We consider the problem of identifying the causal relationships among a set of variables in the presence of both feedback loops and unmeasured confounders. This is a challenging task which, for full identification, typically requires the use of randomized experiments. For linear systems, Eberhardt et al (2010) recently provided a procedure for integrating data from several experiments, and gave a corresponding, but demanding, identifiability condition. In this paper we (i) characterize the underdetermination of the model when the identifiability condition is not fully satisfied, (ii) show that their algorithm is complete with regard to the search space and the assumptions, and (iii) extend the procedure to incorporate the common assumption of faithfulness, and any prior knowledge. The resulting method typically resolves much additional structure and often yields full identification with many fewer experiments. We demonstrate our procedure using simulated data, and apply it to the protein signaling dataset of Sachs et al (2005). 1

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