Sparse Identification of Conditional relationships in Structural Causal Models (SICrSCM) for counterfactual inference

Abstract

Causal models are an essential part of engineering. Physics-based causal models such as Finite Element Models, are prevalent in engineering. However, with the availability of large quantities of sensor data, data-driven causal models are much needed. A major challenge with causal models is capturing complex functional forms and maintaining the interpretability of causal relationships.In this work, an elegant method for automating the selection of the functional form of causal relationships is proposed in the context of counterfactual inference. Sparse Identification of Conditional relationships in Structural Causal Models (SICrSCM) is based on two primary ingredients: a sensible library of basis functions and sparsity to enforce interpretability. The authors propose learning the conditional relationships in a Structural Causal Model (SCM) using a library of candidate polynomial basis functions and enforcing sparsity through Lasso regression to identify essential functions from the library. Under the abduction, intervention and prediction paradigm for counterfactual inference, it is shown that the consequence of finding good approximators is that inference under partial evidence becomes possible when the root nodes of the DAG are observed.The method is illustrated on a simple conceptual example to clearly show the proposed method’s counterfactual inference process and performance. A bridge is built between engineering and statistics by having an intuitive problem, making the concepts accessible for statisticians and engineers.