Core Concepts
PEACE function measures direct causal effects under interventions.
Abstract
The content introduces the Probabilistic Easy Variational Causal Effect (PEACE) function for understanding causal inference. It discusses the application of PEACE to measure direct causal effects in continuous and discrete cases, emphasizing its stability and identifiability criteria. The paper also explores the relationship between divergence, total variation, and PEACE, providing insights into causality through mathematical formulations.
Structure:
Introduction to Causal Reasoning's Role in Human Cognition.
Frameworks in Causal Reasoning: Rubin-Neyman, Pearl, Janzing et al.
Development of a New Generic Causal Framework using Total Variation Concept.
Discussion on Rare Situations and Direct Causal Effects.
Definition and Properties of Probabilistic Easy Variationoal Causal Effect (PEACE).
Generalization of PEACE for Discrete Random Vectors.
Identifiability Criteria and Examples Demonstrating PEACE's Capability.
Stability of PEACE under Small Changes in Joint Distribution.
Extension of PEACE to Positive and Negative Direct Causal Effects.
Conclusion and Examples Supporting the PEACE Framework.
Key Highlights:
Introduction to causal reasoning importance in human cognition.
Comparison of different causal reasoning frameworks like Rubin-Neyman, Pearl, Janzing et al.
Development of a new generic causal framework based on total variation concept.
Stats
"PEACEd(X → Y ) := EZ (NPIEVz d(X → Y ))"
"NPIEVz d(X → Y ) := 4d Σl i=1 |gin(xi, z) − gin(xi−1, z)|P(xi|z)dP(xi−1|z)d"