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15
Algebraic factor analysis: tetrads, pentads and beyond
, 2008
"... Factor analysis refers to a statistical model in which observed variables are conditionally independent given fewer hidden variables, known as factors, and all the random variables follow a multivariate normal distribution. The parameter space of a factor analysis model is a subset of the cone of po ..."
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Cited by 42 (13 self)
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Factor analysis refers to a statistical model in which observed variables are conditionally independent given fewer hidden variables, known as factors, and all the random variables follow a multivariate normal distribution. The parameter space of a factor analysis model is a subset of the cone of positive definite matrices. This parameter space is studied from the perspective of computational algebraic geometry. Gröbner bases and resultants are applied to compute the ideal of all polynomial functions that vanish on the parameter space. These polynomials, known as model invariants, arise from rank conditions on a symmetric matrix under elimination of the diagonal entries of the matrix. Besides revealing the geometry of the factor analysis model, the model invariants also furnish useful statistics for testing goodnessoffit.
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 24 (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.
Adjusted empirical likelihood and its properties
 Journal of Computational and Graphical Statistics
, 2008
"... Computing profile empirical likelihood function is a key step in applications of empirical likelihood which involves constrained maximization. However, in some situations, solutions to the corresponding constraints may not exist. In this case, the convention is to assign a zero value to the profile ..."
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Cited by 18 (2 self)
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Computing profile empirical likelihood function is a key step in applications of empirical likelihood which involves constrained maximization. However, in some situations, solutions to the corresponding constraints may not exist. In this case, the convention is to assign a zero value to the profile empirical likelihood. This convention has at least two limitations. First, it is numerically difficult to determine the nonexistence of any solution; Second, it provides no information on the relative plausibility of these parameter values. In this paper, we use a novel adjustment to the empirical likelihood so that the new method retains all the optimal properties, while guarantees a sensible value at any parameter point. Coupled with this adjustment, we introduce an iterative algorithm with guaranteed convergence. Our simulation indicates that the adjusted empirical likelihood is much faster to compute. The confidence regions constructed via the adjusted empirical likelihood are found to have closer to nominal coverage probabilities without resorting to more complex procedures such as Bartlett correction or bootstrap caliberation. Through some application examples, the method is also shown to be very effective in solving some practical problems associated with the use of empirical likelihood. Some key words: Algorithm, confidence region, constrained maximization, coverage probability, variable selection. 1
On identifying total effects in the presence of latent variables and selection bias
 In Uncertainty in Artificial Intelligence, Proceedings of the TwentyFourth Conference (D. McAllester and
, 2008
"... Assume that causeeffect relationships between variables can be described as a directed acyclic graph and the corresponding linear structural equation model．We consider the identification problem of total effects in the presence of latent variables and selection bias between a treatment variable an ..."
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Cited by 14 (4 self)
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Assume that causeeffect relationships between variables can be described as a directed acyclic graph and the corresponding linear structural equation model．We consider the identification problem of total effects in the presence of latent variables and selection bias between a treatment variable and a response variable. Pearl and his colleagues provided the back door criterion, the front door criterion (Pearl, 2000) and the conditional instrumental variable method (Brito and Pearl, 2002) as identifiability criteria for total effects in the presence of latent variables, but not in the presence of selection bias. In order to solve this problem, we propose new graphical identifiability criteria for total effects based on the identifiable factor models. The results of this paper are useful to identify total effects in observational studies and provide a new viewpoint to the identification conditions of factor models. 1
Wishart distributions for decomposable covariance graph models, Ann. Statist
, 2010
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A MCMC Approach for Learning the Structure of Gaussian Acyclic Directed Mixed Graphs
"... Abstract Graphical models are widely used to encode conditional independence constraints and causal assumptions, the directed acyclic graph (DAG) being one of the most common types of models. However, DAGs are not closed under marginalization: that is, a chosen marginal of a distribution Markov to a ..."
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Abstract Graphical models are widely used to encode conditional independence constraints and causal assumptions, the directed acyclic graph (DAG) being one of the most common types of models. However, DAGs are not closed under marginalization: that is, a chosen marginal of a distribution Markov to a DAG might not be representable with another DAG, unless one discards some of the structural independencies. Acyclic directed mixed graphs (ADMGs) generalize DAGs so that closure under marginalization is possible. In a previous work, we showed how to perform Bayesian inference to infer the posterior distribution of the parameters of a given Gaussian ADMG model, where the graph is fixed. In this paper, we extend this procedure to allow for priors over graph structures.
The Effect Restoration from Measurement Bias in Causal Inference
"... This paper highlights several areas where graphical techniques can be harnessed to address the problem of measurement errors in causal inference. In particulars,the paper discusses the control of partially observable confounders in parametric and non parametric models and the computational problem o ..."
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This paper highlights several areas where graphical techniques can be harnessed to address the problem of measurement errors in causal inference. In particulars,the paper discusses the control of partially observable confounders in parametric and non parametric models and the computational problem of obtaining biasfree effect estimates in such models.
The Graphical Identification for Total Effects by using Surrogate Variables
"... Consider the case where causeeffect relationships between variables can be described as a directed acyclic graph and the corresponding linear structural equation model. This paper provides graphical identifiability criteria for total effects by using surrogate variables in the case where it is dif ..."
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Consider the case where causeeffect relationships between variables can be described as a directed acyclic graph and the corresponding linear structural equation model. This paper provides graphical identifiability criteria for total effects by using surrogate variables in the case where it is difficult to observe a treatment/response variable. The results enable us to judge from graph structure whether a total effect can be identified through the observation of surrogate variables. 1
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"... Graphical identifiability criteria for causal effects in studies with an unobserved treatment/response variable ..."
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Graphical identifiability criteria for causal effects in studies with an unobserved treatment/response variable
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"... On recovering a population covariance matrix in the presence of selection bias ..."
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On recovering a population covariance matrix in the presence of selection bias