Appears in collection : Statistics and Machine Learning at Paris-Saclay (2023 Edition)

It is a common idea that high dimensional data (or features) may lie on low dimensional support making learning easier. In this talk, I will present a very general set-up in which it is possible to recover low dimensional non-linear structures with noisy data, the noise being totally unknown and possibly large. Then I will present minimax rates for the estimation of the support in Hausdorff distance.