Analysis of cause-effect inference by comparing regression errors
This addresses the problem of causal inference for researchers in statistics and machine learning, offering an incremental improvement with a simple, applicable method.
The paper tackles the problem of inferring causal direction between two variables by comparing least-squares regression errors in both directions, showing that errors are smaller in the causal direction under specific assumptions, and provides an algorithm that performs competitively with existing methods on artificial and real-world datasets.
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.