Imaging and Computing Seminar

Lorenzo Rosasco , Brain and Cognitive Sciences, MIT

Spectral Methods for Learning from High Dimensional Data

Learning can be described as the problem of making inference from (possibly small) samples of noisy, high dimensional data. Such a problem is typically ill-posed and ensuring stability is the key to find models that generalize to new data. In this talk I will discuss a general class of learning techniques that draw on the study of spectral properties of suitably defined, data dependent matrices. Stability of the methods is achieved viaspectral filtering, that is discarding components corresponding to small eigenvalues. The efficiency of the approach can be proved using concentration inequalities to study the stability properties of the empirical matrices and their spectra. Such results are dimension independent and suggest that the proposed methods can be efficiently used to learn high dimensions problems. Indeed, an empirical analysis shows that spectral filtering methods achieve state of the art performances in a variety of real world applications.