Towards a Framework for Observational Causality from Time Series: When Shannon Meets Turing

Area of Science:

• Causal inference
• Information theory
• Time series analysis

Background:

• Transfer entropy (TE) quantifies information flow between time series but can obscure complex causal structures.
• Existing methods struggle to differentiate direct and indirect causal associations in multivariate systems.

Purpose of the Study:

• To develop a tensor-based framework for inferring causal structures from time series data.
• To extend the capabilities of causal discovery beyond traditional information-theoretic measures.
• To demonstrate the efficacy of the tensor approach in identifying complex causal relationships.

Main Methods:

• Formulating causal channels as tensors, representing multichannel information transmission.
• Utilizing tensor multiplication to model the cumulative effects of causal cascades.
• Applying information-theoretic analysis to validate the tensor framework.

Main Results:

• The tensor formalism reveals causal structures undetectable by transfer entropy or mutual information alone.
• Bivariate analysis is proven sufficient for inferring causal structure and distinguishing direct/indirect associations in a three-variable system.
• A Data Processing Inequality (DPI) is established for transfer entropy within this framework.

Conclusions:

• Tensor-based methods offer a powerful new approach for advanced causal discovery in time series.
• The framework enhances the interpretability of information flow in complex dynamical systems.
• This work provides theoretical guarantees for causal structure inference using bivariate analysis.