Identification of Possible Common Causes by Intrinsic Dimension Estimation

Abstract

The effect of confounding factors cannot be ignored in real world causal discovery tasks. A common cause is a general confounder between two variables. In this paper, we propose using intrinsic dimension estimation as a necessary condition to determine a possible common cause for two variables. Simulated application showed that the proposed method worked well for both linear and non-linear functions. Testing using different types of noise showed that it generally worked well for different types of added noise. In particular, it worked better than a kernel-based conditional independence test for Poisson noise. Testing of how the estimated intrinsic dimension is affected by different types of distributions showed that the estimated dimension is nearly not affected by the type of distribution. Simulation of mixed pattern showed that the proposed method can still tell a possible common cause when it is mixed with causal relationship. Finally, experiments using variables from the CauseEffectPairs dataset showed that the proposed method can give correct inferred results for real world data.Index Terms-common cause identification, intrinsic dimension, conditional independence test