III: Small: Topics in Temporal Marked Point Processes: Granger Causality, Imperfect Observations and Intervention

事件序列在许多重要的应用程序中无处不在。例如，一场大地震可能引发多次余震，生命早期的一种特定疾病会在以后导致许多症状和疾病。一个基本的问题是不同类型的事件是如何相互关联的，以及一种类型的事件是如何引起另一种类型事件的发生的。该项目的目标是通过利用时间标记点过程的概率和统计方法来解决这个问题，该方法使用历史相关强度函数来模拟事件发生的瞬时可能性。该项目将专门研究因果关系的概念，它为解决如何控制时间标记点过程的问题提供了一个一般框架。为了使这些方法切实可行，该项目还将研究点过程数据有噪声和不完整时的统计学习问题。本研究以健康信息学与电子商务为研究对象。对于医疗保健，该研究有可能揭示疾病进展中有临床意义的合并症，并优化治疗方案，以改善医疗保健结果。对于电子商务，这项研究有可能提高公司的运营效率，增强用户体验。该项目将专注于机器学习和数据挖掘方法和算法，用于建模，学习和控制时间标记点过程。目标是理解和建模当前和未来特定类型事件的发生如何依赖于过去发生的相同和其他类型事件的发生，以及这种动态依赖关系如何在人群和时间中表现出异质性。最终，它将利用时间标记点过程的动态特性知识来设计干预策略，以改变其时间演化，从而达到更理想的结果。该项目的技术核心是开发基于强度的时间标记点过程的因果动态模型，目标是将格兰杰因果关系扩展到时间点过程的背景下。通过系统地研究各种不完全观测下的推理算法，使时间标记点过程的算法更加实用，并开发时间标记点过程时间演化的操纵和控制方法，以获得更理想的结果。

Event sequences are ubiquitous in many important applications. For example, a major earthquake may trigger many after-shocks and a specific disease in early life leads to many symptoms and diseases later on. A fundamental question is how different types of events relate to each other and how one type of event causes the occurrence of another type of event. The objective of this project is to address this question by leveraging the probabilistic and statistical methodology of temporal marked point processes, which models the instantaneous likelihood of an event occurrence using history dependent intensity functions. The project will specifically investigate the notion of causality that provides a general framework for tackling the problem of how to control a temporal marked point process. To make the methods practical, the project will also investigate statistical learning problems when point process data are noisy and incomplete. This research targets health informatics and e-commerce. For healthcare, the research has the potential to uncover clinically meaningful comorbidity in disease progression as well as to optimize treatment regimes for the purpose of improving healthcare outcomes. For e-commerce, the research has the potential to improve companies' operational efficiency and enhance user experiences.This project will focus on machine learning and data mining methodology and algorithms for modeling, learning and control of temporal marked point processes. The goal is in understanding and modeling of how the occurrences of a specific type of events at present and future depend on the occurrences of events of the same and other types happened in the past, and how this dynamic dependency exhibits heterogeneity across a population and across time. Ultimately, it will leverage knowledge of the dynamic properties of temporal marked point processes to design intervention policies to change their time evolution so as to achieve more desirable outcomes. The technical core of the project is to develop intensity based causal dynamic models of temporal marked point processes with the goal to extend Granger causality to the context of temporal point processes, to make algorithms for temporal marked point processes more practical by systematically investigating inference algorithms under a variety of imperfect observations and to develop methods for the manipulation and control of the time evolution of temporal marked point processes in order to achieve more desirable outcomes.