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ML Lunch (March 24): Recovering Block-structured Activations Using Compressive Measurements

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Published on Mar 24, 2014

Speaker: Mladen Kolar

Abstract
In recent years, with the advancement of large-scale data acquisition technology in various engineering, scientific, and socio-economical domains, traditional machine learning and statistical methods have started to struggle with massive amounts of increasingly high-dimensional data. Luckily, in many problems there is a simple structure underlying high-dimensional data that can be exploited to make learning feasible.

In this talk, I will focus on the problem of detection and localization of a contiguous block of weak activation in a large matrix, from a small number of noisy, possibly adaptive, compressive measurements. This is closely related to the problem of compressed sensing, where the task is to estimate a sparse vector using a small number of linear measurements. Contrary to results in compressed sensing, where it has been shown that neither adaptivity nor contiguous structure help much, we show that for reliable localization the magnitude of the weakest signals is strongly influenced by both structure and the ability to choose measurements adaptively while for detection neither adaptivity nor structure reduce the requirement on the magnitude of the signal. We characterize the precise tradeoffs between the various problem parameters, the signal strength and the number of measurements required to reliably detect and localize the block of activation. The sufficient conditions are complemented with information theoretic lower bounds.

Joint work with Sivaraman Balakrishnan, Alessandro Rinaldo and Aarti Singh.

For more ML lunch talks, visit http://www.cs.cmu.edu/~learning/

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