characterization of talagrand s transport entropy inequalities in metric spaces we give a characterization of transport entropy inequalities in metric spaces as an application we deduce that such inequalities are stable under bounded perturbation holley stroock perturbation lemma

concentration of measure inequalities for markov chains and phi mixing processes we prove concentration inequalities for some classes of markov chains and f mixing processes with constants independent of the size of the sample that extend the inequalities for product measures of talagrand the method is based on information inequalities put forward by marton in case of contracting markov chains using a simple duality argument on entropy our results also include the family of logarithmic sobolev inequalities for convex functions applications to bounds on supremum of dependent empirical processes complete this work

development of a formal likelihood function for improved bayesian inference of ephemeral catchments 1 the application of formal bayesian inferential approaches in hydrologic modeling is often criticized for requiring explicit assumptions to be made about the distribution of the errors via the likelihood function these assumptions can be adequate in some situations but often little attention is paid to the selection of an appropriate likelihood function this paper investigates the application of bayesian methods in modeling ephemeral catchments we consider two modeling case studies including a synthetically generated data set and a real data set of an arid australian catchment the case studies investigate some typical forms of the likelihood function which have been applied widely by previous researchers as well as introducing new implementations aimed at better addressing likelihood function assumptions in dry catchments the results of the case studies indicate the importance of explicitly accounting for model residuals that are highly positively skewed due to the presence of many zeros zero inflation arising from the dry spells experienced by the catchment specifically the form of the likelihood function was found to significantly impact the calibrated parameter posterior distributions which in turn have the potential to greatly affect the uncertainty estimates in each application the likelihood function that explicitly accounted for the nonconstant variance of the errors and the zero inflation of the errors resulted in 1 equivalent or better fits to the observed discharge in both timing and volume 2 superior estimation of the uncertainty as measured by the reliability and sharpness metrics and 3 more linear quantile quantile plots indicating the errors were more closely matched to the assumptions of this form of the likelihood function

marginal likelihood from the metropolis hastings output this article provides a framework for estimating the marginal likelihood for the purpose of bayesian model comparisons the approach extends and completes the method presented in chib 1995 by overcoming the problems associated with the presence of intractable full conditional densities the proposed method is developed in the context of mcmc chains produced by the metropolis hastings algorithm whose building blocks are used both for sampling and marginal likelihood estimation thus economizing on prerun tuning effort and programming experiments involving the logit model for binary data hierarchical random effects model for clustered gaussian data poisson regression model for clustered count data and the multivariate probit model for correlated binary data are used to illustrate the performance and implementation of the method these examples demonstrate that the method is practical and widely applicable

minimum complexity regression estimation with weakly dependent observations the minimum complexity regression estimation framework barron 1991 barron and cover 1991 and rissanen 1989 is a general data driven methodology for estimating a regression function from a given list of parametric models using independent and identically distributed i i d observations we extend barron s regression estimation framework to m dependent observations and to strongly mixing observations in particular we propose abstract minimum complexity regression estimators for dependent observations which may be adapted to a particular list of parametric models and establish upper bounds on the statistical risks of the proposed estimators in terms of certain deterministic indices of resolvability assuming that the regression function satisfies a certain fourier transform type representation we examine minimum complexity regression estimators adapted to a list of parametric models based on neural networks and by using the upper bounds for the abstract estimators we establish rates of convergence for the statistical risks of these estimators also as a key tool we extend the classical bernstein inequality from i i d random variables to m dependent processes and to strongly mixing processes

displacement convexity of entropy and related inequalities on graphs we introduce the notion of an interpolating path on the set of probability measures on finite graphs using this notion we first prove a displacement convexity property of entropy along such a path and derive prekopa leindler type inequalities a talagrand transport entropy inequality certain hwi type as well as log sobolev type inequalities in discrete settings to illustrate through examples we apply our results to the complete graph and to the hypercube for which our results are optimal by passing to the limit we recover the classical log sobolev inequality for the standard gaussian measure with the optimal constant

a characterization of dimension free concentration in terms of transportation inequalities the aim of this paper is to show that a probability measure concentrates independently of the dimension like a gaussian measure if and only if it verifies talagrand s t 2 transportation cost inequality this theorem permits us to give a new and very short proof of a result of otto and villani generalizations to other types of concentration are also considered in particular one shows that the poincare inequality is equivalent to a certain form of dimension free exponential concentration the proofs of these results rely on simple large deviations techniques

deviation inequalities for separately lipschitz functionals of composition of random functions abstract we consider a class of non homogeneous markov chains that contains many natural examples next using martingale methods we establish some deviation and moment inequalities for separately lipschitz functions of such a chain under moment conditions on some dominating random variables

on the rate of convergence of regularized boosting classifiers a regularized boosting method is introduced for which regularization is obtained through a penalization function it is shown through oracle inequalities that this method is model adaptive the rate of convergence of the probability of misclassification is investigated it is shown that for quite a large class of distributions the probability of error converges to the bayes risk at a rate faster than n v 2 4 v 1 where v is the vc dimension of the base class whose elements are combined by boosting methods to obtain an aggregated classifier the dimension independent nature of the rates may partially explain the good behavior of these methods in practical problems under tsybakov s noise condition the rate of convergence is even faster we investigate the conditions necessary to obtain such rates for different base classes the special case of boosting using decision stumps is studied in detail we characterize the class of classifiers realizable by aggregating decision stumps it is shown that some versions of boosting work especially well in high dimensional logistic additive models it appears that adding a limited labelling noise to the training data may in certain cases improve the convergence as has been also suggested by other authors

limits to classification and regression estimation from ergodic processes we answer two open questions concerning the existence of universal schemes for classification and regression estimation from stationary ergodic processes it is shown that no measurable procedure can produce weakly consistent regression estimates from every bivariate stationary ergodic process even if the covariate and response variables are restricted to take values in the unit interval it is further shown that no measurable procedure can produce weakly consistent classification rules from every bivariate stationary ergodic process for which the response variable is binary valued the results of the paper are derived via reduction arguments and are based in part on recent work concerning density estimaton from ergodic processes

effective and efficient global optimization for conceptual rainfall runoff models the successful application of a conceptual rainfall runoff crr model depends on how well it is calibrated despite the popularity of crr models reports in the literature indicate that it is typically difficult if not impossible to obtain unique optimal values for their parameters using automatic calibration methods unless the best set of parameters associated with a given calibration data set can be found it is difficult to determine how sensitive the parameter estimates and hence the model forecasts are to factors such as input and output data error model error quantity and quality of data objective function used and so on results are presented that establish clearly the nature of the multiple optima problem for the research crr model sixpar these results suggest that the crr model optimization problem is more difficult than had been previously thought and that currently used local search procedures have a very low probability of successfully finding the optimal parameter sets next the performance of three existing global search procedures are evaluated on the model sixpar finally a powerful new global optimization procedure is presented entitled the shuffled complex evolution sce ua method which was able to consistently locate the global optimum of the sixpar model and appears to be capable of efficiently and effectively solving the crr model optimization problem

optimal aggregation of classifiers in statistical learning classification can be considered as nonparametric estimation of sets where the risk is defined by means of a specific distance between sets associated with misclassification error it is shown that the rates of convergence of classifiers depend on two parameters the complexity of the class of candidate sets and the margin parameter the dependence is explicitly given indicating that optimal fast rates approaching o n 1 can be attained where n is the sample size and that the proposed classifiers have the property of robustness to the margin the main result of the paper concerns optimal aggregation of classifiers we suggest a classifier that automatically adapts both to the complexity and to the margin and attains the optimal fast rates up to a logarithmic factor

exponential inequalities for dynamical measures of expanding maps of the interval we prove an exponential inequality for the absolutely continuous invariant measure of a piecewise expanding map of the interval as an immediate corollary we obtain a concentration inequality we apply these results to the estimation of the rate of convergence of the empirical measure in various metrics and also to the efficiency of the shadowing by sets of positive measure

iterative nonparametric estimation of a log optimal portfolio selection function let stock market vectors form a stationary ergodic sequence for fixed d spl isin n a log optimal portfolio selection function of the past d observed vectors is iteratively estimated on the basis of a training sequence by use of gradients and nonparametric regression strong consistency is obtained under a boundedness and spl alpha mixing condition without further assumptions on the distribution

error bounds for piecewise smooth and switching regression this paper deals with regression problems in which the nonsmooth target is assumed to switch between different operating modes specifically piecewise smooth pws regression considers target functions switching deterministically via a partition of the input space while switching regression considers arbitrary switching laws this paper derives generalization error bounds in these two settings by following the approach based on rademacher complexities for pws regression our derivation involves a chaining argument and a decomposition of the covering numbers of pws classes in terms of the ones of their component function classes and the capacity of the classifier partitioning the input space this yields error bounds with a radical dependence on the number of modes for switching regression the decomposition can be performed directly at the level of the rademacher complexities which yields bounds with a linear dependence on the number of modes by using once more chaining and decomposition at the level of covering numbers we show how to recover a radical dependence examples of applications are given in particular for pws and swichting regression with linear and kernel based component functions

kantorovich duality for general transport costs and applications we introduce a general notion of transport cost that encompasses many costs used in the literature including the classical one and weak transport costs introduced by talagrand and marton in the 90 s and prove a kantorovich type duality theorem as a by product we obtain various applications in different directions we give a short proof of a result by strassen on the existence of a martingale with given marginals we characterize the associated transport entropy inequalities together with the log sobolev inequality restricted to convex concave functions some explicit examples of discrete measures satisfying weak transport entropy inequalities are also given

new concentration inequalities in product spaces we introduce three new ways to measure the distance from a point to a subset of a product space and we prove corresponding concentration inequalities each of them allows to control the fluctuation of a new class of random variables

statistical behavior and consistency of classification methods based on convex risk minimization we study how closely the optimal bayes error rate can be approximately reached using a classification algorithm that computes a classifier by minimizing a convex upper bound of the classification error function the measurement of closeness is characterized by the loss function used in the estimation we show that such a classification scheme can be generally regarded as a nonmaximum likelihood conditional in class probability estimate and we use this analysis to compare various convex loss functions that have appeared in the literature furthermore the theoretical insight allows us to design good loss functions with desirable properties another aspect of our analysis is to demonstrate the consistency of certain classification methods using convex risk minimization this study sheds light on the good performance of some recently proposed linear classification methods including boosting and support vector machines it also shows their limitations and suggests possible improvements

inferential aspects of the skew exponential power distribution when the analysis of real data indicates that normality assumptions are untenable more flexible models that cope with the most prevalent deviations from normality can be adopted in this context the skew exponential power sep distribution warrants special attention because it encompasses distributions having both heavy tails and skewness it allows likelihood inference and it includes the normal model as a special case this article concerns likelihood inference about the parameters of the sep family in particular the information matrix of the maximum likelihood estimators mles is obtained and finite sample properties of the estimators are investigated numerically special attention is given to the properties of the mles and likelihood ratio statistics when the data are drawn from a normal distribution because this case is relevant for using the sep distribution to test for normality application of the sep distribution in robust estimation problems is considered for both independent and depend

transportation cost information inequalities and applications to random dynamical systems and diffusions we first give a characterization of the l1 transportation cost information inequality on a metric space and next find some appropriate sufficient condition to transportation cost information inequalities for dependent sequences applications to random dynamical systems and diffusions are studied

a general framework for nonparametric identification of nonlinear stochastic systems in this paper nonparametric identification of nonlinear autoregressive systems with exogenous inputs narx is considered a general criterion function is introduced for estimating the value of the nonlinear function within the system at any fixed point the criterion function is constructed using a kernel together with a convex objective function not only does this framework include the classical kernel based weighted least squares estimator but also the kernel based l q q geq1 criteria as special cases first we prove that the minimizer of the general criterion function converges to the true function value with probability one second recursive algorithms are proposed to find the estimates which minimize the criterion function and it is shown that these estimates also converge to the true function value with probability one numerical examples are given justifying that the framework guarantees the strong consistency of the estimates and exhibits the robustness against outliers in the observations

estimating a function from ergodic samples with additive noise we study the problem of estimating an unknown function from ergodic samples corrupted by additive noise it is shown that one can consistently recover an unknown measurable function in this setting if the one dimensional 1 d distribution of the samples is comparable to a known reference distribution and the noise is independent of the samples and has known mixing rates the estimates are applied to deterministic sampling schemes in which successive samples are obtained by repeatedly applying a fixed map to a given initial vector and it is then shown how the estimates can be used to reconstruct an ergodic transformation from one of its trajectories

information inequalities and concentration of measure we derive inequalities of the form p q h p r h q r which hold for every choice of probability measures p q r where h p r denotes the relative entropy of p with respect to r and p q stands for a coupling type distance between p and q using the chain rule for relative entropies and then specializing to q with a given support we recover some of talagrand s concentration of measure inequalities for product spaces

quantile hydrologic model selection and model structure deficiency assessment 1 theory a theory for quantile based hydrologic model selection and model structure deficiency assessment is presented the paper demonstrates that the degree to which a model selection problem is constrained by the model structure measured by the lagrange multipliers of the constraints quantifies structural deficiency this leads to a formal definition of model structure deficiency or rigidity model structure deficiency introduces a bias in the prediction of an observed quantile which is often not equal across quantiles structure deficiency is therefore diagnosed when any two quantile predictions for a given model structure cross since unequal bias across quantiles result in quantile predictions crossing the analysis further suggests that the optimal value of quantile specific loss functions order different model structures by its structure deficiencies over a range of quantiles in addition to such novelties quantile hydrologic model selection is a frequentist approach that seeks to complement existing bayesian approaches to hydrological model uncertainty

stability bounds for stationary φ mixing and β mixing processes most generalization bounds in learning theory are based on some measure of the complexity of the hypothesis class used independently of any algorithm in contrast the notion of algorithmic stability can be used to derive tight generalization bounds that are tailored to specific learning algorithms by exploiting their particular properties however as in much of learning theory existing stability analyses and bounds apply only in the scenario where the samples are independently and identically distributed in many machine learning applications however this assumption does not hold the observations received by the learning algorithm often have some inherent temporal dependence this paper studies the scenario where the observations are drawn from a stationary mixing or mixing sequence a widely adopted assumption in the study of non i i d processes that implies a dependence between observations weakening over time we prove novel and distinct stability based generalization bounds for stationary mixing and mixing sequences these bounds strictly generalize the bounds given in the i i d case and apply to all stable learning algorithms thereby extending the use of stability bounds to non i i d scenarios we also illustrate the application of our mixing generalization bounds to general classes of learning algorithms including support vector regression kernel ridge regression and support vector machines and many other kernel regularization based and relative entropy based regularization algorithms these novel bounds can thus be viewed as the first theoretical basis for the use of these algorithms in non i i d scenarios

measure concentration for a class of random processes let x x i i be a stationary random process with a countable alphabet and distribution q let q x k 0 denote the conditional distribution of x x 1 x 2 x n given the k length past write d 1 x 1 0 if 1 x 1 and d 1 x 1 1 otherwise we say that the process x admits a joining with finite distance u if for any two past sequences k 0 k 1 0 and x k 0 x k 1 x 0 there is a joining of q k 0 and q x k 0 say dist 0 x 0 k 0 x k 0 such that the main result of this paper is the following inequality for processes that admit a joining with finite distance

mixing properties of a class of bernoulli processes we prove that stationary very weak bernoulli processes with rate o 1 n vwb o 1 n are strictly very weak bernoulli with rate o 1 n furthermore we discuss the relation between vwb o 1 n and the classical mixing properties for countable state processes in particular we show that vwb o 1 n implies mixing

concentration inequalities for dependent random variables via the martingale method the martingale method is used to establish concentration inequalities for a class of dependent random sequences on a countable state space with the constants in the inequalities expressed in terms of certain mixing coefficients along the way bounds are obtained on martingale differences associated with the random sequences which may be of independent interest as applications of the main result concentration inequalities are also derived for inhomogeneous markov chains and hidden markov chains and an extremal property associated with their martingale difference bounds is established this work complements and generalizes certain concentration inequalities obtained by marton and samson while also providing different proofs of some known results

mirror manifolds in higher dimension we describe mirror manifolds in dimensions different from the familiar case of complex threefolds we isolate certain simplifying features present only in dimension three and supply alternative methods that do not rely on these special characteristics and hence can be generalized to other dimensions although the moduli spaces for calabi yaud folds are not special kahler manifolds whend 3 they still have a restricted geometry and we indicate the new geometrical structures which arise we formulate and apply procedures which allow for the construction of mirror maps and the calculation of order by order instanton corrections to yukawa couplings mathematically these corrections are expected to correspond to calculating chern classes of various parameter spaces hilbert schemes for rational curves on calabi yau manifolds our mirror aided calculations agree with those chern class calculations in the limited number of cases for which the latter can be carried out with current mathematical tools finally we make explicit some striking relations between instanton corrections for various yukawa couplings derived from the associativity of the operator product algebra

mirror symmetry and rational curves on quintic threefolds a guide for mathematicians we give a mathematical account of a recent string theory calcula tion which predicts the number of rational curves on the generic quintic three fold our account involves the interpretation of yukawa couplings in terms of variations of hodge structure a new q expansion principle for functions on the moduli space of calabi yau manifolds and the mirror symmetry phe nomenon recently observed by string theorists department of mathematics duke university durham north carolina 27706 e mail address drm math duke edu this content downloaded from 157 55 39 224 on wed 14 dec 2016 04 59 36 utc all use subject to http about jstor org terms

regularized policy iteration with nonparametric function spaces we study two regularization based approximate policy iteration algorithms namely reg lspi and reg brm to solve reinforcement learning and planning problems in discounted markov decision processes with large state and finite action spaces the core of these algorithms are the regularized extensions of the least squares temporal difference lstd learning and bellman residual minimization brm which are used in the algorithms policy evaluation steps regularization provides a convenient way to control the complexity of the function space to which the estimated value function belongs and as a result enables us to work with rich nonparametric function spaces we derive efficient implementations of our methods when the function space is a reproducing kernel hilbert space we analyze the statistical properties of reg lspi and provide an upper bound on the policy evaluation error and the performance loss of the policy returned by this method our bound shows the dependence of the loss on the number of samples the capacity of the function space and some intrinsic properties of the underlying markov decision process the dependence of the policy evaluation bound on the number of samples is minimax optimal this is the first work that provides such a strong guarantee for a nonparametric approximate policy iteration algorithm

learning theory estimates with observations from general stationary stochastic processes this letter investigates the supervised learning problem with observations drawn from certain general stationary stochastic processes here by general we mean that many stationary stochastic processes can be included we show that when the stochastic processes satisfy a generalized bernstein type inequality a unified treatment on analyzing the learning schemes with various mixing processes can be conducted and a sharp oracle inequality for generic regularized empirical risk minimization schemes can be established the obtained oracle inequality is then applied to derive convergence rates for several learning schemes such as empirical risk minimization erm least squares support vector machines ls svms using given generic kernels and svms using gaussian kernels for both least squares and quantile regression it turns out that for independent and identically distributed i i d processes our learning rates for erm recover the optimal rates for non i i d processes including geometrically mixing markov processes geometrically mixing processes with restricted decay mixing processes and time reversed geometrically mixing processes our learning rates for svms with gaussian kernels match up to some arbitrarily small extra term in the exponent the optimal rates for the remaining cases our rates are at least close to the optimal rates as a by product the assumed generalized bernstein type inequality also provides an interpretation of the so called effective number of observations for various mixing processes

local adaptive importance sampling for multivariate densities with strong nonlinear relationships abstract we consider adaptive importance sampling techniques that use kernel density estimates at each iteration as importance sampling functions these can provide more nearly constant importance weights and more precise estimates of quantities of interest than the sampling importance resampling algorithm when the initial importance sampling function is diffuse relative to the target we propose a new method that adapts to the varying local structure of the target when the target has unusual structure such as strong nonlinear relationships between variables this method provides estimates with smaller mean squared error than alternative methods

on hydrological model complexity its geometrical interpretations and prediction uncertainty knowledge of hydrological model complexity can aid selection of an optimal prediction model out of a set of available models optimal model selection is formalized as selection of the least complex model out of a subset of models that have lower empirical risk this may be considered equivalent to minimizing an upper bound on prediction error defined here as the mathematical expectation of empirical risk in this paper we derive an upper bound that is free from assumptions on data and underlying process distribution as well as on independence of model predictions over time we demonstrate that hydrological model complexity as defined in the presented theoretical framework plays an important role in determining the upper bound the model complexity also acts as a stabilizer to a hydrological model selection problem if it is deemed ill posed we provide an algorithm for computing complexity of any arbitrary hydrological model we also demonstrate that hydrological model complexity has a geometric interpretation as the size of model output space the presented theory is applied to quantify complexities of two hydrological model structures sac sma and sixpar it detects that sac sma is indeed more complex than sixpar we also develop an algorithm to estimate the upper bound on prediction error which is applied on five different rainfall runoff model structures that vary in complexity we show that a model selection problem is stabilized by regularizing it with model complexity complexity regularized model selection yields models that are robust in predicting future but yet unseen data

concentration inequalities for random fields via coupling we present a new and simple approach to concentration inequalities in the context of dependent random processes and random fields our method is based on coupling and does not use information inequalities in case one has a uniform control on the coupling one obtains exponential concentration inequalities if such a uniform control is no more possible then one obtains polynomial or stretched exponential concentration inequalities our abstract results apply to gibbs random fields both at high and low temperatures and in particular to the low temperature ising model which is a concrete example of non uniformity of the coupling

pattern recognition for conditionally independent data in this work we consider the task of relaxing the i i d assumption in pattern recognition or classification aiming to make existing learning algorithms applicable to a wider range of tasks pattern recognition is guessing a discrete label of some object based on a set of given examples pairs of objects and labels we consider the case of deterministically defined labels traditionally this task is studied under the assumption that examples are independent and identically distributed however it turns out that many results of pattern recognition theory carry over a weaker assumption namely under the assumption of conditional independence and identical distribution of objects while the only assumption on the distribution of labels is that the rate of occurrence of each label should be above some positive threshold we find a broad class of learning algorithms for which estimations of the probability of the classification error achieved under the classical i i d assumption can be generalized to the similar estimates for case of conditionally i i d examples

stability and generalization in structured prediction structured prediction models have been found to learn effectively from a few large examples sometimes even just one despite empirical evidence canonical learning theory cannot guarantee generalization in this setting because the error bounds decrease as a function of the number of examples we therefore propose new pac bayesian generalization bounds for structured prediction that decrease as a function of both the number of examples and the size of each example our analysis hinges on the stability of joint inference and the smoothness of the data distribution we apply our bounds to several common learning scenarios including max margin and soft max training of markov random fields under certain conditions the resulting error bounds can be far more optimistic than previous results and can even guarantee generalization from a single large example

a new look at independence the concentration of measure phenomenon in product spaces is a farreaching abstract generalization of the classical exponential inequalities for sums of independent random variables we attempt to explain in the simplest possible terms the basic concepts underlying this phenomenon the basic method to prove concentration inequalities and the meaning of several of the most useful inequalities

data dependent k sub n nn and kernel estimators consistent for arbitrary processes let x sub 1 x sub 2 be an arbitrary random process taking values in a totally bounded subset of a separable metric space associated with x sub i we observe y sub i drawn from an unknown conditional distribution f y x sub i x with continuous regression function m x e y x x the problem of interest is to estimate y sub n based on x sub n and the data x sub i y sub i sub i 1 sup n 1 we construct appropriate data dependent nearest neighbor and kernel estimators and show with a very elementary proof that these are consistent for every process x sub 1 x sub 2

regularization in kernel learning supported in part by australian research council discovery grant dp0559465 and by israel science foundation grant 666 06

an explicit description of the reproducing kernel hilbert spaces of gaussian rbf kernels although gaussian radial basis function rbf kernels are one of the most often used kernels in modern machine learning methods such as support vector machines svms little is known about the structure of their reproducing kernel hilbert spaces rkhss in this work two distinct explicit descriptions of the rkhss corresponding to gaussian rbf kernels are given and some consequences are discussed furthermore an orthonormal basis for these spaces is presented finally it is discussed how the results can be used for analyzing the learning performance of svms

quantile hydrologic model selection and model structure deficiency assessment 2 applications quantile hydrologic model selection and structure deficiency assessment is applied in three case studies the performance of quantile model selection problem is rigorously evaluated using a model structure on the french broad river basin data set the case study shows that quantile model selection encompasses model selection strategies based on summary statistics and that it is equivalent to maximum likelihood estimation under certain likelihood functions it also shows that quantile model predictions are fairly robust the second case study is of a parsimonious hydrological model for dry land areas in western india the case study shows that an intuitive improvement in the model structure leads to reductions in asymmetric loss function values for all considered quantiles the asymmetric loss function is a quantile specific metric that is minimized to obtain a quantile specific prediction model the case study provides evidence that a quantile wise reduction in the asymmetric loss function is a robust indicator of model structure improvement finally a case study of modeling daily streamflow for the guadalupe river basin is presented a model structure that is least deficient for the study area is identified from nine different model structures based on quantile structural deficiency assessment the nine model structures differ in interception routing overland flow and base flow conceptualizations the three case studies suggest that quantile model selection and deficiency assessment provides a robust mechanism to compare deficiencies of different model structures and helps to identify better model structures in addition to its novelty quantile hydrologic model selection is a frequentist approach that seeks to complement existing bayesian approaches to hydrological model uncertainty

a formal likelihood function for parameter and predictive inference of hydrologic models with correlated heteroscedastic and non gaussian errors estimation of parameter and predictive uncertainty of hydrologic models has traditionally relied on several simplifying assumptions residual errors are often assumed to be independent and to be adequately described by a gaussian probability distribution with a mean of zero and a constant variance here we investigate to what extent estimates of parameter and predictive uncertainty are affected when these assumptions are relaxed a formal generalized likelihood function is presented which extends the applicability of previously used likelihood functions to situations where residual errors are correlated heteroscedastic and non gaussian with varying degrees of kurtosis and skewness the approach focuses on a correct statistical description of the data and the total model residuals without separating out various error sources application to bayesian uncertainty analysis of a conceptual rainfall runoff model simultaneously identifies the hydrologic model parameters and the appropriate statistical distribution of the residual errors when applied to daily rainfall runoff data from a humid basin we find that 1 residual errors are much better described by a heteroscedastic first order auto correlated error model with a laplacian distribution function characterized by heavier tails than a gaussian distribution and 2 compared to a standard least squares approach proper representation of the statistical distribution of residual errors yields tighter predictive uncertainty bands and different parameter uncertainty estimates that are less sensitive to the particular time period used for inference application to daily rainfall runoff data from a semiarid basin with more significant residual errors and systematic underprediction of peak flows shows that 1 multiplicative bias factors can be used to compensate for some of the largest errors and 2 a skewed error distribution yields improved estimates of predictive uncertainty in this semiarid basin with near zero flows we conclude that the presented methodology provides improved estimates of parameter and total prediction uncertainty and should be useful for handling complex residual errors in other hydrologic regression models as well

on a mixture of brenier and strassen theorems we give a characterization of optimal transport plans for a variant of the usual quadratic transport cost introduced in 33 optimal plans are composition of a deterministic transport given by the gradient of a continuously differentiable convex function followed by a martingale coupling we also establish some connections with caffarelli s contraction theorem 14

rates of convergence for empirical processes of stationary mixing sequences classical empirical process theory for vapnik cervonenkis classes deals mainly with sequences of independent variables this paper extends the theory to stationary sequences of dependent variables it establishes rates of convergence for mixing and mixing empirical processes indexed by classes of functions the method of proof depends on a coupling of the dependent sequence with sequences of independent blocks to which the classical theory can be applied a uniform o ns 1 s rate of convergence over v c classes is established for sequences whose mixing coefficients decay slightly faster than o n s

a bernstein type inequality for some mixing processes and dynamical systems with an application to learning we establish a bernstein type inequality for a class of stochastic processes that include the classical geometrically mixing processes rio s generalization of these processes as well as many time discrete dynamical systems modulo a logarithmic factor and some constants our bernsteintype inequality coincides with the classical bernstein inequality for i i d data we further use this new bernstein type inequality to derive an oracle inequality for generic regularized empirical risk minimization algorithms and data generated by such processes applying this oracle inequality to support vector machines using the gaussian kernels for both least squares and quantile regression it turns out that the resulting learning rates match up to some arbitrarily small extra term in the exponent the optimal rates for i i d processes

generalization performance of least square regularized regression algorithm with markov chain samples abstract the previously known works describing the generalization of least square regularized regression algorithm are usually based on the assumption of independent and identically distributed i i d samples in this paper we go far beyond this classical framework by studying the generalization of least square regularized regression algorithm with markov chain samples we first establish a novel concentration inequality for uniformly ergodic markov chains then we establish the bounds on the generalization of least square regularized regression algorithm with uniformly ergodic markov chain samples and show that least square regularized regression algorithm with uniformly ergodic markov chains is consistent