Persistence-based Modes Inference
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866908348084912128 |
|---|---|
| author | Henneuse, Hugo |
| author_facet | Henneuse, Hugo |
| contents | We address the problem of estimating multiple modes of a multivariate density using persistent homology, a central tool in Topological Data Analysis. We introduce a method based on the preliminary estimation of the $H_0$-persistence diagram to infer the number of modes, their locations, and the corresponding local maxima. For broad classes of piecewise-continuous functions with geometric control on discontinuities loci, we identify a critical separation threshold between modes, also interpretable in our framework in terms of modes prominence, below which modes inference is impossible and above which our procedure achieves minimax optimal rates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_15449 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Persistence-based Modes Inference Henneuse, Hugo Statistics Theory Algebraic Topology We address the problem of estimating multiple modes of a multivariate density using persistent homology, a central tool in Topological Data Analysis. We introduce a method based on the preliminary estimation of the $H_0$-persistence diagram to infer the number of modes, their locations, and the corresponding local maxima. For broad classes of piecewise-continuous functions with geometric control on discontinuities loci, we identify a critical separation threshold between modes, also interpretable in our framework in terms of modes prominence, below which modes inference is impossible and above which our procedure achieves minimax optimal rates. |
| title | Persistence-based Modes Inference |
| topic | Statistics Theory Algebraic Topology |
| url | https://arxiv.org/abs/2407.15449 |