Persistence Diagram Estimation of Multivariate Piecewise Hölder-continuous Signals - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2024

Persistence Diagram Estimation of Multivariate Piecewise Hölder-continuous Signals

Résumé

To our knowledge, the analysis of convergence rates for persistence diagram estimation from noisy signals had predominantly relied on lifting signal estimation results through sup norm (or other functional norm) stability theorems. We believe that moving forward from this approach can lead to considerable gains. We illustrate it in the setting of Gaussian white noise model. We examine from a minimax perspective, the inference of persistence diagram (for sublevel sets filtration). We show that for piecewise Hölder-continuous functions, with control over the reach of the discontinuities set, taking the persistence diagram coming from a simple histogram estimator of the signal, permit to achieve the minimax rates known for Hölder-continuous functions.
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Dates et versions

hal-04524998 , version 1 (28-03-2024)
hal-04524998 , version 2 (15-05-2024)
hal-04524998 , version 3 (09-07-2024)

Identifiants

  • HAL Id : hal-04524998 , version 2

Citer

Hugo Henneuse. Persistence Diagram Estimation of Multivariate Piecewise Hölder-continuous Signals. 2024. ⟨hal-04524998v2⟩
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