On April 16, 2009 Lorenzo Rosasco from MIT will be delivering a lecture entitled “Inverse Problems: Perspectives in Learning Theory“.

Location: 2237 French Family Science Center

Time: 4:30pm

Abstract: Learing from examples refers to systems that are trained, instead of programmed, with a set of examples. In recent years machine learning techniques have been shown to be useful in a variety of application domains and especially for the analysis of complex high dimensional data sets, such as those found in computer vision or bioinformatics. At a high level the problem of learning can be seen as an inverse problem, where one is interested to recover a model from measurements. However, a further look shows that the two mathematical frameworks seem quite different, as are the requirements: generalization in learning and stability in inverse problems. In this talk we show that in fact the connection between inverse problems and learning goes beyond a simple analogy. If we assume the functions of interest belong to a Hilbert space where functions can be point-wise evaluated, we can cast the problem of learning as an inverse problem defined by a compact linear operator. Building on such connections we can show that different learning principles such as risk penalization, early stopping or lower dimensional projection can be seen as different instances of a general principle. Their analysis builds on operator theoretic results used in inverse problems as well as concentration inequalities for random matrices to deal with the stochastic setting typical of learning.