The new method, called CausalCACTUS, is described in an open-access paper published in the journal Machine Learning on 28 September 2026. It extends an earlier framework known as CACTUS, which generated counterfactual explanations in a compressed latent space learned by a variational autoencoder, while allowing users to specify contextual constraints such as age or family status that the explanation must respect. CausalCACTUS adds what CACTUS lacked: an explicit model of cause and effect among the input features, learned automatically from data rather than supplied by human experts.

The technical core of the approach rests on three pillars. First, the researchers use a causal discovery algorithm called ReX, which trains predictive models for each feature and applies bootstrapped Shapley value attributions to identify which features depend on which. The output is a directed acyclic graph, a map of parent-child relationships such as the chain linking revolving credit utilization to the number of credit lines and then to a person’s debt ratio. Second, this graph is converted into dynamic feasibility constraints during the counterfactual search: a child feature is only allowed to change if at least one of its parents changes as well. Third, a phase-based optimization strategy first drives the search toward any valid counterfactual and then refines it for contextual alignment and minimal distance, with a weighting parameter that gradually shifts emphasis from prediction validity to context preservation.

The counterfactual search itself takes place not in the original feature space but in a four-dimensional latent space learned by a beta-variational autoencoder. This composite model includes an auxiliary classification head that predicts the user-defined context from the latent representation, allowing the optimizer to penalize candidates that drift outside the specified context, for example an applicant older than fifty. A causal distance loss, computed with an adaptive binary mask that is updated at every iteration, penalizes changes to features whose causal parents have not yet been modified. Feature values are also clipped to ranges observed in the training data after each decoding step, keeping every candidate within plausible bounds.

The evaluation covered five publicly available tabular datasets spanning credit risk, income prediction and legal education, ranging from 462 to 16,668 instances, with binary context variables derived from demographic and financial attributes. Against four baseline methods, including LatentCF++, two variants of PrototypeCF and the original CACTUS, CausalCACTUS ranked among the top two on validity in eight of ten comparisons and improved validity over the original CACTUS from roughly 0.7 to around 0.9. More strikingly, it achieved the best context-alignment scores, measured by a local outlier factor computed within the target context, in nine of ten scenarios, and the best causal-compact consistency, a metric combining causal constraint satisfaction with sparsity of changes, in nine of ten configurations.

Statistical analysis reinforced these findings. A Friedman test followed by a Wilcoxon-Holm post-hoc analysis across ten benchmark tasks showed that CausalCACTUS achieved the best average ranks, between 1.0 and 1.4, on proximity, context alignment, compactness and causal consistency. Ablation studies revealed a division of labor between the two new components: the phase-based optimization primarily boosted validity and compactness, while the causal feasibility constraints mainly improved context alignment and causal consistency. The researchers also mapped how the loss-weighting parameter alpha trades validity against context alignment, identifying a balanced setting near 0.7.

A concrete example from the credit dataset illustrates why the framework matters. For a loan applicant over fifty initially classified as high risk, competing methods proposed income changes ranging from a decrease of more than 15,000 dollars to increases exceeding 5,000 dollars, figures the authors describe as implausible for someone at that life stage. CausalCACTUS instead suggested a moderate adjustment of 1,605 dollars, required fewer overall feature modifications, and respected the learned dependency chain between credit utilization, credit lines and debt ratio, which the baseline methods violated. Correlation analysis of feature changes across test instances showed that CausalCACTUS produced strong correlations concentrated on causally related feature pairs, closely matching the learned graph, while baselines either showed weak correlations or correlations misaligned with causal structure.

The authors are candid about the limitations of their approach. Because it relies on a causal graph estimated by a discovery algorithm rather than a fully specified structural causal model, missing edges in the estimated graph could introduce inaccurate dependencies into the search; expert-defined graphs can substitute where reliable domain knowledge exists. The generative model is also a bottleneck: reconstruction errors or misalignment between the latent representation and the underlying causal mechanisms may cause information loss or unintended feature changes. Future work, the team suggests, could replace the beta-variational autoencoder with diffusion models, normalizing flows or causally informed generative variants, and could jointly learn latent representations and causal structures with uncertainty estimates attached to the learned graph.

The implications reach well beyond credit scoring. Counterfactual explanations have been linked to the right to explanation under the General Data Protection Regulation, and as algorithmic decisions spread through finance, hiring and education, the gap between mathematically valid explanations and practically actionable ones becomes a matter of public trust. By showing that causal consistency and user-defined context can be enforced simultaneously in a latent-space search, without demanding a fully specified causal model as a prerequisite, CausalCACTUS offers a template for explanations that a rejected applicant, a loan officer and a regulator could all accept. The source code has been released publicly on GitHub, and the authors point toward extensions to time-series classification and sequential prediction as the next frontier for causally grounded, context-aware explainability.

Subject of Research: Causally consistent and context-aware counterfactual explanations for machine learning classifiers

Article Title: CausalCACTUS: A Causally Consistent and Context-Aware Framework for Counterfactual Explanations

Article References: Wang, Z., García, D., Enguita, J. M., Chatterjee, S., & Jansson, M. (2026). CausalCACTUS: A Causally Consistent and Context-Aware Framework for Counterfactual Explanations. Machine Learning, 115(10), Article 233. https://doi.org/10.1007/s10994-026-07155-2

Image Credits: AI Generated

DOI: 10.1007/s10994-026-07155-2

Keywords: counterfactual explanations, explainable AI, causal discovery, machine learning, variational autoencoder, structural causal models, latent space optimization, algorithmic recourse, model interpretability, context-aware learning, tabular data, GDPR