  We propose a method for learning cyclic causal models from a combination of
observational and interventional equilibrium data. Novel aspects of the
proposed method are its ability to work with continuous data (without assuming
linearity) and to deal with feedback loops. Within the context of biochemical
reactions, we also propose a novel way of modeling interventions that modify
the activity of compounds instead of their abundance. For computational
reasons, we approximate the nonlinear causal mechanisms by (coupled) local
linearizations, one for each experimental condition. We apply the method to
reconstruct a cellular signaling network from the flow cytometry data measured
by Sachs et al. (2005). We show that our method finds evidence in the data for
feedback loops and that it gives a more accurate quantitative description of
the data at comparable model complexity.
