A deterministic analysis of a class of nonlinear regression methods

Abstract

We consider the problem of learning a general class of nonlinear predictors from noisy data. In this context a class of optimal estimators is formed and analyzed in term of performance and convergence. More precisely, we derive bounds on the estimation errors which depend quantitatively on the complexity of the class of candidate models and on the richness properties of the training data. In particular, we show that using a certain class of loss functions in the to-be-minimized performance function yields estimators that can achieve an exact recovery of the true predictor in finite time despite the presence of noise. The results are illustrated with examples throughout the paper.

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BibTeX

@article{bako2026deterministic,
  title = {{A deterministic analysis of a class of nonlinear regression methods}},
  author = {Laurent Bako},
  journal = {Automatica},
  year = {2026},
  month = may,
  doi = {10.1016/j.automatica.2026.113066},
  url = {https://hal.science/hal-05747829v1},
  note = {CC BY 4.0},
}

RIS

TY  - JOUR
TI  - A deterministic analysis of a class of nonlinear regression methods
AU  - Laurent Bako
PY  - 2026
DA  - 2026/05/15
JO  - Automatica
DO  - 10.1016/j.automatica.2026.113066
UR  - https://hal.science/hal-05747829v1
AB  - We consider the problem of learning a general class of nonlinear predictors from noisy data. In this context a class of optimal estimators is formed and analyzed in term of performance and convergence. More precisely, we derive bounds on the estimation errors which depend quantitatively on the complexity of the class of candidate models and on the richness properties of the training data. In particular, we show that using a certain class of loss functions in the to-be-minimized performance function yields estimators that can achieve an exact recovery of the true predictor in finite time despite the presence of noise. The results are illustrated with examples throughout the paper.
SN  - 0005-1098
ER  -

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