a generalizable formulation of conditional logit with diagnostics abstract the conditional logit model is a multinomial logit model that permits the inclusion of choice specific attributes this article shows that the conditional logit model will maximize entropy given a set of attribute value preserving constraints a correspondence between the maximum entropy me and maximum likelihood ml estimates for logit probabilities is established some easily computable and useful diagnostics for logit analysis are provided and it is shown that an evaluation of the relative importance of attributes can be made using the me formulation the me formulation is also generalized to accommodate initial choice probabilities into the logit model an example is given key words choice models entropy kullback leibler discrimination information function relative importance

robust analysis and control for a class of uncertain nonlinear discrete time systems abstract this paper deals with the problem of robust analysis and control of a class of nonlinear discrete time systems with constant uncertain parameters for the analysis problem we use a polynomial lyapunov function and we generalize for nonlinear systems the extended stability notion proposed by oliveira et al 1999 in the context of linear discrete time uncertain systems as a result we propose an lmi optimization problem to maximize an estimate of the domain of attraction and also extend this approach to the synthesis problem by considering parameter dependent lyapunov functions and nonlinear multipliers numerical examples illustrate the approach and show its potential for solving analysis and control problems of nonlinear discrete time systems

probabilistic temporal logics via the modal mu calculus this paper presents a mu calculus based modal logic for describing properties of reactive probabilistic labeled transition systems rpltss and develops a model checking algorithm for determining whether or not states in finite state rpltss satisfy formulas in the logic the logic is based on the distinction between probabilistic systems and nonprobabilistic observations using the modal mu calculus one may specify sets of observations and the semantics of our logic then enable statements to be made about the measures of such sets at various system states the logic may be used to encode a variety of probabilistic modal and temporal logics in addition the model checking problem for it may be reduced to the calculation of solutions to systems of non linear equations finally the logic induces an equivalence on rpltss that coincides with accepted notions of probabilistic bisimulation in the literature

ridge regression biased estimation for nonorthogonal problems in multiple regression it is shown that parameter estimates based on minimum residual sum of squares have a high probability of being unsatisfactory if not incorrect if the prediction vectors are not orthogonal proposed is an estimation procedure based on adding small positive quantities to the diagonal of x x introduced is the ridge trace a method for showing in two dimensions the effects of nonorthogonality it is then shown how to augment x x to obtain biased estimates with smaller mean square error

kernel methods in machine learning we review machine learning methods employing positive definite kernels these methods formulate learning and estimation problems in a reproducing kernel hilbert space rkhs of functions defined on the data domain expanded in terms of a kernel working in linear spaces of function has the benefit of facilitating the construction and analysis of learning algorithms while at the same time allowing large classes of functions the latter include nonlinear functions as well as functions defined on nonvectorial data we cover a wide range of methods ranging from binary classifiers to sophisticated methods for estimation with structured data

sparse kernel regression modeling using combined locally regularized orthogonal least squares and d optimality experimental design the note proposes an efficient nonlinear identification algorithm by combining a locally regularized orthogonal least squares lrols model selection with a d optimality experimental design the proposed algorithm aims to achieve maximized model robustness and sparsity via two effective and complementary approaches the lrols method alone is capable of producing a very parsimonious model with excellent generalization performance the d optimality design criterion further enhances the model efficiency and robustness an added advantage is that the user only needs to specify a weighting for the d optimality cost in the combined model selecting criterion and the entire model construction procedure becomes automatic the value of this weighting does not influence the model selection procedure critically and it can be chosen with ease from a wide range of values

reasoning about probabilistic sequential programs a complete and decidable hoare style calculus for iteration free probabilistic sequential programs is presented using a state logic with truth functional propositional not arithmetical connectives

probabilistic propositional temporal logics we present two closely related propositional probabilistic temporal logics based on temporal logics of branching time as introduced by ben ari pnueli and manna acta inform 20 1983 207 226 emerson and halpern proceedings 14th acm sympos theory of comput 1982 pp 169 179 and emerson and clarke sci comput program 2 1982 241 266 the first logic ptlf is interpreted over finite models while the second logic ptlb which is an extension of the first one is interpreted over infinite models with transition probabilities bounded away from 0 the logic ptlf allows us to reason about finite state sequential probabilistic programs and the logic ptlb allows us to reason about finite state concurrent probabilistic programs without any explicit reference to the actual values of their state transition probabilities a generalization of the tableau method yields deterministic single exponential time decision procedures for our logics and complete axiomatizations of them are given several meta results including the absence of a finite model property for ptlb and the connection between satisfiable formulae of ptlb and finite state concurrent probabilistic programs are also discussed

results on the propositional μ calculus abstract in this paper we define and study a propositional calculus l which consists essentially of propositional modal logic with a least fixpoint operator l is syntactically simpler yet strictly more expressive than propositional dynamic logic pdl for a restricted version we give an exponential time decision procedure small model property and complete deductive system theory subsuming the corresponding results for pdl

multiclass classifiers based on dimension reduction with generalized lda linear discriminant analysis lda has been widely used for dimension reduction of data sets with multiple classes the lda has been recently extended to various generalized lda methods that are applicable regardless of the relative sizes between the data dimension and the number of data items in this paper we propose several multiclass classifiers based on generalized lda glda algorithms taking advantage of the dimension reducing transformation matrix without requiring additional training or parameter optimization a marginal linear discriminant classifier mldc a bayesian linear discriminant classifier bldc and a one dimensional bldc are introduced for multiclass classification our experimental results illustrate that these classifiers produce higher ten fold cross validation accuracy than knn and centroid based classifiers in the reduced dimensional space obtained from glda

robust stability of a class of uncertain markov jump nonlinear systems this note addresses the problem of robust stability analysis for a class of markov jump nonlinear systems subject to polytopic type parameter uncertainty a condition for robust local exponential mean square stability in terms of linear matrix inequalities is developed an estimate of a robust domain of attraction of the origin is also provided the approach is based on a stochastic lyapunov function with polynomial dependence on the system state and uncertain parameters a numerical example illustrates the proposed result

stability analysis of implicit polynomial systems this technical note develops a robust stability analysis method for a class of implicit polynomial systems subject to uncertain constant parameters a polynomial with respect to the state and uncertain parameters lyapunov function is computed to assess the robust local stability of the system and to provide a robust estimate of the domain of attraction the results are given in terms of linear matrix inequalities that are affinely dependent on the system state and uncertain parameters numerical examples illustrate the effectiveness of the developed approach

information indices unification and applications the unified framework of information theoretic statistics was established by kullback 1959 since then numerous information indices have been developed in various contexts this paper represents many of these indices in a unified context the unification thread is the discrimination information function information indices are all logarithmic measures of discrepancy between two probability distributions first we present a summary of informational aspects of the basic information functions a unification of various information theoretic modeling approaches and some explication in terms of traditional measures we then tabulate a unified representation of assortments of information indices developed in the literature for maximum entropy modeling covariate information and influence diagnostics the subjects of these indices include parametric model fitting nonparametric entropy estimation categorical data analysis the linear and exponential family regression and time series the coverage however is not exhaustive the tabulation includes sampling theory and bayesian indices but the focus is on interpretation as descriptive measures and inferential properties are noted tangentially finally applications of some information indices are illustrated through modeling duration data for sprint s churned customer and choice of long distance provider

the propositional dynamic logic of deterministic well structured programs abstract we consider a restricted propositional dynamic logic strict deterministic propositional dynamic logic sdpdl which is appropriate for reasoning about deterministic well structured programs in contrast to pdl for which the validity problem is known to be complete in deterministic exponential time the validity problem for sdpdl is shown to be polynomial space complete we also show that sdpdl is less expressive than pdl and give a complete axiomatization for it the results rely on structure theorems for models of satisfiable sdpdl formulas and the proofs give insight into the effects of nondeterminism on intractability and expressiveness in program logics

effects of collinearity on information about regression coefficients abstract this paper uses information theory to examine effects of nonorthogonality of a regression matrix on data and posterior information about the regression coefficients in the absence of an informative prior the entropy analysis results in collinearity measures that are akin to some well known diagnostics available for the least squares regressions entropy difference and cross entropy analyses are used to quantify collinearity effects on the sample information and posterior distribution information theoretic diagnostics are developed for examining the incremental contribution of additional prior precision to reduction of collinearity effects on the sample and posterior information the proposed collinearity measures are applied to an illustrative example

reasoning about knowledge and probability we provide a model for reasoning about knowledge and probability together we allow explicit mention of probabilities in formulas so that our language has formulas that essentially say according to agent i formula holds with probability at least b the language is powerful enough to allow reasoning about higher order probabilities as well as allowing explicit comparisons of the probabilities an agent places on distinct events we present a general framework for interpreting such formulas and consider various properties that might hold of the interrelationship between agents probability assignments at different states we provide a complete axiomatization for reasoning about knowledge and probability prove a small model property and obtain decision procedures

a decidable propositional dynamic logic with explicit probabilities a propositional version of feldman and harel s pr dl 1982 14th acm sympos on theory of computing pp 181 195 j comput system sci 28 no 2 1984 193 215 is defined and shown to be decidable in double exponential space the logic allows propositional level formulas involving probabilistic programs and contains the full quantified real number theory for dealing with probabilities the decidability proof introduces a succession of abstractions of the notion of a model from the full generality of measure theoretical models down to the finite schematic models which seem to be the most basic structures relating programs and probabilities

assessing the presence of harmful collinearity and other forms of weak data through a test for signal to noise abstract data weaknesses such as collinearity reduce the quality of least squares estimates by inflating parameter variances standard regression diagnostics and statistical tests of hypothesis are unable to indicate such variance inflation and hence cannot detect data weaknesses in this paper then we consider a different means for determining the presence of weak data based on a test for signal to noise in which the size of the parameter variance noise is assessed relative to the magnitude of the parameter signal this test is combined with other collinearity diagnostics to provide a test for the presence of harmful collinearity and or short data the entire procedure is illustrated with an equation from the michigan quarterly econometric model tables of critical values for the test are provided in an appendix

an automata theoretic approach to branching time model checking translating linear temporal logic formulas to automata has proven to be an effective approach for implementing linear time model checking and for obtaining many extensions and improvements to this verification method on the other hand for branching temporal logic automata theoretic techniques have long been thought to introduce an exponential penalty making them essentially useless for model checking recently bernholtz and grumberg 1993 have shown that this exponential penalty can be avoided though they did not match the linear complexity of non automata theoretic algorithms in this paper we show that alternating tree automata are the key to a comprehensive automata theoretic framework for branching temporal logics not only can they be used to obtain optimal decision procedures as was shown by muller et al but as we show here they also make it possible to derive optimal model checking algorithms moreover the simple combinatorial structure that emerges from the automata theoretic approach opens up new possibilities for the implementation of branching time model checking and has enabled us to derive improved space complexity bounds for this long standing problem

solving polynomial systems using a branch and prune approach this paper presents tt newton a branch and prune algorithm used to find all isolated solutions of a system of polynomial constraints tt newton can be characterized as a global search method which uses intervals for numerical correctness and for pruning the search space early the pruning in tt newton consists of enforcing at each node of the search tree a unique local consistency condition called box consistency which approximates the notion of arc consistency well known in artificial intelligence box consistency is parametrized by an interval extension of the constraint and can be instantiated to produce the hansen sengupta narrowing operator used in interval methods as well as new operators which are more effective when the computation is far from a solution tt newton has been evaluated on a variety of benchmarks from kinematics chemistry combustion economics and mechanics on these benchmarks it outperforms the interval methods we are aware of and compares well with textit state of the art continuation methods limitations of tt newton e g a sensitivity to the size of the initial intervals on some problems are also discussed of particular interest is the mathematical and programming simplicity of the method

testing equivalences for processes abstract given a set of processes and a set of tests on these processes we show how to define in a natural way three different equivalences on processes these equivalences are applied to a particular language ccs we give associated complete proof systems and fully abstract models these models have a simple representation in terms of trees

explicitly infinite dimensional bayesian analysis of production technologies abstract the firm s cost function is viewed as a point in a function space and data is viewed as following some probability law that has as its parameters various functionals evaluated at the firm s cost function the fourier flexible form is used to represent a cost function as an infinite dimensional vector whose elements are the parameters of the fourier form this representation is used to assign a prior distribution to the function space a procedure for numerical computation of the posterior distribution of an elasticity of substitution is set forth the ideas are illustrated with an example

algebraic relationships between classical regression and total least squares estimation abstract the total least squares tls technique which is well known in numerical linear algebra and able to compute strongly consistent estimators of the parameters in a linear errors in variables model is compared algebraically with the classical regression estimators using the singular value decomposition and geometric concepts algebraic equivalences and important relationships between the classical regression techniques and tls estimation are established with special reference to problems of collinearity the equivalence between principal component and latent root regression in collinearity problems is proven and the difference between latent root regression and tls estimation is clarified

regional robust stabilisation and domain of attraction estimation for mimo uncertain nonlinear systems with input saturation abstractthe regional robust stabilisation by means of linear time invariant state feedback control for a class of uncertain mimo nonlinear systems with parametric uncertainties and control input saturation is investigated the nonlinear systems are described in a differential algebraic representation and the regional stability is handled considering the largest ellipsoidal domain of attraction doa inside a given polytopic region in the state space a novel set of sufficient linear matrix inequality lmi conditions with new auxiliary decision variables are developed aiming to design less conservative linear state feedback controllers with corresponding larger doas by considering the polytopic description of the saturated inputs a few examples are presented showing favourable comparisons with recently published similar control design methodologies

piecewise linear regularized solution paths we consider the generic regularized optimization problem argmin l y x j efron hastie johnstone and tibshirani ann statist 32 2004 407 499 have shown that for the lasso that is if l is squared error loss and j 1 is the l 1 norm of the optimal coefficient path is piecewise linear that is is piecewise constant we derive a general characterization of the properties of loss l penalty j pairs which give piecewise linear coefficient paths such pairs allow for efficient generation of the full regularized coefficient paths we investigate the nature of efficient path following algorithms which arise we use our results to suggest robust versions of the lasso for regression and classification and to develop new efficient algorithms for existing problems in the literature including mammen and van de geer s locally adaptive regression splines

guaranteed cost control of uncertain nonlinear systems via polynomial lyapunov functions in this paper we consider the problem of guaranteed cost control for a class of uncertain nonlinear systems we derive linear matrix inequality conditions for the regional robust stability and performance problems based on lyapunov functions which are polynomial functions of the state and uncertain parameters the performance index is calculated over a set of initial conditions also we discuss the synthesis problem for a class of affine control systems numerical examples illustrate our method

orthogonalizing em a design based least squares algorithm we introduce an efficient iterative algorithm intended for various least squares problems based on a design of experiments perspective the algorithm called orthogonalizing em oem works for ordinary least squares ols and can be easily extended to penalized least squares the main idea of the procedure is to orthogonalize a design matrix by adding new rows and then solve the original problem by embedding the augmented design in a missing data framework we establish several attractive theoretical properties concerning oem for the ols with a singular regression matrix an oem sequence converges to the moore penrose generalized inverse based least squares estimator for ordinary and penalized least squares with various penalties it converges to a point having grouping coherence for fully aliased regression matrices convergence and the convergence rate of the algorithm are examined finally we demonstrate that oem is highly efficient for large scale least squares and penalized least squares proble

optimal control of uncertain nonlinear quadratic systems abstract this paper addresses the problem of robust and optimal control for the class of nonlinear quadratic systems subject to norm bounded parametric uncertainties and disturbances by using an approach based on the guaranteed cost control theory a technique is proposed to design a state feedback controller ensuring for the closed loop system i the local exponential stability of the zero equilibrium point ii the inclusion of a given region into the domain of exponential stability of the equilibrium point iii the satisfaction of a guaranteed level of performance in terms of boundedness of some optimality indexes in particular a sufficient condition for the existence of a state feedback controller satisfying a prescribed integral quadratic index is provided followed by a sufficient condition for the existence of a state feedback controller satisfying a given l 2 gain disturbance rejection constraint by the proposed design procedures the optimal control problems dealt with here can be efficiently solved as linear matrix inequality lmi optimization problems

control of rational systems using linear fractional representations and linear matrix inequalities abstract every system of the form x f x u y g x u where f and g are rational functions of the state x and linear functions of the input u possesses a linear fractional representation lfr in this lfr the system is viewed as an lti system connected with a diagonal feedback element linear in the state we devise an algorithm for computing lfrs based on this construction we give sufficient conditions for various properties to hold for the open loop system these include checking whether a given polytope is stable finding a lower bound on the decay rate of trajectories initiating in this polytope computing an upper bound on the l2 gain etc all these conditions are obtained by analyzing the properties of a differential inclusion related to the lfr and given as convex optimization problems over linear matrix inequalities lmis we show how to use this approach for static state feedback synthesis we then generalize the results to dynamic output feedback synthesis in the case when f and g are linear in every state coordinate that is not measured extensions towards a class of nonrational and uncertain nonliner systems are discussed

weakly complete axiomatization of exogenous quantum propositional logic a finitary axiomatization for eqpl exogenous quantum propositional logic is presented the axiomatization is shown to be weakly complete relative to an oracle for analytical reasoning the proof is carried out using a non trivial extension of the fagin halpern megiddo technique together with three henkin style completions

on the roles of observations in collinearity in the linear model abstract it is often found that individual observations play an important role in the conditioning of a linear regression problem a state of collinearity is sometimes masked by one or two observations certain other observations may induce collinearity in this article we consider a few measures of collinearity that focus on various aspects of the problem and examine the effect of case deletion on these measures the resulting case deletion diagnostics have the common property that they are all positive and centered around 1 a value larger than 1 corresponds to a collinearity reducing observation whereas a value smaller than 1 indicates a collinearityenhancing effect the diagnostics can be used to assess the effects of multiple observations as well modifications of the results for column equilibrated data are also provided some of the diagnostics involve extensive computation we provide sharp and easily computable upper and lower bounds for these complementing some results in the existing literatu

a bayesian approach to diagnosis of asset pricing models a large literature has arisen which exploits a particular portfolio on the mean variance frontier determining a minimum variance bound on the set of stochastic discount factors state price to probability ratios this paper proposes a new variational characterization of the closely related set of state price densities based on minimization of the kullback leibler information criterion in contrast to the variance bound the resulting information bound automatically satisfies an important positivity constraint furthermore the information bound is determined by a portfolio which maximizes expected cara utility several interpretations of the information bound are given and empirical uses of it are illustrated

computation of lyapunov functions for smooth nonlinear systems using convex optimization linearly parameterized non quadratic lyapunov functions for smooth nonlinear systems are computed numerically using large scale linear or quadratic programming

functional multiple set canonical correlation analysis we propose functional multiple set canonical correlation analysis for exploring associations among multiple sets of functions the proposed method includes functional canonical correlation analysis as a special case when only two sets of functions are considered as in classical multiple set canonical correlation analysis computationally the method solves a matrix eigen analysis problem through the adoption of a basis expansion approach to approximating data and weight functions we apply the proposed method to functional magnetic resonance imaging fmri data to identify networks of neural activity that are commonly activated across subjects while carrying out a working memory task

bisimulation through probabilistic testing abstract we propose a language for testing concurrent processes and examine its strength in terms of the processes that are distinguished by a test by using probabilistic transition systems as the underlying semantic model we show how a testing algorithm can distinguish with a probability arbitrarily close to one between processes that are not bisimulation equivalent we also show a similar result in a slightly stronger form for a new process relation called 2 3 bisimulation which lies strictly between that of simulation and bisimulation finally the ultimately strength of the testing language is shown to identify a new process relation called probabilistic bisimulation which is strictly stronger than bisimulation

optimal weighting of a priori statistics in linear estimation theory abstract many scientific and engineering applications require the determination of the state of a dynamical system at some reference time a common solution technique is to perform a taylor series expansion about a nominal solution and compute linear corrections to this nominal by the use of a set of discrete observations of the dynamical system in cases where the observational data set is ill conditioned statistical information on the nominal solution is commonly incorporated into the solution process in order to provide stability in the computation of the linear corrections this statistical information is generally the uncertainty in the nominal solution known as the a priori covariance this a priori information is typically weighted equally with the observational data in conventional minimum variance or maximum likelihood solution methods often the a priori information available for certain types of dynamical systems is inaccurate or generated by inadequate means it has been shown that the accuracy of the estimates is highly dependent on the choice of the a priori covariance inaccurate a priori information can contribute to large errors in the estimates in ill conditioned problems methods developed herein provide for the optimal weighting of the a priori covariance used in the solution of the linear correction to the nominal solution these methods are demonstrated by their application to a space mechanics simulation in which a satellite s orbit must be precisely determined results are compared to those obtained by conventional minimum variance solution techniques in order to demonstrate the possible improvement in the estimate accuracy achievable by the use of such optimal weighting techniques

simultaneous regression shrinkage variable selection and supervised clustering of predictors with oscar variable selection can be challenging particularly in situations with a large number of predictors with possibly high correlations such as gene expression data in this article a new method called the oscar octagonal shrinkage and clustering algorithm for regression is proposed to simultaneously select variables while grouping them into predictive clusters in addition to improving prediction accuracy and interpretation these resulting groups can then be investigated further to discover what contributes to the group having a similar behavior the technique is based on penalized least squares with a geometrically intuitive penalty function that shrinks some coefficients to exactly zero additionally this penalty yields exact equality of some coefficients encouraging correlated predictors that have a similar effect on the response to form predictive clusters represented by a single coefficient the proposed procedure is shown to compare favorably to the existing shrinkage and variable selection techniques in terms of both prediction error and model complexity while yielding the additional grouping information

some first order probability logics we present some rst order probability logics the logics allow making statements such as p s with the intended meaning the probability of truthfulness of is greater than or equal to s we describe the corresponding probability models we give a sound and complete innitary axiomatic system for the most general of our logics while for some restrictions of this logic we provide nitary axiomatic systems we study the decidability of our logics we discuss some of the related papers c 2000 elsevier science b v all rights reserved

algebraic laws for nondeterminism and concurrency since a nondeterministic and concurrent program may in general communicate repeatedly with its environment its meaning cannot be presented naturally as an input output function as is often done in the denotational approach to semantics in this paper an alternative is put forth first a definition is given of what it is for two programs or program parts to be equivalent for all observers then two program parts are said to be observation congruent if they are in all program contexts equivalent the behavior of a program part that is its meaning is defined to be its observation congruence class the paper demonstrates for a sequence of simple languages expressing finite terminating behaviors that in each case observation congruence can be axiomatized algebraically moreover with the addition of recursion and another simple extension the algebraic language described here becomes a calculus for writing and specifying concurrent programs and for proving their properties

reasoning with time and chance the temporal propositional logic of linear time is generalized to an uncertain world in which random events may occur the formulas do not mention probabilities explicitly i e the only probability appearing explicitly in formulas is probability one this logic is claimed to be useful for stating and proving properties of probabilistic programs it is convenient for proving those properties that do not depend on the specific distribution of probabilities used in the program s random draws the formulas describe properties of execution sequences the models are stochastic systems with state transition probabilities three different axiomatic systems are proposed and shown complete for general models finite models and models with bounded transition probabilities respectively all three systems are decidable by the results of rabin trans amer math soc 141 1969 1 35

correlation weights in multiple regression a general theory on the use of correlation weights in linear prediction has yet to be proposed in this paper we take initial steps in developing such a theory by describing the conditions under which correlation weights perform well in population regression models using ols weights as a comparison we define cases in which the two weighting systems yield maximally correlated composites and when they yield minimally similar weights we then derive the least squares weights for any set of predictors that yield the largest drop in r 2 the coefficient of determination when switching to correlation weights our findings suggest that two characteristics of a model data combination are especially important in determining the effectiveness of correlation weights 1 the condition number of the predictor correlation matrix r xx and 2 the orientation of the correlation weights to the latent vectors of r xx

capturing the intangible concept of information abstract the purpose of this article is to discuss the intricacies of quantifying information in some statistical problems the aim is to develop a general appreciation for the meanings of information functions rather than their mathematical use this theme integrates fundamental aspects of the contributions of kullback lindley and jaynes and bridges chaos to probability modeling a synopsis of information theoretic statistics is presented in the form of a pyramid with shannon at the vertex and a triangular base that signifies three distinct variants of quantifying information discrimination information kullback mutual information lindley and maximum entropy information jaynes examples of capturing information by the maximum entropy me method are discussed it is shown that the me approach produces a general class of logit models capable of capturing various forms of sample and nonsample information diagnostics for quantifying information captured by the me logit models are given and decom

brief paper robust h filter design for a class of discrete time parameter varying systems this paper proposes a robust h filter design method for discrete time linear parameter varying systems with the state space model matrices depending rationally on time varying parameters the system is described by a difference algebraic representation and the parameters admissible values and variations are assumed to belong to given intervals a convex optimization approach in terms of linear matrix inequalities is devised for designing robust filters the filter design is based on lyapunov functions with rational dependence on the system parameters and incorporates information on available bounds on the parameters variation the proposed method can be also applied to the design of gain scheduled h filters numerical examples illustrate the effectiveness of the proposed filter design

a penalized method for multivariate concave least squares with application to productivity analysis abstract we propose a penalized method for the least squares estimator of a multivariate concave regression function this estimator is formulated as a quadratic programing qp problem with o n2 constraints where n is the number of observations computing such an estimator is a very time consuming task and the computational burden rises dramatically as the number of observations increases by introducing a quadratic penalty function we reformulate the concave least squares estimator as a qp with only non negativity constraints this reformulation can be adapted for estimating variants of shape restricted least squares i e the monotonic concave convex least squares the experimental results and an empirical study show that the reformulated problem and its dual are solved significantly faster than the original problem the matlab and r codes for implementing the penalized problems are provided in the paper

decidability and expressiveness for first order logics of probability we consider decidability and expressiveness issues for two first order logics of probability in one the probability is on possible worlds while in the other it is on the domain it turns out that in both cases it takes very little to make reasoning about probability highly undecidable we show that when the probability is on the domain if the language contains only unary predicates then the validity problem is decidable however if the language contains even one binary predicate the validity problem is 21 complete as hard as elementary analysis with free predicate and function symbols with equality in the language even with no other symbol the validity problem is at least as hard as that for elementary analysis 1 hard thus the logic cannot be axiomatized in either case when we put the probability on the set of possible worlds the validity problem is 21 complete with as little as one unary predicate in the language even without equality with equality we get 1 hardness with only a constant symbol we then turn our attention to an analysis of what causes this overwhelming complexity for example we show that if we require rational probabilities then we drop from 21 to 11 in many contexts it suffices to restrict attention to domains of bounded size fortunately the logics are decidable in this case finally we show that although the two logics capture quite different intuitions about probability there is a precise sense in which they are equi expressive

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

finite horizon approximate optimal guaranteed cost control of uncertain nonlinear systems with application to mars entry guidance this paper studies the finite horizon optimal guaranteed cost control gcc problem for a class of time varying uncertain nonlinear systems the aim of this problem is to find a robust state feedback controller such that the closed loop system has not only a bounded response in a finite duration of time for all admissible uncertainties but also a minimal guaranteed cost a neural network nn based approximate optimal gcc design is developed initially by modifying the cost function to account for the nonlinear perturbation of system the optimal gcc problem is transformed into a finite horizon optimal control problem of the nominal system subsequently with the help of the modified cost function together with a parametrized bounding function for all admissible uncertainties the solution to the optimal gcc problem is given in terms of a parametrized hamilton jacobi bellman phjb equation then a nn method is developed to solve offline the phjb equation approximately and thus obtain the nearly optimal gcc policy furthermore the convergence of approximate phjb equation and the robust admissibility of nearly optimal gcc policy are also analyzed finally by applying the proposed design method to the entry guidance problem of the mars lander the achieved simulation results show the effectiveness of the proposed controller

prediction by supervised principal components in regression problems where the number of predictors greatly exceeds the number of observations conventional regression techniques may produce unsatisfactory results we describe a technique called supervised principal components that can be applied to this type of problem supervised principal components is similar to conventional principal components analysis except that it uses a subset of the predictors selected based on their association with the outcome supervised principal components can be applied to regression and generalized regression problems such as survival analysis it compares favorably to other techniques for this type of problem and can also account for the effects of other covariates and help identify which predictor variables are most important we also provide asymptotic consistency results to help support our empirical findings these methods could become important tools for dna microarray data where they may be used to more accurately diagnose and treat cancer

analysis and synthesis of robust control systems via parameter dependent lyapunov functions in this paper the problem of robust stability of systems subject to parametric uncertainties is considered sufficient conditions for the existence of parameter dependent lyapunov functions are given in terms of a criterion which is reminiscent of but less conservative than popov s stability criterion an equivalent frequency domain criterion is demonstrated the relative sharpness of the proposed test and existing stability criteria is then discussed the use of parameter dependent lyapunov functions for robust controller synthesis is then considered it is shown that the search for robustly stabilizing controllers may be limited to controllers with the same order as the original plant a possible synthesis procedure and a numerical example are then discussed

robust observed state feedback design for discrete time systems rational in the uncertainties design of controllers in the form of a state feedback coupled to a state observer is studied in the context of uncertain systems the classical approach by luenberger is revisited results provide a heuristic design procedure that mimics the independent state feedback observer gains design by minimizing the coupling of observation error dynamics on the ideal state feedback dynamics the proposed design and analysis conditions apply to linear systems rationally dependent on uncertainties defined in the cross product of polytopes convex linear matrix inequality results are given thanks to the combination of a new descriptor multi affine representations of systems and the s variable approach stability and h performances are assessed by multi affine parameter dependent lyapunov matrices for both cases of constant and time varying uncertainties or combinations of the two numerical complexity issues and ways to keep it as limited as possible are discussed and illustrated on an academic example

universal weighted mse improvement of the least squares estimator since the seminal work of stein in the 1950s there has been continuing research devoted to improving the total mean squared error mse of the least squares ls estimator in the linear regression model however a drawback of these methods is that although they improve the total mse they do so at the expense of increasing the mse of some of the individual signal components here we consider a framework for developing linear estimators that outperform the ls strategy over bounded norm signals under all weighted mse measures this guarantees for example that both the total mse and the mse of each of the elements will be smaller than that resulting from the ls approach we begin by deriving an easily verifiable condition on a linear method that ensures ls domination for every weighted mse we then suggest a minimax estimator that minimizes the worst case mse over all weighting matrices and bounded norm signals subject to the universal weighted mse domination constraint

maximin effects in inhomogeneous large scale data large scale data are often characterized by some degree of inhomogeneity as data are either recorded in different time regimes or taken from multiple sources we look at regression models and the effect of randomly changing coefficients where the change is either smoothly in time or some other dimension or even without any such structure fitting varying coefficient models or mixture models can be appropriate solutions but are computationally very demanding and often return more information than necessary if we just ask for a model estimator that shows good predictive properties for all regimes of the data then we are aiming for a simple linear model that is reliable for all possible subsets of the data we propose the concept of maximin effects and a suitable estimator and look at its prediction accuracy from a theoretical point of view in a mixture model with known or unknown group structure under certain circumstances the estimator can be computed orders of magnitudes faster than standard penalized regression estimators making computations on large scale data feasible empirical examples complement the novel methodology and theory