Emmy Noether Lectures

2006 Lecturer: Ingrid Daubechies

Mathematical Results and Challenges in Learning Theory

Abstract:

One of the most widespread applications of learning theory is in ubiquitous search engines, which have to (and do!) classify enormous databases according to (almost) arbitrary criteria. Computer scientists have developed powerful algorithms for these very high-dimensional problems, which typically cannot be tackled by gradient-descent or similar optimization methods. These algorithms and the problems they attack provide very interesting mathematical challenges. The talk will discuss in particular the widely applied AdaBoost algorithm and its properties, as well as some variants. It will review joint work with Cynthia Rudin and Rob Schapire (co-inventor, with Freund, of AdaBoost, for which they were awarded the 2003 Gödel prize.)

Brief Biography:

Ingrid Daubechies grew up in Belgium and received both her bachelor’s and Ph.D. degrees (in 1975 and 1980) from the Free University in Brussels. As far as she can remember, she was always interested in mathematics and how things worked, and from an early age, was encouraged by her father, a civil mining engineer, and her mother, a criminologist, to pursue her interest in science. Although she studied to become a physicist, her work has always been very mathematical.

Daubechies held a research position at the Free University until 1987. From 1987 to 1994 she was a member of the technical staff at AT&T Bell Laboratories, during which time she took leaves to spend six months (in 1990) at the University of Michigan, and two years (1991-1993) at Rutgers University. She is now a professor in the Department of Mathematics, the first woman to hold that position, and in the Program in Applied and Computational Mathematics at Princeton University. Her research interests have focused on the mathematical aspects of time-frequency analysis, in particular wavelets, as well as applications. In 1987 she constructed a class of wavelets that were identically zero outside a finite interval, now among the most common type of wavelets used in applications. Currently, she is applying her techniques to learning theory.

Daubechies has received many awards in recognition of her groundbreaking work. In 1984, she received the Louis Empain Prize in Physics, awarded once every five years to a Belgian scientist on the basis of work done before the age of 29. In 1998, she was elected to be a member of the National Academy of Sciences and a Fellow of the Institute of Electrical and Electronics Engineers. The American Mathematical Society awarded her a Leroy P. Steele prize for exposition in 1994 for her book Ten Lectures on Wavelets, as well as the 1997 Ruth Lyttle Satter Prize for “her deep and beautiful analysis of wavelets and their applications.” In 2000, she became the first woman to receive the National Academy of Sciences Award in Mathematics, presented every four years, for excellence in published mathematical research. From 1992 to 1997 she was a fellow of the John D. and Catherine T. MacArthur Foundation. She is a member of the American Academy of Arts and Sciences, the American Mathematical Society, the Mathematical Association of America, the Society for Industrial and Applied Mathematics, and the Institute of Electrical and Electronics Engineers.

Daubechies has been very involved in helping communicate mathematics to the public, in particular in coming up with ideas for the K-12 mathematics curriculum that reflect present-day applications of mathematics. Her husband is also a mathematician, and they have two children, Michael and Carolyn. When she is not working or asleep, she likes to spend time with her family.