statistical mechanics and phase transitions in clustering a new approach to clustering based on statistical physics is presented the problem is formulated as fuzzy clustering and the association probability distribution is obtained by maximizing the entropy at a given average variance the corresponding lagrange multiplier is related to the temperature and motivates a deterministic annealing process where the free energy is minimized at each temperature critical temperatures are derived for phase transitions when existing clusters split it is a hierarchical clustering estimating the most probable cluster parameters at various average variances

hypothesis testing in a mixture case control model summary we consider a problem of testing mixture proportions using two sample data one from group one and the other from a mixture of groups one and two with unknown proportion for being in group two various statistical applications including microarray study infectious epidemiological studies case control studies with contaminated controls clinical trials allowing nonresponders genetic studies for gene mutation and fishery applications can be formulated in this setup under the assumption that the log ratio of probability density functions from the two groups is linear in the observations we propose a generalized score test statistic to test the mixture proportion under some regularity conditions it is shown that this statistic converges to a weighted chi squared random variable under the null hypothesis of 0 where the weight depends only on the sampling fraction of both groups the permutation method is used to provide more reliable finite sample approximation simulation results and two real data applications are presented

gmm based inference with stratified samples when the aggregate shares are known abstract we show how to do efficient moment based inference using the generalized method of moments gmm when data is collected by stratified sampling and the maintained assumption is that the aggregate shares are known

mutual information and conditional mean estimation in poisson channels following the discovery of a fundamental connection between information measures and estimation measures in gaussian channels this paper explores the counterpart of those results in poisson channels in the continuous time setting the received signal is a doubly stochastic poisson point process whose rate is equal to the input signal plus a dark current it is found that regardless of the statistics of the input the derivative of the input output mutual information with respect to the intensity of the additive dark current can be expressed as the expected difference between the logarithm of the input and the logarithm of its noncausal conditional mean estimate the same holds for the derivative with respect to input scaling but with the logarithmic function replaced by x log x similar relationships hold for discrete time versions of the channel where the outputs are poisson random variables conditioned on the input symbols

the balian low theorem for the symplectic form on r2d in this paper we extend the balian low theorem which is a version of the uncertainty principle for gabor weyl heisenberg systems to functions of several variables in particular we first prove the balian low theorem for arbitrary quadratic forms then we generalize further and prove the balian low theorem for differential operators associated with a symplectic basis for the symplectic form on r2d

efficient estimation and stratified sampling abstract in this paper we investigate estimation of a class of semi parametric models the part of the model that is not specified is the marginal distribution of the explanatory variables the sampling is stratified on the dependent variables implying that the explanatory variables are no longer exogenous or ancillary we develop a new estimator for this estimation problem and show that it achieves the semi parametric efficiency bound for this case in addition we show that the estimator applies to a number of sampling schemes that have previously been treated separately

practical codes for photon communication in a recent paper pierce studied the problems of communicating at optical frequencies using photon counting techniques and concluded that at low temperatures we encounter insuperable problems of encoding long before we approach channel capacity in this paper it is shown that even assuming a noiseless model for photon communication for which capacity measured in nats photon is infinite it is unlikely that a signaling efficiency of even 10 nats photon could be achieved practically on the positive side it is shown that pulse position modulation plus reed solomon coding yields practical results in the range of 2 to 3 nats photon

data clustering using a model granular magnet we present a new approach to clustering based on the physical properties of an inhomogeneous ferromagnet no assumption is made regarding the underlying distribution of the data we assign a potts spin to each data point and introduce an interaction between neighboring points whose strength is a decreasing function of the distance between the neighbors this magnetic system exhibits three phases at very low temperatures it is completely ordered all spins are aligned at very high temperatures the system does not exhibit any ordering and in an intermediate regime clusters of relatively strongly coupled spins become ordered whereas different clusters remain uncorrelated this intermediate phase is identified by a jump in the order parameters the spin spin correlation function is used to partition the spins and the corresponding data points into clusters we demonstrate on three synthetic and three real data sets how the method works detailed comparison to the performance of other techniques clearly indicates the relative success of our method

information and asymptotic efficiency in parametric nonparametric models asymptotic lower bounds for estimation of the parameters of models with both parametric and nonparametric components are given in the form of representation theorems for regular estimates and asymptotic minimax bounds the methods used involve i the notion of a hellinger differentiable root density where part of the differentiation is with respect to the nonparametric part of the model to obtain appropriate scores and ii calculation of the effective score for the real or vector finite dimensional parameter of interest as that component of the score function orthogonal to all nuisance parameter scores perhaps infinite dimensional the resulting asymptotic information for estimation of the parametric component of the model is just 4 times the squared l 2 norm of the effective score a corollary of these results is a simple necessary condition for adaptive estimation adaptation is possible only if the scores for the parameter of interest are orthogonal to the scores for the nuisance function or nonparametric part of the model examples considered include the one sample location model with and without symmetry mixture models the two sample shift model and cox s proportional hazards model

characterization on practical photon counting receiver in optical scattering communication we characterize the practical photon counting receiver in optical scattering communication with a finite sampling rate and electrical noise finite small pulse width incurs dead time effect that may lead to sub poisson distribution on the recorded pulses we analyze the first order and second order moments on the number of recorded pulses with a finite sampling rate at the receiver side under two cases where the sampling period is shorter than or equal to the pulse width as well as longer than the pulse width moreover we adopt the maximum likelihood ml detection in order to simplify the analysis we adopt binomial distribution approximation on the number of recorded pulses in each slot a tractable holding time and decision threshold selection rule is provided to maximize the minimal kullback leibler kl distance between the two distributions the performances of proposed sub poisson distribution and the binomial approximation are verified by the experimental results the equivalent photon arrival rate and pulse holding time predicted by the sub poisson model and the associated proposed binomial distribution are well validated by the simulation results where the finite sampling rate and electrical noise are considered the proposed holding time and decision threshold selection rule performs close to the optimal ml receiver

balian low phenomenon for subspace gabor frames in this work the balian low theorem is extended to gabor also called weyl heisenberg frames for subspaces and more particularly its relationship with the unique gabor dual property for subspace gabor frames is pointed out to achieve this goal the subspace gabor frames which have a unique gabor dual of type i resp type ii are defined and characterized in terms of the zak transform for the rational parameter case this characterization is then used to prove the balian low theorem for subspace gabor frames along the same line the same characterization is used to prove a duality theorem for the unique gabor dual property which is an analogue of the ron and shen duality theorem

on the capacity of the discrete time poisson channel the large inputs asymptotic capacity of a peak power and average power limited discrete time poisson channel is derived using a new firm nonasymptotic lower bound and an asymptotic upper bound the upper bound is based on the dual expression for channel capacity and the notion of capacity achieving input distributions that escape to infinity the lower bound is based on a lower bound on the entropy of a conditionally poisson random variable in terms of the differential entropy of its conditional mean

on the capacity of a direct detection photon channel with intertransition constrained binary input the classical directed detection photon channel is modeled by an output nu sub t observed signal describing the photon arrival poisson count process with intensity rate lambda sub t lambda sub 0 where lambda sub t photons s is the channel input information carrying intensity and lambda sub 0 photons s is the dark current intensity upper and lower bounds on the capacity of this channel are presented for two level binary inputs taking on the extreme value lambda sub t in 0 a where a denotes the peak power satisfying an average power constraint e lambda sub t

capacity achieving probability measure for conditionally gaussian channels with bounded inputs a conditionally gaussian channel is a vector channel in which the channel output given the channel input has a gaussian distribution with well behaved input dependent mean and covariance we study the capacity achieving probability measure for conditionally gaussian channels subject to bounded input constraints and average cost constraints many practical communication systems including additive gaussian noise channels certain optical channels fading channels and interference channels fall within this framework subject to bounded input constraint and average cost constraints we show that the channel capacity is achievable and we derive a necessary and sufficient condition for a probability measure to be capacity achieving under certain conditions the capacity achieving measure is proved to be discrete

efficient nonparametric estimation of causal effects in randomized trials with noncompliance causal approaches based on the potential outcome framework provide a useful tool for addressing noncompliance problems in randomized trials we propose a new estimator of causal treatment effects in randomized clinical trials with noncompliance we use the empirical likelihood approach to construct a profile random sieve likelihood and take into account the mixture structure in outcome distributions so that our estimator is robust to parametric distribution assumptions and provides substantial finite sample efficiency gains over the standard instrumental variable estimator our estimator is asymptotically equivalent to the standard instrumental variable estimator and it can be applied to outcome variables with a continuous ordinal or binary scale we apply our method to data from a randomized trial of an intervention to improve the treatment of depression among depressed elderly patients in primary care practices

the capacity of average and peak power limited quadrature gaussian channels the capacity c spl rho sub a spl rho sub p of the discrete time quadrature additive gaussian channel qagc with inputs subjected to normalized average and peak power constraints spl rho sub a and spl rho sub p respectively is considered by generalizing smith s results for the scalar average and peak power constrained gaussian channel it is shown that the capacity achieving distribution is discrete in amplitude envelope having a finite number of mass points with a uniformly distributed independent phase and it is geometrically described by concentric circles it is shown that with peak power being solely the effective constraint a constant envelope with uniformly distributed phase input is capacity achieving for spl rho sub p spl les 7 8 db 4 8 db per dimension the capacity under a peak power constraint is evaluated for a wide range of spl rho sub p by incorporating the theoretical observations into a nonlinear dynamic programming procedure closed form expressions for the asymptotic low and large spl rho sub a and spl rho sub p capacity and the corresponding capacity achieving distribution and for lower and upper bounds on the capacity c spl rho sub a spl rho sub p are developed the capacity c spl rho sub a spl rho sub p provides an improved ultimate upper bound on the reliable information rates transmitted over the qagc with any communication systems subjected to both average and peak power limitations when compared to the classical shannon formula for the capacity of the qagc which does not account for the peak power constraint this is in particular important for systems that operate with restrictive close to 1 average to peak power ratio spl rho sub a spl rho sub p and at moderate power values

gabor schauder bases and the balian low theorem the balian low theorem is a strong form of the uncertainty principle for gabor systems that form orthonormal or riesz bases for l2 r in this paper we investigate the balian low theorem in the setting of schauder bases we prove that new weak versions of the balian low theorem hold for gabor schauder bases but we constructively demonstrate that several variants of the blt can fail for gabor schauder bases that are not riesz bases we characterize a class of gabor schauder bases in terms of the zak transform and product a2 weights the riesz bases correspond to the special case of weights that are bounded away from zero and infinity

inferences for case control and semiparametric two sample density ratio models summary we consider inference in general binary response regression models under retrospective sampling plans prentice pyke 1979 discovered that inference for the odds ratio parameter in a logistic model can be based on a prospective likelihood even though the sampling scheme is retrospective we show that the estimating function obtained from the prospective likelihood is optimal in a class of unbiased estimating functions also we link casecontrol sampling with a two sample biased sampling problem where the ratio of two densities is assumed to take a known parametric form connections between this model and the cox proportional hazards model are pointed out large and small sample size behaviour of the proposed estimators is studied

case control studies with contaminated controls abstract this paper considers inference about a parametric binary choice model when the data consist of two distinct samples the first is a random sample from the people who made choice 1 say with all relevant covariates completely observed the second is a random sample from the whole population with only the covariates observed this is called a contaminated sampling scheme an example might be where we have a random sample of female labor force participants and their covariate values and a second random sample of working age women with covariates whose participant status is unknown we consider the cases in which the fraction of the population making choice 1 is known and that in which it is not for both cases we give semiparametrically efficient procedures for estimating the choice model parameters

semiparametric estimation of a two component mixture model suppose that univariate data are drawn from a mixture of two distributions that are equal up to a shift parameter such a model is known to be nonidentifiable from a nonparametric viewpoint however if we assume that the unknown mixed distribution is symmetric we obtain the identifiability of this model which is then defined by four unknown parameters the mixing proportion two location parameters and the cumulative distribution function of the symmetric mixed distribution we propose estimators for these four parameters when no training data is available our estimators are shown to be strongly consistent under mild regularity assumptions and their convergence rates are studied their finite sample properties are illustrated by a monte carlo study and our method is applied to real data

the discrete time poisson channel at low input powers the asymptotic capacity at low input powers of an average power limited or an average and peak power limited discrete time poisson channel is considered for a poisson channel whose dark current is zero or decays to zero linearly with its average input power e capacity scales like e log 1 e for small e for a poisson channel whose dark current is a nonzero constant capacity scales to within a constant like e log log 1 e for small e

a mapping approach to rate distortion computation and analysis in rate distortion theory results are often derived and stated in terms of the optimizing density over the reproduction space in this paper the problem is reformulated in terms of the optimal mapping from the unit interval with lebesgue measure that would induce the desired reproduction probability density this results in optimality conditions that are random relatives of the known lloyd 1982 optimality conditions for deterministic quantizers the validity of the mapping approach is assured by fundamental isomorphism theorems for measure spaces we show that for the squared error distortion the optimal reproduction random variable is purely discrete at supercritical distortion where the shannon 1948 lower bound is not tight the gaussian source is thus the only source that produces continuous reproduction variables for the entire range of positive rate to analyze the evolution of the optimal reproduction distribution we use the mapping formulation and establish an analogy to statistical mechanics the solutions are given by the distribution at isothermal statistical equilibrium and are parameterized by the temperature in direct correspondence to the parametric solution of the variational equations in rate distortion theory the analysis of an annealing process shows how the number of symbols grows as the system undergoes phase transitions thus an algorithm based on the mapping approach often needs but a few variables to find the exact solution while the blahut 1972 algorithm would only approach it at the limit of infinite resolution finally a quick deterministic annealing algorithm to generate the rate distortion curve is suggested the resulting curve is exact as long as continuous phase transitions in the process are accurately followed

asymptotic efficiency in estimation with conditional moment restrictions abstract in this paper bounds on asymptotic efficiency are derived for a class of non parametric models the data are independent and identically distributed according to some unknown distribution f there is a given function of the data and a parameter the restrictions are that a conditional expectation of this function is zero at some point in the parameter space this point is to be estimated if f is assumed to be a multinomial distribution with known finite support then the problem becomes parametric and the bound can be obtained from the information matrix this bound turns out to depend only upon certain conditional moments and not upon the support of the distribution since a general f can be approximated by a multinomial distribution the multinomial bound applies to the general case

regression analysis based on stratified samples summary jewell 1985 described an iterative method of estimating parameters in the linear regression model from data collected from stratified samples of the dependent variable with no parametric assumptions on the residual distribution the present paper considers an alternative iterative technique which is generally superior in terms of efficiency often by a considerable amount the method is extended to cover stratified sampling on a design variable which is correlated with the dependent variable but is not included as an independent variable regression analysis is often used in the analysis of survey data in situations where complex sampling designs are employed we consider estimation of the p x 1 vector of parameters f3 in the assumed population model e y i x x 3jx under stratified sampling if sample selection is based on values of the independent variables standard regression methods apply however if selection is based on values of the dependent variable y or on a design variable z correlated with the dependent variable but not included as an independent variable ordinary least squares regression estimates are in general asymptotically biased for examples and discussion of previous research see holt smith winter 1980 nathan holt 1980 hausman wise 1982 and jewell

entropy constrained tree structured vector quantizer design current methods for the design of pruned or unbalanced tree structured vector quantizers such as the generalized breiman friedman olshen stone gbfos algorithm proposed in 1980 are effective but suffer from several shortcomings we identify and clarify issues of suboptimality including greedy growing the suboptimal encoding rule and the need for time sharing between quantizers to achieve arbitrary rates we then present the leaf optimal tree design lotd method which with a modest increase in design complexity alters and reoptimizes tree structures obtained from conventional procedures there are two main advantages over existing methods first the optimal entropy constrained nearest neighbor rule is used for encoding at the leaves second explicit quantizer solutions are obtained at all rates without recourse to time sharing we show that performance improvement is theoretically guaranteed simulation results for image coding demonstrate that close to 1 db reduction of distortion for a given rate can be achieved by this technique relative to the gbfos method

least squares regression with data arising from stratified samples of the dependent variable regression analysis is being widely used in the analysis of survey data in situations where complex sampling designs are employed often the selection procedure is based on values of the independent variables in which case standard regression methods apply however the literature abounds with examples where the selection procedure is based on values of the dependent variable for example demets halperin 1977 consider the relationship between serum cholesterol the dependent variable and dietary cholesterol the independent variable from an initial large random sample a smaller subsample was selected with the procedure that only persons with very high or very low initial serum cholesterol were chosen for subsequent measurement of the regression variables in a study of the relationship of blood pressure the dependent variable and certain anthropometric factors in adolescents kotchen et al 1980 performed follow up on a subsample of a previous survey in which individuals in the original highest and lowest blood pressure groups were deliberately oversampled a regression analysis was subsequently performed using standard least square methods finally hausman wise 1982 discuss income maintenance experiments in econometrics where high income families were undersampled from the population in a situation where income is the dependent variable of a subsequent regression analysis there are many reasons why complex sampling designs may be used on the basis of the dependent variable y for example an initial goal of the study may be to estimate the mean of y with high precision for which stratified sampling on the basis of y values may be useful subsequently regression analysis with y as the dependent variable may be desired secondly oversampling extreme values of y is a method of reducing the variances of estimated regression coefficients in cases where it may not be feasible to use traditional efficient designs based on the independent variables for such sampling situations it is now well known that in general ordinary least squares regression estimates will be biased even asymptotically see for example holt smith winter 1980 and nathan holt 1980 various adjusted estimators have been considered which we discuss briefly below

how many clusters an information theoretic perspective clustering provides a common means of identifying structure in complex data and there is renewed interest in clustering as a tool for the analysis of large data sets in many fields a natural question is how many clusters are appropriate for the description of a given system traditional approaches to this problem are based on either a framework in which clusters of a particular shape are assumed as a model of the system or on a two step procedure in which a clustering criterion determines the optimal assignments for a given number of clusters and a separate criterion measures the goodness of the classification to determine the number of clusters in a statistical mechanics approach clustering can be seen as a trade off between energy and entropy like terms with lower temperature driving the proliferation of clusters to provide a more detailed description of the data for finite data sets we expect that there is a limit to the meaningful structure that can be resolved and therefore a minimum temperature beyond which we will capture sampling noise this suggests that correcting the clustering criterion for the bias that arises due to sampling errors will allow us to find a clustering solution at a temperature that is optimal in the sense that we capture maximal meaningful structure without having to define an external criterion for the goodness or stability of the clustering we show that in a general information theoretic framework the finite size of a data set determines an optimal temperature and we introduce a method for finding the maximal number of clusters that can be resolved from the data in the hard clustering limit

efficiency results of mle and gmm estimation with sampling weights this paper examines gmm and ml estimation of econometric models and the theory of hausman tests with sampling weights weighted conditional gmm can be more efficient than weighted conditional mle an inefficient alternative to full information mle under choice based sampling unless regressions have homoscedastic additive disturbances or sampling weights are independent of exogenous variables gmm variances are necessarily smaller without sampling weights if gmm is the same as mle or disturbances are homoscedastic but not in general taking into account the dependence of sampling weights on parameters improves the efficiency of estimation

a p q version of bourgain s theorem let 1 p q satisfy 1 p 1 q 1 we construct an orthonormal basis b n for l 2 r such that p b n and q bn are both uniformly bounded in n here f inf r x a f x 2 dx 1 2 this generalizes a theorem of bourgain and is closely related to recent results on the balian low theorem

deterministic annealing based optimization for zero delay source channel coding in networks this paper studies the problem of global optimization of zero delay source channel codes that map between the source space and the channel space under a given transmission power constraint and for the mean square error distortion particularly we focus on two well known network settings the wyner ziv setting where only a decoder has access to side information and the distributed setting where independent encoders transmit over independent channels to a central decoder prior work derived the necessary conditions for optimality of the encoder and decoder mappings along with a greedy optimization algorithm that imposes these conditions iteratively in conjunction with the heuristic noisy channel relaxation method to mitigate poor local minima while noisy channel relaxation is arguably effective in simple settings it fails to provide accurate global optimization in more complicated settings considered in this paper we propose a powerful nonconvex optimization method based on the concept of deterministic annealing which is derived from information theoretic principles and was successfully employed in several problems including vector quantization classification and regression we present comparative numerical results that show strict superiority of the proposed method over greedy optimization methods as well as prior approaches in literature

improved upper bounds and structural results on the capacity of the discrete time poisson channel new capacity upper bounds are presented for the discrete time poisson channel with no dark current and an average power constraint these bounds are a consequence of techniques developed for the seemingly unrelated problem of upper bounding the capacity of binary deletion and repetition channels previously the best known capacity upper bound in the regime where the average power constraint does not approach zero was due to martinez josa b 2007 which is re derived as a special case of the framework developed in this paper furthermore this framework is carefully instantiated in order to obtain a closed form bound that improves the result of martinez everywhere finally capacity achieving distributions for the discrete time poisson channel are studied under an average power constraint and or a peak power constraint and arbitrary dark current in particular it is shown that the support of the capacity achieving distribution under an average power constraint must only be countably infinite this settles a conjecture of shamai iee proceedings i 1990 in the affirmative previously it was only known that the support must be an unbounded set

dilation of the weyl symbol and balian low theorem the key result of this paper describes the fact that for an important class of pseudodifferential operators the property of invertibility is preserved under minor dilations of their weyl symbols this observation has two implications in time frequency analysis first it implies the stability of general gabor frames under small dilations of the time frequency set previously known only for the case that the time frequency set is a lattice secondly it allows us to derive a new balian low theorem blt for gabor systems with window in the standard window class and with general time frequency families in contrast to the classical versions of blt the new blt does not only exclude orthonormal bases and riesz bases at critical density but indeed it even excludes irregular gabor frames at critical density

a semiparametric two component compound mixture model and its application to estimating malaria attributable fractions summary malaria remains a major epidemiologic problem in many developing countries malaria is defined as the presence of parasites and symptoms usually fever due to the parasites in endemic areas an individual may have symptoms attributable either to malaria or to other causes from a clinical viewpoint it is important to correctly diagnose an individual who has developed symptoms so that the appropriate treatments can be given from an epidemiologic and economic viewpoint it is important to determine the proportion of malaria affected cases in individuals who have symptoms so that policies on intervention program can be developed once symptoms have developed in an individual the diagnosis of malaria can be based on the analysis of the parasite levels in blood samples however even a blood test is not conclusive as in endemic areas many healthy individuals can have parasites in their blood slides therefore data from this type of study can be viewed as coming from a mixture distribution with the components corresponding to malaria and nonmalaria cases a unique feature in this type of data however is the fact that a proportion of the nonmalaria cases have zero parasite levels therefore one of the component distributions is itself a mixture distribution in this article we propose a semiparametric likelihood approach for estimating the proportion of clinical malaria using parasite level data from a group of individuals with symptoms our approach assumes the density ratio for the parasite levels in clinical malaria and nonclinical malaria cases can be modeled using a logistic model we use empirical likelihood to combine the zero and nonzero data the maximum semiparametric likelihood estimate is more efficient than existing nonparametric estimates using only the frequencies of zero and nonzero data on the other hand it is more robust than a fully parametric maximum likelihood estimate that assumes a parametric model for the nonzero data simulation results show that the performance of the proposed method is satisfactory the proposed method is used to analyze data from a malaria survey carried out in tanzania

semiparametric estimation and inference for distributional and general treatment effects summary there is a large literature on methods of analysis for randomized trials with noncompliance which focuses on the effect of treatment on the average outcome the paper considers evaluating the effect of treatment on the entire distribution and general functions of this effect for distributional treatment effects fully non parametric and fully parametric approaches have been proposed the fully non parametric approach could be inefficient but the fully parametric approach is not robust to the violation of distribution assumptions we develop a semiparametric instrumental variable method based on the empirical likelihood approach our method can be applied to general outcomes and general functions of outcome distributions and allows us to predict a subject s latent compliance class on the basis of an observed outcome value in observed assignment and treatment received groups asymptotic results for the estimators and likelihood ratio statistic are derived a simulation study shows that our estimators of various treatment effects are substantially more efficient than the currently used fully non parametric estimators the method is illustrated by an analysis of data from a randomized trial of an encouragement intervention to improve adherence to prescribed depression treatments among depressed elderly patients in primary care practices

efficient approximation of channel capacities we propose an iterative method for approximately computing the capacity of discrete memoryless channels possibly under additional constraints on the input distribution based on duality of convex programming we derive explicit upper and lower bounds for the capacity the presented method requires o m 2 n sqrt log n varepsilon to provide an estimate of the capacity to within varepsilon where n and m denote the input and output alphabet size a single iteration has a complexity o m n we also show how to approximately compute the capacity of memoryless channels having a bounded continuous input alphabet and a countable output alphabet under some mild assumptions on the decay rate of the channel s tail it is shown that discrete time poisson channels fall into this problem class as an example we compute sharp upper and lower bounds for the capacity of a discrete time poisson channel with a peak power input constraint

phase space localization theorem for ondelettes it is proven that an orthonormal basis of ondelettes can never have exponential localization in both position space and momentum space

capacity achieving distributions for the discrete time poisson channel part i general properties and numerical techniques despite being an accepted model for a wide variety of optical channels few general results on optimal signalling for discrete time poisson dtp channels are known among the most significant is that under simultaneous peak and average constraints the capacity achieving distributions are discrete with a finite number of mass points in this paper several fundamental properties of capacity achieving distributions for dtp channels are established in particular we demonstrate that all capacity achieving distributions of the dtp channel have zero as a mass point in the case of only a peak constraint it is further shown that the optimal distribution always has a mass point at the maximum amplitude finally under solely an average power constraint it is shown that a finite number of mass points are insufficient to achieve the capacity in addition to these analytical results a numerical algorithm based on deterministic annealing is presented which can efficiently compute both the channel capacity and the associated optimal input distribution under peak and average power constraints numerical lower bounds based on the envelope of information rates induced by the maxentropic distributions are also shown to be extremely close to the capacity especially in the low power regime

hierarchical gtm constructing localized nonlinear projection manifolds in a principled way it has been argued that a single two dimensional visualization plot may not be sufficient to capture all of the interesting aspects of complex data sets and therefore a hierarchical visualization system is desirable in this paper we extend an existing locally linear hierarchical visualization system phivis in several directions 1 we allow for nonlinear projection manifolds the basic building block is the generative topographic mapping gtm 2 we introduce a general formulation of hierarchical probabilistic models consisting of local probabilistic models organized in a hierarchical tree general training equations are derived regardless of the position of the model in the tree 3 using tools from differential geometry we derive expressions for local directional curvatures of the projection manifold like phivis our system is statistically principled and is built interactively in a top down fashion using the em algorithm it enables the user to interactively highlight those data in the ancestor visualization plots which are captured by a child model we also incorporate into our system a hierarchical locally selective representation of magnification factors and directional curvatures of the projection manifolds such information is important for further refinement of the hierarchical visualization plot as well as for controlling the amount of regularization imposed on the local models we demonstrate the principle of the approach on a toy data set and apply our system to two more complex 12 and 18 dimensional data sets

nonparametric estimation of component distributions in a multivariate mixture suppose k variate data are drawn from a mixture of two distributions each having independent components it is desired to estimate the univariate marginal distributions in each of the products as well as the mixing proportion this is the setting of two class fully parametrized latent models that has been proposed for estimating the distributions of medical test results when disease status is unavailable the problem is one of inference in a mixture of distributions without training data and until now it has been tackled only in a fully parametric setting we investigate the possibility of using nonparametric methods of course when k 1 the problem is not identifiable from a nonparametric viewpoint we show that the problem is almost identifiable when k 2 there the set of all possible representations can be expressed in terms of any one of those representations as a two parameter family furthermore it is proved that when k geq3 the problem is nonparametrically identifiable under particularly mild regularity conditions in this case we introduce root n consistent nonparametric estimators of the 2k univariate marginal distributions and the mixing proportion finite sample and asymptotic properties of the estimators are described

hermitian symplectic geometry and extension theory here we give brief account of hermitian symplectic spaces showing that they are intimately connected to symmetric as well as self adjoint extensions of a symmetric operator furthermore we find an explicit parametrization of the lagrange grassmannian in terms of the unitary matrices this allows us to explicitly describe all self adjoint boundary conditions for the schrodinger operator on the graph in terms of a unitary matrix we show that the asymptotics of the scattering matrix can be expressed simply in terms of this unitary matrix

the wavelet transform time frequency localization and signal analysis two different procedures for effecting a frequency analysis of a time dependent signal locally in time are studied the first procedure is the short time or windowed fourier transform the second is the wavelet transform in which high frequency components are studied with sharper time resolution than low frequency components the similarities and the differences between these two methods are discussed for both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time frequency density finally the notion of time frequency localization is made precise within this framework by two localization theorems

generalized method of moments gmm based inference with stratified samples when the aggregate shares are known abstract we show how to do efficient moment based inference using the generalized method of moments gmm when data is collected by stratified sampling and the maintained assumption is that the aggregate shares are known

capacity achieving input distributions of additive quadrature gaussian mixture noise channels this paper studies the characterization of the optimal input and the computation of the capacity of additive quadrature gaussian mixture gm noise channels under an average power constraint the considered model can be used to represent a wide variety of channels with impulsive interference such as the well known bernoulli gaussian and middleton class a impulsive noise channels as well as multiple access interference channels and cognitive radio channels under imperfect sensing at first we demonstrate that there exists a unique input distribution that achieves the channel capacity and the capacity achieving input distribution has a uniformly distributed phase by examining the kuhn tucker alignment conditions ktcs we further show that if the optimal input amplitude distribution contains an infinite number of mass points on a bounded interval the channel output must be gaussian distributed however by using bernstein s theorem to examine the completely monotonic condition it is shown that the assumption of a gaussian distributed output is not valid as a result there are always a finite number of mass points on any bounded interval in the optimal amplitude distribution in addition by applying a novel bounding technique on the ktc and using the envelop theorem we demonstrate that the optimal amplitude distribution cannot have an infinite number of mass points this gives us the unique solution of the optimal input having discrete amplitude with a finite number of mass points given this discrete nature of the optimal input we then develop a simple method to compute the discrete optimal input and the corresponding capacity our numerical examples show that in many cases the capacity achieving distribution consists of only one or two mass points

two theorems on lattice expansions it is shown that there is a tradeoff between the smoothness and decay properties of the dual functions occurring in the lattice expansion problem more precisely it is shown that if g and g are dual then 1 at least one of h sup 1 2 g and h sup 1 2 g is n in l sup 2 r and 2 at least one of hg and g is not in l sup 2 r here h is the operator 1 4 pi sup 2 d sup 2 dt sup 2 t sup 2 the first result is a generalization of a theorem first stated by r c balian 1987 the second result is new and relies heavily on the fact that when g in w sup 2 2 s with s 1 2 1 2 1 2 1 2 and g 0 than 1 g not in l sup 2 s

mean shift mode seeking and clustering mean shift a simple interactive procedure that shifts each data point to the average of data points in its neighborhood is generalized and analyzed in the paper this generalization makes some k means like clustering algorithms its special cases it is shown that mean shift is a mode seeking process on the surface constructed with a shadow kernal for gaussian kernels mean shift is a gradient mapping convergence is studied for mean shift iterations cluster analysis if treated as a deterministic problem of finding a fixed point of mean shift that characterizes the data applications in clustering and hough transform are demonstrated mean shift is also considered as an evolutionary strategy that performs multistart global optimization

discrete multi gabor expansions a discrete multi gabor expansion dmge is developed to meet the requirements of localized and refined time frequency tf representation of signals the dmge uses multiple windows and their translations and complex modulations as synthesis or analysis waveforms it includes and generalizes the metaplectic translation modulation and dilation representations which are useful in signal analysis uniform nonuniform and proportional time sampling schemes are analyzed the fundamental features and the importance of the dmge are discussed we focus on the construction of dmge and deriving fast algorithms for the computation of related multi analysis sequences with matrix algebra the algorithms derived apply to both multi gabor expansions and uni window gabor expansions another useful feature of the dmge lies in the fact that the multi gabor transform can be realized in a parallel fft based implementation structure examples of dmge and their applications to tf analysis are also discussed

bayes wesml posterior inference from choice based samples abstract in this paper i show that the weighted exogenous sampling likelihood wesml estimator for choice based samples due to manski and lerman 1977 can be given a bayesian interpretation under a multinomial model for the data with improper dirichlet priors bayesian posterior distributions of choice model parameters are computed to study the gains from choice based sampling and the effect of knowledge of population marginal choice probabilities

a simplified approach to computing efficiency bounds in semiparametric models using some standard hilbert space theory a simplified approach to computing efficiency bounds in semiparametric models is presented we use some interesting examples to illustrate this approach and also obtain some results which seem to be new to the literature

large sample theory of estimation in biased sampling regression models i biased sampling regression models were introduced by jewell generalizing the truncated regression model studied by bhattacharya chernoff and yang if the independent variable takes on only a finite number of values as does the stratum variable we show 1 that if the slope of the underlying regression model is assumed known then the nonparametric maximum likelihood estimates of the distribution of the independent and dependent variables a can be calculated from ordinary m estimates b are asymptotically efficient 2 how to construct m estimates of the slope which are always sqrt n consistent asymptotically gaussian and are efficient locally for example if the error distribution is gaussian we support our asymptotics with a small simulation

capacity achieving distributions for the discrete time poisson channel part ii binary inputs discrete time poisson dtp channels exist in many scenarios including space laser communication systems which operate over long distances and which can be corrupted by reflected and scattered light through simulation binary input distributions have been observed to be optimal in many cases however little analytical work exists on conditions for optimality or the form of optimal signalling in this second part the general properties of part i are extended to the case of dtp channels where binary inputs are optimal necessary and sufficient conditions on the optimality of binary i e two mass point distributions are presented by leveraging the general properties of dtp capacity achieving distributions closed form expressions of the capacity achieving distributions are derived in several important special cases including zero dark current and for high dark current numerical results are presented to elucidate the developed analytical work