Kolloquium über Mathematische Statistik und Stochastische Prozesse

Kolloquium über Mathematische
Statistik und Stochastische Prozesse
Dr. Martin Wahl
Humboldt-Universität zu Berlin
06.12.2016, 16:15 Uhr, Hörsaal 5
Non-asymptotic upper bounds for the reconstruction error
of PCA
Abstract:
Principal component analysis (PCA) is a standard tool for dimension reduction. In this talk, we analyse the reconstruction error of PCA and prove
non-asymptotic upper bounds for the corresponding excess risk. These
bounds unify and improve several upper bounds from the literature.
Moreover, the bounds reveal that the excess risk differs considerably from
usually considered subspace distances based on canonical angles. Our
approach relies on the analysis of empirical spectral projectors combined
with concentration inequalities for empirical covariance operators and
empirical eigenvalues. The results are illustrated for covariance matrices
satisfying standard eigenvalue decay assumptions. In addition, corresponding bounds for canonical angle distances are discussed. This is joint
work with Markus Reiß.
Dr. Martin Wahl
Humboldt-Universität zu Berlin
https://www.mathematik.huberlin.de/de/forschung/forschungsgebiete/stochastik/stoch-employees/martinwahl/
Kontakt:
Jun.-Prof. Dr. Mathias Trabs (http://www.math.uni-hamburg.de/home/trabs/)
Universität Hamburg

Download Report