Seminar: Error behavior of least squares in the statistical learning setting

Time:

Venue/Location: Phòng C101, VIASM

Báo cáo viên: Felix Bartel (Chemnitz University of Technology, Germany)

Abstract: With statistical learning we enter a framework in machine learning and individual function approximation. The model is based on randomness in the points and the function evaluations, which includes the scenario of noise. We show that the least squares approximation has the same error as the projection to the ansatz space up to a multiplicative constant provided noise-free samples and logarithmic oversampling. Including noise, we model the classical over- and underfitting behavior one has to balance to achieve the smallest error. This yields a parameter choice question, which can be tackled with cross-validation in an efficient manner. We show that the cross-validaiton score estimates the $L_2$-error and give theoretical guarantes for its concentration.