MELCOT: A Hybrid Learning Architecture with Marginal Preservation for Matrix-Valued Regression
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916974221590528 |
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| author | Tran, Khang Cao, Hieu Pham, Thinh Diep, Nghiem Cao, Tri Nguyen, Binh |
| author_facet | Tran, Khang Cao, Hieu Pham, Thinh Diep, Nghiem Cao, Tri Nguyen, Binh |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_23315 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | MELCOT: A Hybrid Learning Architecture with Marginal Preservation for Matrix-Valued Regression Tran, Khang Cao, Hieu Pham, Thinh Diep, Nghiem Cao, Tri Nguyen, Binh Machine Learning Artificial Intelligence 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. |
| title | MELCOT: A Hybrid Learning Architecture with Marginal Preservation for Matrix-Valued Regression |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2509.23315 |