T-ERC_STG - Tremplin-ERC Starting

Data, geometry and curvature – DataGC

Submission summary

Riemannian data are ubiquitous in modern statistics and machine learning: Low-rank
matrix completion, dictionary learning, matrix factorization, computer vision, shape statistics, optimal
transport, etc. Moreover, in an era where extraordinarily rich, yet also complex and heterogeneous
datasets become available to practitioners, it is becoming urgent to develop tools for extracting information
that is as accurate, robust, computationally tractable and that are adapted to the geometry of
the data. By exploring and further developing the interplays between geometry, curvature, probability
theory and data analysis, DataGC will set the grounds for a non-asymptotic and non-parametric
theory of location estimation on Riemannian manifolds. We will focus on barycenters, centrality regions
and supports of probability distributions, which are paramount in descriptive statistics, data
visualization and statistical inference.

Project coordination

Victor Emmanuel Brunel (Groupe des Ecoles Nationales d'Economie et de Statistique)

The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.

Partner

GENES Groupe des Ecoles Nationales d'Economie et de Statistique

Help of the ANR 112,435 euros
Beginning and duration of the scientific project: March 2022 - 24 Months

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