CAREER: Data-Starved Inference on Point Processes

从表面上看，分析2003年纽约市的大停电，评估交通系统的瓶颈和应急准备，以及成像细胞的遗传活动是非常不同的挑战。然而，这些问题和许多其他重要的问题都是以有限的离散事件测量为特征的，比如一系列系统故障事件，交通网络中通过少量检查点的车辆，或者由基因触发的染料发出的微小光脉冲。本研究的重点是开发基于复杂统计分析的创新理论和计算工具，从少量间接观察到的离散事件中提取有意义的信息。一些教育项目与这些研究追求紧密结合，包括开发新颖的动手学生活动，重点是从间接测量中获取信息。这些课程旨在通过现实世界的例子激发人们对工程学科的兴趣，并最终提高技术素养。高维点过程的数据匮乏推理包括各种各样的基础理论挑战，以及许多关键应用，包括荧光显微镜、网络流量分析、天体物理学和光谱学。本研究包括一个理论和方法框架的发展，用于分析和指导高维、数据匮乏和复杂的基于事件的系统的设计，这些系统可能是动态变化的，用辅助特征向量标记，或支持不规则拓扑。这项工作的教育方面与研究活动紧密结合，有助于进一步推进工程师和整个社会对信号处理挑战和工具的理解。特别是，调查人员正在为中小学生设计外联活动，并开发关于多维和统计信号处理的本科和研究生课程。

On the surface, analyzing the 2003 blackout in New York City, evaluating transportation systems for bottlenecks and emergency preparedness, and imaging a cell's genetic activity are very different challenges. However, these and many other important problems are all characterized by limited measurements of discrete events, such as a cascading series of system failure events, vehicles passing a small number of checkpoints in a transportation network, or tiny pulses of light emitted by a gene-triggered dye. This research is focused on the development of innovative theoretical and computational tools based on sophisticated statistical analyses for extracting meaningful information from small numbers of indirectly observed discrete events. Several educational programs are tightly coupled with these research pursuits, including the development of novel hands-on student activities focused on deriving information from indirect measurements.These programs are designed to stimulate interest in engineering disciplines through real-world examples and ultimately improve technical literacy. Data-starved inference on high-dimensional point processes encompasses a wide variety of fundamental theoretical challenges coupled with many critical applications, including fluorescence microscopy, network traffic analysis, astrophysics, and spectroscopy. This research comprises the development of a theoretical and methodological framework for analyzing and guiding the design of high-dimensional, data-starved, and complex event-based systems which may be dynamically changing, marked with auxiliary feature vectors, or supported on irregular topologies. The educational aspects of this work are tightly integrated with the research activities and help further advance the understanding of signal processing challenges and tools among both engineers and society at large. In particular, the investigators are designing outreach activities for primary and secondary school students and developing undergraduate- and graduate-level courses on multidimensional and statistical signal processing.