combined fuzzy logic and genetic algorithm techniques application to an electromagnetic field problem the influence of a faulted electrical power transmission line on a buried pipeline is investigated the induced electromagnetic field depends on several parameters such as the position of the phase conductors the currents flowing through conducting materials and the earth resistivity a fuzzy logic system was used to simulate the problem it was trained using data derived from finite element method calculations for different configuration cases training set of the above electromagnetic field problem after the training the system was tested for several configuration cases differing significantly from the training cases with satisfactory results it is shown that the proposed method is very time efficient and accurate in calculating electromagnetic fields compared to the time straining finite element method in order to create the rule base for the fuzzy logic system a special incremental learning scheme is used during the training the system is trained using genetic algorithms binary and real genetic encoding were implemented and compared

numerical solution of systems of second order boundary value problems using continuous genetic algorithm in this paper continuous genetic algorithm is introduced as an efficient solver for systems of second order boundary value problems where smooth solution curves are used throughout the evolution of the algorithm to obtain the required nodal values of the unknown variables the solution methodology is based on representing each derivative in the system of differential equations by its finite difference approximation after that the overall residue for all nodes in the given system of differential equations is formulated the solution to the system of differential equations is then converted into the problem of minimizing the overall residue or maximizing the fitness function based on the nodal values generated from the genetic operators three numerical test problems including linear and nonlinear systems were analyzed to illustrate the procedure and confirm the performance of the proposed method in addition to that a convergence and sensitivity analysis to genetic operators and control parameters of the algorithm has been carried out the numerical results show that the proposed algorithm is a robust and accurate procedure for solving systems of second order boundary value problems furthermore the obtained accuracy for the solutions using cga is much better than the results obtained using some modern methods

new estimates for ritz vectors the following estimate for the rayleigh ritz method is proved u u au u sin u u u 1 here a is a bounded self adjoint operator in a real hilbert euclidian space u one of its eigenpairs u a trial subspace for the rayleigh ritz method and u a ritz pair this inequality makes it possible to analyze the fine structure of the error of the rayleigh ritz method in particular it shows that u u c 2 if an eigenvector u is close to the trial subspace with accuracy and a ritz vector u is an approximation to another eigenvector with a different eigenvalue generalizations of the estimate to the cases of eigenspaces and invariant subspaces are suggested and estimates of approximation of eigenspaces and invariant subspaces are proved

a ga based fuzzy modeling approach for generating tsk models this paper proposes a new genetic based modeling method for building simple and well defined tsk models with scatter type input partitions our approach manages all attributes characterizing the structure of a tsk model simultaneously particularly it determines the number of rules the input partition the participating inputs in each rule and the consequent parameters the model building process is divided into two phases in phase one the structure learning task is formulated as a multi objective optimization problem which is resolved using a novel genetic based structure learning gbsl scheme apart from the mean square error mse and the number of rules three additional criteria are introduced in the fitness function for measuring the quality of the partitions optimization of these measures leads to models with representative rules small overlapping and efficient data cover in order to obtain models with accurate data fitting and good local performance the consequent parameters are determined using a local mse function while the overall model is evaluated on the basis of a global mse function the search capabilities of the suggested structure learning scheme are significantly enhanced by including a highly effective local search operator implemented by a micro genetic algorithm and four problem specific operators finally a genetic based parameter learning gbpl scheme is suggested in phase two which performs fine tuning of the initial models obtained after structure learning the performance of the proposed modeling approach is evaluated using a static example and a well known dynamic benchmark problem simulation results demonstrate that our models outperform those suggested by other methods with regard to simplicity model structure and accuracy

shotgun stochastic search for large p regression model search in regression with very large numbers of candidate predictors raises challenges for both model specification and computation for which standard approaches such as markov chain monte carlo mcmc methods are often infeasible or ineffective we describe a novel shotgun stochastic search sss approach that explores interesting regions of the resulting high dimensional model spaces and quickly identifies regions of high posterior probability over models we describe algorithmic and modeling aspects priors over the model space that induce sparsity and parsimony over and above the traditional dimension penalization implicit in bayesian and likelihood analyses and parallel computation using cluster computers we discuss an example from gene expression cancer genomics comparisons with mcmc and other methods and theoretical and simulation based aspects of performance characteristics in large scale regression model searches we also provide software implementing the methods

data driven fuzzy modeling for takagi sugeno kang fuzzy system this paper presents a systematic approach to design first order tagaki sugeno kang tsk fuzzy systems this approach attempts to obtain the fuzzy rules without any assumption about the structure of the data the structure identification and parameter optimization steps in this approach are carried out automatically and are capable of finding the optimal number of the rules with an acceptable accuracy starting with an initial structure the system first tries to improve the structure and then as soon as an improved structure is found it fine tunes its rules parameters then it goes back to improve the structure again to find a better structure and re fine tune the rules parameters this loop continues until a satisfactory solution tsk model is found the proposed approach has successfully been applied to well known benchmark datasets and real world problems the obtained results are compared with those obtained with other methods from the literature experimental studies demonstrate that the predicted properties have a good agreement with the measured data by using the elicited fuzzy model with a small number of rules finally as a case study the proposed approach is applied to the desulfurization process of a real steel industry comparing the proposed approach with some other fuzzy systems and neural networks it is shown that the developed tsk fuzzy system exhibits better results with higher accuracy and smaller size of architecture

selecting fuzzy if then rules for classification problems using genetic algorithms this paper proposes a genetic algorithm based method for selecting a small number of significant fuzzy if then rules to construct a compact fuzzy classification system with high classification power the rule selection problem is formulated as a combinatorial optimization problem with two objectives to maximize the number of correctly classified patterns and to minimize the number of fuzzy if then rules genetic algorithms are applied to this problem a set of fuzzy if then rules is coded into a string and treated as an individual in genetic algorithms the fitness of each individual is specified by the two objectives in the combinatorial optimization problem the performance of the proposed method for training data and test data is examined by computer simulations on the iris data of fisher

identifying a fuzzy model by using the bipartite membership functions the gradient descent method and genetic algorithms have been widely used to refine fuzzy models constructed for the given data this paper approaches from another viewpoint to adjusting the fuzzy model built for the preprocessed data the membership functions defined for each premise variable are equally distributed and fixed in the transformed domain to better identify the fuzzy model either the transformation functions or consequent parts of fuzzy rules or both need to be optimized since adjusting a rule to satisfy one pattern may deteriorate the others performance and result in a lengthy tuning process we then treat each triangular membership function as two disjoint ones such that each fuzzy rule is divided into mutually independent rules this in turn benefits the refinement of consequent parts in the fuzzy rules since adjusting a rule will not affect the others not only the simulation results from the proposed model will be demonstrated but also the results from the conventional approaches will be given for comparisons we use the least squared method to calculate the desired consequent real numbers for the data located in the same region of transformed domain the conformity of the after tuned consequent parts in the fuzzy rules with the desired values further verifies the effectiveness of the presented methodology

simplifying fuzzy modeling by both gray relational analysis and data transformation methods abstract instead of following the traditional approaches which utilize original data patterns to construct the fuzzy model this paper proposes to exploit both gray relational analysis and data transformation techniques to simplify the modeling procedures the transformation method allows us to map the original data to other domains such that there is no need to adjust the membership functions and the fuzzification process is simply taking place on the fixed ones since too many system variables involved may complicate the fuzzy modeling the gray relational method is exploited to select the crucial variables from a finite set of candidates based on the calculated relational degrees between the output and the prospective input variables we can decide which are the important premise variables the proposed methods have definite effects on the model s performance therefore the way to systematically adjust the transformation functions is also investigated ease in selecting the premise variables and minimal effort needed to adjust system parameters are the merits of the proposed work simulation results from two different examples are presented to demonstrate the superiority of the proposed model to the conventional methodologies

finite element galerkin approximation of the eigenvalues and eigenvectors of selfadjoint problems abstract this paper establishes some refined estimates for the approximation of the eigenvalues and eigenvectors of selfadjoint eigenvalue problems by finite element or more generally galerkin methods suppose lambda is an eigenvalue of multiplicity q of a selfajoint problem and let m lambda denote the space of eigenvectors corresponding to lambda keywords hilbert space

on the field of values of oblique projections abstract we highlight some properties of the field of values or numerical range w p of an oblique projector p on a hilbert space i e of an operator satisfying p 2 p if p is neither null nor the identity we present a direct proof showing that w p w i p i e the field of values of an oblique projection coincides with that of its complementary projection we also show that w p is an elliptical disk i e the set of points circumscribed by an ellipse with foci at 0 and 1 and eccentricity 1 p these two results combined provide a new proof of the identity p i p we discuss the influence of the minimal canonical angle between the range and the null space of p on the shape of w p in the finite dimensional case we show a relation between the eigenvalues of matrices related to these complementary projections and present a second proof to the fact that w p is an elliptical disk

fully bayes factors with a generalized g prior for the normal linear model variable selection problem we propose selection criteria based on a fully bayes formulation with a generalization of zellner s g prior which allows for p n a special case of the prior formulation is seen to yield tractable closed forms for marginal densities and bayes factors which reveal new model evaluation characteristics of potential interest

fuzzy modelling and identification with genetic algorithm based learning abstract a ga based learning algorithm is proposed in this paper for the identification of tsk models the algorithm consists of four blocks partition block ga block tuning block and termination block the partition block is to determine an estimated partition of input variables the ga block is to optimise the structure of a tsk model the tuning block is to fine tune the parameters of the tsk model using the gradient descent based approach and the termination block checks that the resultant tsk model is satisfactory the proposed gabl algorithm has the advantage of simplicity flexibility high accuracy and automation the presented numerical examples indicate that the gabl algorithm is effective in constructing a good tsk model for complex nonlinear systems

bayesian regression trees for high dimensional prediction and variable selection abstractdecision tree ensembles are an extremely popular tool for obtaining high quality predictions in nonparametric regression problems unmodified however many commonly used decision tree ensemble methods do not adapt to sparsity in the regime in which the number of predictors is larger than the number of observations a recent stream of research concerns the construction of decision tree ensembles that are motivated by a generative probabilistic model the most influential method being the bayesian additive regression trees bart framework in this article we take a bayesian point of view on this problem and show how to construct priors on decision tree ensembles that are capable of adapting to sparsity in the predictors by placing a sparsity inducing dirichlet hyperprior on the splitting proportions of the regression tree prior we characterize the asymptotic distribution of the number of predictors included in the model and show how this prior can be easily incorporated into existing markov chai

self tuning fuzzy modeling with adaptive membership function rules and hierarchical structure based on genetic algorithm abstract recently fuzzy systems have been used in many fields and places in order to apply the fuzzy system to the various fields the tuning and optimizing method of the fuzzy system is the key issue some self tuning methods have been proposed so far however these conventional self tuning methods do not have sufficient capability of learning in this paper we propose a new supervised self tuning fuzzy modeling which consist of some membership function expressed by the radial basis function with insensitive region learning is carried out by the genetic algorithms the descent method is also utilized for tuning the shapes of the membership function and consequent parts the effectiveness of the proposed methods is shown by some numerical examples

emvs the em approach to bayesian variable selection despite rapid developments in stochastic search algorithms the practicality of bayesian variable selection methods has continued to pose challenges high dimensional data are now routinely analyzed typically with many more covariates than observations to broaden the applicability of bayesian variable selection for such high dimensional linear regression contexts we propose emvs a deterministic alternative to stochastic search based on an em algorithm which exploits a conjugate mixture prior formulation to quickly find posterior modes combining a spike and slab regularization diagram for the discovery of active predictor sets with subsequent rigorous evaluation of posterior model probabilities emvs rapidly identifies promising sparse high posterior probability submodels external structural information such as likely covariate groupings or network topologies is easily incorporated into the emvs framework deterministic annealing variants are seen to improve the effectiveness of our algorithms by mit

approximation of the spectrum of closed operators the determination of normal modes of a rotating basin note univ michigan dept math ann arbor mi 48109 ecole polytech ctr math appl f 91128 palaiseau france descloux j ecole prat hautes etud dept math f 75231 paris 05 france isi document delivery no le068times cited 3cited reference count 17 reference asn article 1981 004doi 10 2307 2007731 record created on 2006 08 24 modified on 2017 05 12

bayesian variable selection in structured high dimensional covariate spaces with applications in genomics we consider the problem of variable selection in regression modeling in high dimensional spaces where there is known structure among the covariates this is an unconventional variable selection problem for two reasons 1 the dimension of the covariate space is comparable and often much larger than the number of subjects in the study and 2 the covariate space is highly structured and in some cases it is desirable to incorporate this structural information in to the model building process we approach this problem through the bayesian variable selection framework where we assume that the covariates lie on an undirected graph and formulate an ising prior on the model space for incorporating structural information certain computational and statistical problems arise that are unique to such high dimensional structured settings the most interesting being the phenomenon of phase transitions we propose theoretical and computational schemes to mitigate these problems we illustrate our methods on two

bayes and empirical bayes multiplicity adjustment in the variable selection problem this paper studies the multiplicity correction effect of standard bayesian variable selection priors in linear regression our first goal is to clarify when and how multiplicity correction happens automatically in bayesian analysis and to distinguish this correction from the bayesian ockham s razor effect our second goal is to contrast empirical bayes and fully bayesian approaches to variable selection through examples theoretical results and simulations considerable differences between the two approaches are found in particular we prove a theorem that characterizes a surprising aymptotic discrepancy between fully bayes and empirical bayes this discrepancy arises from a different source than the failure to account for hyperparameter uncertainty in the empirical bayes estimate indeed even at the extreme when the empirical bayes estimate converges asymptotically to the true variable inclusion probability the potential for a serious difference remains

scalable bayesian model averaging through local information propagation this article shows that a probabilistic version of the classical forward stepwise variable inclusion procedure can serve as a general data augmentation scheme for model space distributions in generalized linear models this latent variable representation takes the form of a markov process thereby allowing information propagation algorithms to be applied for sampling from model space posteriors in particular we propose a sequential monte carlo method for achieving effective unbiased bayesian model averaging in high dimensional problems using proposal distributions constructed using local information propagation the method called lips for local information propagation based sampling is illustrated using real and simulated examples with dimensionality ranging from 15 to 1000 and its performance in estimating posterior inclusion probabilities and in out of sample prediction is compared to those of several other methods namely mcmc bas ibma and lasso in addition it is shown that the latent variab

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

cluster robust error estimates for the rayleigh ritz approximation i estimates for invariant subspaces this is the first part of a paper that deals with error estimates for the rayleigh ritz approximations to the spectrum and invariant subspaces of a bounded hermitian operator in a hilbert or euclidean space this part addresses estimates for the angles between the invariant subspaces and their approximations via the corresponding best approximation errors and residuals and for invariant subspaces corresponding to parts of the discrete spectrum via eigenvalue errors the paper s major concern is to ensure that the estimates in question are accurate and cluster robust i e are not adversely affected by the presence of clustered i e closely situated eigenvalues in the spectrum available estimates of such kind are reviewed and new estimates are derived the paper s main new results introduce estimates for invariant subspaces in which the operator may have clustered eigenvalues whereby not only the distances between eigenvalues in the cluster are not present but also the distances between the cluster and the rest of the spectrum appear in asymptotically insignificant terms only

stability issues on takagi sugeno fuzzy model parametric approach the main objective of this research is to provide a systematic stability analysis technique for fuzzy systems using well established results from robust stability of a family of polynomials the model based takagi sugeno 1985 fuzzy control system is considered and shown to have a dependent coefficient structure involving firing strengths two kharitonov regions via overbounding are established to facilitate the extreme results for stability test in the space of polynomials as well as the complex plane the criterion obtained is a sufficient condition for a fuzzy logic controller three nonlinear examples are demonstrated to show that the systematic approach proposed here can be used to solve fuzzy stability problems fuzzy users concerned over stability issues may find these analytic tools useful

universal approximation by hierarchical fuzzy system with constraints on the fuzzy rule this paper presents a special hierarchical fuzzy system where the outputs of the previous layer are not used in the if parts but used only in the then parts of the fuzzy rules of the current layer the proposed scheme can be shown to be a universal approximator to any continuous function on a compact set if complete fuzzy sets are used in the if parts of the fuzzy rules with singleton fuzzifier and center average defuzzifier from the simulation of ball and beam control system it is demonstrated that the proposed scheme approximates with good accuracy the model nonlinear controller with fewer fuzzy rules than the centralized fuzzy system and its control performance is comparable to that of the nonlinear controller

comment regularization via bayesian penalty mixing ridge regression and the lasso illustrate some of the remarkable successes of penalized likelihood regularization for regression analysis when viewed through the bayesian lens of posterior maximiz

mixtures of g priors for bayesian variable selection zellner s g prior remains a popular conventional prior for use in bayesian variable selection despite several undesirable consistency issues in this article we study mixtures of g priors as an alternative to default g priors that resolve many of the problems with the original formulation while maintaining the computational tractability that has made the g prior so popular we present theoretical properties of the mixture g priors and provide real and simulated examples to compare the mixture formulation with fixed g priors empirical bayes approaches and other default procedures please see arnold zellner s letter and the author s response

spike and slab variable selection frequentist and bayesian strategies variable selection in the linear regression model takes many apparent faces from both frequentist and bayesian standpoints in this paper we introduce a variable selection method referred to as a rescaled spike and slab model we study the importance of prior hierarchical specifications and draw connections to frequentist generalized ridge regression estimation specifically we study the usefulness of continuous bimodal priors to model hypervariance parameters and the effect scaling has on the posterior mean through its relationship to penalization several model selection strategies some frequentist and some bayesian in nature are developed and studied theoretically we demonstrate the importance of selective shrinkage for effective variable selection in terms of risk misclassification and show this is achieved using the posterior from a rescaled spike and slab model we also show how to verify a procedure s ability to reduce model uncertainty in finite samples using a specialized forward selection strategy using this tool we illustrate the effectiveness of rescaled spike and slab models in reducing model uncertainty

asafes2 a novel neuro fuzzy architecture for fuzzy computing based on functional reasoning abstract the functional reasoning or takagi sugeno fuzzy reasoning method is a very promising approach to the task of multi variable non linear function approximation and the design of a fuzzy model and fuzzy controller the proposed architecture asafes2 is a neuro fuzzy function approximator and is the first attempt to combine this reasoning method with stochastic reinforcement learning it can learn a function to a high degree of accuracy at a very great speed and furthermore expresses it in a set of linear relations the main ideas are the fuzzy partitioning of the input space into fuzzy subspaces each corresponding to a possible fuzzy rule and the use of a separate neural unit for every fuzzy subspace in order to calculate the optimum consequence parameters simulation results prove its superiority over back propagation in simple non linear function approximation tasks and over all previous approaches to the box and jenkins gas furnace modelling comparisons are also made with generalized radial basis function networks finally asafes2 as a building block in a learning fuzzy logic controller is applied to the well known cart pole stabilization problem with satisfactory results a new flexible membership function is also presented

galerkin eigenvector approximations how close are galerkin eigenvectors to the best approximation available out of the trial subspace under a variety of conditions the galerkin method gives an approximate eigenvector that approaches asymptotically the projection of the exact eigenvector onto the trial subspace and this occurs more rapidly than the underlying rate of convergence of the approximate eigenvectors both orthogonal galerkin and petrov galerkin methods are considered here with a special emphasis on nonselfadjoint problems thus extending earlier studies by chatelin babuska and osborn and knyazev consequences for the numerical treatment of elliptic pdes discretized either with finite element methods or with spectral methods are discussed new lower bounds to the sep of a pair of operators are developed as well

a method of converting a fuzzy system to a two layered hierarchical fuzzy system and its run time efficiency in classical single layer fuzzy systems fss the number of rules and the run time computational requirements increase exponentially with the number of input domains in this paper we present a method for converting a multidimensional fs to a two layer hierarchical fs that reduces the number of rules and improves the run time efficiency the first layer of the two layer system consists of fss whose rule bases can be represented as linearly independent vectors the second layer constructs linear combinations of the rule base vectors the effectiveness of the hierarchical conversion in reducing the number of rules and improving efficiency is demonstrated on a classic control problem and a simulated higher dimensional fs

a look ahead lanczos algorithm for unsymmetric matrices abstract the two sided lanczos algorithm is known to suffer from serious breakdowns these occur when the associated moment matrix does not permit triangular factorization we modify the algorithm slightly so that it corresponds to using a 2 x 2 pivot in triangular factorization whenever a 1 x 1 pivot would be dangerous the incidence of breakdown is greatly reduced the price paid is that the tridiagonal matrix produced by the algorithm now has bumps whenever a 2 x 2 pivot is used author

hybridizing genetic algorithms with sharing scheme and evolution strategies for designing approximate fuzzy rule based systems genetic algorithms and evolution strategies are combined in order to build a multi stage hybrid evolutionary algorithm for learning constrained approximate mamdani type knowledge bases from examples the genetic algorithm niche concept is used in two of the three stages composing the learning process with the purpose of improving the accuracy of the designed fuzzy rule based systems the proposed genetic fuzzy rule based system is used to solve an electrical engineering problem and the results obtained are compared with other methods presenting different characteristics

bayesian graphical regression we consider the problem of modeling conditional independence structures in heterogenous data in the presence of additional subject level covariates termed graphical regression we propose a novel s

robust error estimates for approximations of non self adjoint eigenvalue problems we present new residual estimates based on kato s square root theorem for spectral approximations of non self adjoint differential operators of convection diffusion reaction type it is not assumed that the eigenvalue vector approximations are obtained from any particular numerical method so these estimates may be applied quite broadly key eigenvalue and eigenvector error results are illustrated in the context of an hp adaptive finite element algorithm for spectral computations where it is shown that the resulting a posteriori error estimates are reliable the efficiency of these error estimates is also strongly suggested empirically

bayesian regression using a prior on the model fit the r2 d2 shrinkage prior prior distributions for high dimensional linear regression require specifying a joint distribution for the unobserved regression coefficients which is inherently difficult we instead propose a ne

a systematic approach for designing multistage fuzzy control systems this paper proposes a systematic approach for designing a multistage fuzzy logic controller mflc for large scale nonlinear systems in designing such a controller the major tasks are to derive fuzzy rule bases determine membership functions of input output variables and design input output scaling factors in this work the fuzzy rule bases are generated by rule generated functions which are based on the negative gradient of a system performance index the membership functions of isosceles triangle of input output variables are fixed in the same cardinality and only the input output scaling factors are optimized from a genetic algorithm based on a fitness function as a result the search space of the parameters is narrowed down to a small space so that the mflc can be quickly constructed and the fuzzy rules and scaling factors can easily be determined the performance of the proposed approach is examined by computer simulations on an inverted pendulum system the performance of single stage structure binary tree structure and skew binary tree structure are compared the binary tree structure has better performance and use fewer fuzzy rules in the illustrative example

fuzzy model predictive control of non linear processes using genetic algorithms abstract this paper introduces a new fuzzy control technique which belongs to the popular family of control algorithms called model predictive controllers the method is based on a dynamic fuzzy model of the process to be controlled which is used for predicting the future behavior of the output variables a non linear optimization problem is then formulated which minimizes the difference between the model predictions and the desired trajectory over the prediction horizon and the control energy over a shorter control horizon the problem is solved on line using a specially designed genetic algorithm which has a number of advantages over conventional non linear optimization techniques the method can be used with any type of fuzzy model and is particularly useful when a direct fuzzy controller cannot be designed due to the complexity of the process and the difficulty in developing fuzzy control rules the method is illustrated via the application to a non linear single input single output reactor where a takagi sugeno model serves as a predictor of the process future behavior

variable selection via gibbs sampling abstract a crucial problem in building a multiple regression model is the selection of predictors to include the main thrust of this article is to propose and develop a procedure that uses probabilistic considerations for selecting promising subsets this procedure entails embedding the regression setup in a hierarchical normal mixture model where latent variables are used to identify subset choices in this framework the promising subsets of predictors can be identified as those with higher posterior probability the computational burden is then alleviated by using the gibbs sampler to indirectly sample from this multinomial posterior distribution on the set of possible subset choices those subsets with higher probability the promising ones can then be identified by their more frequent appearance in the gibbs sample

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

a class of hierarchical fuzzy systems with constraints on the fuzzy rules this paper presents a class of hierarchical fuzzy systems where previous layer outputs are used not in if parts but only in then parts of the fuzzy rules of the current layer the proposed scheme is shown to be a universal approximator to any real continuous function on a compact set if complete fuzzy sets are used in the if parts of the fuzzy rules with singleton fuzzifier and center average defuzzifier from the example of ball and beam control system simulation it is demonstrated that the proposed scheme approximates with high accuracy a model nonlinear controller with fewer fuzzy rules than a centralized fuzzy system and its control performance is comparable to that of a nonlinear controller

on estimators for eigenvalue eigenvector approximations we consider a large class of residuum based a posteriori eigen value eigenvector estimates and present an abstract framework for proving their asymptotic exactness equivalence of the estimator and the error is also established to demonstrate the strength of our abstract approach we present a detailed study of hierarchical error estimators for laplace eigenvalue problems in planar polygonal regions to this end we develop new error analysis for the galerkin approximation which avoids the use of the strengthened cauchy schwarz inequality and the saturation assumption and gives reasonable and explicitly computable upper bounds on the discretization error a brief discussion is also given concerning the design of estimators which are in the same spirit but are based on different a posteriori techniques notably those of gradient recovery type

fast bayesian factor analysis via automatic rotations to sparsity abstractrotational post hoc transformations have traditionally played a key role in enhancing the interpretability of factor analysis regularization methods also serve to achieve this goal by prioritizing sparse loading matrices in this work we bridge these two paradigms with a unifying bayesian framework our approach deploys intermediate factor rotations throughout the learning process greatly enhancing the effectiveness of sparsity inducing priors these automatic rotations to sparsity are embedded within a pxl em algorithm a bayesian variant of parameter expanded em for posterior mode detection by iterating between soft thresholding of small factor loadings and transformations of the factor basis we obtain a dramatic accelerations b robustness against poor initializations and c better oriented sparse solutions to avoid the prespecification of the factor cardinality we extend the loading matrix to have infinitely many columns with the indian buffet process ibp prior the factor dimen

convergence of algorithms of decomposition type for the eigenvalue problem we develop the theory of convergence of a generic gr algorithm for the matrix eigenvalue problem that includes the qr lr sr and other algorithms as special cases our formulation allows for shifts of origin and multiple gr steps the convergence theory is based on the idea that the gr algorithm performs nested subspace iteration with a change of coordinate system at each step thus the convergence of the gr algorithm depends on the convergence of certain sequences of subspaces it also depends on the quality of the coordinate transformation matrices as measured by their condition numbers we show that with a certain obvious shifting strategy the gr algorithm typically has a quadratic asymptotic convergence rate for matrices possessing certain special types of structure cubic convergence can be achieved