- Series
- Stochastics Seminar
- Time
- Tuesday, April 24, 2012 - 4:05pm for 1 hour (actually 50 minutes)
- Location
- skyles 006
- Speaker
- Zongming Ma – The Wharton School, Department of Statistics, University of Pennsylvania
- Organizer
- Karim Lounici
Singular value decomposition is a widely used tool for dimension
reduction in multivariate analysis. However, when used for statistical
estimation in high-dimensional low rank matrix models, singular vectors of
the noise-corrupted matrix are inconsistent for their counterparts of the
true mean matrix. In this talk, we suppose the true singular vectors have
sparse representations in a certain basis. We propose an iterative
thresholding algorithm that can estimate the subspaces spanned by leading
left and right singular vectors and also the true mean matrix optimally
under Gaussian assumption. We further turn the algorithm into a practical
methodology that is fast, data-driven and robust to heavy-tailed noises.
Simulations and a real data example further show its competitive
performance. This is a joint work with Andreas Buja and Dan Yang.