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，不同学科不仅有能力积累各种数据，而且有能力在较长时间内监测观测结果。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特定感兴趣事件发生的时间。这些事件的示例包括医疗保健中的疾病复发、金融中的违约时间、工程中的设备故障等。此类事件发生时间数据的一个主要挑战是它通常不完整;一些数据实例在事件发生前的一段时间内被删除或变得不可观察。由于这一信息缺失，标准的统计和机器学习工具无法轻易应用于分析此类数据。生存分析方法主要由统计界开发，旨在对事件时间数据进行建模，并且通常比标准预测算法更有效，因为它们直接对事件发生的概率进行建模，而不是将标称标签分配给数据实例。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，缺失数据的挑战会因其他几个相关的复杂性而加剧，例如数据中存在相关性，多个实例之间的时间依赖性（在一段时间内收集），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。此类数据对预测分析领域提出了独特的挑战，从而为开发新算法来解决这些问题创造了机会。 该项目提供创新的计算方法，以协助新的科学发现，并为各种时间到事件数据集和应用程序的分析和探索带来实际的变革性影响。 所提出的方法主要在生物医学数据的背景下进行评估，但也适用于其他学科中常见的各种其他形式的时间到事件数据，如社会科学，工程，金融和经济学。该项目构建了新颖的计算和分析算法，可以有效准确地捕获时间到事件数据中的潜在预测模式。该项目旨在构建用于纵向数据分析的新算法，在构建时间到事件模型的同时集成多个源，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，可以捕获一段时间内多个结果的纵向依赖关系。学习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器将其统一为不同输出空间上的多输出回归模型。(ii)多源时间事件模型，可以有效地集成多个信息源，并通过合并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，以解决研究早期阶段缺乏足够的事件训练数据的问题（这是此类事件时间数据中的常见问题）。在这个项目中提出的所有方法都使用真实世界的生物医学数据，包括高维基因组数据和异构电子健康记录进行评估。此外，该项目中开发的算法也将用于解决学生保留问题。

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.