At first glance, modern applications of data processing -- such as
clustering, querying, and search -- bear little resemblance to the
classical Shannon-theoretic problem of lossy compression. However,
the ultimate goal is the same for modern and classical settings; both
demand algorithms which strike a balance between the complexity of the
algorithm output and the utility that it provides. Thus, when we attempt to
establish fundamental performance limits for these "modern" data
processing problems, elements of classical rate distortion theory
Inspired by the challenges associated with extracting useful
information from large datasets, I will discuss compression under
logarithmic loss. Logarithmic loss is a penalty function which
measures the quality of beliefs a user can generate about the original
data upon observing the compressor's output. In this context, we
characterize the tradeoff between the degree to which data can be
compressed and the quality of beliefs an end user can produce.
Notably, our results for compression under logarithmic loss extend to
distributed systems and yield solutions to two canonical problems in
multiterminal source coding.
I will also briefly discuss recent work on compression for
identification, where we seek to compress data in a manner that
preserves the ability to reliably answer queries of a certain form.
This setting stands in stark contrast to the traditional compression
paradigm, where the goal is to reproduce the original data (either
exactly or approximately) from its compressed form. Under certain
assumptions on the data sources, we characterize the tradeoff between
compression rate and the reliability at which queries can be answered.
Bio: Thomas Courtade received the B.S. degree in Electrical Engineering from Michigan Technological University in 2007, and the M.S. and Ph.D. degrees in Electrical Engineering from UCLA in 2008 and 2012, respectively. In 2012, he was awarded the Inaugural Postdoctoral Research Fellowship through the Center for Science of Information. He currently holds this position, and resides at Stanford University. His recent honors include a Distinguished Ph.D. Dissertation award and an Excellence in Teaching award from the UCLA Department of Electrical Engineering and a Best Student Paper Award at the 2012 International Symposium on Information Theory.