Professor of Computer Science, Machine Learning, and Statistics
School of Computer Science
Most of my teaching in the past few years has been related
to the following three courses. The Statistical Machine Learning
course is part of a book project.
15-251: Great Theoretical Ideas in Computer Science
with Anupam Gupta
This course introduces some of the fundamental ideas and techniques in
computer science, in a self-contained way. What is computation? What is computable,
in principle? What is especially easy, or especially hard to compute?
To what extent does the inherent nature of computation shape how we
learn and think about the world? Topics include: representations of
number, induction, ancient and modern arithmetic, basic counting
principles, probability, random walks, number theory, the idea of proof, formal
proof, logic, problem solving methods, polynomial representations,
automata theory, cryptography, infinity, diagonalization,
computability, time complexity, and incompleteness and undecidability.
with Larry Wasserman
Statistical Machine Learning is a second graduate level course in
machine learning, assuming students have taken Machine Learning
(10-701) and Intermediate Statistics (36-705). The term "statistical"
in the title reflects the emphasis on statistical analysis and
methodology, which is the predominant approach in modern machine
The course combines methodology with theoretical foundations and
computational aspects. It treats both the "art" of designing good
learning algorithms and the "science" of analyzing an algorithm's
statistical properties and performance guarantees. Theorems are
presented together with practical aspects of methodology and intuition
to help students develop tools for selecting appropriate methods and
approaches to problems in their own research.
The course includes topics in statistical theory that are now becoming
important for researchers in machine learning, including consistency,
minimax estimation, and concentration of measure. It also presents
topics in computation including elements of convex optimization,
variational methods, randomized projection algorithms, and techniques
for handling large data sets.
with Mor Harchol-Balter
Probability theory has become indispensable in computer science. In
areas such as artificial intelligence and computer science theory,
probabilistic methods and ideas based on randomization are central. In
other areas such as networks and systems, probability is becoming an
increasingly useful framework for handling uncertainty and modeling
the patterns of data that occur in complex systems. This course gives
an introduction to probability as it is used in computer science
theory and practice, drawing on applications and current research
developments as motivation and context. Topics include combinatorial
probability and random graphs, heavy tail distributions, concentration
inequalities, various randomized algorithms, sampling random variables
and computer simulation, and Markov chains and their many
applications, from Web search engines to models of network
protocols. The course assumes only familiarity with basic calculus and
linear algebra; no prior probability and
statistics background is expected. Prerequiste: 15-251.