Direct and Indirect Effects – An Information Theoretic Perspective
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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, and they are unlike existing statistical measures in that they do not involve comparison with a reference (or baseline) value. In addition to endowing IT approaches with an enhanced "resolution", the proposed framework uniquely elucidates the relationship between the IT and statistical perspectives on causality. We provide an identifiability result and demonstrate application of the proposed measures in estimating the causal effect of the El Niño-Southern Oscillation on temperature anomalies in the North American Pacific Northwest.
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