III: Small: New Machine Learning Approaches for Modeling Time-to-Event Data

由于最近数据收集技术的进步，不同学科不仅能够积累各种各样的数据，而且能够在较长时间内监测观测结果。在许多实际应用程序中，监视这些观测值的主要目标是更好地估计某个感兴趣的特定事件发生的时间。这些事件的例子包括医疗保健中的疾病复发、金融中的违约时间、工程中的设备故障等。这种事件时间数据的一个主要挑战是，它往往是不完整的；在事件发生之前的一段时间内，一些数据实例要么被删除，要么变得不可观察。由于这部分信息的缺失，标准的统计和机器学习工具不能轻易地应用于分析这些数据。生存分析方法主要由统计社区开发，旨在为事件时间数据建模，与标准预测算法相比通常更有效，因为它们直接为事件发生的概率建模，而不是为数据实例分配名义标签。更重要的是，它们可以隐式地处理丢失的数据。然而，在许多实际场景中，缺少数据的挑战由于其他一些相关的复杂性而变得更加复杂，例如数据中存在相关性、跨多个实例（在一段时间内收集）的时间依赖性、缺乏来自单一来源的可用信息，以及难以在合理的时间内获取足够的事件数据。这些数据对预测分析领域提出了独特的挑战，因此创造了开发新算法来解决这些问题的机会。该项目提供创新的计算方法，以协助新的科学发现，并为各种时间事件数据集和应用的分析和探索带来实际的变革影响。所提出的方法主要是在生物医学数据的背景下进行评估，但也适用于其他学科（如社会科学、工程、金融和经济学）中常见的各种其他形式的事件时间数据。该项目构建了新颖的计算和分析算法，可以有效和准确地捕获时间到事件数据中的潜在预测模式。该项目旨在构建纵向数据分析的新算法，在构建时间到事件模型时集成多个源，并使用有限的训练数据预测时间事件。具体而言，研究目标是开发以下内容：(i)潜在特征模型，该模型可以捕获一段时间内多个结果的纵向依赖关系。学习不同缺失数据时间窗的多个独立回归模型，然后使用稀疏性正则化器在不同的输出空间上将其统一为一个多输出回归模型。（ii）多源事件时间模型，可以有效地整合多个信息来源，并通过纳入有关实例及其关系的先验知识进行预测。（iii）贝叶斯方法用于早期事件预测，解决研究早期缺乏足够的事件训练数据的问题（这是此类时间到事件数据中常见的问题）。本项目中提出的所有方法都使用现实世界的生物医学数据进行评估，包括高维基因组数据和异构电子健康记录。此外，在这个项目中开发的算法也将用于解决学生滞留的问题。

Due to the advancements in recent data collection technologies, different disciplines have attained the ability to not only accumulate a wide variety of data but also to monitor observations over longer periods of time. In many real-world applications, the primary goal of monitoring these observations is to better estimate the time for a particular event of interest to occur. Examples of these events include disease recurrence in healthcare, time to default in finance, device failure in engineering, etc. A major challenge with such time-to-event data is that it is often incomplete; some data instances are either removed or become unobservable over a period of time before the event occurs. Due to this missing piece of information, standard statistical and machine learning tools cannot readily be applied to analyze such data. Survival analysis methods, primarily developed by the statistics community, aim to model time-to-event data and are usually more effective compared to the standard prediction algorithms as they directly model the probability of occurrence of an event in contrast to assigning a nominal label to the data instance. More importantly, they can implicitly handle missing data. However, in many practical scenarios, the missing data challenges are compounded by several other related complexities such as the presence of correlations within the data, temporal dependencies across multiple instances (collected over a period of time), lack of available information from a single source, and difficulty in acquiring sufficient event data in a reasonable amount of time. Such data poses unique challenges to the field of predictive analytics and thus creates opportunities to develop new algorithms to tackle these issues. This project provides innovative computational methods to assist novel scientific discoveries and bring practical transformational impact to the analysis and exploration of various time-to-event datasets and applications. The proposed methods are primarily being evaluated in the context of biomedical data, but are applicable to various other forms of time-to-event data that is often seen in other disciplines such as social science, engineering, finance, and economics.This project builds novel computational and analytical algorithms that can efficiently and accurately capture the underlying predictive patterns in time-to-event data. The project aims at building new algorithms for longitudinal data analysis, integrate multiple sources while building time-to-event models, and predict temporal events with limited amount of training data. Specifically, the research objectives are to develop the following: (i) Latent feature models that can capture the longitudinal dependencies underlying multiple outcomes over a period of time. Multiple independent regression models for various missing data time windows are learned and then unified into a multi-output regression model over the diverse output space using sparsity regularizers. (ii) Multi-source time-to-event models that can effectively integrate multiple sources of information and make predictions by incorporating prior knowledge about the instances and their relationships. (iii) Bayesian methods for early-stage event prediction to tackle the problem of lack of sufficient training data on events at early stages of studies (which is a common problem in such time-to-event data). All the methods proposed in this project are evaluated using real-world biomedical data including high-dimensional genomic data and heterogeneous electronic health records. In addition, the algorithms developed in this project will also be used to tackle the problem of student retention.