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

大的高维时空数据集，其中测量变量的数量大于样本大小，在现实世界的应用中广泛存在（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）。高维情形下的统计估计和推断与经典情形下的统计估计和推断有着本质的不同（大样本、小变量），许多问题在很大程度上是开放性的，需要新的统计信号处理理论和方法来解决高维数据的回归、聚类、预测、分类等统计问题。一般来说，在不假设特殊的低秩（例如，稀疏的）数据结构。有了这个愿景，目前的研究计划将集中在稀疏信号处理和建模的高维数据，建立理论基础和开发特定应用的新算法。

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.