ultra scalable and efficient methods for hybrid observational and experimental local causal pathway discovery discovery of causal relations from data is a fundamental objective of several scientific disciplines most causal discovery algorithms that use observational data can infer causality only up to a statistical equivalency class thus leaving many causal relations undetermined in general complete identification of causal relations requires experimentation to augment discoveries from observational data this has led to the recent development of several methods for active learning of causal networks that utilize both observational and experimental data in order to discover causal networks in this work we focus on the problem of discovering local causal pathways that contain only direct causes and direct effects of the target variable of interest and propose new discovery methods that aim to minimize the number of required experiments relax common sufficient discovery assumptions in order to increase discovery accuracy and scale to high dimensional data with thousands of variables we conduct a comprehensive evaluation of new and existing methods with data of dimensionality up to 1 000 000 variables we use both artificially simulated networks and in silico gene transcriptional networks that model the characteristics of real gene expression data

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

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

count of eigenvalues in the generalized eigenvalue problem we study isolated and embedded eigenvalues in the generalized eigenvalue problem defined by two self adjoint operators with a positive essential spectrum and a finite number of isolated eigenvalues the generalized eigenvalue problem determines the spectral stability of nonlinear waves in infinite dimensional hamiltonian systems the theory is based on pontryagin s invariant subspace theorem and extends beyond the scope of earlier papers of pontryagin krein grillakis and others our main results are i the number of unstable and potentially unstable eigenvalues equals the number of negative eigenvalues of the self adjoint operators ii the total number of isolated eigenvalues of the generalized eigenvalue problem is bounded from above by the total number of isolated eigenvalues of the self adjoint operators and iii the quadratic forms defined by the two self adjoint operators are strictly positive on the subspace related to the continuous spectrum of the generalized eigenvalue problem applicatio

comparing the areas under two or more correlated receiver operating characteristic curves a nonparametric approach methods of evaluating and comparing the performance of diagnostic tests are of increasing importance as new tests are developed and marketed when a test is based on an observed variable that lies on a continuous or graded scale an assessment of the overall value of the test can be made through the use of a receiver operating characteristic roc curve the curve is constructed by varying the cutpoint used to determine which values of the observed variable will be considered abnormal and then plotting the resulting sensitivities against the corresponding false positive rates when two or more empirical curves are constructed based on tests performed on the same individuals statistical analysis on differences between curves must take into account the correlated nature of the data this paper presents a nonparametric approach to the analysis of areas under correlated roc curves by using the theory on generalized u statistics to generate an estimated covariance matrix

anti integrability in dynamic and variational problems abstract we show using a series of examples that the existence of a singular limit called anti integrable can be useful for proving the existence of chaotic solutions and elucidating some of their properties leading to some new and unexpected results in particular the existence proof of chaotic trajectories in large classes of dynamical systems with discrete time becomes straightforward the method applies even for maps in infinite dimension symplectic or not similar ideas can be used for proving the existence of breathers or self localised modes and of chaotic distributions of breathers in any array of weakly coupled non linear oscillators with continuous time the existence of insulating bipolaronic structures in electron phonon systems electronic self localisation at large electron phonon coupling can also be proven on the same basis

on instability of excited states of the nonlinear schrodinger equation we introduce a new notion of linear stability for standing waves of the nonlinear schrodinger equation nls which requires not only that the spectrum of the linearization be real but also that the generalized kernel be not degenerate and that the signature of all the positive eigenvalues be positive we prove that excited states of the nls are not linearly stable in this more restrictive sense we then give a partial proof that this more restrictive notion of linear stability is a necessary condition to have orbital stability

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

use of the zero norm with linear models and kernel methods we explore the use of the so called zero norm of the parameters of linear models in learning minimization of such a quantity has many uses in a machine learning context for variable or feature selection minimizing training error and ensuring sparsity in solutions we derive a simple but practical method for achieving these goals and discuss its relationship to existing techniques of minimizing the zero norm the method boils down to implementing a simple modification of vanilla svm namely via an iterative multiplicative rescaling of the training data applications we investigate which aid our discussion include variable and feature selection on biological microarray data and multicategory classification

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

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

stability of discrete dark solitons in nonlinear schrodinger lattices we obtain new results on the stability of discrete dark solitons bifurcating from the anti continuum limit of the discrete nonlinear schrodinger equation following the analysis of our previous paper 2005 physica d 212 1 19 we derive a criterion for the stability or instability of discrete dark solitons from the limiting configuration and confirm this criterion numerically we also develop asymptotic calculations of the relevant eigenvalues for a number of prototypical configurations and illustrate their good agreement with the numerical data

variable selection using svm based criteria we propose new methods to evaluate variable subset relevance with a view to variable selection relevance criteria are derived from support vector machines and are based on weight vector w 2 or generalization error bounds sensitivity with respect to a variable experiments on linear and non linear toy problems and real world datasets have been carried out to assess the effectiveness of these criteria results show that the criterion based on weight vector derivative achieves good results and performs consistently well over the datasets we used

local causal and markov blanket induction for causal discovery and feature selection for classification part ii analysis and extensions in part i of this work we introduced and evaluated the generalized local learning gll framework for producing local causal and markov blanket induction algorithms in the present second part we analyze the behavior of gll algorithms and provide extensions to the core methods specifically we investigate the empirical convergence of gll to the true local neighborhood as a function of sample size moreover we study how predictivity improves with increasing sample size then we investigate how sensitive are the algorithms to multiple statistical testing especially in the presence of many irrelevant features next we discuss the role of the algorithm parameters and also show that markov blanket and causal graph concepts can be used to understand deviations from optimality of state of the art non causal algorithms the present paper also introduces the following extensions to the core gll framework parallel and distributed versions of gll algorithms versions with false discovery rate control strategies for constructing novel heuristics for specific domains and divide and conquer local to global learning lgl strategies we test the generality of the lgl approach by deriving a novel lgl based algorithm that compares favorably to the state of the art global learning algorithms in addition we investigate the use of non causal feature selection methods to facilitate global learning open problems and future research paths related to local and local to global causal learning are discussed

on the validity of the variational approximation in discrete nonlinear schrodinger equations abstract the variational approximation is a well known tool to approximate localized states in nonlinear systems in the context of a discrete nonlinear schrodinger equation with a small coupling constant we prove error estimates for the variational approximations of site symmetric bond symmetric and twisted discrete solitons this is shown for various trial configurations which become increasingly more accurate as more parameters are taken it is also shown that the variational approximation yields the correct spectral stability result and controls the oscillatory dynamics of stable discrete solitons for long but finite time intervals

internal modes of discrete solitons near the anti continuum limit of the dnls equation discrete solitons of the discrete nonlinear schrodinger dnls equation are compactly supported in the anti continuum limit of the zero coupling between lattice sites eigenvalues of the linearization of the dnls equation at the discrete soliton determine its spectral stability small eigenvalues bifurcating from the zero eigenvalue near the anti continuum limit were characterized earlier for this model here we analyze the resolvent operator and prove that it is bounded in the neighborhood of the continuous spectrum if the discrete soliton is simply connected in the anti continuum limit this result rules out the existence of internal modes neutrally stable eigenvalues of the discrete spectrum near the anti continuum limit

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

breathers in nonlinear lattices existence linear stability and quantization abstract it has been proved by the principle of anti integrable limit renamed here anti continuous limit and the implicit function theorem that under rather weak hypotheses there exist spatially localized and time periodic solutions breathers in arrays of nonlinear coupled classical oscillators provided the coupling is not too strong the models can be translationally invariant or not and be of any dimension there are also time periodic solutions corresponding to arbitrary distributions on the lattice of such solutions multibreathers the whole set of these solutions can be labeled by a discrete coding sequence the condition that the frequency of the breather or multibreather solution has no harmonics in the phonon spectrum can be discarded for a large subset of spatially extended time periodic solutions called phonobreather which correspond to special codes which can be also spatially chaotic and where no oscillator is at rest these results extend almost without change to models with coupled rotors the existence of rotobreathers which are exact solutions consisting of a single rotor rotating while the other rotors oscillate is proved there are also multirotobreather solutions and phono rotobreathers etc it is also shown that the phase of the single breathers constituting a multibreather or multirotobreather solution can be submitted to a phase torsion these new dynamical structures carry a nonzero energy flow in models with two dimensions and more the phase torsion of multibreather solutions can generate new dynamical solutions with vortices in the energy flow the dynamics of a quantum electron coupled to a classical lattice is also studied within the same approach from the anti continuous limit the existence of two kinds of polarobreathers which are spatially exponentially localized dynamical solutions is proved for a small enough electronic transfer integral the polarobreathers of the first kind include the standard static polaron the lattice configuration is static time independent when the electron is in an excited state i e the electronic oscillator oscillates periodically they can be spatially chaotic a polarobreather of the second kind corresponds to a localized periodic lattice oscillation associated with a localized quasiperiodic electronic oscillation the most simple of these solutions are those for which both the lattice oscillation and the electron wave function are mostly concentrated close to the same single site the standard floquet analysis of the linear stability of the breather and multibreather solutions is shown to be related with the band spectrum property of the newton operator involved in the implicit function theorem the krein theory of bifurcations is reinterpreted from this point of view the linear stability of the single breather and rotobreather solutions is then proved at least at small enough coupling finally it is shown that in the quantum version of translationally invariant classical models where there cannot exist in principle any strictly localized excitation there are narrow bands of excitations consisting of bound states of many bosons which are the quantum counterpart of the classical breathers the bandwidth of these excitations goes exponentially to zero with the number of bound phonons this theory provides simultaneously existence theorems and a new powerful and accurate numerical method for calculating practically any of the solutions which has been formally predicted to exist these numerical applications are currently written elsewhere

computation causation and discovery in science business and policymaking anywhere data are used in prediction two sorts of problems requiring very different methods of analysis often arise the first problems of recognition and classification concerns learning how to use some features of a system to accurately predict other features of that system the second problems of causal discovery concerns learning how to predict those changes to some features of a system that will result if an intervention changes other features this book is about the second more difficult type of problem typical problems of causal discovery are how will a change in commission rates affect the total sales of a company how will a reduction in cigarette smoking among older smokers affect their life expectancy how will a change in the formula a college uses to award scholarships affect its dropout rate these sorts of changes are interventions that directly alter some features of the system and perhaps and this is the question indirectly alter others the contributors discuss recent research and applications using bayes nets or directed graphic representations including representations of feedback of recursive systems the book contains a thorough discussion of foundational issues algorithms proof techniques and applications to economics physics biology educational research and other areas

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

asymptotic stability of breathers in some hamiltonian networks of weakly coupled oscillators we consider a hamiltonian chain of weakly coupled anharmonic oscillators it is well known that if the coupling is weak enough then the system admits families of periodic solutions exponentially localized in space breathers in this paper we prove asymptotic stability in energy space of such solutions the proof is based on two steps first we use canonical perturbation theory to put the system in a suitable normal form in a neighborhood of the breather second we use dispersion in order to prove asymptotic stability the main limitation of the result rests in the fact that the nonlinear part of the on site potential is required to have a zero of order 8 at the origin from a technical point of view the theory differs from that developed for hamiltonian pdes due to the fact that the breather is not a relative equilibrium of the system

introduction to causal inference the goal of many sciences is to understand the mechanisms by which variables came to take on the values they have that is to find a generative model and to predict what the values of those variables would be if the naturally occurring mechanisms were subject to outside manipulations the past 30 years has seen a number of conceptual developments that are partial solutions to the problem of causal inference from observational sample data or a mixture of observational sample and experimental data particularly in the area of graphical causal modeling however in many domains problems such as the large numbers of variables small samples sizes and possible presence of unmeasured causes remain serious impediments to practical applications of these developments the articles in the special topic on causality address these and other problems in applying graphical causal modeling algorithms this introduction to the special topic on causality provides a brief introduction to graphical causal modeling places the articles in a broader context and describes the differences between causal inference and ordinary machine learning classification and prediction problems

variable selection in data mining building a predictive model for bankruptcy we predict the onset of personal bankruptcy using least squares regression although well publicized only 2 244 bankruptcies occur in our dataset of 2 9 million months of credit card activity we use stepwise selection to find predictors of these from a mix of payment history debt load demographics and their interactions this combination of rare responses and over 67 000 possible predictors leads to a challenging modeling question how does one separate coincidental from useful predictors we show that three modifications turn stepwise regression into an effective methodology for predicting bankruptcy our version of stepwise regression 1 organizes calculations to accommodate interactions 2 exploits modern decision theoretic criteria to choose predictors and 3 conservatively estimates p values to handle sparse data and a binary response omitting any one of these leads to poor performance a final step in our procedure calibrates regression predictions with these modifications stepwise regr

chaotic trajectories in the standard map the concept of anti integrability a rigorous proof is given in the standard map associated with a frenkel kontorowa model for the existence of chaotic trajectories with unbounded momenta for large enough coupling constant k k0 these chaotic trajectories with finite entropy per site are coded by integer sequences mi such that the sequence bi mi 1 mi 1 2mi be bounded by some integer b the bound k0 in k depends on b and can be lowered for coding sequences mi fulfilling more restrictive conditions the obtained chaotic trajectories correspond to stationary configurations of the frenkel kontorowa model with a finite non zero photon gap called gap parameter in dimensionless units this property implies that the trajectory or the configuration ui can be uniquely continued as a uniformly continuous function of the model parameter k in some neighborhood of the initial configuration a non zero gap parameter implies that the lyapunov coefficient is strictly positive when it is defined in addition the existence of dilating and contracting manifolds is proven for these chaotic trajectories exotic trajectories such as ballistic trajectories are also proven to exist as a consequence of these theorems the concept of anti integrability emerges from these theorems in the anti integrable limit which can be only defined for a discrete time dynamical system the coordinates of the trajectory at time i do not depend on the coordinates at time i 1 thus at this singular limit the existence of chaotic trajectories is trivial and the dynamical system reduces to a bernoulli shift it is well known that the kam tori of symplectic dynamical originates by continuity from the invariant tori which exists in the integrible limit under certain conditions in a similar way it appears that the chaotic trajectories of dynamical systems originate by continuity from those which exists at the anti integrable limits also under certain conditions

stability of discrete solitons in nonlinear schrodinger lattices we consider the discrete solitons bifurcating from the anti continuum limit of the discrete nonlinear schrodinger nls lattice the discrete soliton in the anti continuum limit represents an arbitrary finite superposition of in phase or anti phase excited nodes separated by an arbitrary sequence of empty nodes by using stability analysis we prove that the discrete solitons are all unstable near the anti continuum limit except for the solitons which consist of alternating anti phase excited nodes we classify analytically and confirm numerically the number of unstable eigenvalues associated with each family of the discrete solitons

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

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

existence and uniqueness for a problem involving hilfer fractional derivative we consider an initial value problem for a class of nonlinear fractional differential equations involving hilfer fractional derivative we prove existence and uniqueness of global solutions in the space of weighted continuous functions the stability of the solution for a weighted cauchy type problem is also analyzed

power and exponentials laws theory and application abstract in this paper we present novel derivatives based on exponential and power law kernel important properties and numerical approximations via riemann liouville caputo for first and second order were obtained we applied the new operators to describe different attractors and the advection diffusion equation interesting simulations were obtained for different values of the fractional orders and we showed that the new operator is useful in practical applications and the numerical simulations show the efficiency and the accuracy of the new derivative to modeling real world problems

the control of the false discovery rate in multiple testing under dependency benjamini and hochberg suggest that the false discovery rate may be the appropriate error rate to control in many applied multiple testing problems a simple procedure was given there as an fdr controlling procedure for independent test statistics and was shown to be much more powerful than comparable procedures which control the traditional familywise error rate we prove that this same procedure also controls the false discovery rate when the test statistics have positive regression dependency on each of the test statistics corresponding to the true null hypotheses this condition for positive dependency is general enough to cover many problems of practical interest including the comparisons of many treatments with a single control multivariate normal test statistics with positive correlation matrix and multivariate t furthermore the test statistics may be discrete and the tested hypotheses composite without posing special difficulties for all other forms of dependency a simple conservative modification of the procedure controls the false discovery rate thus the range of problems for which a procedure with proven fdr control can be offered is greatly increased 1 1 simultaneous hypotheses testing the control of the increased type i error when testing simultaneously a family of hypotheses is a central issue in the area of multiple comparisons rarely are we interested only in whether all hypotheses are jointly true or not which is the test of the intersection null hypothesis in most applications we infer about the individual hypotheses realizing that some of the tested hypotheses are usually true we hope not all and some are not we wish to decide which ones are not true indicating statistical discoveries an important such problem is that of multiple endpoints in a clinical trial a new treatment is compared with an existing one in terms of a large number of potential benefits endpoints

local causal and markov blanket induction for causal discovery and feature selection for classification part i algorithms and empirical evaluation we present an algorithmic framework for learning local causal structure around target variables of interest in the form of direct causes effects and markov blankets applicable to very large data sets with relatively small samples the selected feature sets can be used for causal discovery and classification the framework generalized local learning or gll can be instantiated in numerous ways giving rise to both existing state of the art as well as novel algorithms the resulting algorithms are sound under well defined sufficient conditions in a first set of experiments we evaluate several algorithms derived from this framework in terms of predictivity and feature set parsimony and compare to other local causal discovery methods and to state of the art non causal feature selection methods using real data a second set of experimental evaluations compares the algorithms in terms of ability to induce local causal neighborhoods using simulated and resimulated data and examines the relation of predictivity with causal induction performance our experiments demonstrate consistently with causal feature selection theory that local causal feature selection methods under broad assumptions encompassing appropriate family of distributions types of classifiers and loss functions exhibit strong feature set parsimony high predictivity and local causal interpretability although non causal feature selection methods are often used in practice to shed light on causal relationships we find that they cannot be interpreted causally even when they achieve excellent predictivity therefore we conclude that only local causal techniques should be used when insight into causal structure is sought in a companion paper we examine in depth the behavior of gll algorithms provide extensions and show how local techniques can be used for scalable and accurate global causal graph learning

on classification of intrinsic localized modes for the discrete nonlinear schrodinger equation abstract we consider localized modes discrete breathers of the discrete nonlinear schrodinger equation i d n dt n 1 n 1 2 n n 2 n 1 n z we study the diversity of the steady state solutions of the form n t ei tvn and the intervals of the frequency of their existence the base for the analysis is provided by the anticontinuous limit negative and large enough where all the solutions can be coded by the sequences of three symbols 0 and using dynamical systems approach we show that this coding is valid for 3 4533 and the point is a point of accumulation of saddle node bifurcations also we study other bifurcations of intrinsic localized modes which take place for and give the complete table of them for the solutions with codes consisting of less than four symbols

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples

a new representation formula for the hilfer fractional derivative and its application in the paper we derive an equivalent definition of the generalized riemann liouville derivative derivative in the hilfer sense next we show that the new formula for such derivative is very useful in practical applications

on the spectral theory and dispersive estimates for a discrete schrodinger equation in one dimension based on the recent work komech et al dispersive estimates for 1d discrete schrodinger and klein gordon equations appl anal 85 1487 2006 for compact potentials we develop the spectral theory for the one dimensional discrete schrodinger operator h v n 1 n 1 2 n vn n we show that under appropriate decay conditions on the general potential and a nonresonance condition at the spectral edges the spectrum of h consists of finitely many eigenvalues of finite multiplicities and the essential absolutely continuous spectrum while the resolvent satisfies the limiting absorption principle and the puiseux expansions near the edges these properties imply the dispersive estimates eithpa c h l 2 l 2 t 3 2 for any fixed 52 and any t 0 where pa c h denotes the spectral projection to the absolutely continuous spectrum of h in addition based on the scattering theory for the discrete jost solutions and the previous results by stefanov and kevrekidis asymptotic behaviour of small

sophisticated merging over random partitions a scalable and robust causal discovery approach scalable causal discovery is an essential technology to a wide spectrum of applications including biomedical studies and social network evolution analysis to tackle the difficulty of high dimensionality a number of solutions are proposed in the literature generally dividing the original variable domain into smaller subdomains by computation intensive partitioning strategies these approaches usually suffer significant structural errors when the partitioning strategies fail to recognize true causal edges across the output subdomains such a structural error accumulates quickly with the growing depth of recursive partitioning due to the lack of correction mechanism over causally connected variables when they are wrongly divided into two subdomains finally jeopardizing the robustness of the integrated results this paper proposes a completely different strategy to solve the problem powered by a lightweight random partitioning scheme together with a carefully designed merging algorithm over results from the random partitions based on the randomness properties of the partitioning scheme we design a suite of tricks for the merging algorithm in order to support propagation based significance enhancement maximal acyclic subgraph causal ordering and order sensitive redundancy elimination theoretical studies as well as empirical evaluations verify the genericity effectiveness and scalability of our proposal on both simulated and real world causal structures when the scheme is used in combination with a variety of causal solvers known effective on smaller domains

properties of the scattering matrix and dispersion estimates for jacobi operators we show that for a jacobi operator with coefficients whose j 1 th moments are summable the j th derivative of the scattering matrix is in the wiener algebra of functions with summable fourier coefficients we use this result to improve the known dispersive estimates with integrable time decay for the time dependent jacobi equation in the resonant case