Unexplained Mutual Information: The Robust Tool for Causal Inference in Small Sample Sizes and Outlier-Prone Data

Overview & Synopsis

This study introduces a novel approach to analyzing causality and information flow in complex systems, with a focus on Gaussian linear models. We propose the "unexplained mutual information" (UMI) measure, which quantifies the strength and direction of the relationship between the residuals and the dependent variable. Leveraging UMI, we develop an innovative bidirectional causality test capable of detecting and validating bidirectional causal links -a significant advancement in causal inference techniques. Through extensive empirical evaluation across various vector autoregressive (VAR) models, including those with trends and seasonal components, we demonstrate the effectiveness of our bidirectional causality test. Notably, the test exhibits robust performance even with small time series datasets containing up to 30% outlier observations, making it particularly valuable for practitioners working with limited data. Our research highlights the versatility of UMI as a reliable tool for causality testing, proving its resilience against the presence of outliers in time series data. The proposed methods open up new avenues for uncovering intricate causal patterns within intricate systems, advancing the field of causal inference.