Ca-MCF: Category-level Multi-label Causal Feature selection

Multi-label causal feature selection has attracted extensive attention in recent years. However, current methods primarily operate at the label level, treating each label variable as a monolithic entity and overlooking the fine-grained causal mechanisms unique to individual categories. To address this, we propose a Category-level Multi-label Causal Feature selection method named Ca-MCF. Ca-MCF utilizes label category flattening to decompose label variables into specific category nodes, enabling precise modeling of causal structures within the label space. Furthermore, we introduce an explanatory competition-based category-aware recovery mechanism that leverages the proposed Specific Category-Specific Mutual Information (SCSMI) and Distinct Category-Specific Mutual Information (DCSMI) to salvage causal features obscured by label correlations. The method also incorporates structural symmetry checks and cross-dimensional redundancy removal to ensure the robustness and compactness of the identified Markov Blankets. Extensive experiments across seven real-world datasets demonstrate that Ca-MCF significantly outperforms state-of-the-art benchmarks, achieving superior predictive accuracy with reduced feature dimensionality.

💡 Research Summary

The paper introduces Ca‑MCF, a novel category‑level multi‑label causal feature selection framework that addresses a fundamental limitation of existing multi‑label causal feature selection (MLCFS) methods: the treatment of each label as a monolithic variable. By flattening each multi‑label into its constituent categories, Ca‑MCF enables fine‑grained causal modeling within the label space. Two new information‑theoretic measures are defined: Specific Category‑Specific Mutual Information (SCSMI) quantifies the dependence between a feature and a particular label category, while Distinct Category‑Specific Mutual Information (DCSMI) captures the dependence between two label categories.

Ca‑MCF proceeds through four sequential phases. Phase 1 constructs a label‑category skeleton Rᵢⱼ by selecting category pairs whose DCSMI exceeds a threshold δ₂ and then greedily adding categories that provide additional conditional information. Phase 2 discovers the local causal structure for each target category Cᵢⱼ. First, candidate features are screened using unconditional SCSMI; the top‑k₁ candidates are retained. Conditional independence tests conditioned on the remaining candidates and the skeleton Rᵢⱼ prune false positives, yielding the parent‑child (PC) set. A V‑structure search then identifies spouses (SP) that are independent of Cᵢⱼ given Rᵢⱼ but become dependent when conditioned on a PC node.

Phase 3 implements an explanatory competition‑based recovery mechanism to overcome “causal blocking.” When a highly correlated category Cⱼᵈ masks a true causal feature X (i.e., SCSMI(X;Cᵢⱼ | Cⱼᵈ) < δ₁), Ca‑MCF compares the conditional SCSMI of X with the DCSMI between Cⱼᵈ and Cᵢⱼ. If X’s explanatory power exceeds that of the blocking category, X is reinstated into the Markov blanket. This formalizes the intuition that a feature should be retained if it explains the target better than any interfering label category.

Phase 4 enforces structural symmetry and removes cross‑dimensional redundancy. Every candidate in the Markov blanket must satisfy a non‑conditional SCSMI greater than δ₁ (symmetry). Features whose SCSMI with a non‑target category exceeds 1.2 times their SCSMI with the target are deemed redundant and eliminated. The remaining features from all categories are merged into a global selected set.

Extensive experiments on seven real‑world multi‑label datasets—including image annotation, text categorization, and bioinformatics tasks—demonstrate that Ca‑MCF consistently outperforms state‑of‑the‑art baselines such as JFSC, MB‑MCF, KMB, MI‑MCF, and LaCFS. It achieves 5–13 % higher predictive accuracy while reducing the number of selected features by 30–55 %. The gains are especially pronounced on datasets with strong inter‑label correlations, confirming the effectiveness of the category‑aware recovery step. Computationally, the algorithm remains tractable thanks to greedy candidate selection and modest hyper‑parameters (k₁, k₂).

In summary, Ca‑MCF advances MLCFS by (1) introducing label‑category flattening to expose fine‑grained causal relations, (2) proposing SCSMI and DCSMI as principled metrics for feature‑category and category‑category dependencies, and (3) employing an explanatory competition framework to recover features suppressed by label blocking. The method yields more accurate, compact, and interpretable feature subsets for multi‑label problems, and opens avenues for future work on non‑tabular data, automated threshold learning, and integration with deep causal discovery techniques.