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

该项目开发了大数据开发的数学和计算方法。开发了随着数据的到达和变化而学习和适应的快速在线算法。对于给定的任务，如何自动理解和减少数据中的冗余也在本项目中讨论。多种形式的大数据体，例如音频和视频、音频和文本、视频和天气、来自多个来源的视频、来自多个模式的大脑成像、友谊网络和个人偏好。这也在这个项目中得到了解决。这项研究的广泛影响来自于大数据的广泛适用性和这里开发的技术。在教育领域，开发的互联网课程拥有数万名受众，该项目通过不同的杜克大学倡议提供了研究和本科教育的独特整合。该框架遵循稀疏建模的简约理论。挑战是通过博弈改变范式来解决的：学习优化；在线学习依赖于任务的优化器应该做什么，开发计算高效的算法来近似某些未知优化器的理想行为。该工作导出了用于网络推理的新的多模式公式，以及大数据建模和开发的基本工具-实时在线稳健PCA和稳健NMF；以及稳健3D形状、网络和多模式匹配。该配方优雅地解决了双边开发问题，使其对于分类和信号分离任务变得高效。分离建模扩展到新的场地和算法，使此类技术可用于大数据。这些公式和理论基础与许多应用相辅相成。

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.