Statistical learning theory was introduced in the late 1960's. Until the 1990's it was a purely
theoretical analysis of the problem of function estimation from a given collection of data. In …

The phenomenon of benign overfitting is one of the key mysteries uncovered by deep
learning methodology: deep neural networks seem to predict well, even with a perfect fit to …

This paper investigates ultrafilters in the context of connectivity systems, defined as pairs
$(X, f) $ where $ X $ is a finite set and $ f $ is a symmetric submodular function. Ultrafilters …

Machine learning is one of the fastest growing areas of computer science, with far-reaching
applications. The aim of this textbook is to introduce machine learning, and the algorithmic …

Many modern machine learning models are trained to achieve zero or near-zero training
error in order to obtain near-optimal (but non-zero) test error. This phenomenon of strong …

While quantum state tomography is notoriously hard, most states hold little interest to
practically minded tomographers. Given that states and unitaries appearing in nature are of …

The mathematical theory of machine learning not only explains the current algorithms but
can also motivate principled approaches for the future. This self-contained textbook …

The matrix-completion problem has attracted a lot of attention, largely as a result of the
celebrated Net flix competition. Two popular approaches for solving the problem are nuclear …

We provide an information-theoretic framework for studying the generalization properties of
machine learning algorithms. Our framework ties together existing approaches, including …

A comprehensive introduction to Support Vector Machines and related kernel methods. In
the 1990s, a new type of learning algorithm was developed, based on results from statistical …