no code implementations • 25 Jul 2020 • Emmanuel Caron, Stephane Chretien
Recent extensive numerical experiments in high scale machine learning have allowed to uncover a quite counterintuitive phase transition, as a function of the ratio between the sample size and the number of parameters in the model.
no code implementations • 3 Apr 2018 • Stephane Chretien, Christophe Guyeux, Zhen-Wai Olivier HO
This paper studies the complexity of the stochastic gradient algorithm for PCA when the data are observed in a streaming setting.
no code implementations • 3 Apr 2018 • Stephane Chretien, Zhen-Wai Olivier HO
A problem of paramount importance in both pure (Restricted Invertibility problem) and applied mathematics (Feature extraction) is the one of selecting a submatrix of a given matrix, such that this submatrix has its smallest singular value above a specified level.
no code implementations • 8 Jun 2015 • Stephane Chretien, Tianwen Wei
The subdifferential of convex functions of the singular spectrum of real matrices has been widely studied in matrix analysis, optimization and automatic control theory.