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REX: Causal discovery based on machine learning and explainability techniques

Jesus Renero, Idoia Ochoa, Roberto Maestre

TL;DR

ReX addresses the challenge of causal discovery by integrating machine-learning predictors with Shapley-value explainability to guide the reconstruction of causal graphs under the Causal Markov Condition and faithfulness. The method trains two regressor families (DFN and GBT) to predict each variable from the rest, derives SHAP-based parent sets, bootstraps to stabilize the undirected graph, orients edges via Additive Noise Models and HSIC, and resolves cycles using a SHAP-discrepancy criterion. Across five synthetic data families and real-world datasets (Sachs and finance), ReX achieves high precision and F1 while maintaining low SHD and SID, often outperforming standard causal-discovery baselines. The approach provides interpretable insights by tying feature contributions to potential causal relations and demonstrates robustness to non-linearities and multicollinearity, albeit with substantial computational cost due to SHAP. The work suggests promising directions for scalable SHAP-based causal discovery, including alternative regressors, distributional shift handling, and broader domain applications, with code and data openly available.

Abstract

Explainable Artificial Intelligence (XAI) techniques hold significant potential for enhancing the causal discovery process, which is crucial for understanding complex systems in areas like healthcare, economics, and artificial intelligence. However, no causal discovery methods currently incorporate explainability into their models to derive the causal graphs. Thus, in this paper we explore this innovative approach, as it offers substantial potential and represents a promising new direction worth investigating. Specifically, we introduce ReX, a causal discovery method that leverages machine learning (ML) models coupled with explainability techniques, specifically Shapley values, to identify and interpret significant causal relationships among variables. Comparative evaluations on synthetic datasets comprising continuous tabular data reveal that ReX outperforms state-of-the-art causal discovery methods across diverse data generation processes, including non-linear and additive noise models. Moreover, ReX was tested on the Sachs single-cell protein-signaling dataset, achieving a precision of 0.952 and recovering key causal relationships with no incorrect edges. Taking together, these results showcase ReX's effectiveness in accurately recovering true causal structures while minimizing false positive predictions, its robustness across diverse datasets, and its applicability to real-world problems. By combining ML and explainability techniques with causal discovery, ReX bridges the gap between predictive modeling and causal inference, offering an effective tool for understanding complex causal structures.

REX: Causal discovery based on machine learning and explainability techniques

TL;DR

ReX addresses the challenge of causal discovery by integrating machine-learning predictors with Shapley-value explainability to guide the reconstruction of causal graphs under the Causal Markov Condition and faithfulness. The method trains two regressor families (DFN and GBT) to predict each variable from the rest, derives SHAP-based parent sets, bootstraps to stabilize the undirected graph, orients edges via Additive Noise Models and HSIC, and resolves cycles using a SHAP-discrepancy criterion. Across five synthetic data families and real-world datasets (Sachs and finance), ReX achieves high precision and F1 while maintaining low SHD and SID, often outperforming standard causal-discovery baselines. The approach provides interpretable insights by tying feature contributions to potential causal relations and demonstrates robustness to non-linearities and multicollinearity, albeit with substantial computational cost due to SHAP. The work suggests promising directions for scalable SHAP-based causal discovery, including alternative regressors, distributional shift handling, and broader domain applications, with code and data openly available.

Abstract

Explainable Artificial Intelligence (XAI) techniques hold significant potential for enhancing the causal discovery process, which is crucial for understanding complex systems in areas like healthcare, economics, and artificial intelligence. However, no causal discovery methods currently incorporate explainability into their models to derive the causal graphs. Thus, in this paper we explore this innovative approach, as it offers substantial potential and represents a promising new direction worth investigating. Specifically, we introduce ReX, a causal discovery method that leverages machine learning (ML) models coupled with explainability techniques, specifically Shapley values, to identify and interpret significant causal relationships among variables. Comparative evaluations on synthetic datasets comprising continuous tabular data reveal that ReX outperforms state-of-the-art causal discovery methods across diverse data generation processes, including non-linear and additive noise models. Moreover, ReX was tested on the Sachs single-cell protein-signaling dataset, achieving a precision of 0.952 and recovering key causal relationships with no incorrect edges. Taking together, these results showcase ReX's effectiveness in accurately recovering true causal structures while minimizing false positive predictions, its robustness across diverse datasets, and its applicability to real-world problems. By combining ML and explainability techniques with causal discovery, ReX bridges the gap between predictive modeling and causal inference, offering an effective tool for understanding complex causal structures.
Paper Structure (51 sections, 14 equations, 14 figures, 5 tables, 2 algorithms)

This paper contains 51 sections, 14 equations, 14 figures, 5 tables, 2 algorithms.

Figures (14)

  • Figure 1: Overview of the ReX workflow. The process begins with training regressors (Section \ref{['s:Models-training']}), followed by a bootstrapping procedure (Algorithm \ref{['alg:dag-construction']}) that includes data sampling, computation of SHAP values ($\phi$) to assess feature impact (Section \ref{['ss:computing-shap-values-for-feature-impact']}), selection of candidate parents based on these values (Algorithm \ref{['alg:parent-selection']}, Section \ref{['ss:parents-selection']}), and updating the adjacency matrix (Section \ref{['ss:adjacency-matrix-update']}). Edges are then oriented (Section \ref{['ss:directing-edges']}), and outputs from multiple regressors are combined and pruned to produce the final DAG (Section \ref{['ss:final-dag']}). While parts of the pipeline are general, ReX is specifically designed to leverage Shapley values for assessing feature contributions, as motivated in Section \ref{['ss:mathematical-foundation']}.
  • Figure 2: A visual summary of the intermediate graphs generated by ReX to obtain the final DAG $\mathcal{G}_{\text{\tiny{ReX\xspace}}}$. (a)-(b) represent the unoriented graphs for each of the two regressors after running the steps described in Sections \ref{['s:Models-training']}, \ref{['ss:computing-shap-values-for-feature-impact']}, \ref{['ss:parents-selection']} and \ref{['ss:adjacency-matrix-update']}. (c)-(d) are the result of establishing the direction of each edge presented in (a)-(b), respectively, following the approach described in Section \ref{['ss:directing-edges']}. (e) is the initial DAG resulting from the union of DAGs (c)-(d). (f) is final DAG $\mathcal{G}_{\text{\tiny{ReX\xspace}}}$ resulting from removing cycles and/or bidirectional edged from (e), following the steps described in Section \ref{['ss:final-dag']}. The true DAG is also depicted for comparison. Green arrows represent correctly predicted edges, orange ones edges with the incorrect direction, and red ones edges that are missing in the true DAG.
  • Figure 3: Effect of increasing the number of variables in the input dataset with ReX in the following metrics: (a) F1 score; (b) SHD to true DAG; (c) SID to true DAG; and (d) computation time. Results are computed for the five considered families of synthetic data.
  • Figure 4: Comparative performance of ReX against the benchmark methods PC, NOTEARS, GES, LiNGAM, FCI, and CAM across four key metrics: (a) F1 score; (b) edge difference, (c) precision; and (d) recall. Metrics are computed across all five considered synthetic families, with $p = 10$ features.
  • Figure 5: Benchmark between ReX and compared methods for (a) SHD to true DAG and (b) SID to true DAG metrics.
  • ...and 9 more figures

Theorems & Definitions (4)

  • Definition 1: Causal Markov property
  • Definition 2: Faithfulness
  • Definition 3: Causal-discovery problem
  • Remark