Sparse Signal Processing and Modeling of High Dimensional Spatio-Temporal Data

在实际应用中(例如，功能磁共振成像(FMRI)信号和微阵列基因表达时间序列数据)，被测量变量的数量大于样本大小的大型高维时空数据集被广泛地看到。高维情况下的统计估计和推断与经典情况下(样本量大，变量数少)有根本的不同，许多问题在很大程度上是开放的，需要新的统计信号处理理论和方法来涉及高维数据的回归、聚类、预测、分类等统计问题。一般来说，在高维数据中的估计和推断不可能不假设数据中的特殊的低等级(例如，稀疏)结构。在这一愿景下，当前的研究计划将通过建立理论基础和开发针对特定应用的新算法，专注于稀疏信号处理和高维数据建模。*更具体地说，拟议的研究计划将追求以下主要技术目标：1.研究了高维时间序列数据的稀疏性估计和推断问题。我们的目标是为高维过程的二阶推理建立理论和开发新的算法，这些过程可以是非IID(独立且同分布)、非平稳和非高斯的；开发新的在线稀疏主成分分析(PCA)和在线稀疏独立成分分析(ICA)降维算法，因为PCA和ICA可能是最流行的降维方法；研究激励现实世界的健康应用程序，包括基于帕金森氏病患者的实时功能磁共振神经反馈、基于视频的心脏生理监测，以及用于支持老年人认知康复的基于Kinect/iPad的严肃游戏。*本研究的意义在于对高维时空数据稀疏建模的理论和实践两方面进行了研究。该研究项目的成果将对大数据分析的理论和应用做出重大贡献。事实上，与硬件相关的业务相比，“数据分析”这个概念更具吸引力。作为所谓第三平台时代的关键创新加速器，大数据分析正在重塑许多行业，并给许多研究领域带来革命性的变化。这项拟议的研究将有助于将这一愿景向前推进一小步。该研究项目将为研究生提供接受相关尖端技术培训的机会。

Big high-dimensional spatio-temporal datasets, where the number of measured variables is larger than the sample size, are widely seen in real-world applications (e.g., functional magnetic resonance imaging (fMRI) signals and microarray gene expression time series data). Statistical estimation and inference in high-dimensional situations is fundamentally different from that in the classical setting (with large sample size and smaller number of variables) and many problems are largely open, requiring new statistical signal processing theory and methods involved in regression, clustering, prediction, classification and other statistical problems of high-dimensional data. Generally speaking, estimation and inference in high-dimensional data is not possible without assuming special low-rank (e.g., sparse) structures in the data. With this vision, the current research program will focus on sparse signal processing and modeling of high-dimensional data by both establishing theoretical foundations and developing application-specific novel algorithms. ******More specifically, the proposed research program will pursue the following main technical objectives: 1.) Investigating sparsity-aware estimation and inference problems for high-dimensional time series data. We aim to establish the theory and develop novel algorithms for 2nd-order inference of high-dimensional processes that can be non-iid (independent and identically distributed), non-stationary and non-Gaussian; 2.) Developing novel online sparse Principal Component Analysis (PCA) and online sparse Independent Component Analysis (ICA) algorithms for dimensionality reduction, since PCA and ICA are probably the most popular dimension reduction approaches; and 3.) Investigating motivating real-world health applications, including real-time fMRI based neurofeedback for Parkinson's Disease patients, video-based cardiac physiological monitoring, and Kinect/iPad based serious games for supporting elderly people's cognitive rehabilitation. ******The significance of this research lies in its focus on both the theory and practice of sparse modeling of high dimensional spatio-temporal data. The outcome of this research program will make significant contributions to both the theory and applications of big data analytics. Indeed, the notion “data analytics” is a more attractive capital-lite business than that related to hardware. As one key innovation accelerator in the so-called 3rd Platform era, big data analytics is reshaping many industries and revolutionizing many research areas. The proposed research will help take this vision one tiny step further. The research program will provide an opportunity for the graduate students to be trained in related cutting-edge technologies.