MELCOT融合传统与深度学习，高效处理矩阵回归中的结构保持问题。
MELCOT: A Hybrid Learning Architecture with Marginal Preservation for Matrix-Valued Regression
- 结合边际估计与可学习最优传输，兼顾局部结构与全局特征。
- 在多个数据集上超越所有基线模型，且计算效率高。
- 适合需要保留矩阵空间结构的高维回归任务。
回归在众多领域至关重要，但在高维场景下仍具挑战性，现有方法常丢失空间结构或需大量存储。本文针对矩阵值回归问题（每个样本天然为矩阵形式），提出MELCOT混合架构，融合基于经典机器学习的边际估计（ME）模块与基于深度学习的可学习最优传输（LCOT）模块。ME模块用于估计数据边缘以保持空间信息，LCOT模块则学习复杂全局特征。该设计使MELCOT兼具传统与深度学习方法的优势。在多样数据集和领域上的大量实验表明，MELCOT始终优于所有基线模型，同时保持高效率。
原文摘要 · Abstract (English)
Regression is essential across many domains but remains challenging in high-dimensional settings, where existing methods often lose spatial structure or demand heavy storage. In this work, we address the problem of matrix-valued regression, where each sample is naturally represented as a matrix. We propose MELCOT, a hybrid model that integrates a classical machine learning-based Marginal Estimation (ME) block with a deep learning-based Learnable-Cost Optimal Transport (LCOT) block. The ME block estimates data marginals to preserve spatial information, while the LCOT block learns complex global features. This design enables MELCOT to inherit the strengths of both classical and deep learning methods. Extensive experiments across diverse datasets and domains demonstrate that MELCOT consistently outperforms all baselines while remaining highly efficient.
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