Direct and Indirect Effects -- An Information Theoretic Perspective

TL;DR

This paper introduces new information theoretic measures for quantifying direct, indirect, and total causal effects that can be applied to specific cause values, demonstrated through climate data analysis.

Contribution

It presents novel IT-based causal effect measures that are value-specific and applicable across various domains, with proven identifiability and practical application.

Findings

Proposed measures enable value-specific causal effect estimation.

Application to climate data illustrates measure effectiveness.

Measures are theoretically grounded with an identifiability result.

Abstract

Information theoretic (IT) approaches to quantifying causal influences have experienced some popularity in the literature, in both theoretical and applied (e.g. neuroscience and climate science) domains. While these causal measures are desirable in that they are model agnostic and can capture non-linear interactions, they are fundamentally different from common statistical notions of causal influence in that they (1) compare distributions over the effect rather than values of the effect and (2) are defined with respect to random variables representing a cause rather than specific values of a cause. We here present IT measures of direct, indirect, and total causal effects. The proposed measures are unlike existing IT techniques in that they enable measuring causal effects that are defined with respect to specific values of a cause while still offering the flexibility and general applicability of IT techniques. We provide an identifiability result and demonstrate application of the proposed measures in estimating the causal effect of the El Ni\~no-Southern Oscillation on temperature anomalies in the North American Pacific Northwest.