ABSTRACT

Learning can be described as the problem of making inferences from (possibly small) samples of noisy, high dimensional data. In this talk we will discuss a class of learning techniques that draw on the study of spectral properties of suitably defined, data dependent matrices. Stability of the methods is typically achieved via spectral filtering, that is, discarding components corresponding to small eigenvalues. The efficiency of the approach can be proved using random matrix theory to study the concentration properties of the empirical matrices and their spectra. Numerical experiments support the theoretical findings.