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Karim LOUNICI (Ecole Polytechnique) – "Online PCA: non-asymptotics statistical guarantees for the Krasulina scheme"
Time: 2:00 pm – 3:15 pm
Date: 12st of November 2018
Place: Room 3001.
Karim LOUNICI (Ecole Polytechnique) – “Online PCA: non-asymptotics statistical guarantees for the Krasulina scheme”
Abstract: Principal Component Analysis is a popular method used to analyse the covariance structure $\Sigma$ of a random vector. Recent results on the statistical properties of standard PCA have highlighted the importance of the effective rank as a measure of the intrinsic statistical complexity in the PCA problem. In particular, optimal rates of estimation of the spectral projectors have been established in the offline setting where all the observations are available at once and a batch estimation method is implemented. In the online setting, observations arrive in a stream and our estimate of eigenvalues and spectral projectors are updated every time a new observation is available. This problem has attracted a lot a attention recently but little is known on the statistical properties of the existing methods. In this work, we consider the Krasulina scheme (stochastic gradient ascent scheme) and establish non-asymptotic estimation bounds in probability for the spectral projectors. For this method, the effective rank also plays a central role in the performance of the method, however the obtained rate is slower than that obtained in the offline setting.
Cristina BUTUCEA, Alexandre TSYBAKOV, Julie JOSSE, Eric MOULINES, Mathieu ROSENBAUM