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

该项目为大数据开发开发数学和计算方法。快速和在线算法，学习和适应数据的到来和变化的发展。对于给定的任务，如何自动理解和减少数据中的冗余，也在这个项目中得到了解决。多种形式的大麻烦，例如，音频和视频、音频和文本、视频和天气、来自多媒体的视频、来自多模态的脑成像、友谊网络和个人偏好。这一点在本项目中也得到了解决。这项研究的广泛影响源于大数据的广泛和多样的适用性以及这里开发的技术。在教育竞技场，发达的互联网课程拥有数以万计的观众，该项目通过不同的杜克倡议提供了独特的研究和本科教育的整合。挑战是解决了一个gamechangingparadigm：学习优化，在线学习任务相关的优化器是expectedto做什么，开发计算效率高的算法，以近似的理想行为，有时未知的优化。这项工作导出了用于网络推理的新的多模态公式，以及实时在线鲁棒PCA和鲁棒NMF，大数据建模和开发的基本工具;以及鲁棒的3D形状，网络和多模态匹配。该公式巧妙地解决了双优化问题，使其能够高效地执行分类和信号分离任务。稀疏建模扩展到新的场所和算法，使这些技术可用于大数据。配方和理论基础的补充与众多的应用。

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.