Interpretable, multi-dimensional Evaluation Framework for Causal Discovery from observational i.i.d. Data (2409.19377v2)

Abstract: Nonlinear causal discovery from observational data imposes strict identifiability assumptions on the formulation of structural equations utilized in the data generating process. The evaluation of structure learning methods under assumption violations requires a rigorous and interpretable approach, which quantifies both the structural similarity of the estimation with the ground truth and the capacity of the discovered graphs to be used for causal inference. Motivated by the lack of unified performance assessment framework, we introduce an interpretable, six-dimensional evaluation metric, i.e., distance to optimal solution (DOS), which is specifically tailored to the field of causal discovery. Furthermore, this is the first research to assess the performance of structure learning algorithms from seven different families on increasing percentage of non-identifiable, nonlinear causal patterns, inspired by real-world processes. Our large-scale simulation study, which incorporates seven experimental factors, shows that besides causal order-based methods, amortized causal discovery delivers results with comparatively high proximity to the optimal solution.

• The paper introduces DOS, a composite metric that integrates six performance indicators to measure the accuracy of causal structure estimation.
• The paper conducts comprehensive sensitivity analyses, revealing how methods like AVICI perform robustly under varied experimental conditions and nonlinear challenges.
• The paper’s framework enhances the interpretability and comparability of causal discovery models, offering actionable insights for applications in economics, healthcare, and more.

An Interpretative Evaluation Framework for Causal Discovery from i.i.d. Data

The paper, "How much do we really know about Structure Learning from observational i.i.d. Data? An interpretable, multi-dimensional Evaluation Framework for Causal Discovery," authored by Georg Velev and Stefan Lessmann, provides an in-depth evaluation of causal discovery techniques using a comprehensive and interpretable framework. The focus on nonlinear causal discovery from observational data addresses the stringent identifiability assumptions that are often required in structural equations. This research is conducted within the context of a well-defined simulation framework, considering a variety of experimental factors, and culminates in the introduction of a novel, multi-dimensional evaluation metric called Distance to Optimal Solution (DOS).

Theoretical Foundation and Methodological Contributions

The authors emphasize the importance of causal discovery from observational data for modeling interventional queries and counterfactual outcomes, which have significant implications across fields such as politics, economics, and healthcare. The paper starts by elucidating the theoretical background necessary for understanding the structure learning problem in causal inference, including directed acyclic graphs (DAGs), conditional independence (CI) relations, and causal graphical models (CGMs).

Velev and Lessmann meticulously review existing causal structure learning (CSL) methods and provide a taxonomy that distinguishes combinatorial optimization approaches from continuous optimization techniques. By implementing a large-scale sensitivity analysis on CSL models, the paper explores performance variations under different scenarios, covering aspects such as graph types (ER and SF models), sample sizes, node scales, connectivity, and nonlinear transformations.

Evaluation Framework

One of the key contributions is the introduction of the DOS metric. DOS is derived from six performance indicators: Structural Hamming Distance (SHD), False Positive Rate (FPR), True Positive Rate (TPR), Causal Order Divergence (COD), Structural Intervention Distance (SID), and F1 score. This interpretable metric encapsulates the proximity of the estimated causal structure to the ground truth, integrating multiple facets of performance evaluation into a single composite score.

A notable aspect of the DOS metric is its alignment with TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) from Multi-Criteria Decision Making (MCDM). By normalizing indicators to a common scale [0,1], the DOS metric improves interpretability and facilitates straightforward comparative analysis.

Implications and Sensitivity Analysis

The sensitivity analysis conducted using the Explainable Boosting Machine (EBM) reveals intriguing insights:

• $R^2$-SortnRegress and AVICI are identified as the most robust methods across multiple scenarios.
• Interaction effects play a critical role in real-world applications, notably the scale of the data, which interacts significantly with other factors such as node size and graph connectivity.
• The robustness of amortized variational inference (AVICI) in practical scenarios, especially when dealing with unknown nonlinear causal mechanisms, is highlighted.

The research underscores the significance of normalizing real-world datasets to address issues such as varsortability. It also notes that hybrid bayesian networks, often overlooked in recent studies, display superior performance compared to some contemporary continuous optimization models in causal discovery tasks.

Future Directions and Conclusion

By identifying gaps in current benchmarks, particularly concerning the lack of evaluation frameworks incorporating non-identifiable nonlinear transformations, Velev and Lessmann emphasize the necessity for comprehensive evaluation metrics like DOS. They advocate for further research on hybrid models and suggest extending the DOS framework to real-time data to provide a more thorough evaluation.

In summary, this paper advances the field of causal discovery by providing a rigorous and interpretable evaluation framework. It establishes a robust method to assess CSL techniques across varied scenarios, making a significant step towards more reliable and practical applications of causal inference in diverse domains.