the riemann hilbert approach to strong asymptotics for orthogonal polynomials on 1 1 abstract we consider polynomials that are orthogonal on 1 1 with respect to a modified jacobi weight 1 x 1 x h x with 1 and h real analytic and strictly positive on 1 1 we obtain full asymptotic expansions for the monic and orthonormal polynomials outside the interval 1 1 for the recurrence coefficients and for the leading coefficients of the orthonormal polynomials we also deduce asymptotic behavior for the hankel determinants and for the monic orthogonal polynomials on the interval 1 1 for the asymptotic analysis we use the steepest descent technique for riemann hilbert problems developed by deift and zhou and applied to orthogonal polynomials on the real line by deift kriecherbauer mclaughlin venakides and zhou in the steepest descent method we will use the szeg function associated with the weight and for the local analysis around the endpoints 1 we use bessel functions of appropriate order whereas deift et al use airy functions

on the equivalence of constrained and compound optimal designs abstract constrained and compound optimal designs represent two well known methods for dealing with multiple objectives in optimal design as reflected by two functionals 1 and 2 on the space of information matrices a constrained optimal design is constructed by optimizing 2 subject to a constraint on 1 and a compound design is found by optimizing a weighted average of the functionals 1 1 2 0 1 we show that these two approaches to handling multiple objectives are equivalent

learning equivalence classes of bayesian network structures two bayesian network structures are said to be equivalent if the set of distributions that can be represented with one of those structures is identical to the set of distributions that can be represented with the other many scoring criteria that are used to learn bayesian network structures from data are score equivalent that is these criteria do not distinguish among networks that are equivalent in this paper we consider using a score equivalent criterion in conjunction with a heuristic search algorithm to perform model selection or model averaging we argue that it is often appropriate to search among equivalence classes of network structures as opposed to the more common approach of searching among individual bayesian network structures we describe a convenient graphical representation for an equivalence class of structures and introduce a set of operators that can be applied to that representation by a search algorithm to move among equivalence classes we show that our equivalence class operators can be scored locally and thus share the computational efficiency of traditional operators defined for individual structures we show experimentally that a greedy model selection algorithm using our representation yields slightly higher scoring structures than the traditional approach without any additional time overhead and we argue that more sophisticated search algorithms are likely to benefit much more

uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory we consider asymptotics for orthogonal polynomials with respect to varying exponential weights wn x dx e nv x dx on the line as n the potentials v are assumed to be real analytic with sufficient growth at infinity the principle results concern plancherel rotach type asymptotics for the orthogonal polynomials down to the axis using these asymptotics we then prove universality for a variety of statistical quantities arising in the theory of random matrix models some of which have been considered recently in 31 and also in 4 an additional application concerns the asymptotics of the recurrence coefficients and leading coefficients for the orthonormal polynomials see also 4 the orthogonal polynomial problem is formulated as a riemann hilbert problem following 19 20 the riemann hilbert problem is analyzed in turn using the steepest descent method introduced in 12 and further developed in 11 13 a critical role in our method is played by the equilibrium measure d v for v as analyzed in 8 1999 john wiley sons inc

large sample learning of bayesian networks is np hard in this paper we provide new complexity results for algorithms that learn discrete variable bayesian networks from data our results apply whenever the learning algorithm uses a scoring criterion that favors the simplest structure for which the model is able to represent the generative distribution exactly our results therefore hold whenever the learning algorithm uses a consistent scoring criterion and is applied to a sufficiently large dataset we show that identifying high scoring structures is np hard even when any combination of one or more of the following hold the generative distribution is perfect with respect to some dag containing hidden variables we are given an independence oracle we are given an inference oracle we are given an information oracle we restrict potential solutions to structures in which each node has at most k parents for all k 3 our proof relies on a new technical result that we establish in the appendices in particular we provide a method for constructing the local distributions in a bayesian network such that the resulting joint distribution is provably perfect with respect to the structure of the network

a characterization of markov equivalence classes for acyclic digraphs undirected graphs and acyclic digraphs adgs as well as their mutual extension to chain graphs are widely used to describe dependencies among variables in multivariate distributions in particular the likelihood functions of adg models admit convenient recursive factorizations that often allow explicit maximum likelihood estimates and that are well suited to building bayesian networks for expert systems whereas the undirected graph associated with a dependence model is uniquely determined there may however be many adgs that determine the same dependence markov model thus the family of all adgs with a given set of vertices is naturally partitioned into markov equivalence classes each class being associated with a unique statistical model statistical procedures such as model selection or model averaging that fail to take into account these equivalence classes may incur substantial computational or other inefficiencies here it is shown that each markov equivalence class is uniquely determined by a single chain graph the essential graph that is itself simultaneously markov equivalent to all adgs in the equivalence class essential graphs are characterized a polynomial time algorithm for their construction is given and their applications to model selection and other statistical questions are described

learning linear cyclic causal models with latent variables identifying cause effect relationships between variables of interest is a central problem in science given a set of experiments we describe a procedure that identifies linear models that may contain cycles and latent variables we provide a detailed description of the model family full proofs of the necessary and sufficient conditions for identifiability a search algorithm that is complete and a discussion of what can be done when the identifiability conditions are not satisfied the algorithm is comprehensively tested in simulations comparing it to competing algorithms in the literature furthermore we adapt the procedure to the problem of cellular network inference applying it to the biologically realistic data of the dreamchallenges the paper provides a full theoretical foundation for the causal discovery procedure first presented by eberhardt et al 2010 and hyttinen et al 2010

estimation of directed acyclic graphs through two stage adaptive lasso for gene network inference abstractgraphical models are a popular approach to find dependence and conditional independence relationships between gene expressions directed acyclic graphs dags are a special class of directed graphical models where all the edges are directed edges and contain no directed cycles the dags are well known models for discovering causal relationships between genes in gene regulatory networks however estimating dags without assuming known ordering is challenging due to high dimensionality the acyclic constraints and the presence of equivalence class from observational data to overcome these challenges we propose a two stage adaptive lasso approach called ns dist which performs neighborhood selection ns in stage 1 and then estimates dags by the discrete improving search with tabu dist algorithm within the selected neighborhood simulation studies are presented to demonstrate the effectiveness of the method and its computational efficiency two real data examples are used to demonstrate the p

a recursive method for structural learning of directed acyclic graphs in this paper we propose a recursive method for structural learning of directed acyclic graphs dags in which a problem of structural learning for a large dag is first decomposed into two problems of structural learning for two small vertex subsets each of which is then decomposed recursively into two problems of smaller subsets until none subset can be decomposed further in our approach search for separators of a pair of variables in a large dag is localized to small subsets and thus the approach can improve the efficiency of searches and the power of statistical tests for structural learning we show how the recent advances in the learning of undirected graphical models can be employed to facilitate the decomposition simulations are given to demonstrate the performance of the proposed method

finding optimal bayesian network given a super structure classical approaches used to learn bayesian network structure from data have disadvantages in terms of complexity and lower accuracy of their results however a recent empirical study has shown that a hybrid algorithm improves sensitively accuracy and speed it learns a skeleton with an independency test it approach and constrains on the directed acyclic graphs dag considered during the search and score phase subsequently we theorize the structural constraint by introducing the concept of super structure s which is an undirected graph that restricts the search to networks whose skeleton is a subgraph of s we develop a super structure constrained optimal search cos its time complexity is upper bounded by o m n where m 2 depends on the maximal degree m of s empirically complexity depends on the average degree m and sparse structures allow larger graphs to be calculated our algorithm is faster than an optimal search by several orders and even finds more accurate results when given a sound super structure practically s can be approximated by it approaches significance level of the tests controls its sparseness enabling to control the trade off between speed and accuracy for incomplete super structures a greedily post processed version cos still enables to significantly outperform other heuristic searches

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

a graphical representation of equivalence classes of amp chain graphs this paper deals with chain graph models under alternative amp interpretation a new representative of an amp markov equivalence class called the largest deflagged graph is proposed the representative is based on revealed internal structure of the amp markov equivalence class more specifically the amp markov equivalence class decomposes into finer strong equivalence classes and there exists a distinguished strong equivalence class among those forming the amp markov equivalence class the largest deflagged graph is the largest chain graph in that distinguished strong equivalence class a composed graphical procedure to get the largest deflagged graph on the basis of any amp markov equivalent chain graph is presented in general the largest deflagged graph differs from the amp essential graph which is another representative of the amp markov equivalence class

strong asymptotics of orthogonal polynomials with respect to exponential weights we consider asymptotics of orthogonal polynomials with respect to weights w x dx e q x dx on the real line where q x 2m k 0 qkx k q2m 0 denotes a polynomial of even order with positive leading coefficient the orthogonal polynomial problem is formulated as a riemann hilbert problem following 22 23 we employ the steepest descent type method introduced in 18 and further developed in 17 19 in order to obtain uniform plancherel rotach type asymptotics in the entire complex plane as well as asymptotic formulae for the zeros the leading coefficients and the recurrence coefficients of the orthogonal polynomials c 1999 john wiley sons inc

pc algorithm for nonparanormal graphical models the pc algorithm uses conditional independence tests for model selection in graphical modeling with acyclic directed graphs in gaussian models tests of conditional independence are typically based on pearson correlations and high dimensional consistency results have been obtained for the pc algorithm in this setting analyzing the error propagation from marginal to partial correlations we prove that high dimensional consistency carries over to a broader class of gaussian copula or nonparanormal models when using rank based measures of correlation for graph sequences with bounded degree our consistency result is as strong as prior gaussian results in simulations the rank pc algorithm works as well as the pearson pc algorithm for normal data and considerably better for non normal data all the while incurring a negligible increase of computation time while our interest is in the pc algorithm the presented analysis of error propagation could be applied to other algorithms that test the vanishing of low order partial correlations

the isomonodromy approach to matric models in 2d quantum gravity we consider the double scaling limit in the hermitian matrix model for 2d quantum gravity associated with the measure exp sum limits j 1 n t j z 2j n geqq 3 we show that after the appropriate modification of the contour of integration the cross migdal douglas shenker limit to the painleve i equation in the generic case of the pure gravity is valid and calculate the nonperturbative parameters of the corresponding painleve function our approach is based on the wkb analysis of the l a pair corresponding to the discrete string equation in the framework of the inverse monodromy method here we extend our results which were obtained before for the particular casesn 2 3 our analysis complements the isomonodromy approach proposed by g moore to the general string equations that come from the matrix model in the continuous limit and differ in that we apply the isomonodromy technique to investigate the double scaling limit itself

counting and exploring sizes of markov equivalence classes of directed acyclic graphs when learning a directed acyclic graph dag model via observational data one generally cannot identify the underlying dag but can potentially obtain a markov equivalence class the size the number of dags of a markov equivalence class is crucial to infer causal effects or to learn the exact causal dag via further interventions given a set of markov equivalence classes the distribution of their sizes is a key consideration in developing learning methods however counting the size of an equivalence class with many vertices is usually computationally infeasible and the existing literature reports the size distributions only for equivalence classes with ten or fewer vertices in this paper we develop a method to compute the size of a markov equivalence class we first show that there are five types of markov equivalence classes whose sizes can be formulated as five functions of the number of vertices respectively then we introduce a new concept of a rooted sub class the graph representations of rooted subclasses of a markov equivalence class are used to partition this class recursively until the sizes of all rooted subclasses can be computed via the five functions the proposed size counting is efficient for markov equivalence classes of sparse dags with hundreds of vertices finally we explore the size and edge distributions of markov equivalence classes and find experimentally that in general 1 most markov equivalence classes are half completed and their average sizes are small and 2 the sizes of sparse classes grow approximately exponentially with the numbers of vertices

estimation of sparse directed acyclic graphs for multivariate counts data the next generation sequencing data called high throughput sequencing data are recorded as count data which are generally far from normal distribution under the assumption that the count data follow the poisson log normal distribution this article provides an l1 penalized likelihood framework and an efficient search algorithm to estimate the structure of sparse directed acyclic graphs dags for multivariate counts data in searching for the solution we use iterative optimization procedures to estimate the adjacency matrix and the variance matrix of the latent variables the simulation result shows that our proposed method outperforms the approach which assumes multivariate normal distributions and the log transformation approach it also shows that the proposed method outperforms the rank based pc method under sparse network or hub network structures as a real data example we demonstrate the efficiency of the proposed method in estimating the gene regulatory networks of the ovarian cancer study

stochastic complexity and modeling on demontre un theoreme fondamental qui donne une borne inferieure pour la longueur de code et donc pour les erreurs de prediction on definit les notions d information a priori et d information utile dans les donnees

edge effects in some perturbations of the gaussian unitary ensemble a bordering of gaussian unitary ensemble matrices is considered in which the bordered row consists of zero mean complex gaussians n 0 2 in 0 2 off the diagonal and the real gaussian n 2 on the diagonal we compute the explicit form of the eigenvalue probability function for such matrices as well as that for matrices obtained by repeating the bordering the correlations are in general determinantal and in the single bordering case the explicit form of the correlation kernel is computed in the large n limit it is shown that and or can be tuned to induce a separation of the largest eigenvalue this effect is shown to be controlled by a single parameter universal correlation kernel

simple linear time algorithms to test chordality of graphs test acyclicity of hypergraphs and selectively reduce acyclic hypergraphs chordal graphs arise naturally in the study of gaussian elimination on sparse symmetric matrices acyclic hypergraphs arise in the study of relational data bases rose tarjan and lueker siam j c

optimal structure identification with greedy search in this paper we prove the so called meek conjecture in particular we show that if a dag h is an independence map of another dag g then there exists a finite sequence of edge additions and covered edge reversals in g such that 1 after each edge modification h remains an independence map of g and 2 after all modifications g h as shown by meek 1997 this result has an important consequence for bayesian approaches to learning bayesian networks from data in the limit of large sample size there exists a two phase greedy search algorithm that when applied to a particular sparsely connected search space provably identifies a perfect map of the generative distribution if that perfect map is a dag we provide a new implementation of the search space using equivalence classes as states for which all operators used in the greedy search can be scored efficiently using local functions of the nodes in the domain finally using both synthetic and real world datasets we demonstrate that the two phase greedy approach leads to good solutions when learning with finite sample sizes

uniform asymptotic expansions of the pollaczek polynomials two uniform asymptotic expansions are obtained for the pollaczek polynomials pn cos a b one is for 0 n 0 a b in terms of elementary functions and in descending powers of n the other is for n 2 in terms of a special function closely related to the modified parabolic cylinder functions in descending powers of n this interval contains a turning point and all possible zeros of pn cos in 0 2

a scoring function for learning bayesian networks based on mutual information and conditional independence tests we propose a new scoring function for learning bayesian networks from data using score search algorithms this is based on the concept of mutual information and exploits some well known properties of this measure in a novel way essentially a statistical independence test based on the chi square distribution associated with the mutual information measure together with a property of additive decomposition of this measure are combined in order to measure the degree of interaction between each variable and its parent variables in the network the result is a non bayesian scoring function called mit mutual information tests which belongs to the family of scores based on information theory the mit score also represents a penalization of the kullback leibler divergence between the joint probability distributions associated with a candidate network and with the available data set detailed results of a complete experimental evaluation of the proposed scoring function and its comparison with the well known k2 bdeu and bic mdl scores are also presented

bais a bayesian artificial immune system for the effective handling of building blocks significant progress has been made in theory and design of artificial immune systems aiss for solving hard problems accurately however an aspect not yet widely addressed by the research reported in the literature is the lack of ability of the aiss to deal effectively with building blocks partial high quality solutions coded in the antibody the available aiss present mechanisms for evolving the population that do not take into account the relationship among the variables of the problem potentially causing the disruption of high quality partial solutions this paper proposes a novel ais with abilities to identify and properly manipulate building blocks in optimization problems instead of using cloning and mutation to generate new individuals our algorithm builds a probabilistic model representing the joint probability distribution of the promising solutions and subsequently uses this model for sampling new solutions the probabilistic model used is a bayesian network due to its capability of properly capturing the most relevant interactions among the variables therefore our algorithm called bayesian artificial immune system bais represents a significant attempt to improve the performance of immune inspired algorithms when dealing with building blocks and hence to solve efficiently hard optimization problems with complex interactions among the variables the performance of bais compares favorably with that produced by contenders such as state of the art estimation of distribution algorithms

robustness of design in dose response studies summary we construct experimental designs for dose response studies the designs are robust against possibly misspecified link functions for this they minimize the maximum meansquared error of the estimated dose required to attain a response in 100p of the target population here p might be one particular value p d 0 5 corresponds to ed50 estimation or it might range over an interval of values of interest the maximum of the mean squared error is evaluated over a kolmogorov neighbourhood of the fitted link both the maximum and the minimum must be evaluated numerically the former is carried out by quadratic programming and the latter by simulated annealing

on inclusion driven learning of bayesian networks two or more bayesian network structures are markov equivalent when the corresponding acyclic digraphs encode the same set of conditional independencies therefore the search space of bayesian network structures may be organized in equivalence classes where each of them represents a different set of conditional independencies the collection of sets of conditional independencies obeys a partial order the so called inclusion order this paper discusses in depth the role that the inclusion order plays in learning the structure of bayesian networks in particular this role involves the way a learning algorithm traverses the search space we introduce a condition for traversal operators the inclusion boundary condition which when it is satisfied guarantees that the search strategy can avoid local maxima this is proved under the assumptions that the data is sampled from a probability distribution which is faithful to an acyclic digraph and the length of the sample is unbounded the previous discussion leads to the design of a new traversal operator and two new learning algorithms in the context of heuristic search and the markov chain monte carlo method we carry out a set of experiments with synthetic and real world data that show empirically the benefit of striving for the inclusion order when learning bayesian networks from data

a generalized back door criterion we generalize pearl s back door criterion for directed acyclic graphs dags to more general types of graphs that describe markov equivalence classes of dags and or allow for arbitrarily many hidden variables we also give easily checkable necessary and sufficient graphical criteria for the existence of a set of variables that satisfies our generalized back door criterion when considering a single intervention and a single outcome variable moreover if such a set exists we provide an explicit set that fulfills the criterion we illustrate the results in several examples r code is available in the r package pcalg

optimal designs for dose response models with restricted design spaces in dose response studies the dose range is often restricted due to concerns over drug toxicity and or efficacy we present restricted and unrestricted interval locally optimal designs with respect to a very general class of optimality criteria for estimating the underlying dose response curve the underlying curve belongs to a diversified set of link functions suitable for the dose response studies and having a common canonical form these include the fundamental binary response models the logit and the probit as well as the skewed versions of these models the results are illustrated through the re design of a dose ranging trial conducted at the merck research laboratories zeng and zhu 1997 this work is a generalization of the results of dai and zhu 2002 in terms of the design interval the underlying dose response curve and the optimality criterion

bnc pso structure learning is a very important problem in the field of bayesian networks bns it is also an active research area for more than 2 decades therefore many approaches have been proposed in order to find an optimal structure based on training samples in this paper a particle swarm optimization pso based algorithm is proposed to solve the bn structure learning problem named bnc pso bayesian network construction algorithm using pso edge inserting deleting is employed in the algorithm to make the particles have the ability to achieve the optimal solution while a cycle removing procedure is used to prevent the generation of invalid solutions then the theorem of markov chain is used to prove the global convergence of our proposed algorithm finally some experiments are designed to evaluate the performance of the proposed pso based algorithm experimental results indicate that bnc pso is worthy of being studied in the field of bns construction meanwhile it can significantly increase nearly 15 in the scoring metric values comparing with other optimization based algorithms

learning gaussian tree models analysis of error exponents and extremal structures the problem of learning tree structured gaussian graphical models from independent and identically distributed i i d samples is considered the influence of the tree structure and the parameters of the gaussian distribution on the learning rate as the number of samples increases is discussed specifically the error exponent corresponding to the event that the estimated tree structure differs from the actual unknown tree structure of the distribution is analyzed finding the error exponent reduces to a least squares problem in the very noisy learning regime in this regime it is shown that the extremal tree structure that minimizes the error exponent is the star for any fixed set of correlation coefficients on the edges of the tree if the magnitudes of all the correlation coefficients are less than 0 63 it is also shown that the tree structure that maximizes the error exponent is the markov chain in other words the star and the chain graphs represent the hardest and the easiest structures to learn in the class of tree structured gaussian graphical models this result can also be intuitively explained by correlation decay pairs of nodes which are far apart in terms of graph distance are unlikely to be mistaken as edges by the maximum likelihood estimator in the asymptotic regime

universality for eigenvalue correlations from the unitary ensemble associated with a family of singular weights we study the asymptotic behavior of the eigenvalue correlations for the unitary ensemble associated with a family of singular weights w x exp 1 x2 x 1 1 for 0 when 0 1 2 these are szego class weights and are non szego when 1 2 it is proved that the behavior in the bulk of the spectrum is described in terms of the sine kernel which persists the so called universality results while the local behavior at the edge of the spectrum is described in terms of the airy kernel a specific scaling of the limit reflects the singular behavior of orthogonal polynomials on 1 1 with respect to the weight w x

bayesian optimal designs for estimating a set of symmetrical quantiles we propose multiple objective bayesian optimal designs for the logit model as an example we consider the design problem for estimating several percentiles with possibly unequal interest in each of the percentiles characteristics of these designs are studied and illustrated for the case when the interest lies in estimating the three quartiles we compare these optimal designs with the sequential designs generated via a generalized polya urn model and found the latter to be highly efficient in addition comparisons are made between locally optimal designs and bayesian optimal designs

search for additive nonlinear time series causal models pointwise consistent feasible procedures for estimating contemporaneous linear causal structure from time series data have been developed using multiple conditional independence tests but no such procedures are available for non linear systems we describe a feasible procedure for learning a class of non linear time series structures which we call additive non linear time series we show that for data generated from stationary models of this type two classes of conditional independence relations among time series variables and their lags can be tested efficiently and consistently using tests based on additive model regression combining results of statistical tests for these two classes of conditional independence relations and the temporal structure of time series data a new consistent model specification procedure is able to extract relatively detailed causal information we investigate the finite sample behavior of the procedure through simulation and illustrate the application of this method through analysis of the possible causal connections among four ocean indices several variants of the procedure are also discussed

optimal search on clustered structural constraint for learning bayesian network structure we study the problem of learning an optimal bayesian network in a constrained search space skeletons are compelled to be subgraphs of a given undirected graph called the super structure the previously derived constrained optimal search cos remains limited even for sparse super structures to extend its feasibility we propose to divide the super structure into several clusters and perform an optimal search on each of them further to ensure acyclicity we introduce the concept of ancestral constraints acs and derive an optimal algorithm satisfying a given set of acs finally we theoretically derive the necessary and sufficient sets of acs to be considered for finding an optimal constrained graph empirical evaluations demonstrate that our algorithm can learn optimal bayesian networks for some graphs containing several hundreds of vertices and even for super structures having a high average degree up to four which is a drastic improvement in feasibility over the previous optimal algorithm learnt networks are shown to largely outperform state of the art heuristic algorithms both in terms of score and structural hamming distance

critical edge behavior in the modified jacobi ensemble and the painleve v transcendents we study the jacobi unitary ensemble defined by the perturbed chebyshev weight w x 1 x2 12 tn2 x2 x 1 1 tn 1 the algebraic singularity coalesces with the end point of the support of the weight function namely tn 1 the hard edge as n we use the riemann hilbert approach the method of deift and zhou to obtain the asymptotics of the polynomials orthogonal with respect to w x we show that the universality property is preserved the asymptotic behavior of the eigenvalue correlations in the bulk of the spectrum is described in terms of the sine kernel the main result is on the local behavior at the edge of the spectrum the limit kernel at the edge when tn 1 o n 2 is described by the function for a specific solution of the painleve v equation we also show that when tn varies to a fixed t 1 the painleve v kernel transits to the bessel kernel j 12 on the other hand when tn approaches 1 the painleve v kernel can be approximated by another bessel kernel j 12

learning high dimensional directed acyclic graphs with latent and selection variables we consider the problem of learning causal information between random variables in directed acyclic graphs dags when allowing arbitrarily many latent and selection variables the fci fast causal inference algorithm has been explicitly designed to infer conditional independence and causal information in such settings however fci is computationally infeasible for large graphs we therefore propose the new rfci algorithm which is much faster than fci in some situations the output of rfci is slightly less informative in particular with respect to conditional independence information however we prove that any causal information in the output of rfci is correct in the asymptotic limit we also define a class of graphs on which the outputs of fci and rfci are identical we prove consistency of fci and rfci in sparse high dimensional settings and demonstrate in simulations that the estimation performances of the algorithms are very similar all software is implemented in the r package pcalg

estimating high dimensional intervention effects from observational data we assume that we have observational data generated from an unknown underlying directed acyclic graph dag model a dag is typically not identifiable from observational data but it is possible to consistently estimate the equivalence class of a dag moreover for any given dag causal effects can be estimated using intervention calculus in this paper we combine these two parts for each dag in the estimated equivalence class we use intervention calculus to estimate the causal effects of the covariates on the response this yields a collection of estimated causal effects for each covariate we show that the distinct values in this set can be consistently estimated by an algorithm that uses only local information of the graph this local approach is computationally fast and feasible in high dimensional problems we propose to use summary measures of the set of possible causal effects to determine variable importance in particular we use the minimum absolute value of this set since that is a lower bound on the size of the causal effect we demonstrate the merits of our methods in a simulation study and on a data set about riboflavin production

semiclassical asymptotics of orthogonal polynomials riemann hilbert problem and universality in the matrix model we derive semiclassical asymptotics for the orthogonal polynomials pn z on the line with respect to the exponential weight exp inv z where v z is a double well quartic polynomial in the limit when n n 1 we assume that n n cri for some 0 where cr is the critical value which separates orthogonal polynomials with two cuts from the ones with one cut simultaneously we derive semiclassical asymptotics for the recursive coe cients of the orthogonal polynomials and we show that these coe cients form a cycle of period two which drifts slowly with the change of the ratio n n the proof of the semiclassical asymptotics is based on the methods of the theory of integrable systems and on the analysis of the appropriate matrix riemannhilbert problem as an application of the semiclassical asymptotics of the orthogonal polynomials we prove the universality of the local distribution of eigenvalues in the matrix model with the double well quartic interaction in the presence of two cuts contents

uniform asymptotics of the pollaczek polynomials via the riemann hilbert approach the pollaczek weight is an example of the non szeg class in this paper we investigate the asymptotics of the pollaczek polynomials via the riemannhilbert approach in the analysis the original e

the equivalence of constrained and weighted designs in multiple objective design problems abstract several competing objectives may be relevant in the design of an experiment the competing objectives may not be easy to characterize in a single optimality criterion one approach to these design problems has been to weight each criterion and find the design that optimizes the weighted average of the criteria an alternative approach has been to optimize one criterion subject to constraints on the other criteria an equivalence theorem is presented for the bayesian constrained design problem equivalence theorems are essential in verifying optimality of proposed designs especially when as in most nonlinear design problems numerical optimization is required this theorem is used to show that the results of cook and wong on the equivalence of the weighted and constrained problems apply much more generally the results are applied to bayesian nonlinear design problems with several objectives

reversible mcmc on markov equivalence classes of sparse directed acyclic graphs author s he y jia j yu b abstract graphical models are popular statistical tools which are used to represent dependent or causal complex systems statistically equivalent causal or directed graphical models are said to belong to a markov equivalent class it is of great interest to describe and understand the space of such classes however with currently known algorithms sampling over such classes is only feasible for graphs with fewer than approximately 20 vertices in this paper we design reversible irreducible markov chains on the space of markov equivalent classes by proposing a perfect set of operators that determine the transitions of the markov chain the stationary distribution of a proposed markov chain has a closed form and can be computed easily specifically we construct a concrete perfect set of operators on sparse markov equivalence classes by introducing appropriate conditions on each possible operator algorithms and their accelerated versions are provided to efficiently generate markov chains and to explore properties of markov equivalence classes of sparse directed acyclic graphs dags with thousands of vertices we find experimentally that in most markov equivalence classes of sparse dags 1 most edges are directed 2 most undirected subgraphs are small and 3 the number of these undirected subgraphs grows approximately linearly with the number of vertices institute of mathematical statistics 2013

estimation of particle swarm distribution algorithms combining the benefits of pso and edas this paper presents a novel framework of the estimation of particle swarm distribution algorithms epsdas the aim is to effectively combine particle swarm optimization pso with the estimation of distribution algorithms edas without losing their unique features this aim is achieved by incorporating the following mechanisms 1 selection is applied to the local best solutions in order to obtain more promising individuals for model building 2 a probabilistic model of the problem is built from the selected solutions and 3 new individuals are generated by a stochastic combination of the eda s model sampling method and the pso s particle moving mechanism to exhibit the utility of the epsda framework an extended compact particle swarm optimization ecpso is developed by combining the strengths of the extended compact genetic algorithm ecga with binary pso bpso along the lines of the suggested framework due to its effective nature of harmonizing the global search of ecga with the local search of bpso ecpso is able to discover the optimal solution in a fast and reliable manner experimental results on artificial to real world problems have adduced grounds for the effectiveness of the proposed approach

feature subset selection by bayesian network based optimization abstract a new method for feature subset selection in machine learning fss ebna feature subset selection by estimation of bayesian network algorithm is presented fss ebna is an evolutionary population based randomized search algorithm and it can be executed when domain knowledge is not available a wrapper approach over naive bayes and id3 learning algorithms is used to evaluate the goodness of each visited solution fss ebna based on the eda estimation of distribution algorithm paradigm avoids the use of crossover and mutation operators to evolve the populations in contrast to genetic algorithms in absence of these operators the evolution is guaranteed by the factorization of the probability distribution of the best solutions found in a generation of the search this factorization is carried out by means of bayesian networks promising results are achieved in a variety of tasks where domain knowledge is not available the paper explains the main ideas of feature subset selection estimation of distribution algorithm and bayesian networks presenting related work about each concept a study about the overfitting problem in the feature subset selection process is carried out obtaining a basis to define the stopping criteria of the new algorithm

characterization and greedy learning of interventional markov equivalence classes of directed acyclic graphs the investigation of directed acyclic graphs dags encoding the same markov property that is the same conditional independence relations of multivariate observational distributions has a long tradition many algorithms exist for model selection and structure learning in markov equivalence classes in this paper we extend the notion of markov equivalence of dags to the case of interventional distributions arising from multiple intervention experiments we show that under reasonable assumptions on the intervention experiments interventionalmarkov equivalence defines a finer partitioning of dags than observational markov equivalence and hence improves the identifiability of causal models we give a graph theoretic criterion for two dags being markov equivalent under interventions and show that each interventional markov equivalence class can analogously to the observational case be uniquely represented by a chain graph called interventional essential graph also known as cpdag in the observational case these are key insights for deriving a generalization of the greedy equivalence search algorithm aimed at structure learning from interventional data this new algorithm is evaluated in a simulation study

artificial immune multi objective sar image segmentation with fused complementary features artificial immune systems ais are the computational systems inspired by the principles and processes of the vertebrate immune system ais based algorithms typically mimic the human immune system s characteristics of learning and adaptability to solve some complicated problems here an artificial immune multi objective optimization framework is formulated and applied to synthetic aperture radar sar image segmentation the important innovations of the framework are listed as follows 1 an efficient and robust immune multi objective optimization algorithm is proposed which has the features of adaptive rank clones and diversity maintenance by k nearest neighbor list 2 besides two conflicting fuzzy clustering validity indices are incorporated into this framework and optimized simultaneously and 3 moreover an effective fused feature set for texture representation and discrimination is constructed and researched which utilizes both the gabor filter s ability to precisely extract texture features in low and mid frequency components and the gray level co occurrence probability s glcp ability to measure information in high frequency two experiments with synthetic texture images and sar images are implemented to evaluate the performance of the proposed framework in comparison with other five clustering algorithms fuzzy c means fcm single objective genetic algorithm soga self organizing map som wavelet domain hidden markov models hmtseg and spectral clustering ensemble sce experimental results show the proposed framework has obtained the better performance in segmenting sar images than other five algorithms and behaves insensitive to the speckle noise