A Statistical Approach to Topological Data Analysis

Bertrand Michel 1, 2
2 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : Until very recently, topological data analysis and topological inference methods mostly relied on deterministic approaches. The major part of this habilitation thesis presents a statistical approach to such topological methods. We first develop model selection tools for selecting simplicial complexes in a given filtration. Next, we study the estimation of persistent homology on metric spaces. We also study a robust version of topological data analysis. Related to this last topic, we also investigate the problem of Wasserstein deconvolution. The second part of the habilitation thesis gathers our contributions in other fields of statistics, including a model selection method for Gaussian mixtures, an implementation of the slope heuristic for calibrating penalties, and a study of Breiman’s permutation importance measure in the context of random forests.
Document type :
Habilitation à diriger des recherches
Complete list of metadatas

Cited literature [116 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-01235080
Contributor : Bertrand Michel <>
Submitted on : Friday, November 27, 2015 - 5:15:35 PM
Last modification on : Thursday, March 21, 2019 - 2:42:02 PM
Long-term archiving on : Friday, April 28, 2017 - 10:54:57 PM

Identifiers

  • HAL Id : tel-01235080, version 1

Citation

Bertrand Michel. A Statistical Approach to Topological Data Analysis. Statistics [math.ST]. UPMC Université Paris VI, 2015. ⟨tel-01235080⟩

Share

Metrics

Record views

1233

Files downloads

2971