Causal discovery with endogenous context variables

TL;DR

This paper introduces a new causal discovery method for systems with endogenous context variables, addressing the limitations of naive approaches and providing a sound, causally interpretable algorithm validated by numerical experiments.

Contribution

It proposes an adaptive constraint-based causal discovery algorithm for endogenous context variables, with theoretical soundness and practical validation.

Findings

Naive methods can produce uninformative results in endogenous context settings.

The proposed algorithm outperforms baseline methods in experiments.

Current limitations of the method are identified and discussed.

Abstract

Causal systems often exhibit variations of the underlying causal mechanisms between the variables of the system. Often, these changes are driven by different environments or internal states in which the system operates, and we refer to context variables as those variables that indicate this change in causal mechanisms. An example are the causal relations in soil moisture-temperature interactions and their dependence on soil moisture regimes: Dry soil triggers a dependence of soil moisture on latent heat, while environments with wet soil do not feature such a feedback, making it a context-specific property. Crucially, a regime or context variable such as soil moisture need not be exogenous and can be influenced by the dynamical system variables - precipitation can make a dry soil wet - leading to joint systems with endogenous context variables. In this work we investigate the assumptions for constraint-based causal discovery of context-specific information in systems with endogenous context variables. We show that naive approaches such as learning different regime graphs on masked data, or pooling all data, can lead to uninformative results. We propose an adaptive constraint-based discovery algorithm and give a detailed discussion on the connection to structural causal models, including sufficiency assumptions, which allow to prove the soundness of our algorithm and to interpret the results causally. Numerical experiments demonstrate the performance of the proposed method over alternative baselines, but they also unveil current limitations of our method.