prediction and classification in nonlinear data analysis something old something new something borrowed something blue prediction and classification are two very active areas in modern data analysis in this paper prediction with nonlinear optimal scaling transformations of the variables is reviewed and extended to the use of multiple additive components much in the spirit of statistical learning techniques that are currently popular among other areas in data mining also a classification clustering method is described that is particularly suitable for analyzing attribute value data from systems biology genomics proteomics and metabolomics and which is able to detect groups of objects that have similar values on small subsets of the attributes

approximately optimizing ndcg using pair wise loss abstract the normalized discounted cumulative gain ndcg is used to measure the performance of ranking algorithms much of the work on learning to rank by optimizing ndcg directly or indirectly is based on list wise approaches in our work we approximately optimize a variant of ndcg called ndcg using pair wise approaches ndcg utilizes the linear discounting function we first prove that the dcg error of ndcg is equal to the weighted pair wise loss then on that basis rankboostndcg and ranksvmndcg are proposed to optimize the upper bound of the pair wise 0 1 loss function the experimental results from applying our approaches and ten other state of the art methods to five public datasets show the superiority of the proposed methods especially ranksvmndcg in addition rankboostndcg are less influenced by the initial weight distribution

classification of integrable hydrodynamic chains and generating functions of conservation laws a new approach to classification of integrable hydrodynamic chains is established generating functions of conservation laws are classified by the method of hydrodynamic reductions the n parametric family of explicit hydrodynamic reductions allows us to reconstruct corresponding hydrodynamic chains many new hydrodynamic chains are found

multitask quantile regression under the transnormal model abstractwe consider estimating multitask quantile regression under the transnormal model with focus on high dimensional setting we derive a surprisingly simple closed form solution through rank based covariance regularization in particular we propose the rank based l1 penalization with positive definite constraints for estimating sparse covariance matrices and the rank based banded cholesky decomposition regularization for estimating banded precision matrices by taking advantage of the alternating direction method of multipliers nearest correlation matrix projection is introduced that inherits sampling properties of the unprojected one our work combines strengths of quantile regression and rank based covariance regularization to simultaneously deal with nonlinearity and nonnormality for high dimensional regression furthermore the proposed method strikes a good balance between robustness and efficiency achieves the oracle like convergence rate and provides the provable prediction interval und

flexible discriminant analysis by optimal scoring abstract fisher s linear discriminant analysis is a valuable tool for multigroup classification with a large number of predictors one can find a reduced number of discriminant coordinate functions that are optimal for separating the groups with two such functions one can produce a classification map that partitions the reduced space into regions that are identified with group membership and the decision boundaries are linear this article is about richer nonlinear classification schemes linear discriminant analysis is equivalent to multiresponse linear regression using optimal scorings to represent the groups in this paper we obtain nonparametric versions of discriminant analysis by replacing linear regression by any nonparametric regression method in this way any multiresponse regression technique such as mars or neural networks can be postprocessed to improve its classification performance

on the characterization of a class of fisher consistent loss functions and its application to boosting accurate classification of categorical outcomes is essential in a wide range of applications due to computational issues with minimizing the empirical 0 1 loss fisher consistent losses have been proposed as viable proxies however even with smooth losses direct minimization remains a daunting task to approximate such a minimizer various boosting algorithms have been suggested for example with exponential loss the adaboost algorithm freund and schapire 1995 is widely used for two class problems and has been extended to the multi class setting zhu et al 2009 alternative loss functions such as the logistic and the hinge losses and their corresponding boosting algorithms have also been proposed zou et al 2008 wang 2012 in this paper we demonstrate that a broad class of losses including non convex functions achieve fisher consistency and in addition can be used for explicit estimation of the conditional class probabilities furthermore we provide a generic boosting algorithm that is not loss specific extensive simulation results suggest that the proposed boosting algorithms could outperform existing methods with properly chosen losses and bags of weak learners

identifying risk factors for severe childhood malnutrition by boosting additive quantile regression we investigated the risk factors for childhood malnutrition in india based on the 2005 2006 demographic and health survey by applying a novel estimation technique for additive quantile regression ordinary linear and generalized linear regression models relate the mean of a response variable to a linear combination of covariate effects and as a consequence focus on average properties of the response the use of such a regression model for analyzing childhood malnutrition in developing or transition countries implies that the estimated effects describe the average nutritional status however it is of even greater interest to analyze quantiles of the response distribution such as the 5 or 10 quantile which relate to the risk of extreme malnutrition our investigation is based on a semiparametric extension of quantile regression models where different types of nonlinear effects are included in the model equation leading to additive quantile regression we addressed the variable selection and model c

classical r matrix theory for bi hamiltonian field systems this is a survey of the application of the classical r matrix formalism to the construction of infinite dimensional integrable hamiltonian field systems the main point is the study of bi hamiltonian structures appropriate constructions on poisson noncommutative and loop algebras as well as the central extension procedure are presented the theory is developed for 1 1 and 2 1 dimensional field and lattice soliton systems as well as hydrodynamic systems the formalism presented contains sufficiently many proofs and important details to make it self contained and complete the general theory is applied to several infinite dimensional lie algebras in order to construct both dispersionless and dispersive soliton integrable field systems

reductions and hodograph solutions of the dispersionless kp hierarchy a general scheme for analysing reductions of dispersionless integrable hierarchies is presented it is based on a method for determining the s function by means of a system of first order differential equations compatibility systems of nonlinear partial differential equations of bourlet type characterizing both reductions and hodograph solutions of the dkp hierarchy are obtained wide classes of illustrative explicit examples are exhibited

causal inference by using invariant prediction identification and confidence intervals summary what is the difference between a prediction that is made with a causal model and that with a non causal model suppose that we intervene on the predictor variables or change the whole environment the predictions from a causal model will in general work as well under interventions as for observational data in contrast predictions from a non causal model can potentially be very wrong if we actively intervene on variables here we propose to exploit this invariance of a prediction under a causal model for causal inference given different experimental settings e g various interventions we collect all models that do show invariance in their predictive accuracy across settings and interventions the causal model will be a member of this set of models with high probability this approach yields valid confidence intervals for the causal relationships in quite general scenarios we examine the example of structural equation models in more detail and provide sufficient assumptions under which the set of causal predictors becomes identifiable we further investigate robustness properties of our approach under model misspecification and discuss possible extensions the empirical properties are studied for various data sets including large scale gene perturbation experiments

multivariate adaptive regression splines a new method is presented for flexible regression modeling of high dimensional data the model takes the form of an expansion in product spline basis functions where the number of basis functions as well as the parameters associated with each one product degree and knot locations are automatically determined by the data this procedure is motivated by the recursive partitioning approach to regression and shares its attractive properties unlike recursive partitioning however this method produces continuous models with continuous derivatives it has more power and flexibility to model relationships that are nearly additive or involve interactions in at most a few variables in addition the model can be represented in a form that separately identifies the additive contributions and those associated with the different multivariable interactions

waterbag reductions of the dispersionless discrete kp hierarchy we consider the dispersionless limit of the discrete kp hierarchy we describe a family of n parameter waterbag reductions of the hierarchy and give sufficient conditions for the reduced equations of motion to be hyperbolic using geogdzhaev s method we solve the initial value problem for the reduced system the solution is implicit in generalized hodograph form tsarev s p 1985 sov math dokl 31 488 the relationship of this form of the solution to the properties of the hierarchy the reduction and the initial data is discussed briefly indicating how this construction might be generalized

a view of margin losses as regularizers of probability estimates regularization is commonly used in classifier design to assure good generalization classical regularization enforces a cost on classifier complexity by constraining parameters this is usually combined with a margin loss which favors large margin decision rules a novel and unified view of this architecture is proposed by showing that margin losses act as regularizers of posterior class probabilities in a way that amplifies classical parameter regularization the problem of controlling the regularization strength of a margin loss is considered using a decomposition of the loss in terms of a link and a binding function the link function is shown to be responsible for the regularization strength of the loss while the binding function determines its outlier robustness a large class of losses is then categorized into equivalence classes of identical regularization strength or outlier robustness it is shown that losses in the same regularization class can be parameterized so as to have tunable regularization strength this parameterization is finally used to derive boosting algorithms with loss regularization boostlr three classes of tunable regularization losses are considered in detail canonical losses can implement all regularization behaviors but have no flexibility in terms of outlier modeling shrinkage losses support equally parameterized link and binding functions leading to boosting algorithms that implement the popular shrinkage procedure this offers a new explanation for shrinkage as a special case of loss based regularization finally tunable losses enable the independent parameterization of link and binding functions leading to boosting algorithms of great exibility this is illustrated by the derivation of an algorithm that generalizes both adaboost and logitboost behaving as either one when that best suits the data to classify various experiments provide evidence of the benefits of probability regularization for both classification and estimation of posterior class probabilities

remarks on functional canonical variates alternating least squares methods and ace we discuss properties of some data analytic methods which are intimately related to each other alternating least squares als correspondence analysis and more recently breiman and friedman s ace algorithm the application of these methods to regression produces nonparametric estimators of nonlinear transformations both of the response and the predictors we point out some anomalies as well as some curiosities in the mathematics of these methods and we relate them to some areas in computer aided tomography projection pursuit regression and nonlinear devices in the theory of noise

hydrodynamic reductions of the dispersionless harry dym hierarchy we investigate the reductions of the dispersionless harry dym hierarchy to systems of finitely many partial differential equations these equations must satisfy the compatibility condition and they are diagonalizable and semi hamiltonian by imposing a further constraint the compatibility is reduced to a system of algebraic equations whose solutions are described

statistical analysis of bayes optimal subset ranking the ranking problem has become increasingly important in modern applications of statistical methods in automated decision making systems in particular we consider a formulation of the statistical ranking problem which we call subset ranking and focus on the discounted cumulated gain dcg criterion that measures the quality of items near the top of the rank list similar to error minimization for binary classification direct optimization of natural ranking criteria such as dcg leads to a nonconvex optimization problems that can be np hard therefore a computationally more tractable approach is needed we present bounds that relate the approximate optimization of dcg to the approximate minimization of certain regression errors these bounds justify the use of convex learning formulations for solving the subset ranking problem the resulting estimation methods are not conventional in that we focus on the estimation quality in the top portion of the rank list we further investigate the asymptotic statistical behavior of these formulations under appropriate conditions the consistency of the estimation schemes with respect to the dcg metric can be derived

boosting with the l2 loss this article investigates a computationally simple variant of boosting l2boost which is constructed from a functional gradient descent algorithm with the l2 loss function like other boosting algorithms l2boost uses many times in an iterative fashion a prechosen fitting method called the learner based on the explicit expression of refitting of residuals of l2boost the case with symmetric linear learners is studied in detail in both regression and classification in particular with the boosting iteration m working as the smoothing or regularization parameter a new exponential bias variance trade off is found with the variance complexity term increasing very slowly as m tends to infinity when the learner is a smoothing spline an optimal rate of convergence result holds for both regression and classification and the boosted smoothing spline even adapts to higher order unknown smoothness moreover a simple expansion of a smoothed 0 1 loss function is derived to reveal the importance of the d

dynamical entropy of c algebras and von neumann algebras the definition of the dynamical entropy is extended for automorphism groups ofc algebras as an example the dynamical entropy of the shift of a lattice algebra is studied and it is shown that in some cases it coincides with the entropy density

contrast trees and distribution boosting a method for decision tree induction is presented given a set of predictor variables formula see text and two outcome variables y and z associated with each x the goal is to identify those values of x for which the respective distributions of formula see text and formula see text or selected properties of those distributions such as means or quantiles are most different contrast trees provide a lack of fit measure for statistical models of such statistics or for the complete conditional distribution formula see text as a function of x they are easily interpreted and can be used as diagnostic tools to reveal and then understand the inaccuracies of models produced by any learning method a corresponding contrast boosting strategy is described for remedying any uncovered errors thereby producing potentially more accurate predictions this leads to a distribution boosting strategy for directly estimating the full conditional distribution of y at each x under no assumptions concerning its shape form or parametric representation

dynamical approximation entropies and topological entropy in operator algebras dynamical entropy invariants based on a general approximation approach are introduced for c and w algebra automorphisms this includes a noncommutative extension of topological entropy

the rate of convergence of adaboost the adaboost algorithm was designed to combine many weak hypotheses that perform slightly better than random guessing into a strong hypothesis that has very low error we study the rate at which adaboost iteratively converges to the minimum of the exponential loss unlike previous work our proofs do not require a weak learning assumption nor do they require that minimizers of the exponential loss are finite our first result shows that the exponential loss of adaboost s computed parameter vector will be at most e more than that of any parameter vector of l1 norm bounded by b in a number of rounds that is at most a polynomial in b and 1 e we also provide lower bounds showing that a polynomial dependence is necessary our second result is that within c e iterations adaboost achieves a value of the exponential loss that is at most e more than the best possible value where c depends on the data set we show that this dependence of the rate on e is optimal up to constant factors that is at least 1 e rounds are necessary to achieve within e of the optimal exponential loss

training hard margin support vector machines using greedy stagewise algorithm hard margin support vector machines hm svms suffer from getting overfitting in the presence of noise soft margin svms deal with this problem by introducing a regularization term and obtain a state of the art performance however this disposal leads to a relatively high computational cost in this paper an alternative method greedy stagewise algorithm for svms named gs svms is presented to cope with the overfitting of hm svms without employing the regularization term the most attractive property of gs svms is that its computational complexity in the worst case only scales quadratically with the size of training samples experiments on the large data sets with up to 400 000 training samples demonstrate that gs svms can be faster than libsvm 2 83 without sacrificing the accuracy finally we employ statistical learning theory to analyze the empirical results which shows that the success of gs svms lies in that its early stopping rule can act as an implicit regularization term

hodograph solutions for the manakov santini equation we investigate the integrable 2 1 dimensional manakov santini equation from the lax sato form several particular two and three component reductions are considered so that the manakov santini equation can be reduced to systems of hydrodynamic type then one can construct infinitely many exact solutions of the equation by the hodograph method

the adaboost flow we introduce a dynamical system that we call the adaboost flow the flow is defined by a system of odes with control we show that three algorithms of the adaboost family i the adaboost algorithm of schapire and freund ii the arc gv algorithm of breiman and iii the confidence rated prediction of schapire and singer can be embedded in the adaboost flow the nontrivial part of the adaboost flow equations coincides with the equations of dynamics of the nonperiodic toda system written in terms of spectral variables we provide a novel invariant geometrical description of the adaboost algorithm as a gradient flow on a foliation defined by level sets of the potential function we propose a new approach for constructing boosting algorithms as a continuous time gradient flow on measures defined by various metrics and potential functions finally we explain the similarity of the adaboost algorithm with the perelman s construction for the ricci flow 2015 wiley periodicals inc

building sparse twin support vector machine classifiers in primal space abstract twin support vector machines tsvm obtain faster training speeds than classical support vector machines svm however tsvm augmented vectors lose sparsity in this paper a rapid sparse twin support vector machine stsvm classifier in primal space is proposed to improve the sparsity and robustness of tsvm based on a simple back fitting strategy the stsvm iteratively builds each nonparallel hyperplanes by adding one support vector sv from the corresponding class at one time this process is terminated using an adaptive and stable stopping criterion stsvm learning is implemented by linear equation computing systems through introducing a quadratic function to approximate the empirical risk the computational results on several synthetic and benchmark datasets indicate that the stsvm obtains a sparse separating hyperplane at a low cost without sacrificing its generalization performance

an l_ 2 boosting algorithm for estimation of a regression function an l 2 boosting algorithm for estimation of a regression function from random design is presented which consists of fitting repeatedly a function from a fixed nonlinear function space to the residuals of the data by least squares and by defining the estimate as a linear combination of the resulting least squares estimates splitting of the sample is used to decide after how many iterations of smoothing of the residuals the algorithm terminates the rate of convergence of the algorithm is analyzed in case of an unbounded response variable the method is used to fit a sum of maxima of minima of linear functions to a given data set and is compared with other nonparametric regression estimates using simulated data

on quantum dynamics and statistics of vectors given a sequence of vectors in a hilbert space we propose to use the spectrum of the associated gram matrix as a tool for extracting statistical information on the sequence we examine two simple models in some detail the fractional shift where the sequence is generated by a deterministic unitary dynamics and random normalized vectors in a high dimensional space chosen at a given density in both cases the limiting eigenvalue distribution of the gram matrix is explicitly found we relate our results to the notion of growth entropy and recover in the stochastic case the eigenvalue distribution of the wishart matrices

additive logistic regression a statistical view of boosting boosting is one of the most important recent developments in classification methodology boosting works by sequentially applying a classification algorithm to reweighted versions of the training data and then taking a weighted majority vote of the sequence of classifiers thus produced for many classification algorithms this simple strategy results in dramatic improvements in performance we show that this seemingly mysterious phenomenon can be understood in terms of well known statistical principles namely additive modeling and maximum likelihood for the two class problem boosting can be viewed as an approximation to additive modeling on the logistic scale using maximum bernoulli likelihood as a criterion we develop more direct approximations and show that they exhibit nearly identical results to boosting direct multiclass generalizations based on multinomial likelihood are derived that exhibit performance comparable to other recently proposed multiclass generalizations of boosting in most situations and far superior in some we suggest a minor modification to boosting that can reduce computation often by factors of 10 to 50 finally we apply these insights to produce an alternative formulation of boosting decision trees this approach based on best first truncated tree induction often leads to better performance and can provide interpretable descriptions of the aggregate decision rule it is also much faster computationally making it more suitable to large scale data mining applications

optimal scaling by alternating length constrained nonnegative least squares with application to distance based analysis an important feature of distance based principal components analysis is that the variables can be optimally transformed for monotone spline transformation a nonnegative least squares problem with a length constraint has to be solved in each iteration as an alternative algorithm to lawson and hanson 1974 we propose the alternating length constrained non negative least squares alc nnls algorithm which minimizes the nonnegative least squares loss function over the parameters under a length constraint by alternatingly minimizing over one parameter while keeping the others fixed several properties of the new algorithm are discussed a monte carlo study is presented which shows that for most cases in distance based principal components analysis alc nnls performs as good as the method of lawson and hanson or sometimes even better in terms of the quality of the solution

finitely correlated states on quantum spin chains we study a construction that yields a class of translation invariant states on quantum spin chains characterized by the property that the correlations across any bond can be modeled on a finite dimensional vector space these states can be considered as generalized valence bond states and they are dense in the set of all translation invariant states we develop a complete theory of the ergodic decomposition of such states including the decomposition into periodic neel ordered states the ergodic components have exponential decay of correlations all states considered can be obtained as local functions of states of a special kind so called purely generated states which are shown to be ground states for suitably chosen finite range vbs interactions we show that all these generalized vbs models have a spectral gap our theory does not require symmetry of the state with respect to a local gauge group in particular we illustrate our results with a one parameter family of examples which are not isotropic except for one special case this isotropic model coincides with the one dimensional antiferromagnet recently studied by affleck kennedy lieb and tasaki

the reconstruction approach from interpolation to regression this article introduces an interpolation based method called the reconstruction approach for nonparametric regression based on the fact that interpolation usually has negligible errors compared

boosting as a regularized path to a maximum margin classifier in this paper we study boosting methods from a new perspective we build on recent work by efron et al to show that boosting approximately and in some cases exactly minimizes its loss criterion with an l1 constraint on the coefficient vector this helps understand the success of boosting with early stopping as regularized fitting of the loss criterion for the two most commonly used criteria exponential and binomial log likelihood we further show that as the constraint is relaxed or equivalently as the boosting iterations proceed the solution converges in the separable case to an l1 optimal separating hyper plane we prove that this l1 optimal separating hyper plane has the property of maximizing the minimal l1 margin of the training data as defined in the boosting literature an interesting fundamental similarity between boosting and kernel support vector machines emerges as both can be described as methods for regularized optimization in high dimensional predictor space using a computational trick to make the calculation practical and converging to margin maximizing solutions while this statement describes svms exactly it applies to boosting only approximately

boosting with early stopping convergence and consistency boosting is one of the most significant advances in machine learning for classification and regression in its original and computationally flexible version boosting seeks to minimize empirically a loss function in a greedy fashion the resulting estimator takes an additive function form and is built iteratively by applying a base estimator or learner to updated samples depending on the previous iterations an unusual regularization technique early stopping is employed based on cv or a test set this paper studies numerical convergence consistency and statistical rates of convergence of boosting with early stopping when it is carried out over the linear span of a family of basis functions for general loss functions we prove the convergence of boosting s greedy optimization to the infinimum of the loss function over the linear span using the numerical convergence result we find early stopping strategies under which boosting is shown to be consistent based on i i d samples and we obtain bounds on the rates of convergence for boosting estimators simulation studies are also presented to illustrate the relevance of our theoretical results for providing insights to practical aspects of boosting as a side product these results also reveal the importance of restricting the greedy search step sizes as known in practice through the work of friedman and others moreover our results lead to a rigorous proof that for a linearly separable problem adaboost with e 0 step size becomes an l 1 margin maximizer when left to run to convergence

greedy function approximation a gradient boosting machine function estimation approximation is viewed from the perspective of numerical optimization in function space rather than parameter space a connection is made between stagewise additive expansions and steepest descent minimization a general gradient descent boosting paradigm is developed for additive expansions based on any fitting criterion specific algorithms are presented for least squares least absolute deviation and huber m loss functions for regression and multiclass logistic likelihood for classification special enhancements are derived for the particular case where the individual additive components are regression trees and tools for interpreting such treeboost models are presented gradient boosting of regression trees produces competitive highly robust interpretable procedures for both regression and classification especially appropriate for mining less than clean data connections between this approach and the boosting methods of freund and shapire and friedman hastie and tibshirani are discussed

meromorphic lax representations of 1 1 dimensional multi hamiltonian dispersionless systems rational lax hierarchies introduced by krichever are generalized a systematic construction of infinite multi hamiltonian hierarchies and related conserved quantities is presented the method is based on the classical r matrix approach applied to poisson algebras a proof that poisson operators constructed near different points of laurent expansion of lax functions are equal is given all results are illustrated by several examples

functional gradient ascent for probit regression this paper proposes two gradient based methods to fit a probit regression model by maximizing the sample log likelihood function using the property of the hessian of the objective function the first method performs weighted least square regression in each iteration of the newton raphson framework resulting in probitboost a boosting like algorithm motivated by the gradient boosting algorithm 10 the second proposed approach maximizes the sample log likelihood function by updating the fitted function a small step in the gradient direction performing gradient ascent in functional space resulting in gradient probitboost we also generalize the algorithms to multi class problems by two strategies one of which is to use the gradient ascent to maximize the multi class sample log likelihood function for fitting all the classifiers simultaneously and the second approach uses the one versus all scheme to reduce the multi class problem to a series of binary classification problems the proposed algorithms are tested on typical classification problems including face detection cancer classification and handwritten digit recognition the results show that compared to the alternative methods the proposed algorithms perform similar or better in terms of testing error rates

a tutorial on propensity score estimation for multiple treatments using generalized boosted models the use of propensity scores to control for pretreatment imbalances on observed variables in non randomized or observational studies examining the causal effects of treatments or interventions has become widespread over the past decade for settings with two conditions of interest such as a treatment and a control inverse probability of treatment weighted estimation with propensity scores estimated via boosted models has been shown in simulation studies to yield causal effect estimates with desirable properties there are tools e g the twang package in r and guidance for implementing this method with two treatments however there is not such guidance for analyses of three or more treatments the goals of this paper are twofold 1 to provide step by step guidance for researchers who want to implement propensity score weighting for multiple treatments and 2 to propose the use of generalized boosted models gbm for estimation of the necessary propensity score weights we define the causal quantities that may be of interest to studies of multiple treatments and derive weighted estimators of those quantities we present a detailed plan for using gbm to estimate propensity scores and using those scores to estimate weights and causal effects we also provide tools for assessing balance and overlap of pretreatment variables among treatment groups in the context of multiple treatments a case study examining the effects of three treatment programs for adolescent substance abuse demonstrates the methods

building support vector machines with reduced classifier complexity support vector machines svms though accurate are not preferred in applications requiring great classification speed due to the number of support vectors being large to overcome this problem we devise a primal method with the following properties 1 it decouples the idea of basis functions from the concept of support vectors 2 it greedily finds a set of kernel basis functions of a specified maximum size dmax to approximate the svm primal cost function well 3 it is efficient and roughly scales as o ndmax2 where n is the number of training examples and 4 the number of basis functions it requires to achieve an accuracy close to the svm accuracy is usually far less than the number of svm support vectors

gradient tree boosting for training conditional random fields conditional random fields crfs provide a flexible and powerful model for sequence labeling problems however existing learning algorithms are slow particularly in problems with large numbers of potential input features and feature combinations this paper describes a new algorithm for training crfs via gradient tree boosting in tree boosting the crf potential functions are represented as weighted sums of regression trees which provide compact representations of feature interactions so the algorithm does not explicitly consider the potentially large parameter space as a result gradient tree boosting scales linearly in the order of the markov model and in the order of the feature interactions rather than exponentially as in previous algorithms based on iterative scaling and gradient descent gradient tree boosting also makes it possible to use instance weighting as in c4 5 and surrogate splitting as in cart to handle missing values experimental studies of the effectiveness of these two methods as well as standard imputation and indicator feature methods show that instance weighting is the best method in most cases when feature values are missing at random

functional dissipation microarrays for classification in this article we describe a new method of extracting information from signals called functional dissipation that proves to be very effective for enhancing classification of high resolution texture rich data our algorithm bypasses to some extent the need to have very specialized feature extraction techniques and can potentially be used as an intermediate feature enhancement step in any classification scheme functional dissipation is based on signal transforms but uses the transforms recursively to uncover new features we generate a variety of masking functions and extract features with several generalized matching pursuit iterations in each iteration the recursive process modifies several coefficients of the transformed signal with the largest absolute values according to the specific masking function in this way the greedy pursuit is turned into a slow controlled dissipation of the structure of the signal that for some masking functions enhances separation among classes our case study in this paper is the classification of crystallization patterns of amino acids solutions affected by the addition of small quantities of proteins

prediction games and arcing algorithms the theory behind the success of adaptive reweighting and combining algorithms arcing such as adaboost freund schapire 1996a 1997 and others in reducing generalization error has not been well understood by formulating prediction as a game where one player makes a selection from instances in the training set and the other a convex linear combination of predictors from a finite set existing arcing algorithms are shown to be algorithms for finding good game strategies the minimax theorem is an essential ingredient of the convergence proofs an arcing algorithm is described that converges to the optimal strategy a bound on the generalization error for the combined predictors in terms of their maximum error is proven that is sharper than bounds to date schapire freund bartlett and lee 1997 offered an explanation of why adaboost works in terms of its ability to produce generally high margins the empirical comparison of adaboost to the optimal arcing algorithm shows that their explanation is n

integrability properties of the dispersionless kadomtsev petviashvili hierarchy in the paper we investigate integrability characteristics for the dispersionless kadomtsev petviashvili hierarchy these characteristics include symmetries hamiltonian structures and conserved quantities we give a lax triad to construct a master symmetry and a hierarchy of non isospectral dispersionless kadomtsev petviashvili flows these non isospectral flows together with the known isospectral dispersionless kadomtsev petviashvili flows form a lie algebra which is used to derive two sets of symmetries for the isospectral dispersionless kadomtsev petviashvili hierarchy by means of the master symmetry symmetries noether operator and conserved covariants hamiltonian structures are constructed for both isospectral and non isospectral dispersionless kadomtsev petviashvili hierarchies finally two sets of conserved quantities and their lie algebra are derived for the isospectral dispersionless kadomtsev petviashvili hierarchy

asymptotic properties of large random matrices with independent entries we study the normalized trace gn z n 1 tr h zi 1 of the resolvent of n n real symmetric matrices h 1 jk wjk n j k 1n assuming that their entries are independent but not necessarily identically distributed random variables we develop a rigorous method of asymptotic analysis of moments of gn z for iz 0 where 0 is determined by the second moment of wjk by using this method we find the asymptotic form of the expectation e gn z and of the connected correlator e gn z1 gn z2 e gn z1 e gn z2 we also prove that the centralized trace ngn z e ngn z has the gaussian distribution in the limit n based on these results we present heuristic arguments supporting the universality property of the local eigenvalue statistics for this class of random matrix ensembles

integrable hydrodynamic chains a new approach for derivation of benney type moment chains and integrable hydrodynamic type systems is presented new integrable hydrodynamic chains are constructed all their hydrodynamical reductions are described and integrated new 2 1 integrable hydrodynamic type systems are found

clustering objects on subsets of attributes with discussion read before the royal statistical society at a meeting organized by the research section on wednesday may 5th 2004 professor j t kent in the chair summary a new procedure is proposed for clustering attribute value data when used in conjunction with conventional distance based clustering algorithms this procedure encourages those algorithms to detect automatically subgroups of objects that preferentially cluster on subsets of the attribute variables rather than on all of them simultaneously the relevant attribute subsets for each individual cluster can be different and partially or completely overlap with those of other clusters enhancements for increasing sensitivity for detecting especially low cardinality groups clustering on a small subset of variables are discussed applications in different domains including gene expression arrays are presented