We announce the following DEC Statistics webinar at Bocconi:
Date: Thursday 18 November 2021, h12:00 (Italy time) Speaker: Martin Schlather (University of Mannheim) Title: A Generalized Approach to Principal Component Analysis
Abstract: Principal Component Analysis is a well known procedure to reduce intrinsic complexity of a standardized data set, essentially through simplifying the correlation structure. We provide a substantial extension based on semi-groups, which includes distributions without second moments. We reformulate the PCA as a best low rank approximation defined through a regression problem, which is closely connected to autoencoders and admits solutions under mild assumptions. As a specific example, we apply our general formulation to extreme value distributions. In this case solving the regression problem reduces to a tractable and practically solvable problem for real datasets. As a side effect of our general approach, the perspective on uncorrelated variables is inverted: the assertion that the covariance is zero is not the definition, but a corollary; the fact that uncorrelated variables need not be independent is not a warning, but intrinsic to the definition.
The webinar will be on zoom at: https://unibocconi-it.zoom.us/j/91941945297?pwd=VGhFVGc5OUVHUUFXQ2tlK0xQWkVZ... Meeting ID: 919 4194 5297 Passcode: 932042
Kind regards, Giacomo Zanella