Given data sampled from a number of variables, one is often interested in theunderlying causal relationships in the form of a directed acyclic graph. In thegeneral case, without interventions on some of the variables it is onlypossible to identify the graph up to its Markov equivalence class. However, insome situations one can find the true causal graph just from observationaldata, for example in structural equation models with additive noise andnonlinear edge functions. Most current methods for achieving this rely onnonparametric independence tests. One of the problems there is that the nullhypothesis is independence, which is what one would like to get evidence for.We take a different approach in our work by using a penalized likelihood as ascore for model selection. This is practically feasible in many settings andhas the advantage of yielding a natural ranking of the candidate models. Whenmaking smoothness assumptions on the probability density space, we proveconsistency of the penalized maximum likelihood estimator. We also presentempirical results for simulated scenarios and real two-dimensional data sets(cause-effect pairs) where we obtain similar results as other state-of-the-artmethods.
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