Identifying Total Causal Effects in Linear Models under Partial Homoscedasticity

TL;DR

This paper explores how partial homoscedasticity assumptions can help identify total causal effects in linear models from observational data, providing confidence regions and comparing with stricter error assumptions.

Contribution

It extends causal effect identification methods to partial homoscedasticity settings and develops confidence regions under structure uncertainty.

Findings

Partial homoscedasticity enables causal effect identification.

Confidence regions for effects are constructed under model uncertainty.

Stricter error assumptions improve estimation performance in simulations.

Abstract

A fundamental challenge of scientific research is inferring causal relations based on observed data. One commonly used approach involves utilizing structural causal models that postulate noisy functional relations among interacting variables. A directed graph naturally represents these models and reflects the underlying causal structure. However, classical identifiability results suggest that, without conducting additional experiments, this causal graph can only be identified up to a Markov equivalence class of indistinguishable models. Recent research has shown that focusing on linear relations with equal error variances can enable the identification of the causal structure from mere observational data. Nonetheless, practitioners are often primarily interested in the effects of specific interventions, rendering the complete identification of the causal structure unnecessary. In this work, we investigate the extent to which less restrictive assumptions of partial homoscedasticity are sufficient for identifying the causal effects of interest. Furthermore, we construct mathematically rigorous confidence regions for total causal effects under structure uncertainty and explore the performance gain of relying on stricter error assumptions in a simulation study.