Co-Evolutionary Probabilistic Recovery for Multi-Dimensional Classification with Missing Labels

Multi-dimensional classification (MDC) requires assigning labels to each instance across multiple class dimensions simultaneously, but fully labeling all dimensions is often costly or even impractical. Thus, a setting with missing labels more closely approximates the reality of MDC. Despite its practical relevance, learning from incomplete labels has yet to be investigated in MDC. Existing label completion strategies developed for other learning paradigms cannot be directly applied to MDC, as they typically rely on predefined label correlations or independent recovery assumptions, while overlooking the fact that missing labels may simultaneously obscure the dependencies among multiple class dimensions. Moreover, inaccurate completion can further distort the dependency information available to the learner and introduce unreliable supervision for downstream classifier learning. To address these challenges, we propose CSER, a competitive co-evolutionary framework for probabilistic label recovery. CSER first constructs complementary feature-only and dependency-conditioned class-probability representations from observed labels, and then co-evolves two interacting populations of recovery strategies and pseudo-missing challenges. The challenge population searches for difficult recovery targets that expose weaknesses of current strategies, while the recovery population learns confidence-aware, dimension-wise fusion preferences. A robust strategy is finally selected against accumulated historical challenges and used to recover labels for genuinely missing entries, with multiple imputation propagating the recovered supervision to downstream MDC learning. Experiments on 17 benchmark datasets demonstrate that CSER significantly outperforms MDC baselines equipped with label completion strategies across various label-missing scenarios.