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43
Skincolor modeling and adaptation
 In Proceedings of ACCV'98 (Technical Report CMUCS97146, CS department, CMU
, 1997
"... Abstract. This paper studies a statistical skincolor model and its adaptation. It is revealed that (1) human skin colors cluster in a small region in a color space; (2) the variance of a skin color cluster can be reduced by intensity normalization, and (3) under a certain lighting condition, a skin ..."
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Cited by 140 (6 self)
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Abstract. This paper studies a statistical skincolor model and its adaptation. It is revealed that (1) human skin colors cluster in a small region in a color space; (2) the variance of a skin color cluster can be reduced by intensity normalization, and (3) under a certain lighting condition, a skincolor distribution can be characterized by amultivariate normal distribution in the normalized color space. We then propose an adaptive model to characterize human skincolor distributions for tracking human faces under di erent lighting conditions. The parameters of the model are adapted based on the maximum likelihood criterion. The model has been successfully applied to a realtime face tracker and other applications. 1
Realtime face and facial feature tracking and applications
 In Proceedings of AuditoryVisual Speech Processing (AVSP 98
, 1998
"... A human face provides a variety of di erent communicative functions. In this paper, we present approaches for realtime face/facial feature tracking and their applications. First, we present techniques of tracking human faces. It is revealed that human skincolor can be used as a major feature for tr ..."
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Cited by 20 (0 self)
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A human face provides a variety of di erent communicative functions. In this paper, we present approaches for realtime face/facial feature tracking and their applications. First, we present techniques of tracking human faces. It is revealed that human skincolor can be used as a major feature for tracking human faces. An adaptive stochastic model has been developed to characterize the skincolor distributions. Based on the maximum likelihood method, the model parameters can be adapted for di erent people and different lighting conditions. The feasibility of the model has been demonstrated by the development of a realtime face tracker. We then present a topdown approach for tracking facial features such as eyes, nostrils, and lip corners. These realtime tracking techniques have been successfully applied to many applications such as eyegaze monitoring, head pose tracking, and lipreading. 1.
When Can Association Graphs Admit A Causal Interpretation?
, 1993
"... This paper provides conditions and procedures for deciding if patterns of independencies found in covariance and concentration matrices can be generated by a stepwise recursive process represented by some directed acyclic graph. If such an agreement is found, we know that one or several causal proce ..."
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Cited by 17 (4 self)
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This paper provides conditions and procedures for deciding if patterns of independencies found in covariance and concentration matrices can be generated by a stepwise recursive process represented by some directed acyclic graph. If such an agreement is found, we know that one or several causal processes could be responsible for the observed independencies, and our procedures could then be used to elucidate the graphical structure common to these processes, so as to evaluate their compatibility against substantive knowledge of the domain. If we find that the observed pattern of independencies does not agree with any stepwise recursive process, then there are a number of different possibilities. For instance,  some weak dependencies could have been mistaken for independencies and led to the wrong omission of edges from the covariance or concentration graphs.  some of the observed linear dependencies reflect accidental cancellations or hide actual nonlinear relations, or  the process responsible for the data is nonrecursive, involving aggregated variables, simultenous reciprocal interactions, or mixtures of several causal processes. In order to recognize accidental independencies it would be helpful to conduct several longitudinal studies under slightly varying conditions. In such studies the covariances for the same set of variables is estimated under different conditions and the variations in the conditions would typically affect the numerical values of the parameters. But, if the data were generated by a causal process represented by some directed acyclic graph, then the basic structural properties reflected in the missing edges of that graph should remain unchanged. Under such assumptions, the pattern of independencies that is "implied" by the dag (see Definitio...
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 ..."
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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.
A new algorithm for maximum likelihood estimation in Gaussian graphical models for marginal independence
 In U. Kjærulff and C. Meek (Eds.), Proceedings of the 19th Conference on Uncertainty in Artificial Intelligence
, 2003
"... Graphical models with bidirected edges (↔) represent marginal independence: the absence of an edge between two vertices indicates that the corresponding variables are marginally independent. In this paper, we consider maximum likelihood estimation in the case of continuous variables with a Gaussian ..."
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Cited by 15 (7 self)
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Graphical models with bidirected edges (↔) represent marginal independence: the absence of an edge between two vertices indicates that the corresponding variables are marginally independent. In this paper, we consider maximum likelihood estimation in the case of continuous variables with a Gaussian joint distribution, sometimes termed a covariance graph model. We present a new fitting algorithm which exploits standard regression techniques and establish its convergence properties. Moreover, we contrast our procedure to existing estimation algorithms. 1
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 13 (9 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.
Computationally Efficient Maximum Likelihood Estimation of Structured Covariance Matrices
 IEEE TRANS. SIGNAL PROCESSING
, 1999
"... By invoking the extended invariance principle (EXIP), we present herein a computationally efficient method that provides asymptotic (for large samples) maximum likelihood (AML) estimation for structured covariance matrices and will be referred to as the AML algorithm. A closedform formula for estim ..."
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Cited by 12 (1 self)
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By invoking the extended invariance principle (EXIP), we present herein a computationally efficient method that provides asymptotic (for large samples) maximum likelihood (AML) estimation for structured covariance matrices and will be referred to as the AML algorithm. A closedform formula for estimating Hermitian Toeplitz covariance matrices that makes AML computationally simpler than most existing Hermitian Toeplitz matrix estimation algorithms is derived. Although the AML covariance matrix estimator can be used in a variety of applications, we focus on array processing in this paper. Our simulation study shows that AML enhances the performances of angle estimation algorithms, such as MUSIC, by making them very close to the corresponding CramérRao bound (CRB) for uncorrelated signals. Numerical comparisons with several structured and unstructured covariance matrix estimators are also presented.
Graphical methods for efficient likelihood inference in gaussian covariance models
 Journal of Machine Learning
, 2008
"... Abstract. In graphical modelling, a bidirected graph encodes marginal independences among random variables that are identified with the vertices of the graph. We show how to transform a bidirected graph into a maximal ancestral graph that (i) represents the same independence structure as the origi ..."
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Cited by 7 (2 self)
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Abstract. In graphical modelling, a bidirected graph encodes marginal independences among random variables that are identified with the vertices of the graph. We show how to transform a bidirected graph into a maximal ancestral graph that (i) represents the same independence structure as the original bidirected 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 bidirected 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. 1.
Penalized MaximumLikelihood Estimation of Covariance Matrices with Linear Structure
 IEEE Trans. Signal Processing
, 1996
"... In this paper, a spacealternating generalized expectationmaximization (SAGE) algorithm is presented for the numerical computation of maximumlikelihood (ML) and penalized maximumlikelihood (PML) estimates of the parameters of covariance matrices with linear structure for complex Gaussian processes ..."
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Cited by 6 (0 self)
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In this paper, a spacealternating generalized expectationmaximization (SAGE) algorithm is presented for the numerical computation of maximumlikelihood (ML) and penalized maximumlikelihood (PML) estimates of the parameters of covariance matrices with linear structure for complex Gaussian processes. By using a less informative hiddendata space and a sequential parameterupdate scheme, a SAGEbased algorithm is derived for which convergence of the likelihood is demonstrated to be significantly faster than that of an EMbased algorithm that has been previously proposed. In addition, the SAGE procedure is shown to easily accommodate penalty functions, and a SAGEbased algorithm is derived and demonstrated for forming PML estimates with a quadratic smoothness penalty.