the control of confounding by intermediate variables in epidemiologic studies of the effect of an exposure on disease the crude association of exposure with disease may fail to reflect a causal association due to confounding by one or more covariates most previous discussions of confounding in the epidemiologic literature have considered only point exposure studies that is studies that measure exposure and covariate status only once at start of follow up in this paper we offer definitions of confounding suitable for longitudinal studies that obtain data on exposure covariate and vital status at several points in time an important difference between longitudinal studies and point exposure studies is that in longitudinal studies a time dependent covariate can be simultaneously a confounder and an intermediate variable on the causal pathway from exposure to disease in this paper i propose an estimator the extended standardized risk difference that provides control for confounding by a covariate that is simultaneously a confounder and an intermediate variable

a stable normalized least mean fourth algorithm with improved transient and tracking behaviors the stability problems of the least mean fourth lmf algorithm put a limitation on its tracking capability the paper investigates the possibility of solving this problem via stabilization of the algorithm the analysis is done for a markov plant it is found that the available stable normalized lmf nlmf algorithm has a tracking limitation for high signal to noise ratio the paper presents a new stable nlmf algorithm that is free of this limitation mean square stability of the algorithm is proved expressions are derived for the minimum steady state mean square deviation msd and the corresponding convergence time the new algorithm outperforms the available stable nlmf algorithm in both the transient and steady states the new algorithm is also compared with the nlms algorithm when the adaptation parameter of each algorithm is set to the value that minimizes its steady state msd for large initial msd the algorithm outperforms the nlms algorithm even for gaussian noise for small initial msd the algorithm outperforms the nlms algorithm for sub gaussian noise while the situation is opposite for gaussian noise analytical results are supported by simulations

stability bound of the initial mean square deviation of high order stochastic gradient adaptive filtering algorithms the paper derives the stability bound of the initial mean square deviation of an adaptive filtering algorithm based on minimizing the 2 l th moment of the estimation error with l being an integer greater than 1 the analysis is done for a time invariant plant with even input probability density function dependence of the stability bound on the algorithm step size type of the noise distribution signal to noise ratio snr and l is studied it is shown that the stability bound is decreasing in the step size the stability bound decreases as the tail of the noise probability density function becomes lighter for the same steady state misadjustment this result is surprising since for example it is expected that the stability of the least mean 2 l th algorithm for binary noise distribution is better than that for uniform distribution the stability bound is proportional to the reciprocal of the snr another surprising result finally the stability bound is decreasing in l which implies a limitation on the ability to improve the performance of the adaptive filter by increasing the order of the cost function theoretical results are supported by simulations

mean square convergence analysis of adaline training with minimum error entropy criterion recently the minimum error entropy mee criterion has been used as an information theoretic alternative to traditional mean square error criterion in supervised learning systems mee yields nonquadratic nonconvex performance surface even for adaptive linear neuron adaline training which complicates the theoretical analysis of the method in this paper we develop a unified approach for mean square convergence analysis for adaline training under mee criterion the weight update equation is formulated in the form of block data based on a block version of energy conservation relation and under several assumptions we carry out the mean square convergence analysis of this class of adaptation algorithm including mean square stability mean square evolution transient behavior and the mean square steady state performance simulation experimental results agree with the theoretical predictions very well

on symplectic cobordisms in this note we make several observations concerning symplectic cobordisms among other things we show that every contact 3 manifold has infinitely many concave symplectic fillings and that all overtwisted contact 3 manifolds are symplectic cobordism equivalent

using information on realized effects to determine prospective causal effects the potential outcomes approach to causal inference postulates that each individual has a number of possibly latent outcomes each of which would be observed under a different treatment for any individual some of these outcomes will be unobservable or counterfactual information about post treatment characteristics sometimes allows statements about what would have happened if an individual or group with these characteristics had received a different treatment these are statements about the realized effects of the treatment determining the likely effect of an intervention before making a decision involves inference about effects in populations defined only by characteristics observed before decisions about treatment are made information on realized effects can tighten bounds on these prospectively defined measures of the intervention effect we derive formulae for the bounds and their sampling variances and illustrate these points with data from a hypothetical study of the efficacy of screening mammography

mean square stability analysis of a normalized least mean fourth algorithm for a markov plant recently it has been shown that the stability of the least mean fourth lmf algorithm depends on the nonstationarity of the plant the present paper investigates the possibility of overcoming this problem by normalization of the weight vector update term a rigorous mean square stability analysis is provided for a recent normalized lmf algorithm which is normalized by a term that is second order in the estimation error and fourth order in the regressor the analysis is done for a markov plant with a stationary white input with even probability density function and a stationary zero mean white noise it is proved that the mean square deviation msd of the algorithm is bounded for all finite values of the input variance noise variance initial msd and mean square plant parameter increment analytical results are supported by simulations

adaptive echo cancellation using least mean mixed norm algorithm a novel algorithm for echo cancellation is presented in this work the algorithm consists of simultaneously applying the least mean square lms algorithm to the near end section of the echo canceller and the least mean fourth lmf algorithm to the far end section this new scheme results in a substantial performance improvement over the lms algorithm and other algorithms

bounds on treatment effects from studies with imperfect compliance abstract this article establishes nonparametric formulas that can be used to bound the average treatment effect in experimental studies in which treatment assignment is random but subject compliance is imperfect the bounds provided are the tightest possible given the distribution of assignments treatments and responses the formulas show that even with high rates of noncompliance experimental data can yield useful and sometimes accurate information on the average effect of a treatment on the population

bounds on natural direct effects in the presence of confounded intermediate variables in epidemiological studies we often want to learn about the direct effect of an exposure on an outcome i e the effect that is not relayed by a specific intermediate variable in the literature there are two common definitions of direct effects controlled and natural when the intermediate variable and the outcome have common causes neither the controlled nor the natural direct effect is identified cai et al biometrics 2007 64 3 695 701 derived bounds for the controlled direct effect under a set of hierarchical assumptions in this paper we derive bounds on the natural direct effect under the same assumptions copyright 2008 john wiley sons ltd

an online auc formulation for binary classification the area under the roc curve auc provides a good scalar measure of ranking performance without requiring a specific threshold for performance comparison among classifiers auc is useful for imprecise environments since it operates independently with respect to class distributions and misclassification costs a direct optimization of this auc criterion thus becomes a natural choice for binary classifier design however a direct formulation based on the auc criterion would require a high computational cost due to the drastically increasing input pair features in this paper we propose an online learning algorithm to circumvent this computational problem for binary classification different from those conventional recursive formulations the proposed formulation involves a pairwise cost function which pairs up a newly arrived data point with those of opposite class in stored data moreover with incorporation of a sparse learning into the online formulation the computational effort can be significantly reduced our empirical results on three different scales of public databases show promising potential in terms of classification auc accuracy and computational efficiency

local instrumental variables and latent variable models for identifying and bounding treatment effects this paper examines the relationship between various treatment parameters within a latent variable model when the effects of treatment depend on the recipient s observed and unobserved characteristics we show how this relationship can be used to identify the treatment parameters when they are identified and to bound the parameters when they are not identified

bounds on direct effects in the presence of confounded intermediate variables this article considers the problem of estimating the average controlled direct effect acde of a treatment on an outcome in the presence of unmeasured confounders between an intermediate variable and the outcome such confounders render the direct effect unidentifiable even in cases where the total effect is unconfounded hence identifiable kaufman et al 2005 statistics in medicine 24 1683 1702 applied a linear programming software to find the minimum and maximum possible values of the acde for specific numerical data in this article we apply the symbolic balke pearl 1997 journal of the american statistical association 92 1171 1176 linear programming method to derive closed form formulas for the upper and lower bounds on the acde under various assumptions of monotonicity these universal bounds enable clinical experimenters to assess the direct effect of treatment from observed data with minimum computational effort and they further shed light on the sign of the direct effect and the accuracy of the assessments

pseudoholomorphic curves in symplectizations with applications to the weinstein conjecture in dimension three l in t roduct ion 515 1 1 the weinstein conjecture 515 1 2 the main results 517 1 3 sketch of the proof 522 2 local f redho lm theory 525 2 1 similar i ty principle and consequences 525 2 2 n m as a lmost complex manifold and local fillings 529 2 3 local propert ies of ho lomorphic curves 531 3 bubbl ing off analysis and global fredholm theory 533 3 l grad ien t bounds imply ca bounds 533 3 2 bubbing off analysis of ho lomorphic planes 534 3 3 grad ien t bounds near the boundary 537 4 proof of the main results 544 4 1 set up for a global fredholm theory 544 4 2 bishop s theorem 545 4 3 proof of theorem 5 546 4 4 proof of theorems 8 and 11 547 4 5 uniqueness results for foliations 547 5 appendix 550 5 1 per turbing surfaces 550 5 2 ki l l ing crit ical points of hypersurfaces 552 5 3 adding a thin tube to a sphere 560

polyfolds cobordisms and the strong weinstein conjecture abstract we prove the strong weinstein conjecture for closed contact manifolds that appear as the concave boundary of a symplectic cobordism admitting an essential local foliation by holomorphic spheres

robust matched filtering in ell_ p space a common approach to time delay estimation tde and joint delay doppler estimation jdde for target localization is matched filtering which is equivalent to the cross correlation of the received and transmitted signals the conventional correlation in hilbert space is statistically optimal in white gaussian noise however its performance significantly degrades in the presence of non gaussian noise or clutter in this paper two new concepts called ell p correlation and ell p ambiguity functions which generalize the conventional matched filtering from hilbert space to ell p space are proposed in addition several important mathematical properties of the ell p correlation and ell p ambiguity functions are given and proved compared with conventional ambiguity function the time frequency concentration of the ell p ambiguity function is significantly enhanced i e the delay doppler resolution is improved and the sidelobes are suppressed based on these two newly defined functions a family of tde and jdde algorithms that are robust against impulsive noise or clutter are developed furthermore the cramer rao bounds of tde and jdde for non gaussian noise with arbitrary probability distribution are derived simulation results under several impulsive noise models demonstrate that the performance in terms of robustness resolution and estimation accuracy is substantially improved when compared with the conventional matched filtering and fractional lower order moment based methods

stabilization of high order stochastic gradient adaptive filtering algorithms the paper is concerned with stabilizing the family of adaptive filtering algorithms based on minimizing the 2lth moment of the estimation error with l being an integer greater than 1 stabilization is attained via a proposed normalization of the algorithm mean square stability of the normalized algorithm is proved for a markov plant for all l 1 transient and steady state performances of the algorithm are analyzed for a time invariant plant expressions are derived for the steady state misadjustment and convergence time tradeoff between the transient and steady state performances is evaluated dependence of this tradeoff on the value of l is studied this tradeoff is compared with the tradeoff of the nlms algorithm the proposed algorithm is dramatically superior to the nlms algorithm for sub gaussian noise the superiority increases with l initial mean square deviation and signal to noise ratio analytical results are supported by simulations

improved estimation of controlled direct effects in the presence of unmeasured confounding of intermediate variables adjusting for a causal intermediate is a common analytic strategy for estimating an average causal direct effect acde the acde is the component of the total exposure effect that is not relayed through the specified intermediate even if the total effect is unconfounded the usual acde estimate may be biased when an unmeasured variable affects the intermediate and outcome variables using linear programming optimization to compute non parametric bounds we develop new acde estimators for binary measured variables in this causal structure and use root mean square confounding bias rmsb to compare their performance with the usual stratified estimator in simulated distributions of target populations comprised of the 64 possible potential response types as well as distributions of target populations restricted to subsets of 18 or 12 potential response types defined by monotonicity or no interactions assumptions of unit level causal effects we also consider target population distributions conditioned on fixed outcome risk among the unexposed or fixed true acde in one stratum of the intermediate results show that a midpoint estimator constructed from the optimization bounds has consistently lower rmsb than the usual stratified estimator both unconditionally and conditioned on any risk in the unexposed when conditioning on true acde this midpoint estimator performs more poorly only when conditioned on an extreme true acde in one stratum of the intermediate yet outperforms the stratified estimator in the other stratum when interaction is permitted an alternate limit modified crude estimator can never perform less favourably than the stratified estimator and often has lower rmsb

sharp bounds on causal effects using a surrogate endpoint this paper considers a problem of evaluating the causal effect of a treatment x on a true endpoint y using a surrogate endpoint s in the presence of unmeasured confounders between s and y such confounders render the causal effect of x on y unidentifiable from the causal effect of x on s and the joint probability of s and y to evaluate the causal effect of x on y in such a situation this paper derives closed form formulas for the sharp bounds on the causal effect of x on y based on both the causal effect of x on s and the joint probability of s and y under various assumptions in addition we show that it is not always necessary to observe y to test the null causal effect of x on y under the monotonicity assumption between x and s these bounds enable clinical practitioners and researchers to assess the causal effect of a treatment on a true endpoint using a surrogate endpoint with minimum computational effort

stochastic gradient adaptation under general error criteria examines a family of adaptive filter algorithms of the form w sub k 1 w sub k spl mu f d sub k w sub k sup t x sub k x sub k in which f spl middot is a memoryless odd symmetric nonlinearity acting upon the error such algorithms are a generalization of the least mean square lms adaptive filtering algorithm for even symmetric error criteria for this algorithm family the authors derive general expressions for the mean and mean square convergence of the filter coefficients for both arbitrary stochastic input data and gaussian input data they then provide methods for optimizing the nonlinearity to minimize the algorithm misadjustment for a given convergence rate using the calculus of variations it is shown that the optimum nonlinearity to minimize misadjustment near convergence under slow adaptation conditions is independent of the statistics of the input data and can be expressed as p x p x where p x is the probability density function of the uncorrelated plant noise for faster adaptation under the white gaussian input and noise assumptions the nonlinearity is shown to be x 1 spl mu spl lambda x sup 2 spl sigma sub k sup 2 where spl lambda is the input signal power and spl sigma sub k sup 2 is the conditional error power thus the optimum stochastic gradient error criterion for gaussian noise is not mean square it is shown that the equations governing the convergence of the nonlinear algorithm are exactly those which describe the behavior of the optimum scalar data nonlinear adaptive algorithm for white gaussian input simulations verify the results for a host of noise interferences and indicate the improvement using non mean square error criteria

global stabilization of the least mean fourth algorithm the least mean fourth algorithm has several stability problems its stability depends on the variance and distribution type of the adaptive filter input the noise variance and the initialization of the filter weights the present correspondence provides a global solution to all these stability problems this is achieved by normalizing the weight vector update term by a term that is fourth order in the regressor and second order in the estimation error the former property stabilizes the algorithm against the variance and distribution type of the filter input while the latter stabilizes the algorithm against the noise variance and the weight initialization the obtained algorithm is stable for all values of the step size between 0 and 2 the stability of the algorithm is supported by simulations

weak and strong fillability of higher dimensional contact manifolds for contact manifolds in dimension three the notions of weak and strong symplectic fillability and tightness are all known to be inequivalent we extend these facts to higher dimensions in particular we define a natural generalization of weak fillings and prove that it is indeed weaker at least in dimension five while also being obstructed by all known manifestations of overtwistedness we also find the first examples of contact manifolds in all dimensions that are not symplectically fillable but also cannot be called overtwisted in any reasonable sense these depend on a higher dimensional analogue of giroux torsion which we define via the existence in all dimensions of exact symplectic manifolds with disconnected contact boundary

admissible transverse surgery does not preserve tightness we produce the first examples of closed tight contact 3 manifolds which become overtwisted after performing admissible transverse surgeries along the way we clarify the relationship between admissible transverse surgery and legendrian surgery we use this clarification to study a new invariant of transverse knots namely the range of slopes on which admissible transverse surgery preserves tightness and to provide some new examples of knot types which are not uniformly thick our examples also illuminate several interesting new phenomena including the existence of hyperbolic universally tight contact 3 manifolds whose heegaard floer contact invariants vanish and which are not weakly fillable and the existence of open books with arbitrarily high fractional dehn twist coefficients whose compatible contact structures are not deformations of co orientable taut foliations

formulating tightest bounds on causal effects in studies with unmeasured confounders this paper considers the problem of evaluating the causal effect of an exposure on an outcome in observational studies with both measured and unmeasured confounders between the exposure and the outcome under such a situation maclehose et al epidemiology 2005 16 548 555 applied linear programming optimization software to find the minimum and maximum possible values of the causal effect for specific numerical data in this paper we apply the symbolic balke pearl linear programming method probabilistic counterfactuals semantics computation and applications ph d thesis ucla cognitive systems laboratory 1995 j amer statist assoc 1997 92 1172 1176 to derive the simple closed form expressions for the lower and upper bounds on causal effects under various assumptions of monotonicity these universal bounds enable epidemiologists and medical researchers to assess causal effects from observed data with minimum computational effort and they further shed light on the accuracy of the assessment

identifying direct and indirect effects in a non counterfactual framework summary identifying direct and indirect effects is a common problem in the social science and medical literature and can be described as follows a treatment is administered and a response is recorded however another variable mediates the effect of the treatment on the response in some way channelling a part of the treatment effect the question is how to extricate the direct and channelled indirect effects from one another when it is not possible to intervene on the mediating variable the aim of the paper is to tackle this problem by using a model for direct and indirect effects based on the decision theoretic framework for causal inference

second order convergence analysis of stochastic adaptive linear filtering the convergence of an adaptive filtering vector is studied when it is governed by the mean square error gradient algorithm with constant step size we consider the mean square deviation between the optimal filter and the actual one during the steady state this quantity is known to be essentially proportional to the step size of the algorithm however previous analyses were either heuristic or based upon the assumption that successive observations were independent which is far from being realistic actually in most applications two successive observation vectors share a large number of components and thus they are strongly correlated in this work we deal with the case of correlated observations and prove that the mean square deviation is actually of the same order or less than the step size of the algorithm this result is proved without any boundedness or barrier assumption for the algorithm as it has been done previously in the literature to ensure the nondivergence our assumptions are reduced to the finite strong memory assumption and the finite moments assumption for the observation they are satisfied in a very wide class of practical applications

convergence in distribution of lms type adaptive parameter estimates we study the asymptotic behavior of parameter estimates generated by lms least mean square adaptive estimation algorithms in stationary dependent random situations we show that subject to mild practically reasonable conditions the estimates converge in distribution further we extend this result to prove a more explicit type of convergence in distribution which explains other observed properties we then estimate the moments of this limiting distribution and discuss how this relates to the work of others

stochastic stability analysis for the constant modulus algorithm we derive an easy to compute approximate bound for the range of step sizes for which the constant modulus algorithm cma will remain stable if initialized close to a minimum of the cm cost function our model highlights the influence of the signal constellation used in the transmission system for smaller variation in the modulus of the transmitted symbols the algorithm will be more robust and the steady state misadjustment will be smaller the theoretical results are validated through several simulations for long and short filters and channels

stochastic analysis of a stable normalized least mean fourth algorithm for adaptive noise canceling with a white gaussian reference the least mean fourth lmf algorithm has several stability problems its stability depends on the variance and distribution type of the adaptive filter input the noise variance and the initialization of the filter weights a global solution to these stability problems was presented recently for a normalized lmf nlmf algorithm here a stochastic analysis of the mean square deviation msd of the globally stable nlmf algorithm is provided the analysis is done in the context of adaptive noise canceling with a white gaussian reference input and gaussian binary and uniform desired signals the analytical model is shown to accurately predict the results of monte carlo simulations comparisons of the nlmf and nlms algorithms are then made for various parameter selections it is then shown under what conditions the nlmf algorithm is superior to nlms algorithm for adaptive noise canceling

the least mean fourth lmf adaptive algorithm and its family new steepest descent algorithms for adaptive filtering and have been devised which allow error minimization in the mean fourth and mean sixth etc sense during adaptation the weights undergo exponential relaxation toward their optimal solutions time constants have been derived and surprisingly they turn out to be proportional to the time constants that would have been obtained if the steepest descent least mean square lms algorithm of widrow and hoff had been used the new gradient algorithms are insignificantly more complicated to program and to compute than the lms algorithm their general form is w j 1 w j 2 mu k epsilon j 2k 1 x j where w j is the present weight vector w j 1 is the next weight vector epsilon j is the present error x j is the present input vector mu is a constant controlling stability and rate of convergence and 2k is the exponent of the error being minimized conditions have been derived for weight vector convergence of the mean and of the variance for the new gradient algorithms the behavior of the least mean fourth lmf algorithm is of special interest in comparing this algorithm to the lms algorithm when both are set to have exactly the same time constants for the weight relaxation process the lmf algorithm under some circumstances will have a substantially lower weight noise than the lms algorithm it is possible therefore that a minimum mean fourth error algorithm can do a better job of least squares estimation than a mean square error algorithm this intriguing concept has implications for all forms of adaptive algorithms whether they are based on steepest descent or otherwise

a mean square stability analysis of the least mean fourth adaptive algorithm this paper presents a new convergence analysis of the least mean fourth lmf adaptive algorithm in the mean square sense the analysis improves previous results in that it is valid for non gaussian noise distributions and explicitly shows the dependence of algorithm stability on the initial conditions of the weights analytical expressions are derived presenting the relationship between the step size the initial weight error vector and mean square stability the analysis assumes a white zero mean gaussian reference signal and an independent identically distributed i i d measurement noise with any even probability density function pdf it has been shown by nascimento and bermudez probability of divergence for the least mean fourth lmf algorithm ieee transactions on signal processing vol 54 no 4 pp 1376 1385 apr 2006 that the lmf algorithm is not mean square stable for reference signals whose pdfs have infinite support however the probability of divergence as a function of the step size value tends to rise abruptly only when it moves past a given threshold our analysis provides a simple and yet precise estimate of the region of quick rise in the probability of divergence hence the present analysis is useful for predicting algorithm instability in most practical applications

fast recursive least squares transversal filters for adaptive filtering fast transversal filter ftf implementations of recursive least squares rls adaptive filtering algorithms are presented in this paper substantial improvements in transient behavior in comparison to stochastic gradient or lms adaptive algorithms are efficiently achieved by the presented algorithms the true not approximate solution of the rls problem is always obtained by the ftf algorithms even during the critical initialization period first n iterations of the adaptive filter this true solution is recursively calculated at a relatively modest increase in computational requirements in comparison to stochastic gradient algorithms factor of 1 6 to 3 5 depending upon application additionally the fast transversal filter algorithms are shown to offer substantial reductions in computational requirements relative to existing fast rls algorithms such as the fast kalman algorithms of morf ljung and falconer 1976 and the fast ladder lattice algorithms of morf and lee 1977 1981 they are further shown to attain steady state unnormalized or improve upon first n initialization steps the very low computational requirements of the efficient rls solutions of carayannis manolakis and kalouptsidis 1983 finally several efficient procedures are presented by which to ensure the numerical stability of the transversal filter algorithms including the incorporation of soft constraints into the performance criteria internal bounding and rescuing procedures and dynamic range increasing square root normalized variations of the transversal filters

on symplectic fillings of lens spaces le st be the contact structure naturally induced on the lens space l p q s 3 z pz by the standard contact structure st on the three sphere s 3 we obtain a complete classification of the symplectic fillings of l p q st up to orientation preserving diffeomorphisms in view of our results we formulate a conjecture on the diffeomorphism types of the smoothings of complex two dimensional cyclic quotient singularities

transient analysis of adaptive filters with error nonlinearities the paper develops a unified approach to the transient analysis of adaptive filters with error nonlinearities in addition to deriving earlier results in a unified manner the approach also leads to new performance results without restricting the regression data to being gaussian or white the framework is based on energy conservation arguments and avoids the need for explicit recursions for the covariance matrix of the weight error vector

a unified approach to the steady state and tracking analyses of adaptive filters most adaptive filters are inherently nonlinear and time variant systems the nonlinearities in the update equations tend to lead to difficulties in the study of their steady state performance as a limiting case of their transient performance this paper develops a unified approach to the steady state and tracking analyses of adaptive algorithms that bypasses many of these difficulties the approach is based on the study of the energy flow through each iteration of an adaptive filter and it relies on a fundamental error variance relation

impact of mis specification of the treatment model on estimates from a marginal structural model inverse probability of treatment weighted iptw estimation for marginal structural models msms requires the specification of a nuisance model describing the conditional relationship between treatment allocation and confounders however there is still limited information on the best strategy for building these treatment models in practice we developed a series of simulations to systematically determine the effect of including different types of candidate variables in such models we explored the performance of iptw estimators across several scenarios of increasing complexity including one designed to mimic the complexity typically seen in large pharmacoepidemiologic studies our results show that including pure predictors of treatment i e not confounders in treatment models can lead to estimators that are biased and highly variable particularly in the context of small samples the bias and mean squared error of the msm based iptw estimator increase as the complexity of the problem increases the performance of the estimator is improved by either increasing the sample size or using only variables related to the outcome to develop the treatment model estimates of treatment effect based on the true model for the probability of treatment are asymptotically unbiased we recommend including only pure risk factors and confounders in the treatment model when developing an iptw based msm

dependence of the stability of the least mean fourth algorithm on target weights non stationarity the paper investigates a new stability problem of the least mean fourth lmf algorithm which is the dependence of the algorithm stability on the time variation of the target weights of the adaptive filter the analysis is done in the context of tracking a markov plant with a stationary white gaussian input it is found that the algorithm diverges if the mean square increment of the plant parameter vector exceeds a threshold value that depends on the step size input variance and noise moments the paper also derives a closed form of the steady state mean square deviation without the usual assumption of a strong noise comparison of the tracking capabilities of the lmf and lms algorithms is provided the comparison is done in terms of the minimum mean square deviation attained by each algorithm over the stability range of its step size gaussian uniform and binary distributions of the noise are considered conditions that make one algorithm outperform the other are determined analytical results are supported by simulations

probability of divergence for the least mean fourth algorithm in this paper it is shown that the least mean fourth lmf adaptive algorithm is not mean square stable when the regressor input is not strictly bounded as happens for example if the input has a gaussian distribution for input distributions with infinite support even for the gaussian distribution the lmf always has a nonzero probability of divergence no matter how small the step size is chosen this result is proven for a slight modification of the gaussian distribution in a one tap filter and corroborated with several simulations in addition an upper bound is given for the probability of divergence of lmf as a function of the filter length input power step size and noise variance for the case of gaussian regressors the results reported in this paper provide tools for designers to better understand the behavior of the lmf algorithm and decide on the convenience or not of its use for a given application

the structure of rational and ruled symplectic 4 manifolds this paper investigates the structure of compact symplectic 4 manifolds v w which contain a symplectically embedded copy c of s2 with nonnegative self intersection number such a pair v c w is called minimal if in addition the open manifold v c contains no exceptional curves i e symplectically embedded 2 spheres with self intersection 1 we show that every such pair v c w covers a minimal pair v c c which may be obtained from v by blowing down a finite number of disjoint exceptional curves in v c further the family of manifold pairs v c w under consideration is closed under blowing up and down we next give a complete list of the possible minimal pairs we show that v is symplectomorphic either to p2 with its standard form or to an s2 bundle over a compact surface with a symplectic structure which is uniquely determined by its cohomology class moreover this symplectomorphism may be chosen so that it takes c either to 2 a complex line or quadric in cp2 or in the case when v is a bundle to a fiber or section of the bundle department of mathematics state university of new york at stony brook stony brook new york 11794 3651 e mail address dusa math sunysb edu this content downloaded from 207 46 13 145 on wed 27 apr 2016 05 10 07 utc all use subject to http about jstor org terms

asymptotic analysis of stochastic gradient based adaptive filtering algorithms with general cost functions this paper presents an analysis of stochastic gradient based adaptive algorithms with general cost functions the analysis holds under mild assumptions on the inputs and the cost function the method of analysis is based on an asymptotic analysis of fixed stepsize adaptive algorithms and gives almost sure results regarding the behavior of the parameter estimates whereas previous stochastic analyses typically considered mean and mean square behavior the parameter estimates are shown to enter a small neighborhood about the optimum value and remain there for a finite length of time furthermore almost sure exponential bounds are given for the rate of convergence of the parameter estimates the asymptotic distribution of the parameter estimates is shown to be gaussian with mean equal to the optimum value and covariance matrix that depends on the input statistics specific adaptive algorithms that fall under the framework of this paper are signed error least mean square lms dual sign lms quantized state lms least mean fourth dead zone algorithms momentum algorithms and leaky lms

a class of adaptive step size control algorithms for adaptive filters a class of new adaptive step size control algorithms which is applicable to most of the lms derived tap weight adaptation algorithms is proposed analysis yields a set of difference equations for theoretically calculating the transient behavior of the filter convergence and derives an explicit formula for the steady state excess mean square error emse experiments for some examples prove that the proposed algorithm is highly effective in improving the convergence rate in both transient and tracking phases the theoretically calculated convergence is shown to be in good agreement with that obtained through simulations alternative formulae of the step size adaptation for specific tap weight adaptation algorithms are also proposed

new criteria for blind deconvolution of nonminimum phase systems channels a necessary and sufficient condition for blind deconvolution without observing the input of nonminimum phase linear time invariant systems channels is derived based on this condition several optimization criteria are proposed and their solution is shown to correspond to the desired response these criteria involve the computation only of second and fourth order moments implying a simple tap update procedure the proposed methods are universal in the sense that they do not impose any restrictions on the probability distribution of the unobserved input sequence it is shown that in several important cases e g when the additive noise is gaussian the proposed criteria are essentially unaffected

reasoning about data with directed graphs this paper constructs graphical models for two important analysis problems to demonstrate how graphs can clearly represent complex relationships a powerful property of graphical models called d separation describes the statistical associations in a given graphical model this allows the effects of unmeasured variables to be predicted and suggests conditional analyses which can distinguish conjectured models if an assumption called quasi linearity is made further conclusions can be drawn based on the structure of the graph and d separation making the quasi linearity assumption explicit also contributes to our understanding of which aspects of our causal intuition are based on linearity assumptions the examples that we consider are the scientific interpretation of interventions and the evaluation of the validity of candidate surrogate endpoints for clinical trials intervention studies can be plagued by non compliance with assigned treatment and ambiguity in interpreting results when treatment assignment manipulates multiple factors we show graphically the conclusions that can be drawn under various assumptions the topic of surrogate endpoints is addressed in causal terms and modelled graphically

stochastic system identification with noisy input using cumulant statistics addresses the problem of estimating the parameters of stochastic linear systems when the measurements of the system input as well as the system output are noise contaminated it is assumed that the input is non gaussian and the noises are gaussian the square root of the magnitude of the fourth cumulant of a generalized error signal is proposed as a performance criterion for parameter estimation an optimization algorithm is presented strong consistency of the proposed parameter estimators is proved under certain sufficient conditions both single input single output and multiple input multiple output cases are investigated finally simulation results are presented to illustrate the proposed approach

normalized data nonlinearities for lms adaptation properly designed nonlinearly modified lms algorithms in which various quantities in the stochastic gradient estimate are operated upon by memoryless nonlinearities have been shown to perform better than the lms algorithm in system identification type problems the authors investigate one such algorithm given by w sub k l w sub k spl mu d sub k w sub k sup t x sub k x sub k f x sub k in which the function f x sub k is a scalar function of the sum of the squares of the n elements of the input data vector x sub k this form of algorithm generalizes the so called normalized lms nlms algorithm they evaluate the expected behavior of this nonlinear algorithm for both independent input vectors and correlated gaussian input vectors assuming the system identification model by comparing the nonlinear algorithm s behavior with that of the lms algorithm they then provide a method of optimizing the form of the nonlinearity for the given input statistics in the independent input case they show that the optimum nonlinearity is a single parameter version of the nlms algorithm with an additional constant in the denominator and show that this algorithm achieves a lower excess mean square error mse than the lms algorithm with an equivalent convergence rate additionally they examine the optimum step size sequence for the optimum nonlinear algorithm and show that the resulting algorithm performs better and is less complex to implement than the optimum step size algorithm derived for another form of the nlms algorithm simulations verify the theory and the predicted performance improvements of the optimum normalized data nonlinearity algorithm

a novel family of adaptive filtering algorithms based on the logarithmic cost we introduce a novel family of adaptive filtering algorithms based on a relative logarithmic cost inspired by the competitive methods from the online learning literature the competitive or regret based approaches stabilize or improve the convergence performance of adaptive algorithms through relative cost functions the new family elegantly and gradually adjusts the conventional cost functions in its optimization based on the error amount we introduce important members of this family of algorithms such as the least mean logarithmic square lmls and least logarithmic absolute difference llad algorithms however our approach and analysis are generic such that they cover other well known cost functions as described in the paper the lmls algorithm achieves comparable convergence performance with the least mean fourth lmf algorithm and enhances the stability performance significantly the llad and least mean square lms algorithms demonstrate similar convergence performance in impulse free noise environments while the llad algorithm is robust against impulsive interferences and outperforms the sign algorithm sa we analyze the transient steady state and tracking performance of the introduced algorithms and demonstrate the match of the theoretical analyses and simulation results we show the enhanced stability performance of the lmls algorithm and analyze the robustness of the llad algorithm against impulsive interferences finally we demonstrate the performance of our algorithms in different scenarios through numerical examples