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On the reconstruction error of PCA (Martin Wahl)

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We analyze the reconstruction error of principal component analysis (PCA) and prove non-asymptotic upper bounds for the corresponding excess risk. These bounds unify and improve existing upper bounds from the literature. In particular, they give oracle inequalities under mild eigenvalue conditions. The bounds reveal that the excess risk differs considerably from usually considered subspace distances based on canonical angles. As an application, we analyze the prediction error of principal component regression (PCR). This talk is based on joint work with Markus Reiß.

Dates: 
Tuesday, February 5, 2019 - 11:00
Location: 
Inria Lille - Nord Europe, Room A11
Speaker(s): 
Martin Wahl
Affiliation(s): 
Institut für Mathematik, Humboldt University of Berlin