Compressive sensing as a new paradigm for model building

Abstract

The widely-accepted intuition that the important properties of solids are determined by a few key variables underpins many methods in physics. Though this reductionist paradigm is applicable in many physical problems, its utility can be limited because the intuition for identifying the key variables often does not exist or is difficult to develop. Machine learning algorithms (genetic programming, neural networks, Bayesian methods, etc.) attempt to eliminate the a priori need for such intuition but often do so with increased computational burden and human time. A recently-developed technique in the field of signal processing, compressive sensing (CS), provides a simple, general, and efficient way of finding the key descriptive variables. CS is a new paradigm for model building-we show that its models are just as robust as those built by current state-of-the-art approaches, but can be constructed at a fraction of the computational cost and user effort.

First arXiv submission: 7 pages, 4 figures, submitted to PRB. Second arXiv submission:14 pages, 7 figures. Significant changes made to the text in this revision but content and science is the same, presentation is merely improved. More mathematical detail, clearer discussion of the outcomes, etc

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