On May, 20th to May, 24th 2019 we have the pleasure to welcome Hervé CARDOT (Université de Bourgogne) with us. Hervé will give a talk (see details below) in the Kolloquium für Statistik on Thursday, May 23th 2019. Do not hesitate to pass by his office (Room 4.412, MΛTHEMΛTIKON, INF 205) for a discussion.

Talk:

Kolloquium für Statistik

Thursday, May 23th 2019 14h15

SR7, MΛTHEMΛTIKON, INF 205

Presented by:

Hervé CARDOT (Université de Bourgogne)

Title:

Online robust principal components analysis in Hilbert spaces

Abstract:

Online algorithms based on recursive approaches do not require to store all the data in memory and are useful tools to deal with streaming data as well as massive datasets. They are extremely fast and allow for automatic update when the data are observed sequentially.
In Hilbert spaces, the mean vector and the covariance operator (or covariance matrix for finite dimension spaces) are classical indicators of central location and (multivariate) dispersion that can be estimated sequentially. However, outlying data may be hard to detect automatically for high dimension data and both the mean vector and the covariance matrix can be highly affected by a small proportion of outlying observations.
We present robust indicators of central position and multivariate dispersion based on the geometric median and the median covariation matrix which are relevant tools to perform robust center estimation and robust PCA for variables taking values in separable Hilbert spaces. Such indicators, which can be expressed as the solutions of convex optimization problems, can be efficiently estimated in a recursive and very fast way thanks to averaged stochastic gradient algorithms. Some consistency results are given. Numerical experiments on simulated as well as real high dimensional datasets confirm the effectiveness of such online estimation procedures in comparison to more classical robust techniques, that are generally not designed to deal with large samples of high dimension data.