some aspects of the spline smoothing approach to non parametric regression curve fitting non parametric regression using cubic splines is an attractive flexible and widely applicable approach to curve estimation although the basic idea was formulated many years ago the method is not as widely known or adopted as perhaps it should be the topics and examples discussed in this paper are intended to promote the understanding and extend the practicability of the spline smoothing methodology particular subjects covered include the basic principles of the method the relation with moving average and other smoothing methods the automatic choice of the amount of smoothing and the use of residuals for diagnostic checking and model adaptation the question of providing inference regions for curves and for relevant properties of curves is approached via a finite dimensional bayesian formulation

polar codes for arbitrary dmcs and arbitrary macs polar codes are constructed for arbitrary channels by imposing an arbitrary quasi group structure on the input alphabet just as with usual polar codes the block error probability under successive cancellation decoding is o 2 n 1 2 epsilon where n is the block length encoding and decoding for these codes can be implemented with a complexity of o n log n it is shown that the same technique can be used to construct polar codes for arbitrary multiple access channels by using an appropriate abelian group structure although the symmetric sum capacity is achieved by this coding scheme some points in the symmetric capacity region may not be achieved in the case where the channel is a combination of linear channels we provide a necessary and sufficient condition characterizing the channels whose symmetric capacity region is preserved by the polarization process we also provide a sufficient condition for having a maximal loss in the dominant face

perturbation selection and influence measures in local influence analysis cook s j roy statist soc ser b 48 1986 133 169 local influence approach based on normal curvature is an important diagnostic tool for assessing local influence of minor perturbations to a statistical model however no rigorous approach has been developed to address two fundamental issues the selection of an appropriate perturbation and the development of influence measures for objective functions at a point with a nonzero first derivative the aim of this paper is to develop a differential geometrical framework of a perturbation model called the perturbation manifold and utilize associated metric tensor and affine curvatures to resolve these issues we will show that the metric tensor of the perturbation manifold provides important information about selecting an appropriate perturbation of a model moreover we will introduce new influence measures that are applicable to objective functions at any point examples including linear regression models and linear mixed models are examined to demonstrate the effectiveness of using new influence measures for the identification of influential observations

assessing influence on regression coefficients in generalized linear models summary suggested diagnostics for influence on the estimated regression coefficients in a generalized linear model have generally approximated the effect of deleting a single case we apply the local influence method of cook 1986 to assess the effect of small perturbations of the data including the vector of responses case weights explanatory variables and the components of one case the resulting diagnostics allow one to check for different kinds of influence and may give insight into its workings two examples illustrate some of the diagnostics

diagnostics for mixed model analysis of variance we describe a new method for assessment of model inadequacy in maximum likelihood mixed model analysis of variance in particular we discuss its use in diagnosing perturbations from the usual assumption of constant error variance and from the assumption that each realization of a given random factor has been drawn from the same normal population computer implementation of the procedure is described and an example is presented involving the analysis of filter cartridges used with commercial respirators

deletion diagnostics for generalised estimating equations summary deletion diagnostics are proposed for generalised estimating equations the diagnostics consider leverage and residuals to measure the influence of a subset of observations on the estimated regression parameters and on the estimated values of the linear predictor computational formulae are provided which correspond to the influence of a single observation and of an entire cluster of correlated observations additionally diagnostics are given which approximate the effect of deletion of an arbitrary subset of observations under a model with general covariance structure and arbitrary link function extending proposition 3 of christensen pearson johnson 1992 the proposed measures are applied to medical data

polar codes for q ary channels q 2 r we study polarization for nonbinary channels with input alphabet of size q 2r r 2 3 using arikan s polarizing kernel h2 we prove that the virtual channels that arise in the process of channel evolution converge to q ary channels with capacity 0 1 2 r bits as a result of this analysis we show that polar codes support reliable transmission over discrete memoryless channels with q ary input for all rates below the symmetric capacity of the channel this leads to an explicit transmission scheme for q ary channels the block error probability of decoding using successive cancellation behaves as exp n where n is the code length and is any constant less than 0 5

polar codes for the two user multiple access channel in this paper polar codes for the m user multiple access channel mac with binary inputs are constructed it is shown that arikan s polarization technique applied individually to each user transforms independent uses of an m user binary input mac into successive uses of extremal macs this transformation has a number of desirable properties 1 the uniform sum rate of the original mac is preserved 2 the extremal macs have uniform rate regions that are not only polymatroids but matroids and thus 3 their uniform sum rate can be reached by each user transmitting either uncoded or fixed bits in this sense they are easy to communicate over a polar code can then be constructed with an encoding and decoding complexity of o n log n where n is the block length a block error probability of o exp n1 2 e and capable of achieving the uniform sum rate of any binary input mac with arbitrary many users applications of this polar code construction to channels with a finite field input alphabet and to the additive white gaussian noise channel are also discussed

reinforcement learning in continuous time and space this article presents a reinforcement learning framework for continuous time dynamical systems without a priori discretization of time state and action based on the hamilton jacobi bellman hjb equation for infinite horizon discounted reward problems we derive algorithms for estimating value functions and improving policies with the use of function approximators the processof value function estimation is formulated asthe minimization of a continuous time form of the temporal difference td error update methods based on backward euler approximation and exponential eligibility traces are derived and their correspondences with the conventional residual gradient td 0 and td lambda algorithms are shown for policy improvement two methods a continuous actor critic method and a value gradient based greedy policy are formulated as a special case of the latter a nonlinear feedback control law using the value gradient and the model of the input gain is derived the advantage updating a model free algorithm derived previously is also formulated in the hjbbased framework the performance of the proposed algorithms is first tested in a nonlinear control task of swinging a pendulum up with limited torque it is shown in the simulations that 1 the task is accomplished by the continuous actor critic method in a number of trials several times fewer than by the conventional discrete actor critic method 2 among the continuous policy update methods the value gradient based policy with a known or learned dynamic model performs several times better than the actor critic method and 3 a value function update using exponential eligibility traces is more efficient and stable than that based on euler approximation the algorithms are then tested in a higher dimensional task cartpole swing up this task is accomplished in several hundred trials using the value gradient based policy with a learned dynamic model

perturbation and scaled cook s distance cook s cook 1977 distance is one of the most important diagnostic tools for detecting influential individual or subsets of observations in linear regression for cross sectional data however for many complex data structures e g longitudinal data no rigorous approach has been developed to address a fundamental issue deleting subsets with different numbers of observations introduces different degrees of perturbation to the current model fitted to the data and the magnitude of cook s distance is associated with the degree of the perturbation the aim of this paper is to address this issue in general parametric models with complex data structures we propose a new quantity for measuring the degree of the perturbation introduced by deleting a subset we use stochastic ordering to quantify the stochastic relationship between the degree of the perturbation and the magnitude of cook s distance we develop several scaled cook s distances to resolve the comparison of cook s distance for different subset deletions theoretical and numerical examples are examined to highlight the broad spectrum of applications of these scaled cook s distances in a formal influence analysis

value function based reinforcement learning in changing markovian environments the paper investigates the possibility of applying value function based reinforcement learning rl methods in cases when the environment may change over time first theorems are presented which show that the optimal value function of a discounted markov decision process mdp lipschitz continuously depends on the immediate cost function and the transition probability function dependence on the discount factor is also analyzed and shown to be non lipschitz afterwards the concept of e mdps is introduced which is a generalization of mdps and e mdps in this model the environment may change over time more precisely the transition function and the cost function may vary from time to time but the changes must be bounded in the limit then learning algorithms in changing environments are analyzed a general relaxed convergence theorem for stochastic iterative algorithms is presented we also demonstrate the results through three classical rl methods asynchronous value iteration q learning and temporal difference learning finally some numerical experiments concerning changing environments are presented

influence diagnostics for the cross validated smoothing parameter in spline smoothing abstract this article addresses the problem of influence in estimating the smoothing parameter when fitting a univariate smoothing spline diagnostics are presented that can identify observations that locally influence the choice of smoothing parameter by generalized cross validation either through their case weights or observed responses generalized cross validation and the diagnostic methods are given a frequency interpretation and illustrated with examples

influence analysis for skew normal semiparametric joint models of multivariate longitudinal and multivariate survival data the normality assumption of measurement error is a widely used distribution in joint models of longitudinal and survival data but it may lead to unreasonable or even misleading results when longitudinal data reveal skewness feature this paper proposes a new joint model for multivariate longitudinal and multivariate survival data by incorporating a nonparametric function into the trajectory function and hazard function and assuming that measurement errors in longitudinal measurement models follow a skew normal distribution a monte carlo expectation maximization em algorithm together with the penalized splines technique and the metropolis hastings algorithm within the gibbs sampler is developed to estimate parameters and nonparametric functions in the considered joint models case deletion diagnostic measures are proposed to identify the potential influential observations and an extended local influence method is presented to assess local influence of minor perturbations simulation studies and a real example from a clinical trial are presented to illustrate the proposed methodologies copyright 2017 john wiley sons ltd

detection of influential observation in linear regression a new measure based on confidence ellipsoids is developed for judging the contribution of each data point to the determination of the least squares estimate of the parameter vector in full rank linear regression models it is shown that the measure combines information from the studentized residuals and the variances of the residuals and predicted values two examples are presented

semiparametric estimation of partially linear panel data models in this paper we consider estimating a general partially linear semiparametric panel data model where we allow for some of the regressors to be correlated with the errors we assume the usual empirical case of n large and t small and as in robinson 1988 the proposed instrumental variable estimator is shown to be n consistent

spline smoothing in a partly linear model on donne des estimations qui minimisent la somme des sommes residuelles des carres et une penalite de difficulte

influence diagnostics and outlier tests for semiparametric mixed models summary semiparametric mixed models are useful in biometric and econometric applications especially for longitudinal data maximum penalized likelihood estimators mples have been shown to work well by zhang and co workers for both linear coefficients and nonparametric functions this paper considers the role of influence diagnostics in the mple by extending the case deletion and subject deletion analysis of linear models to accommodate the inclusion of a nonparametric component we focus on influence measures for the fixed effects and provide formulae that are analogous to those for simpler models and readily computable with the mple algorithm we also establish an equivalence between the case or subject deletion model and a mean shift outlier model from which we derive tests for outliers the influence diagnostics proposed are illustrated through a longitudinal hormone study on progesterone and a simulated example

diagnostics for smoothing splines summary diagnostic measures appropriate for use with smoothing splines are derived and their properties are investigated the proposed measures focus on detection of observations which substantially influence the fit and provide additional information over that obtained from examination of residuals alone a numerical example illustrates the technique

a comparison of gcv and gml for choosing the smoothing parameter in the generalized spline smoothing problem the partially improper prior behind the smoothing spline model is used to obtain a generalization of the maximum likelihood gml estimate for the smoothing parameter then this estimate is compared with the generalized cross validation gcv estimate both analytically and by monte carlo methods the comparison is based on a predictive mean square error criteria it is shown that if the true unknown function being estimated is smooth in a sense to be defined then the gml estimate undersmooths relative to the gcv estimate and the predictive mean square error using the gml estimate goes to zero at a slower rate than the mean square error using the gcv estimate if the true function is rough then the gcv and gml estimates have asymptotically similar behavior a monte carlo experiment was designed to see if the asymptotic results in the smooth case were evident in small sample sizes mixed results were obtained for n 32 gcv was somewhat better than gml for n 64 and gcv was decidedly superior for n 128 in the n 32 case gcv was better for smaller sigma 2 and the comparison close for larger sigma 2 the theoretical results are shown to extend to the generalized spline smoothing model which includes the estimate of functions given noisy values of various integrals of them

polar coded modulation a framework is proposed that allows for a joint description and optimization of both binary polar coding and 2m ary digital pulse amplitude modulation pam schemes for the latter the multilevel coding mlc approach as well as bit interleaved coded modulation bicm are considered the conceptual equivalence of polar coding and multilevel coding is covered in detail based on an alternative characterization of the channel polarization phenomenon rules for the optimum choice of the labeling in coded modulation schemes employing polar codes are developed simulation results regarding the error performance of the proposed schemes on the awgn channel are included

bounded parameter markov decision process in this paper we introduce the notion of a em bounded parameter markov decision process as a generalization of the traditional em exact mdp a bounded parameter mdp is a set of exact mdps specified by giving upper and lower bounds on transition probabilities and rewards all the mdps in the set share the same state and action space bounded parameter mdps can be used to represent variation or uncertainty concerning the parameters of sequential decision problems bounded parameter mdps can also be used in aggregation schemes to represent the variation in the transition probabilities for different base states aggregated together in the same aggregate state we introduce em interval value functions as a natural extension of traditional value functions an interval value function assigns a closed real interval to each state representing the assertion that the value of that state falls within that interval an interval value function can be used to bound the performance of a policy over the set of exact mdps associated with a given bounded parameter mdp we describe an iterative dynamic programming algorithm called em interval policy evaluation which computes an interval value function for a given bounded parameter mdp and specified policy interval policy evaluation on a policy policy computes the most restrictive interval value function that is sound i e that bounds the value function for policy in every exact mdp in the set defined by the bounded parameter mdp a simple modification of interval policy evaluation results in a variant of value iteration bellman57 that we call em interval value iteration which computes a policy for an bounded parameter mdp that is optimal in a well defined sense

deletion diagnostics for the generalised linear mixed model with independent random effects the generalised linear mixed model glmm is widely used for modelling environmental data however such data are prone to influential observations which can distort the estimated exposure response curve particularly in regions of high exposure deletion diagnostics for iterative estimation schemes commonly derive the deleted estimates based on a single iteration of the full system holding certain pivotal quantities such as the information matrix to be constant in this paper we present an approximate formula for the deleted estimates and cook s distance for the glmm which does not assume that the estimates of variance parameters are unaffected by deletion the procedure allows the user to calculate standardised dfbetas for mean as well as variance parameters in certain cases such as when using the glmm as a device for smoothing such residuals for the variance parameters are interesting in their own right in general the procedure leads to deleted estimates of mean parameters which are corrected for the effect of deletion on variance components as estimation of the two sets of parameters is interdependent the probabilistic behaviour of these residuals is investigated and a simulation based procedure suggested for their standardisation the method is used to identify influential individuals in an occupational cohort exposed to silica the results show that failure to conduct post model fitting diagnostics for variance components can lead to erroneous conclusions about the fitted curve and unstable confidence intervals

case deletion diagnostics for mixed models mixed linear models arise in many areas of application standard estimation methods for mixed models are sensitive to bizarre observations such influential observations can completely distort an analysis and lead to inappropriate actions and conclusions we develop case deletion diagnostics for detecting influential observations in mixed linear models diagnostics for both fixed effects and variance components are proposed computational formulas are given that make the procedures feasible the methods are illustrated using examples

kernel smoothing in partial linear models on considere deux methodes d estimation l une reliee aux splines de lissage partiels l autre motivee par une analyse de residus partielle

e mdps learning in varying environments in this paper e mdp models are introduced and convergence theorems are proven using the generalized mdp framework of szepesvari and littman using this model family we show that q learning is capable of finding near optimal policies in varying environments the potential of this new family of mdp models is illustrated via a reinforcement learning algorithm called event learning which separates the optimization of decision making from the controller we show that event learning augmented by a particular controller which gives rise to an e mdp enables near optimal performance even if considerable and sudden changes may occur in the environment illustrations are provided on the two segment pendulum problem

rate splitting multiple access for discrete memoryless channels it is shown that the encoding decoding problem for any asynchronous m user discrete memoryless multiple access channel can be reduced to corresponding problems for at most 2m 1 single user discrete memoryless channels this result which extends a similar result for gaussian channels reduces the seemingly hard task of finding good multiple access codes to the much better understood task of finding good codes for single user channels as a by product some interesting properties of the capacity region of m user asynchronous discrete memoryless channels are derived

polar codes for arbitrary classical quantum channels and arbitrary cq macs we prove polarization theorems for arbitrary classical quantum cq channels the input alphabet is endowed with an arbitrary abelian group operation and an arikan style transformation is applied using this operation it is shown that as the number of polarization steps becomes large the synthetic cq channels polarize to deterministic homomorphism channels that project their input to a quotient group of the input alphabet this result is used to construct polar codes for arbitrary cq channels and arbitrary cq multiple access channels the encoder can be implemented in o n log n operations where n is the blocklength of the code a quantum successive cancellation decoder for the constructed codes is proposed it is shown that the probability of error of this decoder decays faster than 2 n beta for any beta

high dimensional influence measure influence diagnosis is important since presence of influential observations could lead to distorted analysis and misleading interpretations for high dimensional data it is particularly so as the increased dimensionality and complexity may amplify both the chance of an observation being influential and its potential impact on the analysis in this article we propose a novel high dimensional influence measure for regressions with the number of predictors far exceeding the sample size our proposal can be viewed as a high dimensional counterpart to the classical cook s distance however whereas the cook s distance quantifies the individual observation s influence on the least squares regression coefficient estimate our new diagnosis measure captures the influence on the marginal correlations which in turn exerts serious influence on downstream analysis including coefficient estimation variable selection and screening moreover we establish the asymptotic distribution of the proposed influence measure by letting the predictor dimension go to infinity availability of this asymptotic distribution leads to a principled rule to determine the critical value for influential observation detection both simulations and real data analysis demonstrate usefulness of the new influence diagnosis measure

influence diagnostics for linear longitudinal models abstract influence diagnostics are important for analyzing cross sectional regression studies because they allow the analyst to understand the impact of individual observations on the estimated regression model in this article we consider the role of influence diagnostics in subject specific longitudinal models diagnostics are proposed under both fixed and random subject effects our approach is based on subject deletion which in this setting involves deleting a group of correlated observations we develop partial influence statistics to understand the combined impact of observations from a subject on population parameters simple computational formulas make the procedures feasible finally we illustrate the use of our new influence statistics by examining a dataset to model a taxpayer s charitable givings

channel polarization a method for constructing capacity achieving codes for symmetric binary input memoryless channels a method is proposed called channel polarization to construct code sequences that achieve the symmetric capacity i w of any given binary input discrete memoryless channel b dmc w the symmetric capacity is the highest rate achievable subject to using the input letters of the channel with equal probability channel polarization refers to the fact that it is possible to synthesize out of n independent copies of a given b dmc w a second set of n binary input channels wn i 1 les i les n such that as n becomes large the fraction of indices i for which i wn i is near 1 approaches i w and the fraction for which i wn i is near 0 approaches 1 i w the polarized channels wn i are well conditioned for channel coding one need only send data at rate 1 through those with capacity near 1 and at rate 0 through the remaining codes constructed on the basis of this idea are called polar codes the paper proves that given any b dmc w with i w 0 and any target rate r i w there exists a sequence of polar codes cfrn nges1 such that cfrn has block length n 2n rate ges r and probability of block error under successive cancellation decoding bounded as pe n r les o n 1 4 independently of the code rate this performance is achievable by encoders and decoders with complexity o n logn for each

source and channel polarization over finite fields and reed solomon matrices polarization phenomenon over any finite field fq with size q being a power of a prime is considered this problem is a generalization of the original proposal of channel polarization by arikan for the binary field as well as its extension to a prime field by sasoglu telatar and arikan in this paper a necessary and sufficient condition of a matrix over a finite field fq is shown under which any source and channel are polarized furthermore the result of the speed of polarization for the binary alphabet obtained by arikan and telatar is generalized to arbitrary finite field it is also shown that the asymptotic error probability of polar codes is improved by using the reed solomon matrices which can be regarded as a natural generalization of the 2 2 binary matrix used in the original proposal by arikan

semiparametric stochastic mixed models for longitudinal data abstract we consider inference for a semiparametric stochastic mixed model for longitudinal data this model uses parametric fixed effects to represent the covariate effects and an arbitrary smooth function to model the time effect and accounts for the within subject correlation using random effects and a stationary or nonstationary stochastic process we derive maximum penalized likelihood estimators of the regression coefficients and the nonparametric function the resulting estimator of the nonparametric function is a smoothing spline we propose and compare frequentist inference and bayesian inference on these model components we use restricted maximum likelihood to estimate the smoothing parameter and the variance components simultaneously we show that estimation of all model components of interest can proceed by fitting a modified linear mixed model we illustrate the proposed method by analyzing a hormone dataset and evaluate its performance through simulations