Analysis of cause-effect inference by comparing regression errors
  We address the problem of inferring the causal direction between two
variables by comparing the least-squares errors of the predictions in both
possible directions. Under the assumption of an independence between the
function relating cause and effect, the conditional noise distribution, and the
distribution of the cause, we show that the errors are smaller in causal
direction if both variables are equally scaled and the causal relation is close
to deterministic. Based on this, we provide an easily applicable algorithm that
only requires a regression in both possible causal directions and a comparison
of the errors. The performance of the algorithm is compared with various
related causal inference methods in different artificial and real-world data
sets.
