The M-Tensor Format: Optimality in High Dimensional Regression for Nonlinear Models with Scarce Data
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910016479428608 |
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| author | Cloarec, Rémi Rodriguez, Sebastian Kestelyn, Xavier Chinesta, Francisco |
| author_facet | Cloarec, Rémi Rodriguez, Sebastian Kestelyn, Xavier Chinesta, Francisco |
| contents | We present a nonlinear regression framework based on tensor algebra tailored to high dimensional contexts where data is scarce. We exploit algebraic properties of a partial tensor product, namely the m-tensor product, to leverage structured equations with separated variables. The proposed method combines kernel properties along with tensor algebra to prevent the curse of dimensionality and tackle approximations up to hundreds of parameters while avoiding the fixed point strategy. This formalism allows us to provide different regularization techniques fit for low amount of data with a high number of parameters while preserving well-known matrix-based properties. We demonstrate complexity scaling on a general benchmark and dynamical systems to show robustness for engineering problems and ease of implementation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_08509 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The M-Tensor Format: Optimality in High Dimensional Regression for Nonlinear Models with Scarce Data Cloarec, Rémi Rodriguez, Sebastian Kestelyn, Xavier Chinesta, Francisco Computational Engineering, Finance, and Science 15A23, 15A69, 65D40 We present a nonlinear regression framework based on tensor algebra tailored to high dimensional contexts where data is scarce. We exploit algebraic properties of a partial tensor product, namely the m-tensor product, to leverage structured equations with separated variables. The proposed method combines kernel properties along with tensor algebra to prevent the curse of dimensionality and tackle approximations up to hundreds of parameters while avoiding the fixed point strategy. This formalism allows us to provide different regularization techniques fit for low amount of data with a high number of parameters while preserving well-known matrix-based properties. We demonstrate complexity scaling on a general benchmark and dynamical systems to show robustness for engineering problems and ease of implementation. |
| title | The M-Tensor Format: Optimality in High Dimensional Regression for Nonlinear Models with Scarce Data |
| topic | Computational Engineering, Finance, and Science 15A23, 15A69, 65D40 |
| url | https://arxiv.org/abs/2602.08509 |