@phdthesis{michel:tel-01235080, TITLE = {{A Statistical Approach to Topological Data Analysis}}, AUTHOR = {Michel, Bertrand}, URL = {https://theses.hal.science/tel-01235080}, SCHOOL = {{UPMC Universit{\'e} Paris VI}}, YEAR = {2015}, MONTH = Nov, KEYWORDS = {topological data analysis ; topological inference ; persistent homology ; non parametric statistics ; model selection ; Wasserstein metrics ; mixture models ; slope heuristics ; random forests ; permutation importance measure. ; analyse topologique des donn{\'e}es ; inf{\'e}rence topologique ; homologie persistante ; statistique non param{\'e}trique ; s{\'e}lection de mod{\`e}les ; bootstrap ; d{\'e}convolution ; m{\'e}triques Wasserstein ; mod{\`e}les de m{\'e}lange ; heuristique de pente ; for{\^e}ts al{\'e}atoires ; mesure d'importance par permutation}, TYPE = {Habilitation {\`a} diriger des recherches}, PDF = {https://theses.hal.science/tel-01235080/file/ManuscritHDR_MichelB.pdf}, HAL_ID = {tel-01235080}, HAL_VERSION = {v1}, }