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Modeling Discrete Interventional Data using Directed Cyclic Graphical Models
"... We outline a representation for discrete multivariate distributions in terms of interventional potential functions that are globally normalized. This representation can be used to model the effects of interventions, and the independence properties encoded in this model can be represented as a direct ..."
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We outline a representation for discrete multivariate distributions in terms of interventional potential functions that are globally normalized. This representation can be used to model the effects of interventions, and the independence properties encoded in this model can be represented as a directed graph that allows cycles. In addition to discussing inference and sampling with this representation, we give an exponential family parametrization that allows parameter estimation to be stated as a convex optimization problem; we also give a convex relaxation of the task of simultaneous parameter and structure learning using group ℓ1regularization. The model is evaluated on simulated data and intracellular flow cytometry data. 1
Causal Modelling Combining Instantaneous and Lagged Effects: an Identifiable Model Based on NonGaussianity
"... Causal analysis of continuousvalued variables typically uses either autoregressive models or linear Gaussian Bayesian networks with instantaneous effects. Estimation of Gaussian Bayesian networks poses serious identifiability problems, which is why it was recently proposed to use nonGaussian model ..."
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Causal analysis of continuousvalued variables typically uses either autoregressive models or linear Gaussian Bayesian networks with instantaneous effects. Estimation of Gaussian Bayesian networks poses serious identifiability problems, which is why it was recently proposed to use nonGaussian models. Here, we show how to combine the nonGaussian instantaneous model with autoregressive models. We show that such a nonGaussian model is identifiable without prior knowledge of network structure, and we propose an estimation method shown to be consistent. This approach also points out how neglecting instantaneous effects can lead to completely wrong estimates of the autoregressive coefficients. 1.
Estimation of a Structural Vector Autoregression Model Using NonGaussianity
"... Analysis of causal effects between continuousvalued variables typically uses either autoregressive models or structural equation models with instantaneous effects. Estimation of Gaussian, linear structural equation models poses serious identifiability problems, which is why it was recently proposed ..."
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Analysis of causal effects between continuousvalued variables typically uses either autoregressive models or structural equation models with instantaneous effects. Estimation of Gaussian, linear structural equation models poses serious identifiability problems, which is why it was recently proposed to use nonGaussian models. Here, we show how to combine the nonGaussian instantaneous model with autoregressive models. This is effectively what is called a structural vector autoregression (SVAR) model, and thus our work contributes to the longstanding problem of how to estimate SVAR’s. We show that such a nonGaussian model is identifiable without prior knowledge of network structure. We propose computationally efficient methods for estimating the model, as well as methods to assess the significance of the causal influences. The model is successfully applied on financial and brain imaging data.
A Tractable PseudoLikelihood Function for Bayes Nets Applied to Relational Data
"... Bayes nets (BNs) for relational databases are a major research topic in machine learning and artificial intelligence. When the database exhibits cyclic probabilistic dependencies, measuring the fit of a BN model to relational data with a likelihood function is a challenge [5, 36, 28, 9]. A common ap ..."
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Bayes nets (BNs) for relational databases are a major research topic in machine learning and artificial intelligence. When the database exhibits cyclic probabilistic dependencies, measuring the fit of a BN model to relational data with a likelihood function is a challenge [5, 36, 28, 9]. A common approach to difficulties in defining a likelihood function is to employ a pseudolikelihood; a prominent example is the pseudo likelihood defined for Markov Logic Networks (MLNs). This paper proposes a new pseudo likelihood P ∗ for Parametrized Bayes Nets (PBNs) [32] and other relational versions of Bayes nets. The pseudo loglikelihood L ∗ = ln(P ∗ ) is similar to the singletable BN loglikelihood, where row counts in the data table are replaced by frequencies in the database. We introduce a new type of semantics based on the concept of random instantiations (groundings) from classic AI research [12, 1]: The measure L ∗ is the expected loglikelihood of a random instantiation of the 1storder variables in the PBN. The standard moralization method for converting a PBN to an MLN provides another interpretation of L ∗ : the measure is closely related to the loglikelihood and to the pseudo loglikelihood of the moralized PBN. For parameter learning, the L ∗maximizing estimates are the empirical conditional frequencies in the databases. For structure learning, we show that the state of the art learnandjoin method of Khosravi et al. [18] implicitly maximizes the L ∗ measure. The measure provides a theoretical foundation for this algorithm, while the algorithm’s empirical success provides experimental validation for its usefulness.
Structure learning in causal cyclic networks
 In JMLR Workshop and Conference Proceedings
, 2010
"... Cyclic graphical models are unnecessary for accurate representation of joint probability distributions, but are often indispensable when a causal representation of variable relationships is desired. For variables with a cyclic causal dependence structure, DAGs are guaranteed not to recover the corre ..."
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Cyclic graphical models are unnecessary for accurate representation of joint probability distributions, but are often indispensable when a causal representation of variable relationships is desired. For variables with a cyclic causal dependence structure, DAGs are guaranteed not to recover the correct causal structure, and therefore may yield false predictions about the outcomes of perturbations (and even inference.) In this paper, we introduce an approach to generalize Bayesian Network structure learning to structures with cyclic dependence. We introduce a structure learning algorithm, prove its performance given reasonable assumptions, and use simulated data to compare its results to the results of standard Bayesian network structure learning. We then propose a modified, heuristic algorithm with more modest data requirements, and test its performance on a reallife dataset from molecular biology, containing causal, cyclic dependencies. c○2010 S. Itani and M. OhannessianITANI OHANNESSIAN SACHS NOLAN DAHLEH 1.
DirectLiNGAM: A direct method for learning a linear nongaussian structural equation model
 J. of Machine Learning Research
"... ..."
NeuroImage xxx (2009) xxx–xxx Contents lists available at ScienceDirect
"... journal homepage: www.elsevier.com/locate/ynimg Six problems for causal inference from fMRI ..."
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journal homepage: www.elsevier.com/locate/ynimg Six problems for causal inference from fMRI
On Causal Discovery with Cyclic Additive Noise Models
"... We study a particular class of cyclic causal models, where each variable is a (possibly nonlinear) function of its parents and additive noise. We prove that the causal graph of such models is generically identifiable in the bivariate, Gaussiannoise case. We also propose a method to learn such model ..."
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We study a particular class of cyclic causal models, where each variable is a (possibly nonlinear) function of its parents and additive noise. We prove that the causal graph of such models is generically identifiable in the bivariate, Gaussiannoise case. We also propose a method to learn such models from observational data. In the acyclic case, the method reduces to ordinary regression, but in the more challenging cyclic case, an additional term arises in the loss function, which makes it a special case of nonlinear independent component analysis. We illustrate the proposed method on synthetic data. 1