Distances between finite-horizon linear behaviors
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866916771418603520 |
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| author | Padoan, Alberto Coulson, Jeremy |
| author_facet | Padoan, Alberto Coulson, Jeremy |
| contents | The paper introduces a class of distances for linear behaviors over finite time horizons. These distances allow for comparisons between finite-horizon linear behaviors represented by matrices of possibly different dimensions. They remain invariant under coordinate changes, rotations, and permutations, ensuring independence from input-output partitions. Moreover, they naturally encode complexity-misfit trade-offs for Linear Time-Invariant (LTI) behaviors, providing a principled solution to a longstanding puzzle in behavioral systems theory. The resulting framework characterizes modeling as a minimum distance problem, identifying the Most Powerful Unfalsified Model (MPUM) as optimal among all systems unfalsified by a given dataset. Finally, we illustrate the value of these metrics in a time series anomaly detection task, where their finer resolution yields superior performance over existing distances. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_22849 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Distances between finite-horizon linear behaviors Padoan, Alberto Coulson, Jeremy Optimization and Control Systems and Control The paper introduces a class of distances for linear behaviors over finite time horizons. These distances allow for comparisons between finite-horizon linear behaviors represented by matrices of possibly different dimensions. They remain invariant under coordinate changes, rotations, and permutations, ensuring independence from input-output partitions. Moreover, they naturally encode complexity-misfit trade-offs for Linear Time-Invariant (LTI) behaviors, providing a principled solution to a longstanding puzzle in behavioral systems theory. The resulting framework characterizes modeling as a minimum distance problem, identifying the Most Powerful Unfalsified Model (MPUM) as optimal among all systems unfalsified by a given dataset. Finally, we illustrate the value of these metrics in a time series anomaly detection task, where their finer resolution yields superior performance over existing distances. |
| title | Distances between finite-horizon linear behaviors |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2503.22849 |