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It is generally difficult to make any statements about the expectedprediction error in an univariate setting without further knowledge about howthe data were generated. Recent work showed that knowledge about the realunderlying causal structure of a data generation process has implications forvarious machine learning settings. Assuming an additive noise and anindependence between data generating mechanism and its input, we draw a novelconnection between the intrinsic causal relationship of two variables and theexpected prediction error. We formulate the theorem that the expected error ofthe true data generating function as prediction model is generally smaller whenthe effect is predicted from its cause and, on the contrary, greater when thecause is predicted from its effect. The theorem implies an asymmetry in theerror depending on the prediction direction. This is further corroborated withempirical evaluations in artificial and real-world data sets.

Error Asymmetry in Causal and Anticausal Regression