an sos based control lyapunov function design for polynomial fuzzy control of nonlinear systems this paper deals with a sum of squares sos based control lyapunov function clf design for polynomial fuzzy control of nonlinear systems the design starts with exactly replacing smooth nonlinear systems dynamics with polynomial fuzzy models which are known as universal approximators next global stabilization conditions represented in terms of sos are provided in the framework of the clf design i e a stabilizing controller with nonparallel distributed compensation form is explicitly designed by applying sontag s control law once a clf for a given nonlinear system is constructed furthermore semiglobal stabilization conditions on operation domains are derived in the same fashion as in the global stabilization conditions both global and semiglobal stabilization problems are formulated as sos optimization problems which reduce to numerical feasibility problems five design examples are given to show the effectiveness of our proposed approach over the existing linear matrix inequality and sos approaches

continuous takagi sugeno s models reduction of the number of lmi conditions in various fuzzy control design technics fuzzy models of the takagi sugeno type enable representation of a wide class of nonlinear models conditions about their stabilization can be derived systematically usually these conditions are written as linear matrix inequality lmi problems in this paper we use a collection of properties concerning matrices to extend the area of solutions involving the feedback control laws we will work out with continuous fuzzy models and supply results about the stabilization the regulator problem and also hinfin control solutions based on a reduced number of decision variables implying a reduced number of lmi conditions are also proposed we show that a good tradeoff can been obtained

hierarchical bayesian formulations for selecting variables in regression models the objective of finding a parsimonious representation of the observed data by a statistical model that is also capable of accurate prediction is commonplace in all domains of statistical applications the parsimony of the solutions obtained by variable selection is usually counterbalanced by a limited prediction capacity on the other hand methodologies that assure high prediction accuracy usually lead to models that are neither simple nor easily interpretable regularization methodologies have proven to be useful in addressing both prediction and variable selection problems the bayesian approach to regularization constitutes a particularly attractive alternative as it is suitable for high dimensional modeling offers valid standard errors and enables simultaneous estimation of regression coefficients and complexity parameters via computationally efficient mcmc techniques bayesian regularization falls within the versatile framework of bayesian hierarchical models which encompasses a variety of other approaches suited for variable selection such as spike and slab models and the mc3 approach in this article we review these bayesian developments and evaluate their variable selection performance in a simulation study for the classical small p large n setting the majority of the existing bayesian methodology for variable selection deals only with classical linear regression here we present two applications in the contexts of binary and survival regression where the bayesian approach was applied to select markers prognostically relevant for the development of rheumatoid arthritis and for overall survival in acute myeloid leukemia patients copyright 2012 john wiley sons ltd

robust static output feedback stabilization for nonlinear discrete time systems with time delay via fuzzy control approach this paper addresses the problem of designing robust static output feedback controllers for nonlinear discrete time interval systems with time delays both in states and in control input in the approach we do not directly employ the lyapunov approach as do in most of traditional fuzzy control design approaches instead sufficient conditions for guaranteeing the robust stability for the considered systems are derived in terms of the matrix spectral norm of the closed loop fuzzy system the stability conditions are further formulated into linear matrix inequalities so that the desired controller can be easily obtained by using the matlab linear matrix inequality lmi toolbox finally an example is provided to illustrate the effectiveness of the proposed approach

on solutions of the initial value problem for the nonlinear schrodinger equations on considere le probleme aux valeurs initiales pour l equation de schrodinger non lineaire de la forme iu t u f u 2 u t x r r n u 0 x x x r n on etudie la regularite des solutions quand les fonctions initiales ne sont pas regulieres

conjugate lyapunov functions for saturated linear systems based on a recent duality theory for linear differential inclusions ldis the condition for stability of an ldi in terms of one lyapunov function can be easily derived from that in terms of its conjugate function this paper uses a particular pair of conjugate functions the convex hull of quadratics and the maximum of quadratics for the purpose of estimating the domain of attraction for systems with saturation nonlinearities to this end the nonlinear system is locally transformed into a parametertized ldi system with an effective approach which enables optimization on the parameter of the ldi along with the optimization of the lyapunov functions the optimization problems are derived for both the convex hull and the max functions and the domain of attraction is estimated with both the convex hull of ellipsoids and the intersection of ellipsoids a numerical example demonstrates the effectiveness of this paper s methods

a monte carlo approach to nonnormal and nonlinear state space modeling abstract a solution to multivariate state space modeling forecasting and smoothing is discussed we allow for the possibilities of nonnormal errors and nonlinear functionals in the state equation the observational equation or both an adaptive monte carlo integration technique known as the gibbs sampler is proposed as a mechanism for implementing a conceptually and computationally simple solution in such a framework the methodology is a general strategy for obtaining marginal posterior densities of coefficients in the model or of any of the unknown elements of the state space missing data problems including the k step ahead prediction problem also are easily incorporated into this framework we illustrate the broad applicability of our approach with two examples a problem involving nonnormal error distributions in a linear model setting and a one step ahead prediction problem in a situation where both the state and observational equations are nonlinear and involve unknown parameters

local shrinkage rules levy processes and regularized regression we use l evy processes to generate joint prior distributions and therefore penalty functions for a location parameter b b1 bp as p grows large this generalizes the class of local global shrinkage rules based on scale mixtures of normals illuminates new connections among disparate methods and leads to new results for computing posterior means and modes under a wide class of priors we extend this framework to large scale regularized regression problems where p n and provide comparisons with other methodologies

stability analysis of polynomial fuzzy models via polynomial fuzzy lyapunov functions in this paper the stability of continuous time polynomial fuzzy models by means of a polynomial generalization of fuzzy lyapunov functions is studied fuzzy lyapunov functions have been fruitfully used in the literature for local analysis of takagi sugeno models a particular class of the polynomial fuzzy ones based on a recent taylor series approach which allows a polynomial fuzzy model to exactly represent a nonlinear model in a compact set of the state space it is shown that a refinement of the polynomial lyapunov function so as to make it share the fuzzy structure of the model proves advantageous conditions thus obtained are tested via available sos software

bayesian estimation of density via multiple sequential inversions of two dimensional images with application to electron microscopy we present a new bayesian methodology to learn the unknown material density of a given sample by inverting its two dimensional images that are taken with a scanning electron microscope an image results from a sequence of projections of the convolution of the density function with the unknown microscopy correction function that we also learn from the data thus learning of the unknowns demands multiple inversions we invoke a novel design of experiment involving imaging at multiple values of the parameter that controls the subsurface depth from which information about the density structure is carried to result in the image real life material density functions are characterized by high density contrasts and are highly discontinuous implying that they exhibit correlation structures that do not vary smoothly in the absence of training data modeling such correlation structures of real material density functions is not possible so we discretize the material sample and treat values of the density functi

stabilization with relaxed controls cannot in general be stabilized using a continuous closed loop control u x even if each state separately can be driven asymptotically to the origin an example is analyzed in section 2 in this paper we examine the possibility of stabilizing such systems with a continuous closed loop relaxed control we find indeed that the family of systems stabilizable with relaxed controls is larger than the family of those stabilizable with ordinary controls an even larger class is obtained if the continuity of the closed loop at the origin is not required the latter class includes all one dimensional systems for which states can be driven asymptotically to the origin this result does not hold in two dimensional systems and we provide a counter example it should be pointed that relaxed control type stabilization is used both in theory and in practice the method is known as dither we shall comment on the similarities lyapunov functions for the system 1 help us in the construction of the continuous closed loop stabilizers in fact we find that the existence of a smooth lyapunov function is equivalent to the existence of a stabilizing closed loop which is continuous except possibly at the origin an additional condition on the lyapunov function implies the continuity at the origin as well we present these results in section 4 after a brief introduction of closed loop relaxed controls notations and terminology in section 3 prior to that in section 2 we discuss an example illustrating the power of relaxed controls in the particular case of systems linear in the controls relaxed controls can be replaced by ordinary controls this is discussed in section 5 the role of lyapunov functions in the stability and stabilization theories is of course well known examples of systems with lyapunov functions are available in the literature we display some in section 6 along with general comments on the construction applications and counterexamples including one which cannot be continuously stabilized yet possesses a nonsmooth lyapunov function closed loop stabilization with ordinary controls is analyzed extensively in the literature see sontag 8 sussmann ll and references therein lyapunov functions techniques in stabil

pseudodifferential operator with a nonanalytic symbol on a half line we study the initial boundary value problem for the nonlinear pseudodifferential equations with nonanalytic symbol we study traditionally important problems of a theory of nonlinear partial differential equations such as global in time existence of solutions to the initial boundary value problem and the asymptotic behavior of solutions for large time

structuring shrinkage some correlated priors for regression this paper develops a rich class of sparsity priors for regression effects that encourage shrinkage of both regression effects and contrasts between effects to zerowhilst leaving sizeable real effects largely unshrunk the construction of these priors uses some properties of normal gamma distributions to include design features in the prior specification but has general relevance to any continuous sparsity prior specific prior distributions are developed for serial dependence between regression effects and correlation within groups of regression effects

decoupling shrinkage and selection in bayesian linear models a posterior summary perspective selecting a subset of variables for linear models remains an active area of research this article reviews many of the recent contributions to the bayesian model selection and shrinkage prior literature a posterior variable selection summary is proposed which distills a full posterior distribution over regression coefficients into a sequence of sparse linear predictors

stability and performance for saturated systems via quadratic and nonquadratic lyapunov functions in this paper we develop a systematic lyapunov approach to the regional stability and performance analysis of saturated systems in a general feedback configuration the only assumptions we make about the system are well posedness of the algebraic loop and local stability problems to be considered include the estimation of the domain of attraction the reachable set under a class of bounded energy disturbances and the nonlinear l2 gain the regional analysis is established through an effective treatment of the algebraic loop and the saturation deadzone function this treatment yields two forms of differential inclusions a polytopic differential inclusion pdi and a norm bounded differential inclusion ndi that contain the original system adjustable parameters are incorporated into the differential inclusions to reflect the regional property the main idea behind the regional analysis is to ensure that the state remain inside the level set of a certain lyapunov function where the pdi or the ndi is valid with quadratic lyapunov functions conditions for stability and performances are derived as linear matrix inequalities lmis to obtain less conservative conditions we use a pair of conjugate non quadratic lyapunov functions the convex hull quadratic function and the max quadratic function these functions yield bilinear matrix inequalities bmis as conditions for stability and guaranteed performance level the bmi conditions cover the corresponding lmi conditions as special cases hence the bmi results are guaranteed to be as good as the lmi results in most examples the bmi results are significantly better than the lmi results

the bayesian lasso the lasso estimate for linear regression parameters can be interpreted as a bayesian posterior mode estimate when the regression parameters have independent laplace i e double exponential priors gibbs sampling from this posterior is possible using an expanded hierarchy with conjugate normal priors for the regression parameters and independent exponential priors on their variances a connection with the inverse gaussian distribution provides tractable full conditional distributions the bayesian lasso provides interval estimates bayesian credible intervals that can guide variable selection moreover the structure of the hierarchical model provides both bayesian and likelihood methods for selecting the lasso parameter slight modifications lead to bayesian versions of other lasso related estimation methods including bridge regression and a robust variant

sos based stability analysis of polynomial fuzzy model based control systems via polynomial membership functions this paper presents stability analysis of polynomial fuzzy model based fmb control systems using the sum of squares sos approach recently stability analysis of the polynomial fuzzy control systems which is a generalized form of the well known takagi sugeno t s fmb control systems has been reported in the form of sos based stability conditions lack of information on the relations between membership functions and premise variables in the existing stability analysis approaches causes conservatism of their results in this paper to derive relaxed stability conditions for polynomial fmb control systems membership functions which are approximated with polynomials and carrying relations between membership functions and premise variables are brought into the stability analysis considering a polynomial fmb control system and based on the lyapunov stability theory stability conditions in the form of fuzzy summations are derived where each term contains product of membership functions of the polynomial fuzzy model and polynomial fuzzy controller each product term is approximated by a polynomial in order to obtain better approximation the operating domain of membership functions is partitioned to subregions then sos based stability conditions for all subregions are derived unlike some published stability analysis approaches the proposed one can be employed for stability analysis of polynomial fuzzy control systems under imperfect premise matching of which the fuzzy model and fuzzy controller do not share the same membership functions the solution of the sos based stability conditions can be found numerically using sostools which is a free third party matlab toolbox numerical examples are given to illustrate the effectiveness of the proposed stability conditions

brief paper nonlinear control design for linear differential inclusions via convex hull of quadratics this paper presents a nonlinear control design method for robust stabilization and robust performance of linear differential inclusions ldis a recently introduced non quadratic lyapunov function the convex hull of quadratics will be used for the construction of nonlinear state feedback laws design objectives include stabilization with maximal convergence rate disturbance rejection with minimal reachable set and least l 2 gain conditions for stabilization and performances are derived in terms of bilinear matrix inequalities bmis which cover the existing linear matrix inequality lmi conditions as special cases numerical examples demonstrate the advantages of using nonlinear feedback control over linear feedback control for ldis it is also observed through numerical computation that nonlinear control strategies help to reduce control effort substantially

an approach to fuzzy control of nonlinear systems stability and design issues presents a design methodology for stabilization of a class of nonlinear systems first the authors represent a nonlinear plant with a takagi sugeno fuzzy model then a model based fuzzy controller design utilizing the concept of the so called parallel distributed compensation is employed the main idea of the controller design is to derive each control rule so as to compensate each rule of a fuzzy system the design procedure is conceptually simple and natural moreover the stability analysis and control design problems can be reduced to linear matrix inequality lmi problems therefore they can be solved efficiently in practice by convex programming techniques for lmis the design methodology is illustrated by application to the problem of balancing and swing up of an inverted pendulum on a cart

ep gig priors and applications in bayesian sparse learning in this paper we propose a novel framework for the construction of sparsity inducing priors in particular we define such priors as a mixture of exponential power distributions with a generalized inverse gaussian density ep gig ep gig is a variant of generalized hyperbolic distributions and the special cases include gaussian scale mixtures and laplace scale mixtures furthermore laplace scale mixtures can subserve a bayesian framework for sparse learning with nonconvex penalization the densities of ep gig can be explicitly expressed moreover the corresponding posterior distribution also follows a generalized inverse gaussian distribution we exploit these properties to develop em algorithms for sparse empirical bayesian learning we also show that these algorithms bear an interesting resemblance to iteratively reweighted l2 or l1 methods finally we present two extensions for grouped variable selection and logistic regression

elastic net regression modeling with the orthant normal prior the elastic net procedure is a form of regularized optimization for linear regression that provides a bridge between ridge regression and the lasso the estimate that it produces can be viewed as a bayesian posterior mode under a prior distribution implied by the form of the elastic net penalty this article broadens the scope of the bayesian connection by providing a complete characterization of a class of prior distributions that generate the elastic net estimate as the posterior mode the resulting model based framework allows for methodology that moves beyond exclusive use of the posterior mode by considering inference based on the full posterior distribution two characterizations of the class of prior distributions are introduced a properly normalized direct characterization which is shown to be conjugate for linear regression models and an alternate representation as a scale mixture of normal distributions prior distributions are proposed for the regularization parameters resulting in an infi

a universal construction of artstein s theorem on nonlinear stabilization abstract this note presents an explicit proof of the theorem due to artstein which states that the existence of a smooth control lyapunov function implies smooth stabilizability moreover the result is extended to the real analytic and rational cases as well the proof uses a universal formula given by an algebraic function of lie derivatives this formula originates in the solution of a simple riccati equation

the spike and slab lasso abstractdespite the wide adoption of spike and slab methodology for bayesian variable selection its potential for penalized likelihood estimation has largely been overlooked in this paper we bridge this gap by cross fertilizing these two paradigms with the spike and slab lasso procedure for variable selection and parameter estimation in linear regression we introduce a new class of self adaptive penalty functions that arise from a fully bayes spike and slab formulation ultimately moving beyond the separable penalty framework a virtue of these non separable penalties is their ability to borrow strength across coordinates adapt to ensemble sparsity information and exert multiplicity adjustment the spike and slab lasso procedure harvests efficient coordinate wise implementations with a path following scheme for dynamic posterior exploration we show on simulated data that the fully bayes penalty mimics oracle performance providing a viable alternative to cross validation we develop theory for the s

a new lmi based approach to relaxed quadratic stabilization of t s fuzzy control systems this paper proposes a new quadratic stabilization condition for takagi sugeno t s fuzzy control systems the condition is represented in the form of linear matrix inequalities lmis and is shown to be less conservative than some relaxed quadratic stabilization conditions published recently in the literature a rigorous theoretic proof is given to show that the proposed condition can include previous results as special cases in comparison with conventional conditions the proposed condition is not only suitable for designing fuzzy state feedback controllers but also convenient for fuzzy static output feedback controller design the latter design work is quite hard for t s fuzzy control systems based on the lmi based conditions derived one can easily synthesize controllers for stabilizing t s fuzzy control systems since only a set of lmis is involved the controller design is quite simple and numerically tractable finally the validity and applicability of the proposed approach are successfully demonstrated in the control of a continuous time nonlinear system

new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi the problems of relaxed quadratic stability conditions fuzzy observer designs and h controller designs for t s fuzzy systems have been studied first new stability conditions are obtained by relaxing the stability conditions derived in previous papers secondly new fuzzy observers based on the relaxed stability conditions for the t s fuzzy systems have been proposed thirdly two sufficient lmi conditions which guarantee the existence of the h controllers based on fuzzy observers for the t s fuzzy systems have been proposed the conditions are not only simple but also consider the interactions among the fuzzy subsystems finally by some examples using the lmi technique we show that the regulators the fuzzy observers and the h controller designs based on new observers for the t s fuzzy systems are very practical and efficient

approaches to quadratic stability conditions and h sub spl infin control designs for t s fuzzy systems in this paper the problems of quadratic stability conditions and h sub spl infin control designs for takagi sugeno t s fuzzy systems have been studied first a new quadratic stability condition which is more simple than that in a previous paper has been proposed second two new sufficient conditions in the terms of linear matrix inequalities lmis which guarantee the existence of the state feedback h sub spl infin control for the t s fuzzy systems have been proposed the conditions are not only simple but also consider the interactions among the fuzzy subsystems finally based on the lmis the h sub spl infin controller designing methods for the t s fuzzy systems have been given

a note on posterior moments for a normal mean with double exponential prior summary general results on the behaviour of the posterior mean and variance of the mean of a normal distribution with known variance using a double exponential prior are derived and complement the conjectures and particular examples given by pericchi and smith 1992 and pericchi and walley 1991

relaxed stabilization criterion for t s fuzzy systems by minimum type piecewise lyapunov function based switching fuzzy controller this paper proposes the minimum type piecewise lyapunov function based switching fuzzy controller that switches accompanying the piecewise lyapunov function by applying this switching fuzzy controller with the minimum type piecewise lyapunov function the relaxed stabilization criterion is obtained for continuous takagi sugeno t s fuzzy systems some conditions of the relaxed stabilization criterion are represented by bilinear matrix inequalities bmis which contain some bilinear terms as the product of a full matrix and a scalar according to the literature the path following method is very effective for this kind of bmi problem hence it is utilized to obtain solutions of the criterion xie et al in 1997 chose two types i e minimum type and maximum type of piecewise lyapunov functions as the lyapunov function candidates the reasons for why this study only chooses the minimum type piecewise lyapunov function as the lyapunov function candidate are illustrated moreover the numerical example shows the relaxation of the proposed criterion

new approaches to relaxed quadratic stability condition of fuzzy control systems this paper deals with the quadratic stability conditions of fuzzy control systems that relax the existing conditions reported in the previous literatures two new conditions are proposed and shown to be useful in analyzing and designing fuzzy control systems the first one employs the s procedure to utilize information regarding the premise parts of the fuzzy systems the next one enlarges the class of fuzzy control systems whose stability is ensured by representing the interactions among the fuzzy subsystems in a single matrix and solving it by linear matrix inequality the relationships between the suggested stability conditions and the conventional well known stability conditions reported in the previous literatures are also discussed and it is shown in a rigorous manner that the second condition of this paper includes the conventional conditions finally some examples and simulation results are presented to illustrate the effectiveness of the stability conditions

bayesian lasso regression summary the lasso estimate for linear regression corresponds to a posterior mode when independent double exponential prior distributions are placed on the regression coefficients this paper intro duces new aspects of the broader bayesian treatment of lasso regression a direct characterization of the regression coefficients posterior distribution is provided and computation and inference under this characterization is shown to be straightforward emphasis is placed on point estima tion using the posterior mean which facilitates prediction of future observations via the posterior predictive distribution it is shown that the standard lasso prediction method does not neces sarily agree with model based bayesian predictions a new gibbs sampler for bayesian lasso regression is introduced

convergent lmi relaxations for quadratic stabilizability and mathscr h _ infty control of takagi sugeno fuzzy systems this paper investigates the quadratic stabilizability of takagi sugeno t s fuzzy systems by means of parallel distributed state feedback compensators using finsler s lemma a new design condition assuring the existence of such a controller is formulated as a parameter dependent linear matrix inequality lmi with extra matrix variables and parameters in the unit simplex algebraic properties of the system parameters and recent results of positive polynomials are used to construct lmi relaxations that differently from most relaxations in the literature provide certificates of convergence to solve the control design problem due to the degrees of freedom obtained with the extra variables the conditions presented in this paper are an improvement over earlier results based only on polya s theorem and can be viewed as an alternative to the use of techniques based on the relaxation of quadratic forms an extension to cope with guaranteed h infin attenuation levels is also given with proof of asymptotic convergence to the global optimal controller under quadratic stability the efficiency of the proposed approach in terms of precision and computational effort is demonstrated by means of numerical comparisons with other methods from the literature

stability analysis and region of attraction estimation using piecewise polynomial lyapunov functions polynomial fuzzy model approach this paper proposes sum of squares sos methodologies for stability analysis and region of attraction roa estimation for nonlinear systems represented by polynomial fuzzy models via piecewise polynomial lyapunov functions pplfs at first two sos based global stability criteria are proposed by applying maximum type and minimum type pplfs respectively it is known that less conservative results can be obtained by reducing global stability to local stability since it is usually the case for nonlinear systems that the stability cannot be reached globally therefore based on the two types of pplfs two local stability criteria are further proposed with the algorithms that enlarge the estimated roa as much as possible the constraints for checking global and local stability and enlarging the estimated roa are represented in terms of bilinear sos problems hence the path following method is applied to solve the bilinear sos problems in the proposed methodologies finally some examples are provided to illustrate the utility of the proposed methodologies

a convex approach to robust stability for linear systems with uncertain scalar parameters in this paper robust stability for linear systems with several uncertain complex and or real scalar parameters is studied a countable family of conditions sufficient for robust stability is given in terms of solvability of some simple linear matrix inequalities lmis these conditions are of increasing precision and it is shown conversely that robust stability implies solvability of these lmis from a certain rank and beyond this result constitutes an extension of the characterization by solvability of lyapunov inequality of the asymptotic stability for usual linear systems it is based on the search of parameter dependent quadratic lyapunov functions polynomial of increasing degree in the parameters

asymptotically necessary and sufficient conditions for stability and performance in fuzzy control applications of polya s theorem stability and performance requirements in fuzzy control of takagi sugeno systems are usually stated as fuzzy summations i e sums of terms related to lyapunov functions which are weighted by membership functions or products of them this paper presents an application to fuzzy control of polya s theorems on positive forms on the standard simplex the result provides a set of progressively less conservative sufficient conditions for proving positivity of fuzzy summations such conditions are less and less conservative as a complexity parameter n increases particular cases of such conditions are those in c h fang y s liu s w kau l hong c h lee a new lmi based approach to relaxed quadratic stabilization of t s fuzzy control systems ieee trans fuzzy systems 14 2006 286 397 x liu q zhang new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi automatica 39 9 2003 1571 1582 with n 2 and 3 respectively the proposed conditions are asymptotically exact i e necessary and sufficient when n tends to infinity or equivalently when a tolerance parameter tends to zero

exact and approximate posterior moments for a normal location parameter the forms of first and second posterior moments for a normal location parameter are identified for a rather general class of prior distributions exact and approximate illustrations are given where the prior distribution is double exponential or student t respectively

ott sudan ostrovskiy equation on a half line abstract we consider the initial boundary value problem for the ott sudan ostrovskiy equation on a half line we study traditionally important problems of the theory of nonlinear partial differential equations such as global in time existence of solutions to the initial boundary value problem and the asymptotic behavior of solutions for large time

bayesian group factor analysis with structured sparsity latent factor models are the canonical statistical tool for exploratory analyses of low dimensional linear structure for a matrix of p features across n samples we develop a structured bayesian group factor analysis model that extends the factor model to multiple coupled observation matrices in the case of two observations this reduces to a bayesian model of canonical correlation analysis here we carefully define a structured bayesian prior that encourages both element wise and column wise shrinkage and leads to desirable behavior on high dimensional data in particular our model puts a structured prior on the joint factor loading matrix regularizing at three levels which enables element wise sparsity and unsupervised recovery of latent factors corresponding to structured variance across arbitrary subsets of the observations in addition our structured prior allows for both dense and sparse latent factors so that covariation among either all features or only a subset of features can be recovered we use fast parameter expanded expectation maximization for parameter estimation in this model we validate our method on simulated data with substantial structure we show results of our method applied to three high dimensional data sets comparing results against a number of state of the art approaches these results illustrate useful properties of our model including i recovering sparse signal in the presence of dense effects ii the ability to scale naturally to large numbers of observations iii flexible observation and factor specific regularization to recover factors with a wide variety of sparsity levels and percentage of variance explained and iv tractable inference that scales to modern genomic and text data sizes

on switched regulator design of uncertain nonlinear systems using takagi sugeno fuzzy models this paper is concerned with the design of state feedback switched controllers for a class of uncertain nonlinear plants described by takagi sugeno t s fuzzy models the proposed methodology eliminates the need to find the membership function expressions to implement the control law which is relevant in cases where the membership function depends on uncertain parameters the design of the switched controllers is based on a minimum type lyapunov function and the minimization of the time derivative of this lyapunov function the conditions of the new stability criterion are represented by a kind of bilinear matrix inequalities bmis that has been solved by the path following method a numerical example and the nonlinear control design of a magnetic levitator with uncertainties illustrate the procedure

a new sum of squares design framework for robust control of polynomial fuzzy systems with uncertainties this paper presents a new sum of squares sos for brevity design framework for robust control of polynomial fuzzy systems with uncertainties two kinds of robust stabilization conditions are derived in terms of sos one is global sos robust stabilization conditions that guarantee the global and asymptotical stability of polynomial fuzzy control systems the other is semiglobal sos robust stabilization conditions the latter is available for very complicated systems that are difficult to guarantee the global and asymptotical stability of polynomial fuzzy control systems the main feature of all the sos robust stabilization conditions derived in this paper are to be expressed as nonconvex formulations with respect to polynomial lyapunov function parameters and polynomial feedback gains since a typical transformation from nonconvex sos design conditions to convex sos design conditions often results in some conservative issues the new design framework presented in this paper gives key ideas to avoid the conservative issues the first key idea is that we directly solve nonconvex sos design conditions without applying the typical transformation the second key idea is that we bring a so called copositivity concept these ideas provide some advantages in addition to relaxations to solve our sos robust stabilization conditions efficiently we introduce a gradient algorithm formulated as a minimizing optimization problem of the upper bound of the time derivative of an sos polynomial that can be regarded as a candidate of polynomial lyapunov functions three design examples are provided to illustrate the validity and applicability of the proposed design framework the examples demonstrate advantages of our new sos design framework for the existing linear matrix inequality approaches and the existing convex sos approach

conjugate convex lyapunov functions for dual linear differential inclusions tools from convex analysis are used to show how stability properties and lyapunov inequalities translate when passing from a linear differential inclusion ldi to its dual in particular it is proved that a convex positive definite function is a lyapunov function for an ldi if and only if its convex conjugate is a lyapunov function for the ldis dual examples show how such duality effectively doubles the number of tools available for assessing stability of ldis

bayesian generalized kernel mixed models we propose a fully bayesian methodology for generalized kernel mixed models gkmms which are extensions of generalized linear mixed models in the feature space induced by a reproducing kernel we place a mixture of a point mass distribution and silverman s g prior on the regression vector of a generalized kernel model gkm this mixture prior allows a fraction of the components of the regression vector to be zero thus it serves for sparse modeling and is useful for bayesian computation in particular we exploit data augmentation methodology to develop a markov chain monte carlo mcmc algorithm in which the reversible jump method is used for model selection and a bayesian model averaging method is used for posterior prediction when the feature basis expansion in the reproducing kernel hilbert space is treated as a stochastic process this approach can be related to the karhunen loeve expansion of a gaussian process gp thus our sparse modeling framework leads to a flexible approximation method for gps

on scale mixtures of normal distributions summary the exponential power family of distributions of box tiao 1973 is shown to be a subset of the class of scale mixtures of normals the corresponding mixing distributions are explicitly obtained identifying a close relationship between the exponential power family and a further class of normal scale mixtures namely the stable distributions

a descriptor system approach to fuzzy control system design via fuzzy lyapunov functions there has been a flurry of research activities in the analysis and design of fuzzy control systems based on linear matrix inequalities lmis this paper presents a descriptor system approach to fuzzy control system design using fuzzy lyapunov functions the design conditions are still cast in terms of lmis but the proposed approach takes advantage of the redundancy of descriptor systems to reduce the number of lmi conditions which leads to less computational requirement to obtain relaxed lmi conditions new types of fuzzy controller and fuzzy lyapunov function are proposed a salient feature of the lmi conditions derived in this paper is to relate the feasibility of the lmis to the switching speed of each linear subsystem to be exact to the lower bounds of time derivatives of membership functions to illustrate the validity and applicability of the proposed approach two design examples are provided the first example shows that the lmi conditions based on the fuzzy lyapunov function are less conservative than those based on a common standard lyapunov function the second example illustrates the utility of the fuzzy lyapunov function approach in comparison with a piecewise lyapunov function approach

mixtures envelopes and hierarchical duality summary we develop a connection between mixture and envelope representations of objective functions that arise frequently in statistics we refer to this connection by using the term hierarchical duality our results suggest an interesting and previously underexploited relationship between marginalization and profiling or equivalently between the fenchel moreau theorem for convex functions and the bernstein widder theorem for laplace transforms we give several different sets of conditions under which such a duality result obtains we then extend existing work on envelope representations in several ways including novel generalizations to variance mean models and to multivariate gaussian location models this turns out to provide an elegant missing data interpretation of the proximal gradient method which is a widely used algorithm in machine learning we show several statistical applications in which the framework proposed leads to easily implemented algorithms including a robust version of the fused lasso non linear quantile regression via trend filtering and the binomial fused double pareto model code for the examples is available on github at https github com jgscott hierduals

lmi based relaxed nonquadratic stabilization conditions for nonlinear systems in the takagi sugeno s form this paper presents the stabilization analysis for a class of nonlinear systems that are represented by a takagi and sugeno ts discrete fuzzy model takagi and sugeno ieee trans systems man cybern 15 1 1985 116 the main result given here concerns their stabilization using new control laws and new nonquadratic lyapunov functions new relaxed conditions and linear matrix inequality based design are proposed that allow outperforming previous results found in the literature two examples are also provided to demonstrate the efficiency of the approaches

homogeneous polynomially nonquadratic stabilization of discrete time takagi sugeno systems via nonparallel distributed compensation law this paper considers stability of discrete time nonlinear systems in takagi sugeno t s form this problem has been studied for more than 20 years with many sufficient conditions and the asymptotically necessary and sufficient ans conditions with respect to the common quadratic lyapunov function having being obtained this paper considers general forms of homogeneous polynomially nonquadratic lyapunov hpnql function and homogeneous polynomially parameterized nonparallel distributed compensation hpp non pdc law by generalization of the procedure based on polya s theorem and techniques used for parameter dependent linear matrix inequality pd lmi which have been studied previously in different contexts ans stability conditions with respect to the general hpnql function are obtained

the horseshoe estimator for sparse signals this paper proposes a new approach to sparsity called the horseshoe estimator the horseshoe is a close cousin of other widely used bayes rules arising from for example double exponential and cauchy priors in that it is a member of the same family of multivariate scale mixtures of normals but the horseshoe enjoys a number of advantages over existing approaches including its robustness its adaptivity to dierent sparsity patterns and its analytical tractability we prove two theorems that formally characterize both the horseshoe s adeptness at large outlying signals and its super ecient rate of convergence to the correct estimate of the sampling density in sparse situations finally using a combination of real and simulated data we show that the horseshoe estimator corresponds quite closely to the answers one would get by pursuing a full bayesian model averaging approach using a discrete mixture prior to model signals and noise

the bayesian bridge summary we propose the bayesian bridge estimator for regularized regression and classification two key mixture representations for the bayesian bridge model are developed a scale mixture of normal distributions with respect to an stable random variable a mixture of bartlett fejer kernels or triangle densities with respect to a two component mixture of gamma random variables both lead to markov chain monte carlo methods for posterior simulation and these methods turn out to have complementary domains of maximum efficiency the first representation is a well known result due to west and is the better choice for collinear design matrices the second representation is new and is more efficient for orthogonal problems largely because it avoids the need to deal with exponentially tilted stable random variables it also provides insight into the multimodality of the joint posterior distribution which is a feature of the bridge model that is notably absent under ridge or lasso type priors we prove a theorem that extends this representation to a wider class of densities representable as scale mixtures of beta distributions and we provide an explicit inversion formula for the mixing distribution the connections with slice sampling and scale mixtures of normal distributions are explored on the practical side we find that the bayesian bridge model outperforms its classical cousin in estimation and prediction across a variety of data sets both simulated and real we also show that the markov chain monte carlo algorithm for fitting the bridge model exhibits excellent mixing properties particularly for the global scale parameter this makes for a favourable contrast with analogous markov chain monte carlo algorithms for other sparse bayesian models all methods described in this paper are implemented in the r package bayesbridge an extensive set of simulation results is provided in two on line supplemental files

functional horseshoe priors for subspace shrinkage we introduce a new shrinkage prior on function spaces called the functional horseshoe fhs prior that encourages shrinkage toward parametric classes of functions unlike other shrinkage priors f

bayes and empirical bayes methods for reduced rank regression models in matched case control studies matched case control studies are popular designs used in epidemiology for assessing the effects of exposures on binary traits modern studies increasingly enjoy the ability to examine a large number of exposures in a comprehensive manner however several risk factors often tend to be related in a nontrivial way undermining efforts to identify the risk factors using standard analytic methods due to inflated type i errors and possible masking of effects epidemiologists often use data reduction techniques by grouping the prognostic factors using a thematic approach with themes deriving from biological considerations we propose shrinkage type estimators based on bayesian penalization methods to estimate the effects of the risk factors using these themes the properties of the estimators are examined using extensive simulations the methodology is illustrated using data from a matched case control study of polychlorinated biphenyls in relation to the etiology of non hodgkin s lymphoma

a sum of squares approach to modeling and control of nonlinear dynamical systems with polynomial fuzzy systems this paper presents a sum of squares sos approach for modeling and control of nonlinear dynamical systems using polynomial fuzzy systems the proposed sos based framework provides a number of innovations and improvements over the existing linear matrix inequality lmi based approaches to takagi sugeno t s fuzzy modeling and control first we propose a polynomial fuzzy modeling and control framework that is more general and effective than the well known t s fuzzy modeling and control secondly we obtain stability and stabilizability conditions of the polynomial fuzzy systems based on polynomial lyapunov functions that contain quadratic lyapunov functions as a special case hence the stability and stabilizability conditions presented in this paper are more general and relaxed than those of the existing lmi based approaches to t s fuzzy modeling and control moreover the derived stability and stabilizability conditions are represented in terms of sos and can be numerically partially symbolically solved via the recently developed sostools to illustrate the validity and applicability of the proposed approach a number of analysis and design examples are provided the first example shows that the sos approach renders more relaxed stability results than those of both the lmi based approaches and a polynomial system approach the second example presents an extensive application of the sos approach in comparison with a piecewise lyapunov function approach the last example is a design exercise that demonstrates the viability of the sos based approach to synthesizing a stabilizing controller

the calculation of posterior distributions by data augmentation abstract the idea of data augmentation arises naturally in missing value problems as exemplified by the standard ways of filling in missing cells in balanced two way tables thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze this device is used to great advantage by the em algorithm dempster laird and rubin 1977 in solving maximum likelihood problems in situations when the likelihood cannot be approximated closely by the normal likelihood maximum likelihood estimates and the associated standard errors cannot be relied upon to make valid inferential statements from the bayesian point of view one must now calculate the posterior distribution of parameters of interest if data augmentation can be used in the calculation of the maximum likelihood estimate then in the same cases one ought to be able to use it in the computation of the posterior distribution it is the purpose of this article to explain how this can be done the basic idea