AF: SMALL: Learning to Parsimoniously Model and Compute with Big Data

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This project develops mathematical and computational approaches for big data exploitation. Fast and onlinealgorithms that learn and adapt as data arrives and changes are developed. How to automaticallyunderstand and reduce redundancy in the data, for a given task, is also addressed in this project. Big datacomes in multiple forms, e.g., audio and video, audio and text, video and weather, video from multiplesources, brain imaging from multiple modalities, friendship networks and individual preferences. This isalso addressed in this project. The broad impact of the research is born in the large and diverseapplicability of big data and in the techniques here developed. In the education arena, the developedInternet classes have an audience of tens of thousands, and the project provides unique integration ofresearch and undergraduate education via different Duke initiatives.The framework follows the parsimony theory of sparse modeling. Challenges are addressed with a gamechangingparadigm: learning to optimize; on-line learning what the task-dependent optimizer is expectedto do, developing computationally efficient algorithms to approximate the ideal behavior of sometimesunknown optimizers. The work derives novel multi-modal formulations for network inference, and realtimeon-line robust PCA and robust NMF, fundamental tools in big data modeling and exploitation; aswell as robust 3D shape, networks, and multi-modal matching. The formulation elegantly solves bileveloptimization problems rendering it efficient for classification and signal separation tasks. Sparsemodeling is extended to new venues and algorithms, making such techniques usable for big data. Theformulations and theoretical foundations are complemented with numerous applications.