Cauchy-MMA: Multi-Metric autoencoder ensemble with adaptive cauchy loss for High-Dimensional incomplete data collaborative filtering.

High-dimensional incomplete data often suffers from severe outlier interference and rigid loss constraints, which significantly limit the performance of collaborative filtering. Although multi-metric autoencoders improve representation learning by fusing multiple metrics, their static loss functions fail to dynamically balance robustness and generalization. To address this issue, we propose Cauchy-MMA, a novel framework that integrates multi-metric autoencoders with adaptive Cauchy loss. The core innovations include: (1) exploiting the outlier-resistant property of the Cauchy distribution to construct a robust loss that suppresses gradient explosion caused by outliers; (2) designing a continuous and fully differentiable parameter adaptation mechanism to dynamically adjust penalties according to error magnitudes; and (3) adaptively integrating two adaptive Cauchy loss variants with four static losses to form a six-branch collaborative learning system. Theoretical analysis establishes sublinear regret bounds for the ensemble aggregation, proves asymptotic convergence of suboptimal model weights, and derives a strict boundedness guarantee for the adaptive loss influence function. Extensive experiments on four real-world datasets demonstrate that Cauchy-MMA achieves highly competitive performance against recent graph-based and robust baselines across rating prediction and Top-K recommendation tasks, and substantially mitigates performance deterioration under strong outlier interference.