 
Decentralized hypothesis testing problems
Martin Wainwright
Department of Statistics
Department of Electrical Engineering and Computer Sciences and Statistics
UC Berkeley, California
Many modern scientific and engineering applications are based on an
inherently decentralized setup, in which data is distributed
throughout a network, and cannot be aggregated at a central location
due to various forms of communication constraints. An important
example of such a decentralized system is a sensor network: a set of
spatiallydistributed sensors collect data from the environment (e.g.,
temperature, humidity etc.) but are permitted to transmit only a
compressed version back to a central location or fusion center. It is
frequently of interest to solve statistical inference problems in such
a decentralized setting.
We consider the problem of testing a binary hypothesis in a
decentralized setting. More concretely, the goal is to design
compression rules at the sensors (which determine the messages that
are relayed to the fusion center), as well as a decision function at
the fusion center so as to minimize the overall probability of error.
In contrast to most previous work (which focuses on the case when the
underlying distributions have known parametric forms), we consider the
problem of learning compression rules based on a set of empirical
samples. We propose a computationally efficient technique based on
regularized forms of of the empirical risk and kernel methods, and
analyze its statistical properties. Part of the analysis is based on
a connection between surrogates to the 01 loss, and the class of
$f$divergences (or AliSilvey distances).
Joint work with XuanLong Nguyen and Michael Jordan, UC Berkeley
