MELCOT: A Hybrid Learning Architecture with Marginal Preservation for Matrix-Valued Regression
This addresses regression challenges for domains with matrix-valued data, offering improved performance and efficiency, though it appears incremental as a hybrid of existing methods.
The paper tackles the problem of matrix-valued regression in high-dimensional settings by proposing MELCOT, a hybrid model that integrates marginal estimation with learnable-cost optimal transport, and it demonstrates consistent outperformance over baselines across diverse datasets.
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.