Statistical Learning and Modeling: Methodology and Algorithm

我的研究项目侧重于开发新的统计工具来分析、建模和解释复杂的系统，如人体动力学和医学研究中产生的高维多模态数据。这项研究处于现代统计学习和“传统”统计思想的交叉点。本研究有两个研究方向：(1)开发有效的统计模型和算法来描述、分析和解释人类行为数据，如电子邮件通信、紧急呼叫等；(2)开发用于分析高维多模态数据的自动统计学习工具。******第一个研究方向的最终目标是提出一个不需要领域知识且可解释的灵活模型。在未来五年内，我们希望实现的短期目标包括：(1)扩展当前的非参数自激点过程，即一个模型除了模拟激振和爆发现象外，还包含空间和时间信息，使其具有随位置和时间变化的分支系数函数，以满足现实世界的条件；(2)针对非参数自激点过程中背景函数和触发函数的估计，提出了一种基于期望最大化的局部对数似然估计方法；(3)进一步，研究非参数自激点过程的短期预测算法，预测未来事件发生的时间和次数。******为了克服分析来自多个来源的高维多模态数据的困难，在第二个研究方向上，我们建议开发一种混合方法，将统计学、计算拓扑和深度学习的方法交互结合起来。提出的研究包括三个短期目标：(1)三维面部成像中的颅面形态分析；(2)多元时间序列分析；(3)结构化和非结构化到结构化数据的联合分析。******在第一个研究方向上开发的方法可以很容易地适应并应用于其他领域，如社交网络和恐怖主义数据。在第二个研究方向上开发的新模型将有可能提高阻塞性睡眠呼吸暂停患者的诊断准确性，并导致开发新的工具来分析其他研究领域出现的高维多模态数据集。**

My research program focuses on developing new statistical tools to analyze, model, and interpret complex systems such as human dynamics and high-dimensional multimodal data arising from medical research. This research lies at the intersection of modern statistical learning and "traditional" statistical ideas. This proposed research has two research directions: (1) Develop efficient statistical models and algorithms for describing, analyzing and interpreting human behaviour data, such as e-mail communication, emergency calls etc.; (2) Develop automated statistical learning tools for analyzing high dimensional multimodal data.******The ultimate goal of the first research direction is to propose a flexible model, which does not require domain knowledge and is interpretable. The short term objectives we want to accomplish over the next five years include: (1) Extend the current nonparametric self-exciting point process, i.e., a model incorporates both spatial and temporal information besides modeling exciting and bursts phenomena, to have a branch coefficient function depending on location and time in order to satisfy real world conditions; (2) An Expectation Maximization based local log likelihood estimation will be proposed to reduce computational cost in estimating background and triggering functions in nonparametric self-exciting point processes; (3) Further, a short-term forecast algorithm for nonparametric self-exciting point processes will be developed to predict the time and number of the occurrence of future events. ******To overcome the difficulties in analyzing high-dimensional multimodal data from multiple sources, in the second research direction, we propose to develop a hybrid approach that interactively combines methods from statistics, computational topology and deep learning. The proposed research includes three short-term objectives: (1) Analysis of craniofacial morphology in 3D facial imaging; (2) Analysis of multivariate time series; (3) Joint analysis of structured and unstructured to structured data. ******The methods developed in the first research direction can be easily adapted and applied to other areas such as social networks and terrorist data. The new model developed in the second research direction will potentially enhance the diagnostic accuracy of Obstructive Sleep Apnea patients and lead to the development of new tools to analyze high-dimensional multimodal datasets arising in other research areas. **