Support Vector Machines for Censored Data

医学研究的最新进展，包括与人类基因组研究有关的进展，导致了个性化医学的发展。个性化医疗是指根据患者的基因特征和其他个人生物医学信息为患者量身定做的医疗。开发个性化的医疗方案是具有挑战性的，因为它涉及从高维患者数据中学习。此外，来自个性化医学临床研究的数据通常会受到审查，即数据没有得到充分的观察，例如，由于患者在研究过程中退出。虽然审查数据的统计分析是一个很发达的领域，但现有的大多数统计工具都是在限制性假设下开发的，这些假设往往不适用于高维数据环境。因此，重要的是开发一种可以应用于当今高维数据集的被审查数据的分析方法。在这个项目中，我们将开发新的机器学习技术，既可以处理高维数据，也可以处理审查数据。我们将开发的算法不仅适用于个性化医学领域，而且还适用于高维删失数据普遍存在的其他学科，如工程学、经济学和社会学。首先，我们将为不同类型的删失数据开发支持向量学习技术，包括右删失数据、区间删失数据、当前状态数据以及带有删失数据的多阶段决策问题。然后我们将研究这些估计量的理论性质，包括它们的有限样本性质和它们的渐近行为。为了实现这一目标，我们将开发新的方法，包括用于审查数据的新的有限样本工具。最后，我们将把我们开发的工具应用于真实世界的数据。我们将使用理论工具、模拟和对真实世界数据的分析来将所提出的学习方法与现有方法进行比较。最后，我们将为我们研究的每一种不同的算法开发软件。该软件将被开发成可以集成到现有的机器学习软件中。

Recent advances in medical research, including those related to the study of the human genome, have led to the development of personalized medicine. Personalized medicine describes medical treatment that is tailored to a patient based on the patient's genetic profile and other personal biomedical information. Developing personalized medical treatment regimens is challenging since it involves learning from high-dimensional patient data. Moreover, data from personalized-medicine clinical studies are typically subject to censoring, i.e., the data are not fully observed, due, for example, to patients dropping out during the course of a study. While statistical analysis of censored data is a well-developed area, most of the existing statistical tools were developed under restrictive assumptions that often do not hold for high-dimensional data settings. It is therefore important to develop an approach for analysis of censored data that can be applied to today's high-dimensional data sets. In this project we will develop novel machine learning techniques that can handle both high-dimensional and censored data. The algorithms that we will develop will be applicable not only in the field of personalized medicine, but also in other disciplines in which high-dimensional censored data are common, such as engineering, economics, and sociology.In this research, we will extend the framework of support vector machines (SVMs) to censored data. First, we will develop support vector learning techniques for different types of censored data, including right censored data, interval censoring, current status data, and multistage decision problems with censored data. We will then study the theoretical properties of these estimators, including their finite-sample properties and their asymptotic behavior. For this goal we will develop novel methodology, including new finite-sample tools for censored data. Finally, we will apply the tools that we develop to real-world data. We will compare the proposed learning methods with existing methods using theoretical tools, simulation, and analysis of real-world data. Finally, we will develop software for each of the different algorithms that we study. This software will be developed such that it can be integrated into existing machine learning software.