On Causal Discovery with Cyclic Additive Noise Models

Part of Advances in Neural Information Processing Systems 24 (NIPS 2011)

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Joris M. Mooij, Dominik Janzing, Tom Heskes, Bernhard Schölkopf


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.