the complex parameter rao test the rao test is an important method in signal detection in the presence of unknown parameters the traditional approach to the problem when the unknown parameters are complex valued is to form a corresponding real valued parameter vector and then to use the real rao test alternatively we present a complex parameter rao test by reformulating the calculations with respect to the complex valued quantities directly two important examples of the application of the complex parameter rao test are given to illustrate the procedure

parametric glrt for multichannel adaptive signal detection this paper considers the problem of detecting a multichannel signal in the presence of spatially and temporally colored disturbance a parametric generalized likelihood ratio test glrt is developed by modeling the disturbance as a multichannel autoregressive ar process maximum likelihood ml parameter estimation underlying the parametric glrt is examined it is shown that the ml estimator for the alternative hypothesis is nonlinear and there exists no closed form expression to address this issue an asymptotic ml aml estimator is presented which yields asymptotically optimum parameter estimates at reduced complexity the performance of the parametric glrt is studied by considering challenging cases with limited or no training signals for parameter estimation such cases especially when training is unavailable are of great interest in detecting signals in heterogeneous fast changing or dense target environments but generally cannot be handled by most existing multichannel detectors which rely more heavily on training at an adequate level compared with the recently introduced parametric adaptive matched filter pamf and parametric rao detectors the parametric glrt achieves higher data efficiency offering improved detection performance in general

propagation of probabilities means and variances in mixed graphical association models abstract a scheme is presented for modeling and local computation of exact probabilities means and variances for mixed qualitative and quantitative variables the models assume that the conditional distribution of the quantitative variables given the qualitative is multivariate gaussian the computational architecture is set up by forming a tree of belief universes and the calculations are then performed by local message passing between universes the asymmetry between the quantitative and qualitative variables sets some additional limitations for the specification and propagation structure approximate methods when these are not appropriately fulfilled are sketched it has earlier been shown how to exploit the local structure in the specification of a discrete probability model for fast and efficient computation thereby paving the way for exploiting probability based models as parts of realistic systems for planning and decision support the purpose of this article is to extend this computational s

sign patterns that require almost unique rank abstract a sign pattern matrix is a matrix whose entries are from the set 0 for a real matrix b sgn b is the sign pattern matrix obtained by replacing each positive respectively negative zero entry of b by respectively 0 for a sign pattern matrix a the sign pattern class of a denoted q a is defined as b sgn b a the minimum rank mr a maximum rank mr a of a sign pattern matrix a is the minimum maximum of the ranks of the real matrices in q a several results concerning sign patterns a that require almost unique rank that is to say the sign patterns a such that mr a mr a 1 are established and are extended to sign patterns a for which the spread is d mr a mr a a complete characterization of the sign patterns that require almost unique rank is obtained

distance between populations using mixed continuous and categorical variables summary a general form of the location model is considered for mixed continuous and categorical variables observed in a number of different populations and some special cases of practical interest are cited the distance between any two populations is derived for each of these models estimation of parameters in these distance measures is discussed and the methods are illustrated by application to previously published data

variational learning of a dirichlet process of generalized dirichlet distributions for simultaneous clustering and feature selection this paper introduces a novel enhancement for unsupervised feature selection based on generalized dirichlet gd mixture models our proposal is based on the extension of the finite mixture model previously developed in 1 to the infinite case via the consideration of dirichlet process mixtures which can be viewed actually as a purely nonparametric model since the number of mixture components can increase as data are introduced the infinite assumption is used to avoid problems related to model selection i e determination of the number of clusters and allows simultaneous separation of data in to similar clusters and selection of relevant features our resulting model is learned within a principled variational bayesian framework that we have developed the experimental results reported for both synthetic data and real world challenging applications involving image categorization automatic semantic annotation and retrieval show the ability of our approach to provide accurate models by distinguishing between relevant and irrelevant features without over or under fitting the data

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

model based gaussian and non gaussian clustering abstract the classification maximum likelihood approach is sufficiently general to encompass many current clustering algorithms including those based on the sum of squares criterion and on the criterion of friedman and rubin 1967 however as currently implemented it does not allow the specification of which features orientation size and shape are to be common to all clusters and which may differ between clusters also it is restricted to gaussian distributions and it does not allow for noise we propose ways of overcoming these limitations a reparameterization of the covariance matrix allows us to specify that some features but not all be the same for all clusters a practical framework for non gaussian clustering is outlined and a means of incorporating noise in the form of a poisson process is described an approximate bayesian method for choosing the number of clusters is given the performance of the proposed methods is studied by simulation with encouraging results the methods are applied to the analysis of a data set arising in the study of diabetes and the results seem better than those of previous analyses rh

invariance nonlinear models and asymptotic tests the invariance properties of some well known asymptotic tests are studied three types of invariance are considered invariance to the representation of the null hypothesis invariance to one to one transformations of the parameter space reparameterizations and invariance to one to one transformations of the model variables such as changes in measurement units tests that are not invariant include the wald test and generalized versions of it a widely used variant of the lagrange multiplier test neyman s c a test and a generalized version of the latter for all these tests we show that simply changing measurement units can lead to vastly different answers even when equivalent null hypotheses are tested this problem is illustrated by considering regression models with box cox transformations on the variables we observe in particular that various consistent estimators of the information matrix lead to test procedures with different invariance properties general sufficient conditions are then established under which the generalized c a test becomes invariant to reformulations of the null hypothesis and or to one to one transformations of the parameter space as well as to transformations of the variables in many practical cases where wald type tests lack invariance we find that special formulations of the generalized c a test are invariant and hardly more costly to compute than wald tests this computational simplicity stands in contrast with other invariant tests such as the likelihood ratio test we conclude that noninvariant asymptotic tests should be avoided or used with great care further in many situations the suggested implementation of the generalized c a test often yields an attractive substitute to the wald test which is not invariant and to other invariant tests which are more costly to perform

the adaptive coherence estimator a uniformly most powerful invariant adaptive detection statistic we show that the adaptive coherence estimator ace is a uniformly most powerful ump invariant detection statistic this statistic is relevant to a scenario appearing in adaptive array processing in which there are auxiliary signal free training data vectors that can be used to form a sample covariance estimate for clutter and interference suppression the result is based on earlier work by bose and steinhardt who found a two dimensional 2 d maximal invariant when test and training data share the same noise covariance their 2 d maximal invariant is given by kelly s generalized likelihood ratio test glrt statistic and the adaptive matched filter amf we extend the maximal invariant framework to the problem for which the ace is a glrt the test data shares the same covariance structure as the training data but the relative power level is not constrained in this case the maximal invariant statistic collapses to a one dimensional 1 d scalar which is also the ace statistic furthermore we show that the probability density function for the ace possesses the property of total positivity which establishes that it has monotone likelihood ratio thus a threshold test on the ace is ump invariant this means that it has a claim to optimality having the largest detection probability out of the class of detectors that are also invariant to affine transformations on the data matrix that leave the hypotheses unchanged this requires an additional invariance not imposed by bose and steinhardt invariance to relative scaling of test and training data the ace is invariant and has a constant false alarm rate cfar with respect to such scaling whereas kelly s glrt and the amf are invariant and cfar only with respect to common scaling

response models for mixed binary and quantitative variables summary a number of special representations are considered for the joint distribution of qualitative mostly binary and quantitative variables in addition to the conditional gaussian models and to conditional gaussian regression chain models some emphasis is placed on models derived from an underlying multivariate normal distribution and on models in which discrete probabilities are specified linearly in terms of unknown parameters the possibilities for choosing between the models empirically are examined as well as the testing of independence and conditional independence and the estimation of parameters often the testing of independence is exactly or nearly the same for a number of different models

markov properties of nonrecursive causal models this paper aims to solve an often noted incompatibility between graphical chain models which elucidate the conditional independence structure of a set of random variables and simultaneous equations systems which focus on direct linear interactions and correlations between random variables various authors have argued that the incompatibility arises mainly from the fact that in a simultaneous equations system e g a lisrel model reciprocal causality is possible whereas this is not so in the case of graphical chain models in this article it is shown that this view is not correct in fact the definition of the markov property embodied in a graph can be generalized to a wider class of graphs which includes certain nonrecursive graphs the resulting class of reciprocal graph probability models strictly includes the class of chain graph probability models the class of lattice conditional independence probability models is also strictly included it is shown that the resulting methodology is directly applicable to quite general simultaneous equations systems that are subject to mild restrictions only provided some adjustments are made general simultaneous equations systems can be handled as well in all cases consistency with the lisrel methodology is maintained

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

rational realization of maximum eigenvalue multiplicity of symmetric tree sign patterns abstract a sign pattern is a matrix whose entries are elements of 0 it describes the set of real matrices whose entries have the signs in the pattern a graph that allows loops but not multiple edges describes the set of symmetric matrices having a zero nonzero pattern of entries determined by the absence or presence of edges in the graph dealba et al l m dealba t l hardy i r hentzel l hogben a wangsness minimum rank and maximum eigenvalue multiplicity of symmetric tree sign patterns linear algebra appl in press doi 10 1016 j laa 2006 02 018 gave algorithms for the computation of maximum multiplicity and minimum rank of matrices associated with a tree sign pattern or tree and an algorithm to obtain an integer matrix realizing minimum rank we extend these results by giving algorithms to obtain a symmetric rational matrix realizing the maximum multiplicity of a rational eigenvalue among symmetric matrices associated with a symmetric tree sign pattern or tree

rational realizations of the minimum rank of a sign pattern matrix abstract a sign pattern matrix is a matrix whose entries are from the set 0 the minimum rank of a sign pattern matrix a is the minimum of the ranks of the real matrices whose entries have signs equal to the corresponding entries of a it is conjectured that the minimum rank of every sign pattern matrix can be realized by a rational matrix the equivalence of this conjecture to several seemingly unrelated statements are established for some special cases such as when a is entrywise nonzero or the minimum rank of a is at most 2 or the minimum rank of a is at least n 1 where a is m n the conjecture is shown to hold connections between this conjecture and the existence of positive rational solutions of certain systems of homogeneous quadratic polynomial equations with each coefficient equal to either 1 or 1 are investigated

minimum rank matrices with prescribed graph abstract we study properties of real symmetric matrices with prescribed graph and lowest possible rank we concentrate on the case where the graph is a tree and give an algorithm for computing the minimum possible rank in this case a more general problem is also considered

ideal parent structure learning for continuous variable bayesian networks bayesian networks in general and continuous variable networks in particular have become increasingly popular in recent years largely due to advances in methods that facilitate automatic learning from data yet despite these advances the key task of learning the structure of such models remains a computationally intensive procedure which limits most applications to parameter learning this problem is even more acute when learning networks in the presence of missing values or hidden variables a scenario that is part of many real life problems in this work we present a general method for speeding structure search for continuous variable networks with common parametric distributions we efficiently evaluate the approximate merit of candidate structure modifications and apply time consuming exact computations only to the most promising ones thereby achieving significant improvement in the running time of the search algorithm our method also naturally and efficiently facilitates the addition of useful new hidden variables into the network structure a task that is typically considered both conceptually difficult and computationally prohibitive we demonstrate our method on synthetic and real life data sets both for learning structure on fully and partially observable data and for introducing new hidden variables during structure search

adaptive array detection of uncertain rank one waveforms adaptive array detection of known within a complex scaling rank one space time waveforms in unknown spatial noise has received considerable attention the two published solutions are the adaptive matched filter and the glrt we expand on this work to consider the case of rank one waveforms that are uncertain i e only partially known more precisely we model the space time steering vector as the kronecker product of two vectors each of which is unknown but is known to lie in a known subspace applications for such a model include detection in the presence of multipath and spectral or polarization diversity in both radar processing and wireless communication using the principle of invariance we construct detectors based on the maximal invariant we show that the snr required to achieve a given detection probability for a given false alarm rate is only weakly impacted by waveform uncertainty thus our detector approaches the performance of earlier detectors which entail known waveforms

the minimum rank problem a counterexample we provide a counterexample to a recent conjecture that the minimum rank over the reals of every sign pattern matrix can be realized by a rational matrix we use one of the equivalences of the conjecture and some results from projective geometry as a consequence of the counterexample we show that there is a graph for which the minimum rank of the graph over the reals is strictly smaller than the minimum rank of the graph over the rationals we also make some comments on the minimum rank of sign pattern matrices over different subfields of r

invariance and the wald test abstract many models and hypotheses of interest in econometrics are invariant to certain types of data transformations such as measurement unit changes dagenais and dufour econometrica 59 1991 1601 economics letters 38 1992 251 and dufour and dagenais j statist plann inference 32 1992 111 have shown that wald tests are not invariant in general to such data transformations in this paper i provide a simple set of sufficient conditions to ensure that a wald test for a null hypothesis is invariant to such a data transformation i then use this set of conditions to help account for certain features of the monte carlo results from gregory and weall economics letters 22 1986 203 on the properties of a variety of wald tests for sargan s common factor restriction sargan econometrica 48 1980 879 in the first order autoregressive distributed lag model

separating function estimation tests a new perspective on binary composite hypothesis testing in this paper we study some relationships between the detection and estimation theories for a binary composite hypothesis test h0 against h1 and a related estimation problem we start with a one dimensional 1d space for the unknown parameter space and one sided hypothesis problems and then extend out results into more general cases for one sided tests we show that the uniformly most powerful ump test is achieved by comparing the minimum variance and unbiased estimator mvue of the unknown parameter with a threshold thus for the case where the ump test does not exist the mvue of the unknown parameter does not exist either therefore for such cases a good estimator of the unknown parameter is deemed as a good decision statistic for the test for a more general class of composite testing with multiple unknown parameters we prove that the mvue of a separating function sf can serve as the optimal decision statistic for the ump unbiased test where the sf is continuous differentiable positive for all parameters under h1 and is negative for the parameters under h0 we then prove that the ump unbiased statistic is equal to the mvue of an sf in many problems with multiple unknown parameters the ump test does not exist for such cases we show that if one detector between two detectors has a better receiver operating characteristic roc curve then using its decision statistic we can estimate the sf more e accurately in probability for example the sf is the signal to noise ratio snr in some problems these results motivate us to introduce new suboptimal sf estimator tests sfets which are easy to derive for many problems finally we provide some practical examples to study the relationship between the decision statistic of a test and the estimator of its corresponding sf

rational solutions of certain matrix equations abstract a sign pattern is a matrix whose entries are from the set 0 for a real matrix b sgn b is the sign pattern obtained by replacing each positive respectively negative zero entry of b by respectively 0 for a sign pattern a the sign pattern class of a denoted q a is defined as b sgn b a the purpose of this note is to prove the following theorem let a b and c be real matrices such that ab c suppose that the zero bipartite graph of c this is the same as the complement of the bipartite graph of c is a forest then there exist rational perturbations a b and c of a b and c respectively in the same corresponding sign pattern classes such that a b c

an adaptive detector for deterministic signals in noise of unknown spectra using the rao test an adaptive detector for a known deterministic signal of unknown amplitude in gaussian noise of unknown spectra is described the detector is based on the rao test which is asymptotically equivalent to the generalized likelihood ratio the detector achieves constant false alarm probability in the presence of large changes in input noise bandwidth and variance while providing optimum detection performance the results are supported by simulation

generalized matched subspace filter for nonindependent noise based on ica we propose a generalization of the matched subspace filter for the detection of unknown signals in a background of non gaussian and nonindependent noise the generalization is based on a modification of the rao test by including a linear transformation derived from independent component analysis ica receiver operating characteristic roc curves computed for simulated examples illustrate the significant improvement achieved with the generalized solution

a new parametric adaptive nonstationarity detector and application techniques for hypothesis testing can be used to solve a broad class of nonstationarity detection problems which is a key issue in a variety of applications to achieve lower complexity and to deal with real time detection in practical applications we develop a new adaptive nonstationarity detector by exploiting a parametric model a weighted maximum a posteriori map estimator is developed to estimate the parameters associated with the parametric model we then derive a regularized wald test from the weighted map estimate which is adaptively implemented by a regularized recursive least squares rls algorithm several important issues are discussed including model order selection forgetting factor and regularization parameter selection for rls and numerically stable implementation using qr decomposition which are intrinsic parts of the proposed parametric adaptive detector simulation results are presented to illustrate the efficiency of the proposed nonstationarity detector with adaptive estimation and automatic model selection especially for slowly varying type of nonstationarity such as time varying spectrums and speeches

dimensionality reduction in unsupervised learning of conditional gaussian networks this paper introduces a novel enhancement for unsupervised learning of conditional gaussian networks that benefits from feature selection our proposal is based on the assumption that in the absence of labels reflecting the cluster membership of each case of the database those features that exhibit low correlation with the rest of the features can be considered irrelevant for the learning process thus we suggest performing this process using only the relevant features then every irrelevant feature is added to the learned model to obtain an explanatory model for the original database which is our primary goal a simple and thus efficient measure to assess the relevance of the features for the learning process is presented additionally the form of this measure allows us to calculate a relevance threshold to automatically identify the relevant features the experimental results reported for synthetic and real world databases show the ability of our proposal to distinguish between relevant and irrelevant features and to accelerate learning while still obtaining good explanatory models for the original database

on the invariance coincidence and statistical equivalence of the glrt rao test and wald test three common techniques to discriminate between alternatives in a binary hypothesis testing problem are the generalized likelihood ratio test glrt the rao test and the wald test in this paper we investigate some characteristics of the corresponding decision statistics and provide their expressions for some problems of particular interest in statistical signal processing first of all we focus on the invariance of the rao and wald tests with respect to transformations leaving the testing problem unaltered then we introduce necessary and sufficient conditions in order for their decision statistics to coincide with twice the logarithm of the glrt statistic finally we present some detection problems usually encountered in practical signal processing applications where the decision variables of the three quoted tests are equivalent namely related by strictly monotonic transformations

hierarchical interaction models lauritzen and wermuth have proposed a class of models for mixed qualitative and continuous data defined by two properties that the continuous variables are normally distributed given the qualitative variables and that a set of conditional independence relations hold between specified pairs of variables the present paper examines an extension to this class called hierarchical interaction models a compact form for model representation is described and an estimation algorithm is given some properties of the models a compact form for model representation is described and an estimation algorithm is given some properties of the models concerning marginalization and conditioning are examined the class includes and generalizes hierarchical log linear models standard fixed effect anova multivariate anova and multivariate regression models

adaptive double subspace signal detection in gaussian background part i homogeneous environments in this two part paper we consider the problem of adaptive multidimensional multichannel signal detection in gaussian noise with unknown covariance matrix the test data primary data is assumed as a collection of sample vectors arranged as the columns of a rectangular data array the rows and columns of the signal matrix are both assumed to lie in known subspaces but with unknown coordinates due to this feature of the signal structure we name this kind of signal as the double subspace signal part i of this paper focuses on the adaptive detection in homogeneous environments while part ii deals with the adaptive detection in partially homogeneous environments precisely in this part we derive the generalized likelihood ratio test glrt rao test wald test as well as their two step variations in homogeneous environments three types of spectral norm tests snts are also introduced all these detectors are shown to possess the constant false alarm rate cfar property moreover we discuss the differences between them and show how they work another contribution is that we investigate various special cases of these detectors remarkably some of them are well known existing detectors while some others are still new at the stage of performance evaluation conducted by monte carlo simulations both matched and mismatched signals are dealt with for each case more than one scenario is considered

simple linear time algorithms to test chordality of graphs test acyclicity of hypergraphs and selectively reduce acyclic hypergraphs chordal graphs arise naturally in the study of gaussian elimination on sparse symmetric matrices acyclic hypergraphs arise in the study of relational data bases rose tarjan and lueker siam j c

adaptive radar detectors based on the observed fim modified versions of rao wald and durbin tests are considered exploiting an estimator of the fisher information matrix fim in place of the exact one they are asymptotically equivalent under some technical conditions to the standard counterparts and rely on the use of the observed fim ofim which is proportional to the negative hessian of the log likelihood the developed framework is applied to the problem of adaptive radar detection of a point like target in homogeneous or partially homogeneous interference remarkably for both the scenarios it is shown that rao wald and durbin tests with ofim are statistically equivalent to the generalized likelihood ratio test glrt for the specific detection problem namely kelly s detector for the homogeneous environment and the adaptive coherence estimator ace s kraut and l l scharf the cfar adaptive subspace detector is a scale invariant glrt ieee trans signal process vol 47 no 9 pp 2538 2541 sep 1999 also known as adaptive normalized matched filter anmf e conte m lops and g ricci asymptotically optimum radar detection in compound gaussian clutter ieee trans aerosp electron syst vol 31 no 2 pp 617 625 apr 1995 for the partially homogeneous scenario this provides a new interpretation of the mentioned glrts laying the foundations for a better understanding of their theoretical validity

graphical regression models for polytomous variables when modeling the relationship between two nominal categorical variables it is often desirable to include covariates to understand how individuals differ in their response behavior typically however not all the relevant covariates are available with the result that the measured variables cannot fully account for the associations between the nominal variables under the assumption that the observed and unobserved variables follow a homogeneous conditional gaussian distribution this paper proposesrc m regression models to decompose the residual associations between the polytomous variables based on goodman s 1979 1985 rc m association model a distinctive feature ofrc m regression models is that they facilitate the joint estimation of effects due to manifest and omitted continuous variables without requiring numerical integration therc m regression models are illustrated using data from the high school and beyond study tatsuoka lohnes 1988

regression models for a bivariate discrete and continuous outcome with clustering abstract developmental toxicity studies of laboratory animals play a crucial role in the testing and regulation of chemicals and pharmaceutical compounds exposure to developmental toxicants typically causes a variety of adverse effects such as fetal malformations and reduced fetal weight at term in this article we discuss regression methods for jointly analyzing bivariate discrete and continuous outcomes that are motivated by the statistical problems that arise in analyzing data from developmental toxicity studies we focus on marginal regression models that is models in which the marginal expectation of the bivariate response vector is related to a set of covariates by some known link functions in these models the regression parameters for the marginal expectation are of primary scientific interest whereas the association between the binary and continuous response is considered to be a nuisance characteristic of the data we describe a likelihood based approach based on the general location mode

from boolean to sign pattern matrices abstract a nonnegative sign pattern matrix is a matrix whose entries are from the set 0 a nonnegative sign pattern matrix can also be viewed as a boolean matrix by replacing each entry with 1 in this paper some interesting connections between nonnegative sign pattern matrices and boolean matrices are investigated in particular the relations between the minimum rank and the boolean row or column rank are explored the idempotent boolean matrices that allow idempotence are identified and the nonnegative sign patterns that allow various types of nonnegative or positive generalized inverses are characterized

association models and canonical correlation in the analysis of cross classifications having ordered categories abstract the association models considered in goodman 1979a for the analysis of cross classifications having ordered categories are presented in a somewhat different form in the present article to facilitate comparison of the results obtained using these models with those obtained using the earlier canonical correlation approach both the association models and the canonical correlation approach can provide meaningful scores for the row and column categories and these scores can be used to partition into relevant components the usual chi squared statistic for testing the null hypothesis of statistical independence between the row classification and column classification however while the usual procedure for testing the statistical significance of chi squared components is invalid when these components are based on the canonical correlations a corresponding procedure is valid when these components are obtained with the association models the components of association obtained with the association mo

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

graphical and recursive models for contingency tables summary we discuss two classes of models for contingency tables graphical and recursive models both of which arise from restrictions that are expressible as conditional independencies of variable pairs the first of these is a subclass of hierarchical log linear models each of its models can be represented by an undirected graph in the second class each model corresponds to a particular kind of a directed graph instead and can be characterized by a nontrivial factorization of the joint distribution in terms of response variables we derive decomposable or multiplicative models as the intersecting class this result has useful consequences for exploratory types of analysis as well as for the model interpretation we can give an aid for detecting well fitting decomposable models in a transformation of the observed contingency table and each decomposable model may be interpreted with the help of an undirected or directed graph

matched subspace detectors we formulate a general class of problems for detecting subspace signals in subspace interference and broadband noise we derive the generalized likelihood ratio glr for each problem in the class we then establish the invariances for the glr and argue that these are the natural invariances for the problem in each case the glr is a maximal invariant statistic and the distribution of the maximal invariant statistic is monotone this means that the glr test glrt is the uniformly most powerful invariant detector we illustrate the utility of this finding by solving a number of problems for detecting subspace signals in subspace interference and broadband noise in each case we give the distribution for the detector and compute performance curves

minimal sufficient causation and directed acyclic graphs notions of minimal sufficient causation are incorporated within the directed acyclic graph causal framework doing so allows for the graphical representation of sufficient causes and minimal sufficient causes on causal directed acyclic graphs while maintaining all of the properties of causal directed acyclic graphs this in turn provides a clear theoretical link between two major conceptualizations of causality one counterfactual based and the other based on a more mechanistic understanding of causation the theory developed can be used to draw conclusions about the sign of the conditional covariances among variables

a maximal invariant framework for adaptive detection with structured and unstructured covariance matrices we introduce a framework for exploring array detection problems in a reduced dimensional space by exploiting the theory of invariance in hypothesis testing this involves calculating a low dimensional basis set of functions called the maximal invariant the statistics of which are often tractable to obtain thereby making analysis feasible and facilitating the search for tests with some optimality property using this approach we obtain a locally most powerful invariant test for the unstructured covariance case and show that all invariant tests can be expressed in terms of the previously published kelly s generalized likelihood ratio glrt and robey s adaptive matched filter amf test statistics applying this framework to structured covariance matrices corresponding to stochastic interferers in a known subspace for which the glrt is unavailable we obtain the maximal invariant and propose several new invariant detectors that are shown to perform as well or better than existing ad hoc detectors these invariant tests are unaffected by most nuisance parameters hence the variation in the level of performance is sharply reduced this framework facilitates the search for such tests even when the usual glrt is unavailable

feature selection with svd entropy some modification and extension many approaches have been developed for dimensionality reduction these approaches can broadly be categorized into supervised and unsupervised methods in case of supervised dimensionality reduction for any input vector the target value is known which can be a class label also in a supervised approach our objective is to select a subset of features that has adequate discriminating power to predict the target value this target value for an input vector is absent in case of an unsupervised approach in an unsupervised scheme we mainly try to find a subset that can capture the inherent structure of the data such as the neighborhood relation or the cluster structure in this work we first study a singular value decomposition svd based unsupervised feature selection approach proposed by varshavsky et al then we propose a modification of this method to improve its performance an svd entropy based supervised feature selection algorithm is also developed in this paper performance evaluation of the algorithms is done on altogether 13 benchmark and one synthetic data sets the quality of the selected features is assessed using three indices sammon s error se cluster preservation index cpi and misclassification error mce using a 1 nearest neighbor 1 nn classifier besides showing the improvement of the modified unsupervised scheme over the existing one we have also made a comparative study of the modified unsupervised and the proposed supervised algorithms with one well known unsupervised and two popular supervised feature selection methods respectively our results reveal the effectiveness of the proposed algorithms in selecting relevant features

invariance and optimality of cfar detectors in binary composite hypothesis tests we investigate the relationship between constant false alarm rate cfar and invariant tests we introduce the minimal invariant group mig we show that for a family of distributions the unknown parameters are eliminated from the distribution of the maximal invariant statistic under the mig while the maximum information of the observed signal is preserved we prove that any invariant test with respect to mig is cfar and conversely for any cfar test an invariant statistic exists with respect to an mig under some mild conditions moreover for a given cfar test we propose a systematic method for deriving an enhanced test i e a function of observations exists such that the likelihood ratio lr of the maximal invariant of its mig gives an enhanced test furthermore we introduce the uniformly most powerful cfar ump cfar test as the optimal cfar bound among all cfar tests we then prove that the ump cfar test for the minimally invariant hypothesis testing problem is given by the lr of the maximal invariant under mig for some problems this test mp cfar depends on the unknown parameters of the alternative hypothesis however provides an upper performance bound for all suboptimal cfar tests we also propose three suboptimal novel cfar tests among which one is asymptotically optimal

model order selection rules for covariance structure classification in radar the adaptive classification of the interference covariance matrix structure for radar signal processing applications is addressed in this paper this represents a key issue because many detection architectures are synthesized assuming a specific covariance structure which may not necessarily coincide with the actual one due to the joint action of the system and environment uncertainties the considered classification problem is cast in terms of a multiple hypotheses test with some nested alternatives and the theory of model order selection mos is exploited to devise suitable decision rules several mos techniques such as the akaike takeuchi and bayesian information criteria are adopted and the corresponding merits and drawbacks are discussed at the analysis stage illustrating examples for the probability of correct model selection are presented showing the effectiveness of the proposed rules

collapsibility and response variables in contingency tables summary various definitions of the collapsibility of a hierarchical log linear model for a multidimensional contingency table are considered and shown to be equivalent necessary and sufficient conditions for collapsibility are found in terms of the generating class it is shown that log linear models are appropriate for tables with response and explanatory variables if and only if they are collapsible onto the explanatory variables some key word8 collapsibility contingency table graphical model interaction graph log linear model response variable s sufficiency shown to be closely related some models have the property that relations between a set of the classifying factors may be studied by examination of the table of marginal totals formed by summing over the remaining factors such models are said to be collapsible onto the given set of factors collapsibility has important consequences for hypothesis testing and model selection and can be useful in data reduction we consider various definitions of collapsibility and show their equivalence furthermore necessary and sufficient conditions for collapsi bility are found in terms of the generating class many tables analysed in practice involve response variables simple examples one of which is given in 3 suffice to show the importance of distinguishing between response and explanatory variables first that inappropriate models may be avoided and second that natural and relevant models that are not log linear may be considered this paper characterizes appropriate and inappropriate log linear models for tables with response variables and some alternative approaches for the analysis of such tables are briefly considered we consider a multidimensional contingency table n based on a set of classifying factors f for a given subset a of f we are interested in the table of marginal totals na that is to say the table of cell counts summed over the remaining factors ac that is the complement of a in f we identify a hierarchical log linear model l that is the set of probabilities p e l with its generating class whose elements generators are given in square brackets thus for example the model ab bcd for a 4 way table corresponds

maximum likelihood estimation for mixed continuous and categorical data with missing values summary maximum likelihood procedures for analysing mixed continuous and categorical data with missing values are presented the general location model of olkin tate 1961 and extensions introduced by krzanowski 1980 1982 form the basis for our methods maximum likelihood estimation with incomplete data is achieved by an application of the em algorithm dempster laird rubin 1977 special cases of the algorithm include orchard woodbury s 1972 algorithm for incomplete normal samples fuchs s 1982 algorithms for log linear modelling of partially classified contingency tables and day s 1969 algorithm for multivariate normal mixtures applications include a imputation of missing values b logistic regression and discriminant analysis with missing predictors and unclassified observations c linear regression with missing continuous and categorical predictors and d parametric cluster analysis with incomplete data methods are illustrated using data from the st louis risk research project some key word8 cluster analysis discriminant analysis em algorithm incomplete data linear regression logistic regression log linear model mixture model

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

minimum ranks of sign patterns and zero nonzero patterns and point hyperplane configurations abstract a sign pattern matrix is a matrix whose entries are from the set 0 the minimum rank respectively rational minimum rank of a sign pattern matrix a is the minimum of the ranks of the real respectively rational matrices whose entries have signs equal to the corresponding entries of a a sign pattern a is said to be condensed if a has no zero row or column and no two rows or columns are identical or negatives of each other a zero nonzero pattern matrix is a matrix whose entries are from the set 0 where indicates a nonzero entry many of the sign pattern notions carry over to zero nonzero patterns assuming that the ground field is r in this paper a direct connection between condensed m n sign patterns and zero nonzero patterns with minimum rank r and m point n hyperplane configurations in r r 1 is established in particular condensed sign patterns and zero nonzero patterns with minimum rank 3 are closely related to point line configurations on the plane using this connection we construct the smallest known sign pattern whose minimum rank is 3 but whose rational minimum rank is greater than 3 it is proved that for any sign pattern or zero nonzero pattern a if the number of zero entries on each column of a is at most 2 then the rational and real minimum ranks of a are equal further it is shown that for any zero nonzero pattern a with minimum rank r 3 if the number of zero entries on each column of a is at most r 1 then the rational minimum rank of a is also r a few related conjectures and open problems are raised

random distortion testing and optimality of thresholding tests this paper addresses the problem of testing whether the mahalanobis distance between a random signal and a known deterministic model 0 exceeds some given non negative real number or not when has unknown probability distribution and is observed in additive independent gaussian noise with positive definite covariance matrix when is deterministic unknown we prove the existence of thresholding tests on the mahalanobis distance to 0 that have specified level and maximal constant power mcp the mcp property is a new optimality criterion involving wald s notion of tests with uniformly best constant power ubcp on ellipsoids for testing the mean of a normal distribution when the signal is random with unknown distribution constant power maximality extends to maximal constant conditional power mccp and the thresholding tests on the mahalanobis distance to 0 still verify this novel optimality property our results apply to the detection of signals in independent and additive gaussian noise in particular for a large class of possible model mismatches mccp tests can guarantee a specified false alarm probability in contrast to standard neyman pearson tests that may not respect this constraint

rao test for adaptive detection in gaussian interference with unknown covariance matrix this paper deals with the problem of detecting a signal known up to a scaling factor in the presence of gaussian disturbance with unknown covariance matrix a new detector based on the rao test criterion is introduced and its invariance properties and constant false alarm rate cfar behavior are studied at the analysis stage the performance of the new receiver is assessed also in comparison with some classical adaptive radar detectors both in the matched as well as in the mismatched signal case remarkably the rao test may achieve a matched detection performance which is commensurate with that of the generalized likelihood ratio test glrt based detectors if a sufficient number of training data is available moreover it also exhibits better rejection capabilities of mismatched signals than the counterparts in the last part of the work a two stage detector whose second stage coincides with the rao test is devised it represents a suitable means to restore the detection performance of the plain rao test in the presence of a small number of training data finally the performance of the aforementioned two stage processor is analyzed in closed form and the cfar behavior is proved

gaussian markov distributions over finite graphs on s interesse aux modeles de selection de covariance introduites par dempster 1972 et etudies par wermuth 1976

on substantive research hypotheses conditional independence graphs and graphical chain models summary graphs consisting of points and lines or arrows as connections between selected pairs of points are used to formulate hypotheses about relations between variables points stand for variables connections represent associations when a missing connection is interpreted as a conditional independence the graph characterizes a conditional independence structure as well statistical models called graphical chain models correspond to special types of graphs which are interpreted in this fashion examples are used to illustrate how conditional independences are reflected in summary statistics derived from the models and how the graphs help to identify analogies and equivalences between different models graphical chain models are shown to provide a unifying concept for many statistical techniques that in the past have proven to be useful in analyses of data they also provide tools for new types of analysis

feature subset selection by bayesian network based optimization abstract a new method for feature subset selection in machine learning fss ebna feature subset selection by estimation of bayesian network algorithm is presented fss ebna is an evolutionary population based randomized search algorithm and it can be executed when domain knowledge is not available a wrapper approach over naive bayes and id3 learning algorithms is used to evaluate the goodness of each visited solution fss ebna based on the eda estimation of distribution algorithm paradigm avoids the use of crossover and mutation operators to evolve the populations in contrast to genetic algorithms in absence of these operators the evolution is guaranteed by the factorization of the probability distribution of the best solutions found in a generation of the search this factorization is carried out by means of bayesian networks promising results are achieved in a variety of tasks where domain knowledge is not available the paper explains the main ideas of feature subset selection estimation of distribution algorithm and bayesian networks presenting related work about each concept a study about the overfitting problem in the feature subset selection process is carried out obtaining a basis to define the stopping criteria of the new algorithm

cfar detection of multidimensional signals an invariant approach the paper deals with constant false alarm rate cfar detection of multidimensional signals embedded in gaussian noise with unknown covariance we attack the problem by resorting to the principle of invariance which proves a valuable statistical tool for ensuring a priori namely at the design stage the cfar property in this context we determine a maximal invariant statistic with respect to a proper group of transformations that leave unaltered the hypothesis testing problem under study devise the optimum invariant detector and show that no uniformly most powerful invariant umpi test exists thus we establish the conditions an invariant detector must fulfill in order to ensure the cfar property finally we discuss several suboptimal implementable invariant receivers and remarkably show that the generalized likelihood ratio test glrt detector is a member of this class the performance analysis which has been carried out in the presence of a gaussian signal array shows that the proposed detectors exhibit a quite acceptable loss with respect to the optimum neyman pearson detector

statistics and causal inference abstract problems involving causal inference have dogged at the heels of statistics since its earliest days correlation does not imply causation and yet causal conclusions drawn from a carefully designed experiment are often valid what can a statistical model say about causation this question is addressed by using a particular model for causal inference holland and rubin 1983 rubin 1974 to critique the discussions of other writers on causation and causal inference these include selected philosophers medical researchers statisticians econometricians and proponents of causal modeling

an approximation to maximum likelihood estimates in reduced models summary an approximation to the maximum likelihood estimates of the parameters in a model can be obtained from the corresponding estimates and information matrices in an extended model i e a model with additional parameters the approximation is close provided that the data are consistent with the first model applications are described to log linear models for discrete data to models for multivariate normal distributions with special covariance matrices and to mixed discrete continuous models

asymptotically optimal cfar detectors this paper investigates the asymptotic optimality of the constant false alarm rate cfar tests obtained using the minimal invariant group mig reduction we show that the cfar tests obtained after mig reduction using the wald test is a separating function estimation test sfet and that the generalized likelihood ratio test glrt and the rao test are asymptotically sfet using maximum likelihood estimation mle under some mild conditions thus they are asymptotically optimal in order to find an improved test and motivated by the invariance property of the mle of induced maximal invariant we maximize the asymptotic probability of detection of the sfet using the mle after reduction we propose a systematic method allowing to derive the asymptotically optimal separating function aosf this aosf is obtained as the euclidean distance of the transformed parameters under two hypotheses such that the gradient of the transformed parameters is the cholesky decomposition of the fisher information matrix fim i e the fim is transformed into an identity matrix interestingly the aosf estimation test aosfet using mle simplifies to the wald cfar wherever the fim does not depend on the unknown parameters the simulation results show that the proposed aosfet usually outperforms the glrt wald test and rao test

improved likelihood ratio statistics for covariance selection models summary the expected value of the likelihood ratio statistic for covariance selection models when this statistic has a closed form is derived correct to terms of order n 2 n being the sample size then a bartlett type correction factor is available for such statistics by simulation the practical use of such a correction factor is illustrated and is compared with an alternative correction factor in a special case the null density of the corrected statistic is also considered

maximum likelihood estimation in graphical models with missing values in this paper we discuss maximum likelihood estimation when some observations are missing in mixed graphical interaction models assuming a conditional gaussian distribution as introduced by lauritzen wermuth 1989 for the saturated case ml estimation with missing values via the em algorithm has been proposed by little schluchter 1985 we expand their results to the special restrictions in graphical models and indicate a more efficient way to compute the e step the main purpose of the paper is to show that for certain missing patterns the computational effort can considerably be reduced

ranks of dense alternating sign matrices and their sign patterns abstract in this paper an explicit formula for the ranks of dense alternating sign matrices is obtained the minimum rank and the maximum rank of the sign pattern of a dense alternating sign matrix are determined some related results and examples are also provided

an invariant approach to adaptive radar detection under covariance persymmetry in this paper we propose a systematic and unifying framework to deal with adaptive radar detection in the presence of gaussian interference sharing a persymmetric covariance structure first we determine the group of transformations which leaves the considered hypothesis testing problem unaltered then after reduction by sufficiency we determine a maximal invariant statistic which is a four dimensional vector and significantly compresses the original observation space its first two components are the one step and the two step generalized likelihood ratio test decision statistics respectively whereas its last two entries represent an ancillary statistic we provide also the exact statistical characterization of the maximal invariant which is exploited to synthesize both the optimum and the locally optimum in the low signal to interference plus noise ratio regime invariant receivers finally some sub optimum decision rules based on theoretically solid design criteria are discussed and their performances are analyzed in comparison with the benchmark invariant test

propagating imprecise probabilities in bayesian networks abstract often experts are incapable of providing exact probabilities likewise samples on which the probabilities in networks are based must often be small and preliminary in such cases the probabilities in the networks are imprecise the imprecision can be handled by second order probability distributions it is convenient to use beta or dirichlet distributions to express the uncertainty about probabilities the problem of how to propagate point probabilities in a bayesian network now is transformed into the problem of how to propagate dirichlet distributions in bayesian networks it is shown that the propagation of dirichlet distributions in bayesian networks with incomplete data results in a system of probability mixtures of beta binomial and dirichlet distributions approximate first order probabilities and their second order probability density functions are obtained by stochastic simulation a number of properties of the propagation of imprecise probabilities are discussed by the use of examples an important property is that the imprecision of inferences increases rapidly as new premises are added to an argument the imprecision can be used as a pruning criterion in a network to keep the number of variables involved in an inferential argument small thus imprecision may be used as an ockam s razor in bayesian networks