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.

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

A principal aim of many sciences is to model causal systems well enough to provide insight into their structures and mechanisms and to provide reliable predictions about the effects of policy interventions. To

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