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147
A linear nongaussian acyclic model for causal discovery
 J. Machine Learning Research
, 2006
"... In recent years, several methods have been proposed for the discovery of causal structure from nonexperimental data. Such methods make various assumptions on the data generating process to facilitate its identification from purely observational data. Continuing this line of research, we show how to ..."
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Cited by 101 (28 self)
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In recent years, several methods have been proposed for the discovery of causal structure from nonexperimental data. Such methods make various assumptions on the data generating process to facilitate its identification from purely observational data. Continuing this line of research, we show how to discover the complete causal structure of continuousvalued data, under the assumptions that (a) the data generating process is linear, (b) there are no unobserved confounders, and (c) disturbance variables have nonGaussian distributions of nonzero variances. The solution relies on the use of the statistical method known as independent component analysis, and does not require any prespecified timeordering of the variables. We provide a complete Matlab package for performing this LiNGAM analysis (short for Linear NonGaussian Acyclic Model), and demonstrate the effectiveness of the method using artificially generated data and realworld data.
A Bayesian Approach to Causal Discovery
, 1997
"... We examine the Bayesian approach to the discovery of directed acyclic causal models and compare it to the constraintbased approach. Both approaches rely on the Causal Markov assumption, but the two differ significantly in theory and practice. An important difference between the approaches is that t ..."
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Cited by 100 (1 self)
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We examine the Bayesian approach to the discovery of directed acyclic causal models and compare it to the constraintbased approach. Both approaches rely on the Causal Markov assumption, but the two differ significantly in theory and practice. An important difference between the approaches is that the constraintbased approach uses categorical information about conditionalindependence constraints in the domain, whereas the Bayesian approach weighs the degree to which such constraints hold. As a result, the Bayesian approach has three distinct advantages over its constraintbased counterpart. One, conclusions derived from the Bayesian approach are not susceptible to incorrect categorical decisions about independence facts that can occur with data sets of finite size. Two, using the Bayesian approach, finer distinctions among model structuresboth quantitative and qualitativecan be made. Three, information from several models can be combined to make better inferences and to better ...
Nonlinear causal discovery with additive noise models
"... The discovery of causal relationships between a set of observed variables is a fundamental problem in science. For continuousvalued data linear acyclic causal models with additive noise are often used because these models are well understood and there are wellknown methods to fit them to data. In ..."
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Cited by 78 (30 self)
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The discovery of causal relationships between a set of observed variables is a fundamental problem in science. For continuousvalued data linear acyclic causal models with additive noise are often used because these models are well understood and there are wellknown methods to fit them to data. In reality, of course, many causal relationships are more or less nonlinear, raising some doubts as to the applicability and usefulness of purely linear methods. In this contribution we show that in fact the basic linear framework can be generalized to nonlinear models. In this extended framework, nonlinearities in the datagenerating process are in fact a blessing rather than a curse, as they typically provide information on the underlying causal system and allow more aspects of the true datagenerating mechanisms to be identified. In addition to theoretical results we show simulations and some simple real data experiments illustrating the identification power provided by nonlinearities. 1
Stratified exponential families: Graphical models and model selection
 ANNALS OF STATISTICS
, 2001
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A probabilistic model for componentbased shape synthesis
 ACM Transactions on Graphics
, 2012
"... We present an approach to synthesizing shapes from complex domains, by identifying new plausible combinations of components from existing shapes. Our primary contribution is a new generative model of componentbased shape structure. The model represents probabilistic relationships between properties ..."
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Cited by 58 (8 self)
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We present an approach to synthesizing shapes from complex domains, by identifying new plausible combinations of components from existing shapes. Our primary contribution is a new generative model of componentbased shape structure. The model represents probabilistic relationships between properties of shape components, and relates them to learned underlying causes of structural variability within the domain. These causes are treated as latent variables, leading to a compact representation that can be effectively learned without supervision from a set of compatibly segmented shapes. We evaluate the model on a number of shape datasets with complex structural variability and demonstrate its application to amplification of shape databases and to interactive shape synthesis.
Optimization by learning and simulation of Bayesian and Gaussian networks
, 1999
"... Estimation of Distribution Algorithms (EDA) constitute an example of stochastics heuristics based on populations of individuals every of which encode the possible solutions to the optimization problem. These populations of individuals evolve in succesive generations as the search progresses  organ ..."
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Cited by 54 (7 self)
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Estimation of Distribution Algorithms (EDA) constitute an example of stochastics heuristics based on populations of individuals every of which encode the possible solutions to the optimization problem. These populations of individuals evolve in succesive generations as the search progresses  organized in the same way as most evolutionary computation heuristics. In opposition to most evolutionary computation paradigms which consider the crossing and mutation operators as essential tools to generate new populations, EDA replaces those operators by the estimation and simulation of the joint probability distribution of the selected individuals. In this work, after making a review of the different approaches based on EDA for problems of combinatorial optimization as well as for problems of optimization in continuous domains, we propose new approaches based on the theory of probabilistic graphical models to solve problems in both domains. More precisely, we propose to adapt algorit...
Learning Bayesian Networks: A unification for discrete and Gaussian domains
 PROCEEDINGS OF ELEVENTH CONFERENCE ON UNCERTAINTY INARTI CIAL INTELLIGENCE
, 1995
"... We examine Bayesian methods for learning Bayesian networks from a combination of prior knowledge and statistical data. In particular, we unify the approaches we presented at last year's conference for discrete and Gaussian domains. We derive a general Bayesian scoring metric, appropriate for bo ..."
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Cited by 53 (5 self)
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We examine Bayesian methods for learning Bayesian networks from a combination of prior knowledge and statistical data. In particular, we unify the approaches we presented at last year's conference for discrete and Gaussian domains. We derive a general Bayesian scoring metric, appropriate for both domains. We then use this metric in combination with wellknown statistical facts about the Dirichlet and normal{Wishart distributions to derive our metrics for discrete and Gaussian domains.
Learning Bayesian networks with the bnlearn R package
 Journal of Statistical Software
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Bayesian Network Analysis of Signaling Networks: A Primer
, 2005
"... Highthroughput proteomic data can be used to reveal the connectivity of signaling networks and the influences between signaling molecules. We present a primer on the use of Bayesian networks for this task. Bayesian networks have been successfully used to derive causal influences among biological si ..."
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Cited by 44 (0 self)
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Highthroughput proteomic data can be used to reveal the connectivity of signaling networks and the influences between signaling molecules. We present a primer on the use of Bayesian networks for this task. Bayesian networks have been successfully used to derive causal influences among biological signaling molecules (for example, in the analysis of intracellular multicolor flow cytometry). We discuss ways to automatically derive a Bayesian network model from proteomic data and to interpret the resulting model.
Bayesian Estimation and Testing of Structural Equation Models
 Psychometrika
, 1999
"... The Gibbs sampler can be used to obtain samples of arbitrary size from the posterior distribution over the parameters of a structural equation model (SEM) given covariance data and a prior distribution over the parameters. Point estimates, standard deviations and interval estimates for the parameter ..."
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Cited by 43 (10 self)
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The Gibbs sampler can be used to obtain samples of arbitrary size from the posterior distribution over the parameters of a structural equation model (SEM) given covariance data and a prior distribution over the parameters. Point estimates, standard deviations and interval estimates for the parameters can be computed from these samples. If the prior distribution over the parameters is uninformative, the posterior is proportional to the likelihood, and asymptotically the inferences based on the Gibbs sample are the same as those based on the maximum likelihood solution, e.g., output from LISREL or EQS. In small samples, however, the likelihood surface is not Gaussian and in some cases contains local maxima. Nevertheless, the Gibbs sample comes from the correct posterior distribution over the parameters regardless of the sample size and the shape of the likelihood surface. With an informative prior distribution over the parameters, the posterior can be used to make inferences about the parameters of underidentified models, as we illustrate on a simple errorsinvariables model.