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Binary models for marginal independence
 JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B
, 2005
"... A number of authors have considered multivariate Gaussian models for marginal independence. In this paper we develop models for binary data with the same independence structure. The models can be parameterized based on Möbius inversion and maximum likelihood estimation can be performed using a versi ..."
Abstract

Cited by 16 (2 self)
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A number of authors have considered multivariate Gaussian models for marginal independence. In this paper we develop models for binary data with the same independence structure. The models can be parameterized based on Möbius inversion and maximum likelihood estimation can be performed using a version of the Iterated Conditional Fitting algorithm. The approach is illustrated on a simple example. Relations to multivariate logistic and dependence ratio models are discussed.
Partial inversion for linear systems and partial closure of independence graphs
 BIT, Numer. Math
"... We introduce and study a calculus for realvalued square matrices, called partial inversion, and an associated calculus for binary square matrices. The first, applied to systems of recursive linear equations, generates new sets of parameters for different types of statistical joint response models. ..."
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Cited by 14 (11 self)
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We introduce and study a calculus for realvalued square matrices, called partial inversion, and an associated calculus for binary square matrices. The first, applied to systems of recursive linear equations, generates new sets of parameters for different types of statistical joint response models. The corresponding generating graphs are directed and acyclic. The second calculus, applied to matrix representations of independence graphs, gives chain graphs induced by such a generating graph. Chain graphs are more complex independence graphs associated with recursive joint response models. Missing edges in independence graphs coincide with structurally zero parameters in linear systems. A wide range of consequences of an assumed independence structure can be derived by partial closure, but computationally efficient algorithms still need to be developed for applications to very large graphs.
Covariance Chains
 Bernoulli
, 2006
"... Covariance matrices which can be arranged in tridiagonal form are called covariance chains. They are used to clarify some issues of parameter equivalence and of independence equivalence for linear models in which a set of latent variables influences a set of observed variables. For this purpose, ort ..."
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Cited by 12 (8 self)
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Covariance matrices which can be arranged in tridiagonal form are called covariance chains. They are used to clarify some issues of parameter equivalence and of independence equivalence for linear models in which a set of latent variables influences a set of observed variables. For this purpose, orthogonal decompositions for covariance chains are derived first in explicit form. Covariance chains are also contrasted to concentration chains, for which estimation is explicit and simple. For this purpose, maximumlikelihood equations are derived first for exponential families when some parameters satisfy zero value constraints. From these equations explicit estimates are obtained, which are asymptotically efficient, and they are applied to covariance chains. Simulation results confirm the satisfactory behaviour of the explicit covariance chain estimates also in moderatesize samples.
Matrix representations and independencies in directed acyclic graphs
 Ann. Statist
, 2008
"... For a directed acyclic graph, there are two known criteria to decide whether any specific conditional independence statement is implied for all distributions factorized according to the given graph. Both criteria are based on special types of path in graphs. They are called separation criteria becau ..."
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Cited by 10 (9 self)
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For a directed acyclic graph, there are two known criteria to decide whether any specific conditional independence statement is implied for all distributions factorized according to the given graph. Both criteria are based on special types of path in graphs. They are called separation criteria because independence holds whenever the conditioning set is a separating set in a graph theoretical sense. We introduce and discuss an alternative approach using binary matrix representations of graphs in which zeros indicate independence statements. A matrix condition is shown to give a new path criterion for separation and to be equivalent to each of the previous two path criteria. 1. Introduction. We
Hifh dimensional sparse covariance estimation via directed acyclic graphs
, 2009
"... We present a graphbased technique for estimating sparse covariance matrices and their inverses from highdimensional data. The method is based on learning a directed acyclic graph (DAG) and estimating parameters of a multivariate Gaussian distribution based on a DAG. For inferring the underlying DA ..."
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Cited by 3 (1 self)
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We present a graphbased technique for estimating sparse covariance matrices and their inverses from highdimensional data. The method is based on learning a directed acyclic graph (DAG) and estimating parameters of a multivariate Gaussian distribution based on a DAG. For inferring the underlying DAG we use the PCalgorithm [27] and for estimating the DAGbased covariance matrix and its inverse, we use a Cholesky decomposition approach which provides a positive (semi)definite sparse estimate. We present a consistency result in the highdimensional framework and we compare our method with the Glasso [12, 8, 2] for simulated and real data.
BY NANNY WERMUTH
, 2008
"... Undetected confounding may severely distort the effect of an explanatory variable on a response variable, as defined by a stepwise datagenerating process. The best known type of distortion, which we call direct confounding, arises from an unobserved explanatory variable common to a response and its ..."
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Undetected confounding may severely distort the effect of an explanatory variable on a response variable, as defined by a stepwise datagenerating process. The best known type of distortion, which we call direct confounding, arises from an unobserved explanatory variable common to a response and its main explanatory variable of interest. It is relevant mainly for observational studies, since it is avoided by successful randomization. By contrast, indirect confounding, which we identify in this paper, is an issue also for intervention studies. For general stepwisegenerating processes, we provide matrix and graphical criteria to decide which types of distortion may be present, when they are absent and how they are avoided. We then turn to linear systems without other types of distortion, but with indirect confounding. For such systems, the magnitude of distortion in a leastsquares regression coefficient is derived and shown to be estimable, so that it becomes possible to recover the effect of the generating process from the distorted coefficient.
Matrix representations and independencies in
"... For a directed acyclic graph, there are two known criteria to decide whether any specific conditional independence statement is implied for all distributions factorizing according to the given graph. Both criteria are based on special types of path in graphs. They are called separation criteria beca ..."
Abstract
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For a directed acyclic graph, there are two known criteria to decide whether any specific conditional independence statement is implied for all distributions factorizing according to the given graph. Both criteria are based on special types of path in graphs. They are called separation criteria because independence holds whenever the conditioning set is a separating set in a graph theoretical sense. We introduce and discuss an alternative approach using binary matrix representations of graphs in which zeros indicate independence statements. A matrix condition is shown to give a new path criterion for separation and to be equivalent to each of the previous two path criteria. Key words: Conditional independence, edge matrix, parent graph, partial closure, partial inversion, separation criteria, stepwise data generating process. 1