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Robust Inference and Communication: Theory, Algorithms and Performance Analysis

Co-PIs Sean P. Meyn and Venugopal V. Veeravalli 2008–2012

Project Summary This proposal is written in response to the growing need for new techniques for inference and communication in complex environments, as well as techniques to evaluate their performance. The proposed research consists of two complementary tracks. The first concerns methods for constructing inference and decoding algorithms for complex models, with possible modeling uncertainty, based on the geometry surrounding Kullback-Leibler (K-L) divergence and related methods developed by the PIs in recent research.

The second track treats performance evaluation and performance improvement. Both performance evaluation and algorithm selection will be performed using Monte-Carlo or related sample path learning techniques. These approaches are chosen primarily because of their ease of application when compared to deterministic techniques involving numerical integration.

Monte-Carlo techniques comes at a price in the form of high variance. The foundations of variance reduction techniques for simulation are very similar to the foundations of Information Theory based on K-L divergence. We will develop techniques for simulation and learning in concert with research on hypothesis testing and communication to construct faster algorithms for performance evaluation and adaptation.

The proposed research tasks are divided into three concurrent and inter-related projects:

Project 1: Robust hypothesis testing, with an emphasis on quickest change detection.

Project 2: Robust and efficient communication, with an emphasis on coding for wireless channels.

Project 3: Simulation and learning for optimizing algorithms developed under Projects 1 and 2.

In view of the tremendous practical importance of the basic problems considered, it is expected that even modest theoretical advances can have strong practical impact. Conversely, engineering insights gained by the use of practical simulation, learning and coding algorithms, are likely to lead to significant developments in the underlying statistical theory. 

 

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