In this talk I will present some thoughts on a few basic issues and
recent trends in machine learning. I will then describe new work we
have been doing to develop an intuitive theoretical framework for one of
these recent trends, the use of kernel methods. Kernel methods have
proven to be very powerful tools in machine learning, allowing simple
learning algorithms to be used in situations where fairly complex
decision surfaces are needed. They also have an existing fairly
well-developed theory. However, there has been a large gap between the
"theoretical story" and practical intuition surrounding kernel methods,
which our framework aims to narrow. An interesting feature of our
proposed framework is that it can also be applied to clustering. In
particular, I will discuss how it can be used to provide a new approach
to analyzing clustering problems and the types of information needed to
solve them, and how we should perhaps expand our concept of what it
means to cluster well.
Portions of this talk
include work joint with Nina Balcan and Santosh Vempala.