a characterization of markov equivalence classes for acyclic digraphs undirected graphs and acyclic digraphs adgs as well as their mutual extension to chain graphs are widely used to describe dependencies among variables in multivariate distributions in particular the likelihood functions of adg models admit convenient recursive factorizations that often allow explicit maximum likelihood estimates and that are well suited to building bayesian networks for expert systems whereas the undirected graph associated with a dependence model is uniquely determined there may however be many adgs that determine the same dependence markov model thus the family of all adgs with a given set of vertices is naturally partitioned into markov equivalence classes each class being associated with a unique statistical model statistical procedures such as model selection or model averaging that fail to take into account these equivalence classes may incur substantial computational or other inefficiencies here it is shown that each markov equivalence class is uniquely determined by a single chain graph the essential graph that is itself simultaneously markov equivalent to all adgs in the equivalence class essential graphs are characterized a polynomial time algorithm for their construction is given and their applications to model selection and other statistical questions are described

generalizing capacity new definitions and capacity theorems for composite channels we consider three capacity definitions for composite channels with channel side information at the receiver a composite channel consists of a collection of different channels with a distribution characterizing the probability that each channel is in operation the shannon capacity of a channel is the highest rate asymptotically achievable with arbitrarily small error probability under this definition the transmission strategy used to achieve the capacity must achieve arbitrarily small error probability for all channels in the collection comprising the composite channel the resulting capacity is dominated by the worst channel in its collection no matter how unlikely that channel is we therefore broaden the definition of capacity to allow for some outage the capacity versus outage is the highest rate asymptotically achievable with a given probability of decoder recognized outage the expected capacity is the highest average rate asymptotically achievable with a single encoder and multiple decoders where channel side information determines the channel in use the expected capacity is a generalization of capacity versus outage since codes designed for capacity versus outage decode at one of two rates rate zero when the channel is in outage and the target rate otherwise while codes designed for expected capacity can decode at many rates expected capacity equals shannon capacity for channels governed by a stationary ergodic random process but is typically greater for general channels the capacity versus outage and expected capacity definitions relax the constraint that all transmitted information must be decoded at the receiver we derive channel coding theorems for these capacity definitions through information density and provide numerical examples to highlight their connections and differences we also discuss the implications of these alternative capacity definitions for end to end distortion source channel coding and separation

global identifiability of linear structural equation models structural equation models are multivariate statistical models that are defined by specifying noisy functional relationships among random variables we consider the classical case of linear relationships and additive gaussian noise terms we give a necessary and sufficient condition for global identifiability of the model in terms of a mixed graph encoding the linear structural equations and the correlation structure of the error terms global identifiability is understood to mean injectivity of the parametrization of the model and is fundamental in particular for applicability of standard statistical methodology

chain graph models and their causal interpretations chain graphs are a natural generalization of directed acyclic graphs and undirected graphs however the apparent simplicity of chain graphs belies the subtlety of the conditional independence hypotheses that they represent there are many simple and apparently plausible but ultimately fallacious interpretations of chain graphs that are often invoked implicitly or explicitly these interpretations also lead to flawed methods for applying background knowledge to model selection we present a valid interpretation by showing how the distribution corresponding to a chain graph may be generated from the equilibrium distributions of dynamic models with feed back these dynamic interpretations lead to a simple theory of intervention extending the theory developed for directed acyclic graphs finally we contrast chain graph models under this interpretation with simultaneous equation models which have traditionally been used to model feed back in econometrics

structural intervention distance for evaluating causal graphs causal inference relies on the structure of a graph often a directed acyclic graph dag different graphs may result in different causal inference statements and different intervention distributions to quantify such differences we propose a pre metric between dags the structural intervention distance sid the sid is based on a graphical criterion only and quantifies the closeness between two dags in terms of their corresponding causal inference statements it is therefore well suited for evaluating graphs that are used for computing interventions instead of dags it is also possible to compare cpdags completed partially dags that represent markov equivalence classes the sid differs significantly from the widely used structural hamming distance and therefore constitutes a valuable additional measure we discuss properties of this distance and provide a reasonably efficient implementation with software code available on the first author s home page

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

a recursive method for structural learning of directed acyclic graphs in this paper we propose a recursive method for structural learning of directed acyclic graphs dags in which a problem of structural learning for a large dag is first decomposed into two problems of structural learning for two small vertex subsets each of which is then decomposed recursively into two problems of smaller subsets until none subset can be decomposed further in our approach search for separators of a pair of variables in a large dag is localized to small subsets and thus the approach can improve the efficiency of searches and the power of statistical tests for structural learning we show how the recent advances in the learning of undirected graphical models can be employed to facilitate the decomposition simulations are given to demonstrate the performance of the proposed method

successive refinement of information characterization of the achievable rates let r spl middot be the rate distortion function assume that we want to describe a source with distortion no larger than spl delta sub 1 from the rate distortion theory we know that we need to do so at a rate r sub 1 no smaller than r spl delta sub 1 spl lsqb bits symbol spl rsqb if it turns out that a more accurate description at distortion spl delta sub 2 spl delta sub 2

graphical methods for efficient likelihood inference in gaussian covariance models in graphical modelling a bi directed graph encodes marginal independences among random variables that are identified with the vertices of the graph we show how to transform a bi directed graph into a maximal ancestral graph that i represents the same independence structure as the original bi directed graph and ii minimizes the number of arrowheads among all ancestral graphs satisfying i here the number of arrowheads of an ancestral graph is the number of directed edges plus twice the number of bi directed edges in gaussian models this construction can be used for more efficient iterative maximization of the likelihood function and to determine when maximum likelihood estimates are equal to empirical counterparts

half trek criterion for generic identifiability of linear structural equation models a linear structural equation model relates random variables of interest and corresponding gaussian noise terms via a linear equation system each such model can be represented by a mixed graph in which directed edges encode the linear equations and bidirected edges indicate possible correlations among noise terms we study parameter identifiability in these models that is we ask for conditions that ensure that the edge coefficients and correlations appearing in a linear structural equation model can be uniquely recovered from the covariance matrix of the associated distribution we treat the case of generic identifiability where unique recovery is possible for almost every choice of parameters we give a new graphical condition that is sufficient for generic identifiability and can be verified in time that is polynomial in the size of the graph it improves criteria from prior work and does not require the directed part of the graph to be acyclic we also develop a related necessary condition and examine the gap between sufficient and necessary conditions through simulations on graphs with 25 or 50 nodes as well as exhaustive algebraic computations for graphs with up to five nodes

causal reasoning with ancestral graphs causal reasoning is primarily concerned with what would happen to a system under external interventions in particular we are often interested in predicting the probability distribution of some random variables that would result if some other variables were forced to take certain values one prominent approach to tackling this problem is based on causal bayesian networks using directed acyclic graphs as causal diagrams to relate post intervention probabilities to pre intervention probabilities that are estimable from observational data however such causal diagrams are seldom fully testable given observational data in consequence many causal discovery algorithms based on data mining can only output an equivalence class of causal diagrams rather than a single one this paper is concerned with causal reasoning given an equivalence class of causal diagrams represented by a partial ancestral graph we present two main results the first result extends pearl 1995 s celebrated do calculus to the context of ancestral graphs in the second result we focus on a key component of pearl s calculus the property of invariance under interventions and give stronger graphical conditions for this property than those implied by the first result the second result also improves the earlier similar results due to spirtes et al 1993

distortion minimization in gaussian layered broadcast coding with successive refinement a transmitter without channel state information wishes to send a delay limited gaussian source over a slowly fading channel the source is coded in superimposed layers with each layer successively refining the description in the previous one the receiver decodes the layers that are supported by the channel realization and reconstructs the source up to a distortion the expected distortion is minimized by optimally allocating the transmit power among the source layers for two source layers the allocation is optimal when power is first assigned to the higher layer up to a power ceiling that depends only on the channel fading distribution all remaining power if any is allocated to the lower layer for convex distortion cost functions with convex constraints the minimization is formulated as a convex optimization problem in the limit of a continuum of infinite layers the minimum expected distortion is given by the solution to a set of linear differential equations in terms of the density of the fading distribution as the number of channel uses per source symbol tends to zero the power distribution that minimizes expected distortion converges to the one that maximizes expected capacity

minimum expected distortion in gaussian source coding with fading side information an encoder subject to a rate constraint wishes to describe a gaussian source under squared error distortion the decoder besides receiving the encoder s description also observes side information consisting of uncompressed source symbol subject to slow fading and noise the decoder knows the fading realization but the encoder knows only its distribution the rate distortion function that simultaneously satisfies the distortion constraints for all fading states was derived by heegard and berger a layered encoding strategy is considered in which each codeword layer targets a given fading state when the side information channel has two discrete fading states the expected distortion is minimized by optimally allocating the encoding rate between the two codeword layers for multiple fading states the minimum expected distortion is formulated as the solution of a convex optimization problem with linearly many variables and constraints through a limiting process on the primal and dual solutions it is shown that single layer rate allocation is optimal when the fading probability density function is continuous and quasiconcave e g rayleigh rician nakagami and log normal in particular under rayleigh fading the optimal single codeword layer targets the least favorable state as if the side information was absent

discussion latent variable graphical model selection via convex optimization we want to congratulate the authors for a thought provoking and very interesting paper sparse modeling of the concentration matrix has enjoyed popularity in recent years it has been framed as a computationally convenient convex 1constrained estimation problem in yuan and lin 2007 and can be applied readily to higher dimensional problems the authors argue we think correctly that the sparsity of the concentration matrix is for many applications more plausible after the effects of a few latent variables have been removed the most attractive point about their method is surely that it is formulated as a convex optimization problem latent variable fitting and sparse graphical modeling of the conditional distribution of the observed variables can then be obtained through a single fitting procedure practical aspects the method deserves wide adoption but this will only be realistic if software is made available for example as an r package not many users will go to the trouble of implementing the method on their own so we will strongly urge the authors to do so an imputation method in the absence of readily available software it is worth thinking whether the proposed fitting procedure can be approximated by methods involving known and well tested computational techniques the concentration matrix of observed and hidden variables is k ko koh k ho kh where we have deviated from the notation in the paper by omitting the asterisk the proposed estimator sn ko of ko was defined as

stratified exponential families graphical models and model selection we describe a hierarchy of exponential families which is useful for distinguishing types of graphical models undirected graphical models with no hidden variables are linear exponential families lefs directed acyclic graphical dag models and chain graphs with no hidden variables including dag models with several families of local distributions are curved exponential families cefs graphical models with hidden variables are what we term stratified exponential families sefs a sef is a finite union of cefs of various dimensions satisfying some regularity conditions we also show that this hierarchy of exponential families is noncollapsing with respect to graphical models by providing a graphical model which is a cef but not a lef and a graphical model that is a sef but not a cef finally we show how to compute the dimension of a stratified exponential family these results are discussed in the context of model selection of graphical models

joint source channel codes for mimo block fading channels we consider transmission of a continuous amplitude source over an l block rayleigh fading mt x mr multiple input multiple output mimo channel when the channel state information is only available at the receiver since the channel is not ergodic shannon s source channel separation theorem becomes obsolete and the optimal performance requires a joint source channel approach our goal is to minimize the expected end to end distortion particularly in the high signal to noise ratio snr regime the figure of merit is the distortion exponent defined as the exponential decay rate of the expected distortion with increasing snr we provide an upper bound and lower bounds for the distortion exponent with respect to the bandwidth ratio among the channel and source bandwidths for the lower bounds we analyze three different strategies based on layered source coding concatenated with progressive superposition or hybrid digital analog transmission in each case by adjusting the system parameters we optimize the distortion exponent as a function of the bandwidth ratio we prove that the distortion exponent upper bound can be achieved when the channel has only one degree of freedom that is l 1 and min mt mr 1 when we have more degrees of freedom our achievable distortion exponents meet the upper bound for only certain ranges of the bandwidth ratio we demonstrate that our results which were derived for a complex gaussian source can be extended to more general source distributions as well

hybrid digital analog hda joint source channel codes for broadcasting and robust communications we consider the problem of transmitting a band limited gaussian source on an additive band limited gaussian noise channel the well known threshold effect dictates that the more powerful a code is the more sensitive it is to the exact knowledge of the channel noise a code is said to be robust if it is asymptotically optimal for a wide range of channel noise thus robust codes have a graceful degradation characteristic and are free of the threshold effect it is demonstrated that robust codes exist whenever the source and channel bandwidths are equal in the unequal bandwidth case a collection of nearly robust joint source channel codes is constructed using a hybrid digital analog hda coding technique for designing nearly robust codes a matched tandem code whose channel encoder s output is partially fully matched to its input is proposed and the existence of an asymptotically optimal matched tandem code is shown the nearly robust codes achieve the shannon limit theoretically optimum distortion and have a less severe threshold effect finally for the case of two different noise conditions the distortion regions of these codes are determined

towards integrative causal analysis of heterogeneous data sets and studies we present methods able to predict the presence and strength of conditional and unconditional dependencies correlations between two variables y and z never jointly measured on the same samples based on multiple data sets measuring a set of common variables the algorithms are specializations of prior work on learning causal structures from overlapping variable sets this problem has also been addressed in the field of statistical matching the proposed methods are applied to a wide range of domains and are shown to accurately predict the presence of thousands of dependencies compared against prototypical statistical matching algorithms and within the scope of our experiments the proposed algorithms make predictions that are better correlated with the sample estimates of the unknown parameters on test data this is particularly the case when the number of commonly measured variables is low the enabling idea behind the methods is to induce one or all causal models that are simultaneously consistent with fit all available data sets and prior knowledge and reason with them this allows constraints stemming from causal assumptions e g causal markov condition faithfulness to propagate several methods have been developed based on this idea for which we propose the unifying name integrative causal analysis inca a contrived example is presented demonstrating the theoretical potential to develop more general methods for co analyzing heterogeneous data sets the computational experiments with the novel methods provide evidence that causally inspired assumptions such as faithfulness often hold to a good degree of approximation in many real systems and could be exploited for statistical inference code scripts and data are available at www mensxmachina org

kernel based object tracking a new approach toward target representation and localization the central component in visual tracking of nonrigid objects is proposed the feature histogram based target representations are regularized by spatial masking with an isotropic kernel the masking induces spatially smooth similarity functions suitable for gradient based optimization hence the target localization problem can be formulated using the basin of attraction of the local maxima we employ a metric derived from the bhattacharyya coefficient as similarity measure and use the mean shift procedure to perform the optimization in the presented tracking examples the new method successfully coped with camera motion partial occlusions clutter and target scale variations integration with motion filters and data association techniques is also discussed we describe only a few of the potential applications exploitation of background information kalman tracking using motion models and face tracking

successive refinement of information the successive refinement of information consists of first approximating data using a few bits of information then iteratively improving the approximation as more and more information is supplied the goal is to achieve an optimal description at each stage in general an ongoing description which is rate distortion optimal whenever it is interrupted is sought it is shown that in order to achieve optimal successive refinement the necessary and sufficient conditions are that the solutions of the rate distortion problem can be written as a markov chain in particular all finite alphabet signals with hamming distortion satisfy these requirements it is also shown that the same is true for gaussian signals with squared error distortion and for laplacian signals with absolute error distortion a simple counterexample with absolute error distortion and a symmetric source distribution which shows that successive refinement is not always achievable is presented

active appearance models we describe a new method of matching statistical models of appearance to images a set of model parameters control modes of shape and gray level variation learned from a training set we construct an efficient iterative matching algorithm by learning the relationship between perturbations in the model parameters and the induced image errors

joint response graphs and separation induced by triangular systems summary we consider joint probability distributions generated recursively in terms of univariate conditional distributions satisfying conditional independence restrictions the independences are captured by missing edges in a directed graph a matrix form of such a graph called the generating edge matrix is triangular so the distributions that are generated over such graphs are called triangular systems we study consequences of triangular systems after grouping or reordering of the variables for analyses as chain graph models i e for alternative recursive factorizations of the given density using joint conditional distributions for this we introduce families of linear triangular equations which do not require assumptions of distributional form the strength of the associations that are implied by such linear families for chain graph models is derived the edge matrices of chain graphs that are implied by any triangular system are obtained by appropriately transforming the generating edge matrix it is shown how induced independences and dependences can be studied by graphs by edge matrix calculations and via the properties of densities some ways of using the results are illustrated

variable rate channel capacity this paper introduces the notions of variable to fixed and fixed to variable channel capacity without feedback for channels that satisfy the strong converse these notions coincide with the conventional shannon capacity for channels that do not behave ergodically the conventional fixed rate shannon capacity only depends on least favorable channel conditions while the variable rate capacity notions are able to capture the whole range of channel states and their likelihood even in the absence of any side information about channel state at the transmitter particular emphasis is placed on memoryless channels that are governed by finitely valued states we show that single user variable to fixed channel capacity is intimately connected to the capacity region of broadcast channels with degraded message sets and we give an expression for the fixed to variable capacity

systematic lossy source channel coding the fundamental limits of systematic communication are analyzed in systematic transmission the decoder has access to a noisy version of the uncoded raw data analog or digital the coded version of the data is used to reduce the average reproduced distortion d below that provided by the uncoded systematic link and or increase the rate of information transmission unlike the case of arbitrarily reliable error correction d spl rarr 0 for symmetric sources channels where systematic codes are known to do as well as nonsystematic codes we demonstrate that the systematic structure may degrade the performance for nonvanishing d we characterize the achievable average distortion and we find necessary and sufficient conditions under which systematic communication does not incur loss of optimality the wyner ziv 1976 rate distortion theorem plays a fundamental role in our setting the general result is applied to several scenarios for a gaussian bandlimited source and a gaussian channel the invariance of the bandwidth signal to noise ratio snr in decibels product is established and the optimality of systematic transmission is demonstrated bernoulli sources transmitted over binary symmetric channels and over certain gaussian channels are also analyzed it is shown that if nonnegligible bit error rate is tolerated systematic encoding is strictly suboptimal

the streaming dmt of fading channels we study sequential transmission of a stream of messages over a block fading multi input multi output mimo channel a new message arrives in each coherence block and the decoder is required to output each message after a delay of t coherence blocks we establish the optimal diversity multiplexing tradeoff dmt and show that it can be achieved using a simple interleaving of messages the converse is based on an outage amplification technique which appears to be new we also discuss another coding scheme based on a sequential tree code this coding scheme only requires the knowledge of delay at the decoder and yet realizes the optimal dmt we finally discuss some extensions when multiple messages at uniform intervals arrive within each coherence period

on the choice of a model to fit data from an exponential family let x 1 cdots x n be iid observations coming from an exponential family the problem of interest is this given a finite number of models m j smoothly curved manifolds in mathbb r k choose the best model to fit the observations with some penalty for choosing models with dimensions which are too large a result of schwarz is made more specific and is extended to the case where the models are curved manifolds if s y n j is up to a constant c n independent of the model the log of the posterior probability of the j th model where the sample mean y n 1 n sum n i 1 x i has been replaced by y schwarz suggested an asymptotic expansion of s y n j whose leading terms are gamma y n j n sup psi in m j cap theta y psi b psi frac 1 2 k j log n in the case where the models are affine subspaces of mathbb r k we establish a similar asymptotic expansion including the next term with uniform bounds for y in a compact neighborhood of nabla b theta where theta is the true value of the parameter we suggest a criterion for the choice of the best model that consists of maximizing the three leading terms in the expansion s y n j we show that the criterion gives the correct model with probabilities p n theta rightarrow 1 as n rightarrow infty

computing maximum likelihood estimates in recursive linear models with correlated errors in recursive linear models the multivariate normal joint distribution of all variables exhibits a dependence structure induced by a recursive or acyclic system of linear structural equations these linear models have a long tradition and appear in seemingly unrelated regressions structural equation modelling and approaches to causal inference they are also related to gaussian graphical models via a classical representation known as a path diagram despite the models long history a number of problems remain open in this paper we address the problem of computing maximum likelihood estimates in the subclass of bow free recursive linear models the term bow free refers to the condition that the errors for variables i and j be uncorrelated if variable i occurs in the structural equation for variable j we introduce a new algorithm termed residual iterative conditional fitting ricf that can be implemented using only least squares computations in contrast to existing algorithms ricf has clear convergence properties and yields exact maximum likelihood estimates after the first iteration whenever the mle is available in closed form

causal discovery with continuous additive noise models we consider the problem of learning causal directed acyclic graphs from an observational joint distribution one can use these graphs to predict the outcome of interventional experiments from which data are often not available we show that if the observational distribution follows a structural equation model with an additive noise structure the directed acyclic graph becomes identifiable from the distribution under mild conditions this constitutes an interesting alternative to traditional methods that assume faithfulness and identify only the markov equivalence class of the graph thus leaving some edges undirected we provide practical algorithms for finitely many samples resit regression with subsequent independence test and two methods based on an independence score we prove that resit is correct in the population setting and provide an empirical evaluation

markovian acyclic directed mixed graphs for discrete data acyclic directed mixed graphs admgs are graphs that contain directed rightarrow and bidirected leftrightarrow edges subject to the constraint that there are no cycles of directed edges such graphs may be used to represent the conditional independence structure induced by a dag model containing hidden variables on its observed margin the markovian model associated with an admg is simply the set of distributions obeying the global markov property given via a simple path criterion m separation we first present a factorization criterion characterizing the markovian model that generalizes the well known recursive factorization for dags for the case of finite discrete random variables we also provide a parameterization of the model in terms of simple conditional probabilities and characterize its variation dependence we show that the induced models are smooth consequently markovian admg models for discrete variables are curved exponential families of distributions

piecewise affine kernel tracking for non planar targets since the multiple kernel representation opened in tracking the possibility of representing several features of the target in the same model tracking multiple features using kernel based methods has received a great attention in spite of these efforts the formulation has been reduced to tracking planar targets or targets rotating inside a plane parallel to the image plane the aim of this paper is to extend the multi kernel tracking to cope with situations different to those to this end we consider the triangular mesh described by the centers of the kernels and we develop the estimation of a set of affine transforms one at each mesh triangle subject to the constraints that each affine transform of a triangle must be compatible with the affine transforms coming from contiguous triangles the method is applied to sequences including face and car tracking results show an outperformance respect to previous kernel tracking methods which generally work with a too restricted set of movements

measurement bias and effect restoration in causal inference summary this paper highlights several areas where graphical techniques can be harnessed to address the problem of measurement errors in causal inference in particular it discusses the control of unmeasured confounders in parametric and nonparametric models and the computational problem of obtaining bias free effect estimates in such models we derive new conditions under which causal effects can be restored by observing proxy variables of unmeasured confounders with without external studies

ancestral graph markov models this paper introduces a class of graphical independence models that is closed under marginalization and conditioning but that contains all dag independence models this class of graphs called maximal ancestral graphs has two attractive features there is at most one edge between each pair of vertices every missing edge corresponds to an independence relation these features lead to a simple parameterization of the corresponding set of distributions in the gaussian case

on the distortion snr exponent of hybrid digital analog space time coding we consider the transmission of a real independent and identically distributed i i d analog source over a quasi static m input n output multiple input multiple output mimo block fading channel the relevant performance criterion is end to end average quadratic distortion d versus channel signal to noise ratio snr for given spectral efficiency eta defined as the ratio of the source bandwidth over the channel bandwidth in the limit of high snr we define the distortion snr exponent a eta as the largest a such that d esdot snr a over all possible source channel coding schemes of spectral efficiency eta we find a simple upper bound on a eta an achievable lower bound asep eta achievable by separated tandem source channel coding and a tighter lower bound ahybrid eta achievable by new hybrid digital analog space time coding schemes as a corollary we have that a eta is completely determined for the scalar case m n 1 and for the bandwidth compression case eta ges 2 min m n expiicit and simple construction of hybrid space time codes achieving ahybrid eta are also given

covariate selection for the nonparametric estimation of an average treatment effect observational studies in which the effect of a nonrandomized treatment on an outcome of interest is estimated are common in domains such as labour economics and epidemiology such studies often rel

a broadcast approach for a single user slowly fading mimo channel a broadcast transmission strategy for the slowly fading gaussian multiple input multiple output mimo channel is introduced this broadcast strategy is an extension of the single input single output siso broadcast approach perfect channel state information csi is assumed known at the receiver end only this strategy facilitates to adapt the reliably decoded rate to the actual channel state without having any feedback link to the transmitter transmission of layered coded information is motivated by the theory of majorization we derive the basic equations characterizing achievable rates of the strategy several ad hoc approximations to the achievable region are considered and their performance is compared with the siso setting and the ergodic capacity it has been demonstrated that a single layer outage approach is reasonably efficient in the mimo setting in terms of the average reliably decoded rate a multiple access channel mac broadcast approach is also applied for the mimo case and demonstrated to be relatively efficient

distortion bounds for broadcasting with bandwidth expansion we consider the problem of broadcasting a single gaussian source to two listeners over a gaussian broadcast channel with rho channel uses per source sample where rho 1 a distortion pair d1 d2 is said to be achievable if one can simultaneously achieve a mean squared error mse d1 at receiver 1 and d2 at receiver 2 the main result of this correspondence is an outer bound for the set of all achievable distortion pairs that is we find necessary conditions under which d1 d2 is achievable we then apply this result to the problem of point to point transmission over a gaussian channel with unknown signal to noise ratio snr and rho 1 we show that if a system must be optimal at a certain snrmin then asymptotically the system distortion cannot decay faster than o 1 snr as for achievability we show that a previously reported scheme due to mittal and phamdo 2002 is optimal at high snr we introduce two new schemes for broadcasting with bandwidth expansion combining digital and analog transmissions we finally show how a system with a partial feedback returning from the bad receiver to the transmitter and to the good receiver achieves a distortion pair that lies on the outer bound derived here

on the causal interpretation of acyclic mixed graphs under multivariate normality abstract in multivariate statistics acyclic mixed graphs with directed and bidirected edges are widely used for compact representation of dependence structures that can arise in the presence of hidden i e latent or unobserved variables indeed under multivariate normality every mixed graph corresponds to a set of covariance matrices that contains as a full dimensional subset the covariance matrices associated with a causally interpretable acyclic digraph this digraph generally has some of its nodes corresponding to hidden variables we seek to clarify for which mixed graphs there exists an acyclic digraph whose hidden variable model coincides with the mixed graph model restricting to the tractable setting of chain graphs and multivariate normality we show that decomposability of the bidirected part of the chain graph is necessary and sufficient for equality between the mixed graph model and some hidden variable model given by an acyclic digraph

likelihood ratio tests and singularities many statistical hypotheses can be formulated in terms of polynomial equalities and inequalities in the unknown parameters and thus correspond to semi algebraic subsets of the parameter space we consider large sample asymptotics for the likelihood ratio test of such hypotheses in models that satisfy standard probabilistic regularity conditions we show that the assumptions of chernoff s theorem hold for semi algebraic sets such that the asymptotics are determined by the tangent cone at the true parameter point at boundary points or singularities the tangent cone need not be a linear space and limiting distributions other than chi square distributions may arise while boundary points often lead to mixtures of chi square distributions singularities give rise to nonstandard limits we demonstrate that minima of chi square random variables are important for locally identifiable models and in a study of the factor analysis model with one factor we reveal connections to eigenvalues of wishart matrices

on the multicast capacity of the wireless broadcast channel for a multicast network in which a common source is transmitted to n users the problem of maximizing the average rate subject to a coverage constraint minimum quality of service is studied considering such a network with single antenna nodes and assuming that the channel state information is available only at the receiver side the highest expected rate achievable by a random user in the network called the expected typical rate is derived in two scenarios hard coverage constraint and soft coverage constraint in the first case the coverage is expressed in terms of the outage probability while in the second case the expected rate should satisfy a certain minimum requirement it is shown that the optimum solution achieving the highest expected typical rate for given coverage requirements in both cases is achieved by an infinite layer superposition code for which the optimal power allocation among different layers is derived the analysis is extended to a scenario with multiple transmit antennas for the miso case a suboptimal coding scheme is proposed which is shown to be asymptotically optimal when the number of transmit antennas grows at least logarithmically with the number of users in the network

marginalization and collapsibility in graphical interaction models the behaviour of a graphical interaction model under marginalization is discussed a graphical interaction model is called collapsible onto a set of variables if the class of marginal distributions is the same as that implied by the related subgraph the necessary and sufficient condition for collapsibility is found and it is shown that collapsibility is equivalent to a range of other important statistical properties of the model

multiple collaborative kernel tracking those motion parameters that cannot be recovered from image measurements are unobservable in the visual dynamic system this paper studies this important issue of singularity in the context of kernel based tracking and presents a novel approach that is based on a motion field representation which employs redundant but sparsely correlated local motion parameters instead of compact but uncorrelated global ones this approach makes it easy to design fully observable kernel based motion estimators this paper shows that these high dimensional motion fields can be estimated efficiently by the collaboration among a set of simpler local kernel based motion estimators which makes the new approach very practical