Classification of a mixture of Gaussians from noisy compressive measurements: Fundamental limits, designs and geometrical interpretation

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• Dr. Miguel Rodrigues, University College London
• Wednesday 29 January 2014, 11:00-12:00
• Department of Electrical and Electronic Engineering, Room 408.

If you have a question about this talk, please contact Patrick Kelly.

Compressive sensing (CS) is an emerging paradigm that offers the means to simultaneously sense and compress a signal without any loss of information. The sensing process is based on the projection of the signal of interest onto a set of vectors, which are typically constituted randomly, and the recovery process is based on the resolution of an inverse problem. The result that has captured the imagination of the signal and information processing community is that it is possible to perfectly reconstruct a n-dimensional s-sparse signal (sparse in some orthonormal dictionary or frame) with overwhelming probability with only O(slog(n/s)) linear random measurements or projections using tractable l1 minimization methods or iterative methods, like greedy matching pursuit.

The focus of compressive sensing has been primarily on exact or near-exact signal reconstruction from the set of linear signal measurements. However, it is also natural to leverage the paradigm to perform other relevant information processing tasks, such as detection, classification and estimation of certain parameters, from the set of compressive measurements. One could in fact argue that the paradigm is a better fit to information processing tasks such as signal detection, signal classification or pattern recognition rather than signal reconstruction, since it may be easier to discriminate between signal classes than reconstruct an entire signal using only partial information about the source signal.

The focus of this talk is on the classification of a mixture of Gaussians from noisy compressive measurements. By leveraging analogies between the compressive classification problem and the multiple-antenna wireless communications problem, we argue that it is possible to construct performance characterizations that encapsulate not only the standard phase transition notion (that captures the presence of absence of a misclassification error probability floor) but also other more refined notions such as the diversity gain and the measurement gain. We also argue that it is possible to use the new characterizations as a proxy to design optimal projections/measurements for compressive classification problems: such measurements lead to considerable performance gains in relation to random ones. It is also shown that the performance characterizations and the designs are imbued with considerable geometrical significance.

The talk also shows how the fundamental limits associated with the classification of a mixture of Gaussians translate into fundamental limits associated with the reconstruction of the mixture: in particular, we provide a characterization of the number of measurements that is both necessary and sufficient to reconstruct the mixture that it is much sharper than standard characterizations in the literature. In addition, the talk illustrates how such results apply to image compression.

This represents joint work with Hugo Reboredo (University of Porto, Portugal), Francesco Renna (University of Porto, Portugal), Lawrence Carin (Duke University, USA ) and Robert Calderbank (Duke University, USA )

Bio: Miguel Rodrigues is a Senior Lecturer with the Department of Electronic and Electrical Engineering, University College London, U.K. He was previously with the Department of Computer Science, University of Porto, Portugal, rising through the ranks from Assistant to Associate Professor, where he also led the Information Theory and Communications Research Group at Instituto de Telecomunicações – Porto. He received the Licenciatura degree in Electrical Engineering from the Faculty of Engineering of the University of Porto, Portugal in 1998 and the Ph.D. degree in Electronic and Electrical Engineering from University College London, UK in 2002. He has carried out postdoctoral research work both at Cambridge University, UK, as well as Princeton University, USA , in the period 2003 to 2007. He has also held visiting appointments at Princeton University, USA ., Duke University, USA , Cambridge University, UK and University College London, UK in the period 2007 to 2013.

His research interests are in the general areas of information theory, communications theory and statistical signal processing. He was the recipient of the IEEE Communications and Information Theory Societies Joint Paper Award in 2011 for the work on Wireless Information-Theoretic Security (with M. Bloch, J. Barros and S. W. McLaughlin). He was also the recipient of the the Prize Engenheiro António de Almeida, the Prize Engenheiro Cristiano Spratley, and the Merit Scholarship from the University of Porto, and the best student poster prize at the 2nd IMA Conference on Mathematics in Communications. He has also been awarded doctoral and postdoctoral research fellowships from the Portuguese Foundation for Science and Technology, and research fellowships from Foundation Calouste Gulbenkian.

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