimation problems robust estimation in scaled gaussian distributions and kronecker structured models maximum likelihood estimation in these settings involves non convex minimizations we show that these problems are in fact g convex this leads to straight forward analysis allows the use of standard optimization methods and paves the road to various extensions via additional g convex regularization

iterative adaptive kronecker mimo radar beamformer description and convergence analysis we introduce an iterative procedure for design of adaptive kl variate linear beamformers that are structured as the kronecker product of k variate transmit and l variate receive beamformers we focus on mimo radar applications for scenarios where only joint transmit and receive adaptive beamforming can efficiently mitigate multi mode propagated backscatter interference this is because the direction of departure dod on one interference mode and the direction of arrival doa on the other coincide with those of a target respectively we introduce a markov model for the adaptive iterative routine specify its convergence condition and derive final stable signal to interference plus noise ratio sinr performance characteristics simulation results demonstrate high accuracy of the analytical derivations in addition we demonstrate that for the considered class of multiple input multiple output mimo radar interference scenarios the diagonally loaded sample matrix inversion smi algorithm provides additional performance improvement and convergence rate for this iterative adaptive kronecker beamformer

parameter estimation problems with singular information matrices the case of a singular fisher information matrix fim represents a significant complication for the theory of the cramer rao lower bound crb that is usually handled by resorting to the pseudoinverse of the fisher matrix we take a different approach in which the crb is derived as the solution to an unconstrained quadratic maximization problem which enables us to handle the singular case in a simple yet rigorous manner when the fisher matrix is singular except under unusual circumstances any estimator having the specified bias derivatives that figure in the crb must have infinite variance

robust stabilization of systems with multiple real pole uncertainties the robust stabilization of systems with several uncertain real poles is discussed necessary and sufficient conditions of existence of a controller in terms is obtained of an interpolation problem are given the interpolating function is obtained directly for a particular case two examples are shown for the synthesis of a controller an explicit solution of the controller for plants without zeros in the right hand plane rhp and without known poles in the rhp is given this shows the practical utility of the method to the design of robust stabilizers

covariance estimation in high dimensions via kronecker product expansions this paper presents a new method for estimating high dimensional covariance matrices the method permuted rank penalized least squares prls is based on a kronecker product series expansion of the true covariance matrix assuming an i i d gaussian random sample we establish high dimensional rates of convergence to the true covariance as both the number of samples and the number of variables go to infinity for covariance matrices of low separation rank our results establish that prls has significantly faster convergence than the standard sample covariance matrix scm estimator the convergence rate captures a fundamental tradeoff between estimation error and approximation error thus providing a scalable covariance estimation framework in terms of separation rank similar to low rank approximation of covariance matrices the mse convergence rates generalize the high dimensional rates recently obtained for the ml flip flop algorithm for kronecker product covariance estimation we show that a class of block toeplitz covariance matrices is approximatable by low separation rank and give bounds on the minimal separation rank r that ensures a given level of bias simulations are presented to validate the theoretical bounds as a real world application we illustrate the utility of the proposed kronecker covariance estimator for spatio temporal linear least squares prediction of multivariate wind speed measurements

canonical coordinates are the right coordinates for low rank gauss gauss detection and estimation in this correspondence our aim is to establish a connection between low rank detection low rank estimation and canonical coordinates the key to this connection is the observation that gauss gauss detectors and estimators share canonical coordinates in the case where the underlying model is a signal plus noise model we show that in gauss gauss detection j divergence is a function of squared canonical correlations and hence is invariant to nonsingular transformations of the data channels further we show that j divergence has a special decomposition in canonical coordinates impelling their use for rank reduction canonical coordinates have been found earlier to be fundamental for low rank estimation as they decompose three important performance measures namely the relative volume of error concentration ellipse processing gain and information rate this correspondence shows that canonical coordinates are also fundamental for low rank detection making them more useful in signal processing and communication problems when low rank modeling is required to achieve computational efficiency or robustness against noise and model uncertainties

on cores and stable sets for fuzzy games in this paper cores and stable sets for games with fuzzy coalitions are introduced and their relations studied for convex fuzzy games it turns out that all cores coincide and that the core is the unique stable set also relations between cores and stable sets of fuzzy clan games are discussed

asymptotically optimal detection in unknown colored noise via autoregressive modeling the problem of detecting a known signal in colored gaussian noise of unknown covariance is addressed the noise is modeled as an autoregressive process of known order but unknown coefficients by employing the theory of generalized likelihood ratio testing a detector structure is derived and then analyzed for performance it is proven that for large data records the detection performance is identical to that of an optimal prewhitener and matched filter and therefore the detector itself is optimal simulation results indicate that the data record length necessary for the asymptotic results to apply can be quite small thus the proposed detector is well suited for practical applications

gemini graph estimation with matrix variate normal instances undirected graphs can be used to describe matrix variate distributions in this paper we develop new methods for estimating the graphical structures and underlying parameters namely the row and column covariance and inverse covariance matrices from the matrix variate data under sparsity conditions we show that one is able to recover the graphs and covariance matrices with a single random matrix from the matrix variate normal distribution our method extends with suitable adaptation to the general setting where replicates are available we establish consistency and obtain the rates of convergence in the operator and the frobenius norm we show that having replicates will allow one to estimate more complicated graphical structures and achieve faster rates of convergence we provide simulation evidence showing that we can recover graphical structures as well as estimating the precision matrices as predicted by theory

efficient algorithms for the solution of block linear systems with toeplitz entries abstract this paper is concerned with the development of fast solvers for block linear systems with toeplitz entries two algorithms are described the first utilizes block permutations to unravel the nesting structure of the associated matrix the second has a block schur type format and features highly parallel potential

high dimensional semiparametric bigraphical models in multivariate analysis a gaussian bigraphical model is commonly used for modelling matrix valued data in this paper we propose a semiparametric extension of the gaussian bigraphical model called the nonparanormal bigraphical model a projected nonparametric rank based regularization approach is employed to estimate sparse precision matrices and produce graphs under a penalized likelihood framework theoretically our semiparametric procedure achieves the parametric rates of convergence for both matrix estimation and graph recovery empirically our approach outperforms the parametric gaussian model for non gaussian data and is competitive with its parametric counterpart for gaussian data extensions to the categorical bigraphical model and the missing data problem are discussed copyright 2013 oxford university press

convex fuzzy games and participation monotonic allocation schemes in this paper the cone of convex cooperative fuzzy games is studied as in the classical case of convex crisp games these games have a large core and the fuzzy shapley value is the barycenter of the core surprisingly the core and the weber set coincide as in the classical case but the coincidence of these sets for a fuzzy game does not imply automatically convexity as in the crisp case participation monotonic allocation schemes pamas are introduced and it turns out that each core element of a convex fuzzy game is pamas extendable

linear production games with fuzzy control the aim of this paper is to analyse linear production with committee control situations arising when controllers face the possibility of graduating their options in order to model these situations we consider several kinds of fuzzy controls which can be modelled as different simple fuzzy games an lp game which is an extension of lp games with committee control introduced in curiel et al on balanced games and games with committee control or spectrum 11 1989 83 88 is obtained and its core is studied

robust kronecker product pca for spatio temporal covariance estimation kronecker pca involves the use of a space versus time kronecker product decomposition to estimate spatio temporal covariances in this paper the addition of a sparse correction factor is considered which corresponds to a model of the covariance as a sum of kronecker products of low separation rank and a sparse matrix this sparse correction extends the diagonally corrected kronecker pca of greenewald and hero 2014 to allow for sparse unstructured outliers anywhere in the covariance matrix e g arising from variables or correlations that do not fit the kronecker model well or from sources such as sensor noise or sensor failure we introduce a robust pca based algorithm to estimate the covariance under this model an extension to toeplitz temporal factors is also provided producing a parameter reduction for temporally stationary measurement modeling high dimensional mse performance bounds are given for these extensions finally the proposed extension of kronpca is evaluated on both simulated and real data coming from yeast cell cycle experiments this establishes the practical utility of robust kronecker pca in biological and other applications

on kronecker and linearly structured covariance matrix estimation the estimation of covariance matrices is an integral part of numerous signal processing applications in many scenarios there exists prior knowledge on the structure of the true covariance matrix e g it might be known that the matrix is toeplitz in addition to hermitian given the available data and such prior structural knowledge estimates using the known structure can be expected to be more accurate since more data per unknown parameter is available in this work we study the case when a covariance matrix is known to be the kronecker product of two factor matrices and in addition the factor matrices are toeplitz we devise a two step estimator to accurately solve this problem the first step is a maximum likelihood ml based closed form estimator which has previously been shown to give asymptotically in the number of samples efficient estimates when the relevant factor matrices are hermitian or persymmetric the second step is a re weighting of the estimates found in the first steps such that the final estimate satisfies the desired toeplitz structure we derive the asymptotic distribution of the proposed two step estimator and conclude that the estimator is asymptotically statistically efficient and hence asymptotically ml through monte carlo simulations we further show that the estimator converges to the relevant cramer rao lower bound for fewer samples than existing methods

statistical analysis of subspace based estimation of reduced rank linear regressions a number of signal processing and system identification problems include linear regressions with a reduced rank regression matrix a typical step in subspace based algorithms is to apply the singular value decomposition svd to compute a low rank factorization however it is not clear how certain weighting matrices should be defined for best possible accuracy we present a statistical analysis of the estimate of the reduced rank regression matrix and we discuss a couple of approaches for finding weighting matrices

rank reduction for modeling stationary signals rank reduction is developed as a general principle for trading off model bias and model variance in the analysis and synthesis of signals the principle is applied to three basic problems stationary time series modeling stationary time series whitening and vector quantization each problem brings its own surprises and insights

a space frequency analysis of meg background processes abstract in meg source localization the estimated source parameters will be more reliable when the spatiotemporal covariance of the noise and background activity is taken into account since this covariance is in general too large to estimate based on the data and to invert efficiently different parametrizations have been proposed in the literature these models can be seen as special cases of the general decomposition of the covariance into a sum of kronecker products of spatial matrices xn and temporal matrices tn van loan 2000 in this study we investigate the assumption of the matrices tn being toeplitz if so the covariance matrix in the space frequency domain will have an approximate block diagonal structure facilitating inversion which is a prerequisite for source localization in this study we address the question whether the toeplitz approximation is valid for data sets obtained in visual evoked field auditory evoked field somatosensory evoked field experiments and data sets containing spontaneous activity it turns out that on average 87 is in the block diagonal of the sample covariance which is close to the values obtained for real toeplitz matrices tn this implies that the space frequency domain is very interesting for source localization since the major part of the entire covariance can be incorporated in that domain straightforwardly finally the two major processes in the background activity are characterized in terms of their spatial and frequency patterns yielding a focal and a non focal pattern in 8 of 10 data sets analyzed in this study the focal pattern represents the alpha frequency at parieto occipital areas whereas the non focal pattern is more widespread both in space and in frequency

tensor graphical lasso teralasso the paper introduces a multiway tensor generalization of the bigraphical lasso which uses a two way sparse kronecker sum multivariate normal model for the precision matrix to model parsimoniously conditional dependence relationships of matrix variate data based on the cartesian product of graphs we call this tensor graphical lasso generalization teralasso we demonstrate by using theory and examples that the teralasso model can be accurately and scalably estimated from very limited data samples of high dimensional variables with multiway co ordinates such as space time and replicates statistical consistency and statistical rates of convergence are established for both the bigraphical lasso and teralasso estimators of the precision matrix and estimators of its support non sparsity set respectively we propose a scalable composite gradient descent algorithm and analyse the computational convergence rate showing that the composite gradient descent algorithm is guaranteed to converge at a geometric rate to the global minimizer of the teralasso objective function finally we illustrate teralasso by using both simulation and experimental data from a meteorological data set showing that we can accurately estimate precision matrices and recover meaningful conditional dependence graphs from high dimensional complex data sets

low rank detection of multichannel gaussian signals using block matrix approximation the exact design of an m channel matched filter with l taps requires the solution of an ml spl times ml block system of linear equations with toeplitz entries practical cases where m 50 and l 100 are not uncommon when the individual sensors of an array are closely spaced the temporal and spatial correlation of the resulting vector noise process may be modeled in a separable fashion in this case the noise covariance block matrix attains a special structure where all block entries are just weighted versions of each other it is shown that in this case the complexity of the detector design can be reduced drastically by a factor of ml compared to a conventional multichannel matched filter design procedure it is further shown that the separable vector noise model facilitates a complete exploitation of the rank properties of noise and data matrices a constructive procedure for the design of low rank detectors in the multichannel case is derived these detectors consist of two consecutive blocks a data and noise dependent compression stage which maps the significant signal energy into a subspace of minimal dimension followed by a minimal set of independent matched filters which point in the subspace directions in which the signal is much stronger than the noise this low rank detector concept enables discrimination with little or no performance penalty at a minimal computational cost

a clt on the snr of diagonally loaded mvdr filters this paper studies the fluctuations of the signal to noise ratio snr of minimum variance distorsionless response mvdr filters implementing diagonal loading in the estimation of the covariance matrix previous results in the signal processing literature are generalized and extended by considering both spatially as well as temporarily correlated samples specifically a central limit theorem clt is established for the fluctuations of the snr of the diagonally loaded mvdr filter under both supervised and unsupervised training settings in adaptive filtering applications our second order analysis is based on the nash poincare inequality and the integration by parts formula for gaussian functionals as well as classical tools from statistical asymptotic theory numerical evaluations validating the accuracy of the clt confirm the asymptotic gaussianity of the fluctuations of the snr of the mvdr filter

low rank detectors for gaussian random vectors a constructive procedure is presented for designing low rank detectors which maximize the divergence between hypotheses about the covariance structure of gaussian signals the detectors are constructed from the eigenstructure of a signal to noise ratio matrix we show that the unity eigenvalues of this matrix provide no information about the covariance structure and the rank of the detector may be reduced with no performance penalty more generally we show that in certain situations small eigenvalues may provide more information for discrimination than large eigenvalues this leads to a systematic procedure for reducing the rank of a quadratic detector several examples are discussed

reduction of robust stabilization problems to standard h problems for classes of systems with structured uncertainty we consider the problem of robustly stabilizing a family of linear time invariant systems with a linear time invariant controller for classes of robust stabilization problems with unmodelled dynamics recent breakthroughs in h theory lead to solution via two riccati equations for systems with structured real uncertainty however a similar comprehensive theory does not exist the objective of this paper is to delineate classes of linear time invariant systems with structured uncertainty either real or complex for which a similar solution to the robust stabilization problem is possible the theory has the following salient features first for classes of uncertainty structures no conservatism is introduced for structured real parametric uncertainty we make a connection with h theory that does not amount to any crude overbounding via complex discs the stabilizability conditions we obtain are not only sufficient but also necessary the second salient feature in the theory is a special weighting function which we construct for example for the case when the structured uncertainty enters only in the denominator the robust stabilization problem is replaced by a standard h sensitivity minimization problem with our special weighting function a similar h complementary sensitivity problem is associated with numerator uncertainty

modified nevanlinna pick interpolation and feedback stabilization of linear plants with uncertainty in the gain factor abstract this paper is a sequel to an earlier work in which we applied classical novnnlinna pick interpolation to the stabilization of a single input output plant with uncertainly in the gain factor by means of an asymptotically stable control and feedback sensor in this present work we show that for the proper design we need a modification of the classical interpolation procedure a point not clearly brought out in our previous paper

covariate adjusted tensor classification in high dimensions in contemporary scientific research it is often of great interest to predict a categorical response based on a high dimensional tensor i e multi dimensional array and additional covariates mo

bi iteration svd subspace tracking algorithms we present a class of fast subspace tracking algorithms that arise from a straightforward extension of bauer s 1957 classical bi iteration to the sequential processing case the bi iteration concept has an unexpected potential in subspace tracking our new bi svd subspace trackers are well structured and show excellent convergence properties they outperform the tqr svd subspace tracking algorithm detailed comparisons confirm our claims an application to rank and data adaptive signal reconstruction is also discussed

maximum likelihood array processing for stochastic coherent sources maximum likelihood ml estimation in array signal processing for the stochastic noncoherent signal case is well documented in the literature we focus on the equally relevant case of stochastic coherent signals explicit large sample realizations are derived for the ml estimates of the noise power and the singular signal covariance matrix the asymptotic properties of the estimates are examined and some numerical examples are provided in addition we show the surprising fact that the ml estimates of the signal parameters obtained by ignoring the information that the sources are coherent coincide in large samples with the ml estimates obtained by exploiting the coherent source information thus the ml signal parameter estimator derived for the noncoherent case or its large sample realizations asymptotically achieves the lowest possible estimation error variance corresponding to the coherent cramer rao bound

low rank adaptive filters we introduce a class of adaptive filters based on sequential adaptive eigendecomposition subspace tracking of the data covariance matrix these new algorithms are completely rank revealing and hence they can perfectly handle the following two relevant data cases where conventional recursive least squares rls methods fail to provide satisfactory results 1 highly oversampled smooth data with rank deficient of almost rank deficient covariance matrix and 2 noise corrupted data where a signal must be separated effectively from superimposed noise this paper contradicts the widely held belief that rank revealing algorithms must be computationally more demanding than conventional recursive least squares a spatial rls adaptive filter has a complexity of o n sup 2 operations per time step where n is the filter order the corresponding low rank adaptive filter requires only o nr operations per time step where r spl les n denotes the rank of the data covariance matrix thus low rank adaptive filters can be computationally less or even much less demanding depending on the order rank ratio n r or the compressibility of the signal simulation results substantiate our claims this paper is devoted to the theory and application of fast orthogonal iteration and bi iteration subspace tracking algorithms

reduced rank linear regression and weighted low rank approximations this paper addresses parameter estimation in reduced rank linear regressions this estimation problem has applications in several subject areas including system identification sensor array processing econometrics and statistics a new estimation procedure based on instrumental variable principles is derived and analyzed the proposed method is designed to handle noise that is both spatially and temporally autocorrelated an asymptotical analysis shows that the proposed method outperforms previous methods when the noise is temporally correlated and that it is asymptotically efficient otherwise a numerical study indicates that the performance is significantly improved also for finite sample set sizes in addition the cramer rao lower bound crb on unbiased estimator covariance for the data model is derived a statistical test for rank determination is also developed an important step in the new algorithm is the weighted low rank approximation wlra as the wlra lacks a closed form solution in its general form two new noniterative and approximate solutions are derived both of them asymptotically optimal when part of the estimation procedure proposed here these methods are also interesting in their own right since the wlra has several applications

signal detection via spectral theory of large dimensional random matrices results on the spectral behavior of random matrices as the dimension increases are applied to the problem of detecting the number of sources impinging on an array of sensors a common strategy to solve this problem is to estimate the multiplicity of the smallest eigenvalue of the spatial covariance matrix r of the sensed data existing approaches rely on the closeness of the noise eigenvalues of sample covariance matrix to each other and therefore the sample size has to be quite large when the number of sources is large in order to obtain a good estimate the theoretical analysis presented focuses on the splitting of the spectrum of sample covariance matrix into noise and signal eigenvalues it is shown that when the number of sensors is large the number of signals can be estimated with a sample size considerably less than that required by previous approaches

a generalized linear production model a unifying model we introduce a generalized linear production model whose attractive feature being that the resources held by any subset of producerss is not restricted to be the vector sum of the resources held by the members ofs we provide sufficient conditions for the non emptiness of the core of the associated generalized linear production game and show that if the core of the game is not empty then a solution in it can be produced from a dual optimal solution to the associated linear programming problem our generalized linear production model is a proper generalization of the linear production model introduced by owen and it can be used to analyze cooperative games which cannot be studied in the ordinary linear production model framework we use the generalized model to show that the cooperative game induced by a network optimization problem in which players are the nodes of the network has a non empty core we further employ our model to prove the non emptiness of the core of two other classes of cooperative games which were not previously studied in the literature and we also use our generalized model to provide an alternative proof for the non emptiness of the core of the class of minimum cost spanning tree games thus it appears that the generalized linear production model is a unifying model which can be used to explain the non emptiness of the core of cooperative games generated by various seemingly different optimization models

totally balanced games arising from controlled programming problems a cooperative game in characteristic function form is obtained by allowing a number of individuals to esercise partial control over the constraints of a generally nonlinear mathematical programming problem either directly or through committee voting conditions are imposed on the functions defining the programming problem and the control system which suffice to make the game totally balanced this assures a nonempty core and hence a stable allocation of the full value of the programming problem among the controlling palyers in the linear case the core is closely related to the solutions of the dual problem applications are made to a variety of economic models including the transferable utility trading economies of shapley and shubik and a multishipper one commodity transshipment model with convex cost functions and concave revenue functions dropping the assumption of transferable utility leads to a class of controlled multiobjective or pareto programming problems which again yield totally balanced games

bilinear probabilistic principal component analysis probabilistic principal component analysis ppca is a popular linear latent variable model for performing dimension reduction on 1 d data in a probabilistic manner however when used on 2 d data such as images ppca suffers from the curse of dimensionality due to the subsequently large number of model parameters to overcome this problem we propose in this paper a novel probabilistic model on 2 d data called bilinear ppca bppca this allows the establishment of a closer tie between bppca and its nonprobabilistic counterpart moreover two efficient parameter estimation algorithms for fitting bppca are also developed experiments on a number of 2 d synthetic and real world data sets show that bppca is more accurate than existing probabilistic and nonprobabilistic dimension reduction methods

on estimation of covariance matrices with kronecker product structure the estimation of signal covariance matrices is a crucial part of many signal processing algorithms in some applications the structure of the problem suggests that the underlying true covariance matrix is the kronecker product of two valid covariance matrices examples of such problems are channel modeling for multiple input multiple output mimo communications and signal modeling of eeg data in applications it may also be that the kronecker factors in turn can be assumed to possess additional linear structure the maximum likelihood ml method for the associated estimation problem has been proposed previously it is asymptotically efficient but has the drawback of requiring an iterative search for the maximum of the likelihood function two methods that are fast and noniterative are proposed in this paper both methods are shown to be asymptotically efficient the first method is a noniterative variant of a well known alternating maximization technique for the likelihood function it performs on par with ml in simulations but has the drawback of not allowing for extra structure in addition to the kronecker structure the second method is based on covariance matching principles and does not suffer from this drawback however while the large sample performance is the same it performs somewhat worse than the first estimator in small samples in addition the cramer rao lower bound for the problem is derived in a compact form the problem of estimating the kronecker factors and the problem of detecting if the kronecker structure is a good model for the covariance matrix of a set of samples are related therefore the problem of detecting the dimensions of the kronecker factors based on the minimum values of the criterion functions corresponding to the two proposed estimation methods is also treated in this work

cooperative fuzzy games we derive versions of known results dealing with core equilibria and shapley values of cooperative games in the case of cooperative fuzzy games i e games defined on fuzzy subsets of the set of n players a fuzzy coalition is an n vector i associating with each player i his rate of participation i 0 1 in the fuzzy coalition and the real number v is the coalition worth assumed to be positively homogeneous if also v is superadditive or equivalently concave the fuzzy game with side payments has a nonempty core associated with the coalition worth function for any ordinary game with side payments is a fuzzy extension thereof viz the fuzzy game whose coalition worth function is the least positively homogeneous superadditive function majorizing the coalition worth function of the original game the fuzzy extension always has a nonempty core moreover if the original game has a nonempty core it coincides with that of its fuzzy extension analogous results are established for games without side payments an axiomatization of values of fuzzy games with side payments is also given the results are applied to show that the set of walras equilibria coincides with the fuzzy core of an economy

an axiomatic approach of the discrete choquet integral as a tool to aggregate interacting criteria the most often used operator to aggregate criteria in decision making problems is the classical weighted arithmetic mean however in many problems the criteria considered interact and a substitute to the weighted arithmetic mean has to be adopted we show that under rather natural conditions the discrete choquet integral is an adequate aggregation operator that extends the weighted arithmetic mean by taking into consideration of the interaction among criteria the axiomatic that supports the choquet integral is presented and an intuitive approach is proposed as well

inference for time varying signals using locally stationary processes abstract locally stationary processes lsps in silverman s sense defined by the modulation in time of a stationary covariance function are valuable in stochastic modelling of time varying signals however for practical applications methods to conduct reliable parameter inference from measured data are required in this paper we address the lack of suitable methods for estimating the parameters of the lsp model by proposing a novel inference method the proposed method is based on the separation of the two factors defining the lsp covariance function in order to take advantage of their individual structure and divide the inference problem into two simpler sub problems the method s performance is tested in a simulation study and compared with traditional sample covariance based estimation an illustrative example of parameter estimation from eeg data measured during a memory encoding task is provided

performance analysis of a class of transient detection algorithms a unified framework the detection of short duration nonstationary signals which are commonly referred to as transients is often performed in the time frequency transform domain an analytical framework within which the performance of different detectors based on linear transforms can be easily compared for different classes of signals is developed a given class of transients is modeled as a signal existing in a linear subspace plus a mismatch signal closed form expressions are derived for the best and the worst detection performance for all possible transients in a given class using this framework the performance of detectors based on the gabor transform and on the short time fourier transform is evaluated and compared

on convergence of kronecker graphical lasso algorithms this paper studies iteration convergence of kronecker graphical lasso kglasso algorithms for estimating the covariance of an i i d gaussian random sample under a sparse kronecker product covariance model and mse convergence rates the kglasso model originally called the transposable regularized covariance model by allen transposable regularized covariance models with an application to missing data imputation ann appl statist vol 4 no 2 pp 764 790 2010 implements a pair of ell 1 penalties on each kronecker factor to enforce sparsity in the covariance estimator the kglasso algorithm generalizes glasso introduced by yuan and lin model selection and estimation in the gaussian graphical model biometrika vol 94 pp 19 35 2007 and banerjee model selection through sparse maximum likelihood estimation for multivariate gaussian or binary data j mach learn res vol 9 pp 485 516 mar 2008 to estimate covariances having kronecker product form it also generalizes the unpenalized ml flip flop ff algorithm of dutilleul the mle algorithm for the matrix normal distribution j statist comput simul vol 64 pp 105 123 1999 and werner on estimation of covariance matrices with kronecker product structure ieee trans signal process vol 56 no 2 pp 478 491 feb 2008 to estimation of sparse kronecker factors we establish that the kglasso iterates converge pointwise to a local maximum of the penalized likelihood function we derive high dimensional rates of convergence to the true covariance as both the number of samples and the number of variables go to infinity our results establish that kglasso has significantly faster asymptotic convergence than glasso and ff simulations are presented that validate the results of our analysis for example for a sparse 10 thinspace 000 times 10 thinspace 000 covariance matrix equal to the kronecker product of two 100 times 100 matrices the root mean squared error of the inverse covariance estimate using ff is 2 times larger than that obtainable using kglasso for sample size of n 100

polarimetric detection in compound gaussian clutter with kronecker structured covariance matrix in this paper we consider polarimetric adaptive detection in compound gaussian clutter whose covariance matrix cm has a kronecker structure we derive the cramer rao bound of a kronecker structured cm estimate and analyze the constant false alarm rate property of the adaptive subspace matched filter detector that uses kronecker structured estimates we provide a general expression for the average signal to clutter ratio loss scrl as a function of the mean square error of the covariance estimate the aforementioned expression is helpful in determining how many samples are required in order to achieve a desired average scrl level in practical scenarios based on that expression we show that the required sample size can be effectively reduced by exploiting the kronecker structure of the clutter cm we also derive the asymptotic detection performance of the adaptive subspace matched filter the analysis of scrl and detection performance can be extended to more general scenarios especially when the maximum likelihood estimate of the structured cm involves solving fixed point equations numerical simulations validate the merits of the proposed methods

estimating stationary dipoles from meg eeg data contaminated with spatially and temporally correlated background noise the stationary dipole model for the inverse problem of magnetoencephalographic meg and electroencephalographic eeg data is extended by including spatio temporal correlations of the background noise for that purpose the spatio temporal covariances are described as a kronkecker product of a spatial and a temporal covariance matrix the maximum likelihood method is used to estimate this kronecker product from a series of trials of meg eeg data a simulation study shows that the inclusion of the background noise generally improves the dipole estimate substantially when the frequency of the source time functions however coincides with the frequency contents of the covariance function the dipole estimate worsens when the temporal correlations are included the inclusion of spatial correlations always improves the estimates

robust estimation of structured covariance matrix for heavy tailed elliptical distributions this paper considers the problem of robustly estimating a structured covariance matrix with an elliptical underlying distribution with a known mean in applications where the covariance matrix naturally possesses a certain structure taking the prior structure information into account in the estimation procedure is beneficial to improving the estimation accuracy we propose incorporating the prior structure information into tyler s m estimator and formulating the problem as minimizing the cost function of tyler s estimator under the prior structural constraint first the estimation under a general convex structural constraint is introduced with an efficient algorithm for finding the estimator derived based on the majorization minimization mm algorithm framework then the algorithm is tailored to several special structures that enjoy a wide range of applications in signal processing related fields namely sum of rank one matrices toeplitz and banded toeplitz structure in addition two types of non convex structures i e the kronecker structure and the spiked covariance structure are also discussed where it is shown that simple algorithms can be derived under the guidelines of mm the algorithms are guaranteed to converge to a stationary point of the problems furthermore if the constraint set is geodesically convex such as the kronecker structure set then the algorithm converges to a global minimum numerical results show that the proposed estimator achieves a smaller estimation error than the benchmark estimators at a lower computational cost

testing separability of space time functional processes summaryseparability is a common simplifying assumption on the covariance structure of spatiotemporal functional data we present three tests of separability one a functional extension of the monte carlo likelihood method of mitchell et al 2006 and two based on quadratic forms our tests are based on asymptotic distributions of maximum likelihood estimators and do not require monte carlo simulation the main theoretical contribution of this paper is the specification of the joint asymptotic distribution of these estimators which can be used to derive many other tests the main methodological finding is that one of the quadratic form methods which we call a norm approach emerges as a clear winner in terms of finite sample performance in nearly every setting we considered this approach focuses directly on the frobenius distance between the spatiotemporal covariance function and its separable approximation we demonstrate the efficacy of our methods via simulations and application to irish wind data

asymptotic performance of a distributed detection system in correlated gaussian noise the authors consider the detection of a constant signal in noise with a large set of geographically dispersed sensors the noise at the sensors is correlated gaussian two correlation models are considered one where the correlation coefficient between any two sensors decreases geometrically as the sensor separation increases and one in which the correlation coefficient between any two sensors is a constant for both correlation models the asymptotic as the number of sensors becomes large performances of a distributed detection system and a central system are examined

maximum likelihood estimation for the tensor normal distribution algorithm minimum sample size and empirical bias and dispersion recently there has been a growing interest in the analysis of multi dimensional data arrays e g when a univariate response is sampled in 3 d space or when a multivariate response is sampled in time and 2 d space in this article we scrutinize the problem of maximum likelihood estimation mle for the tensor normal distribution of order 3 or more which is characterized by the separability of its variance covariance structure there is one variance covariance matrix per dimension in the 3 d case the system of likelihood equations for the three variance covariance matrices has no analytical solution and therefore needs to be solved iteratively we studied the convergence of an iterative three stage algorithm mle 3d that we propose for this determined the minimum sample size required for matrix estimates to exist and computed by simulation the empirical bias and dispersion of the kronecker product of the three variance covariance matrix estimators in eight scenarios we found that the standardized bias and a matrix measure of dispersion decrease monotonically and tend to vanish with increasing sample size so the kronecker product estimator is consistent an example with 3 d spatial measures of glucose content in the brain is also presented finally results are discussed and the 4 d case is presented with simulation results in an appendix software is available for interested users

non euclidian metrics and the robust stabilization of systems with parameter uncertainty this paper considers from a complex function theoretic point of view certain kinds of robust synthesis problems in particular we use a certain kind of metric on the disk the hyperbolic metric which allows us to reduce the problem of robust stabilization of systems with many types of real and complex parameter variations to an easily solvable problem in non euclidian geometry it is shown that several apparently different problems can be treated in a unified general framework a new result on the gain margin problem for multivariable plants is also given finally we apply our methods to systems with real zero or pole variations

robust stabilization some extensions of the gain margin maximization problem considers robust stabilization for siso systems with linear dependence on a real uncertain parameter which may occur either in the numerator or denominator of the plant transfer function the authors show necessary and sufficient conditions for the existence of robust controllers their structure and parameterization can be obtained from the corresponding nevanlinna pick interpolation problems this work extends the previously known case of an uncertain gain parameter