Machine learning has been highly successful in data-intensive applications but is often
hampered when the data set is small. Recently, Few-shot Learning (FSL) is proposed to …

This paper surveys quantum learning theory: the theoretical aspects of machine learning
using quantum computers. We describe the main results known for three models of learning …

The remarkable practical success of deep learning has revealed some major surprises from
a theoretical perspective. In particular, simple gradient methods easily find near-optimal …

We describe the new field of the mathematical analysis of deep learning. This field emerged
around a list of research questions that were not answered within the classical framework of …

Flexible estimation of heterogeneous treatment effects lies at the heart of many statistical
applications, such as personalized medicine and optimal resource allocation. In this article …

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

Pattern Analysis is the process of finding general relations in a set of data, and forms the
core of many disciplines, from neural networks, to so-called syntactical pattern recognition …

Weak Convergence Page 1 1.3 Weak Convergence In this section IDl and IE are metric spaces
with metrics d and e, respectively. The set of all continuous, bounded functions f: IDl 1--+ IR is …

Concentration inequalities deal with deviations of functions of independent random
variables from their expectation. In the last decade new tools have been introduced making …

This package includes both Mathematical Statistics: Basic Ideas and Selected Topics,
Volume I, Second Edition, as well as Mathematical Statistics: Basic Ideas and Selected …