Discovering Mechanistic Causality from Time Series: A Behavioral-System Approach

TL;DR

This paper introduces a control-based causality discovery method called BeCaus, which identifies true mechanistic causality from time series data by leveraging system dynamics and trajectory spaces, overcoming limitations of traditional statistical tests.

Contribution

The paper presents the BeCaus test, a novel control-theoretic approach for causality detection that distinguishes causal structures and handles unobserved inputs in complex systems.

Findings

The BeCaus test can distinguish independence, causality, and latent causes in linear systems.

Conditions for causality discoverability in linear time-invariant systems are established.

Preliminary case study suggests potential for extending the method to nonlinear systems.

Abstract

Identifying ``true causality'' is a fundamental challenge in complex systems research. Widely adopted methods, like the Granger causality test, capture statistical dependencies between variables rather than genuine driver-response mechanisms. This critical gap stems from the absence of mathematical tools that reliably reconstruct underlying system dynamics from observational time-series data. In this paper, we introduce a new control-based method for causality discovery through the behavior-system theory, which represents dynamical systems via trajectory spaces and has been widely used in data-driven control. Our core contribution is the \textbf{B}ehavior-\textbf{e}nabled \textbf{Caus}ality test (the BeCaus test), which transforms causality discovery into solving fictitious control problems. By exploiting the intrinsic asymmetry between system inputs and outputs, the proposed method operationalizes our conceptualization of mechanistic causality: variable $X$ is a cause of $Y$ if $X$ (partially) drives the evolution of $Y$. We establish conditions for linear time-invariant systems to be causality-discoverable, i.e., conditions for the BeCaus test to distinguish four basic causal structures (independence, full causality, partial causality, and latent-common-cause relation). Notably, our approach accommodates open systems with unobserved inputs. Moreover, an exploratory case study indicates the new method's potential extensibility to nonlinear systems.