CBMM Research Meeting: Do we really need to train by minimizing a loss functional?

March 28, 2023 - 4:00 pm

H. N. Mhaskar - Claremont Graduate University, Claremont.


The fundamental problem of machine learning is often formulated as the problem of function approximation. For example, we have data of the form {(xj,yj)}, where yj is the class label for xj, and we want to approximate the class label as a function of the input x. The standard way for this approximation is to minimize a loss functional, usually with some regularization. Surprisingly, even though the problem is posed as a problem of function approxi- mation, approximation theory has played only a marginal role in this theory. We describe our efforts to explore why this might be the case, and also to develop approximation theory/harmonic analysis tools more meaningfully and directly applicable to machine learning. We also argue that classification problems are better treated as generalized signal separation problems rather than function approximation problems.


MIT Building 46
March 28, 2023
4:00 pm
McGovern Reading Room (46-5165)