ICWS Seminar
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Multiuser Information-Theoretic Games: Classical and New Examples
Mokshay Madiman, Yale University
March 13, 2008
4:00 p.m.
Room 141 CSL
ABSTRACT
Cooperative games are ubiquitous in information theory, and arise most
frequently in the characterization of fundamental limits in various
scenarios involving multiple users. Examples include classical settings
in network information theory such as Slepian-Wolf source coding and
multiple access channels, classical settings in statistics such as
robust hypothesis testing, and new settings at the intersection of
networking and statistics such as distributed estimation problems for
sensor networks. Cooperative game theory allows one to understand
aspects of all of these problems from a fresh and unifying perspective
that treats users as players in a game, sometimes leading to new
insights.
The first part of the talk reviews basic notions from
cooperative game theory and the fundamental connection to classical
problems. The second part of the talk focuses on fundamental limits of
distributed estimation, motivated by a toy model for sensor networks. In
distributed estimation, it is of interest to relate the minimax risks of
estimating a parameter for users who have access to different sets of
observations. We present some insights into this question in the case of
a location parameter, where each user sees either the concatenation or
the sum of observations from a set of sources. Using the game theoretic
framework from the first part, we apply our results to design and
resource allocation problems for sensor networks. If time permits, we
will also mention a surprising connection to results of fundamental
interpretive importance in probability, such as the fact that the
entropy of the normalized sums in the central limit theorem increases
monotonically to the Gaussian entropy.
The talk will cover in part joint work with Andrew Barron
(Yale), Abram Kagan (Maryland), and Tinghui Yu (Maryland).
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ICWS Seminar Series is supported by a grant from Rockwell Collins