Causal analysis of continuous-valued 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 non-Gaussian models. Here, we show how to combine the non-Gaussian instantaneous model with autoregressive models. We show that such a non-Gaussian 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.

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

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 pseudo-likelihood; 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 log-likelihood L ∗ = ln(P ∗ ) is similar to the single-table BN log-likelihood, 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 log-likelihood of a random instantiation of the 1st-order 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 log-likelihood 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 learn-and-join 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.

Analysis of causal effects between continuous-valued 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 non-Gaussian models. Here, we show how to combine the non-Gaussian instantaneous model with autoregressive models. This is effectively what is called a structural vector autoregression (SVAR) model, and thus our work contributes to the long-standing problem of how to estimate SVAR’s. We show that such a non-Gaussian 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 direct method for estimating a causal ordering

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journal homepage: www.elsevier.com/locate/ynimg Six problems for causal inference from fMRI

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, Gaussian-noise 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

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Independent component analysis is a probabilistic method for learning a linear transform of a random vector. The goal is to find components which are maximally independent and non-Gaussian (non-normal). Its fundamental difference to classical multivariate statistical methods is in the assumption of non-Gaussianity, which enables the identification of original, underlying components, in contrast to classical methods. The basic theory of ICA was mainly developed in the 1990’s and summarized, for example, in our monograph in 2001. Here, we provide an overview of some recent developments in the theory since the year 2000. The main topics are: analysis of causal relations, testing independent components, analysing multiple data sets (three-way data), modelling dependencies between the components, and improved methods for estimating the basic model. Key words: independent component analysis, blind source separation, non-Gaussianity, causal analysis. 1.