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，而且还能够监测更长时间的观测。在许多实际应用中，监视这些观测的主要目标是更好地估计感兴趣的特定事件发生的时间。这些事件的示例包括医疗保健中的疾病复发、财务中的违约时间、工程中的设备故障等。此类事件间隔时间数据的主要挑战是它通常是不完整的；一些数据实例在事件发生之前的一段时间内要么被删除，要么变得不可观察。由于这一信息的缺失，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。主要由统计界开发的生存分析方法旨在对到事件的时间数据进行建模，并且通常比标准预测算法更有效，因为与为数据实例分配名义标签相比，它们直接对事件发生的概率进行建模。更重要的是，它们可以隐式处理丢失的数据。然而，在许多实际情况下，丢失数据的挑战由于其他几个相关的复杂性而变得更加复杂，例如数据中存在相关性、跨多个实例的时间依赖关系(在一段时间内收集)、从单一来源缺乏可用的信息、以及在合理的时间内获取足够的事件数据的困难。这些数据对预测分析领域提出了独特的挑战，从而创造了开发新算法来解决这些问题的机会。该项目提供了创新的计算方法，以协助新的科学发现，并为分析和探索各种事件间隔数据集和应用程序带来实际的变革影响。建议的方法主要在生物医学数据的背景下进行评估，但也适用于在社会科学、工程学、金融学和经济学等其他学科中常见的各种其他形式的事件间隔时间数据。该项目构建了新的计算和分析算法，可以高效而准确地捕获事件间隔时间数据中潜在的预测模式。该项目旨在构建新的纵向数据分析算法，在构建事件间隔时间模型的同时集成多个来源，并使用有限的训练数据预测时间事件。具体地说，研究目标是开发以下内容：(I)能够捕捉一段时间内多种结果背后的纵向相关性的潜在特征模型。学习针对各种缺失数据时间窗口的多个独立回归模型，然后使用稀疏正则化将其统一到不同输出空间上的多输出回归模型。(2)多源时间-事件模型，该模型可以有效地集成多个信息源，并通过纳入关于实例及其关系的先验知识来进行预测。(3)早期事件预测的贝叶斯方法，以解决研究早期阶段缺乏关于事件的足够训练数据的问题(这是此类事件间隔时间数据中的一个常见问题)。本项目中提出的所有方法都使用真实世界的生物医学数据进行了评估，包括高维基因组数据和不同种类的电子健康记录。此外，本项目开发的算法还将用于解决留学生问题。

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.