Theory and Applications of Random Forests

本研究发展了随机森林的理论，特别是为了更好地促进其在实际环境中的使用。理论上的考虑包括平衡性、子树、节点分布、节点分裂、变量深度和其他新颖的树概念。这些概念用于改进随机森林在高维和低维问题中的预测和变量选择。提高统计方法（如树）性能的最简单技术之一是对多个数据实例取其平均值。这种平均过程通常被称为集成学习，并且已经引起了相当大的关注，因为它被广泛观察到结合初级学习器可以产生具有优越预测性能的预测器。最成功的树集成学习器之一是随机森林。随机森林在经验上取得了相当大的成功，但对它仍有许多未知之处。本研究旨在提高我们对随机森林的理解，并利用这些知识来提高其在实际环境中的应用。这项研究的重点是心血管疾病，这是发达国家的头号死亡原因，癌症患者的癌症分期和预后，以及识别和开发骨髓增生综合征的基因型特征，骨髓增生综合征是一种血液干细胞异质性疾病，目前尚无治愈性药物治疗。

This research develops theory for random forests specifically for the purpose of better facilitating its use in practical settings. Theoretical considerations include balancedness, subtrees, node distributions, node splitting, depth of variables, and other novel tree concepts. These concepts are used to improve prediction and variable selection for random forests in both high and low-dimensional problems. One of the simplest techniques for improving the performance of a statistical method such as a tree is to take its average over multiple instances of the data. This averaging process is often referred to as ensemble learning and has attracted considerable attention as it has been widely observed that combining elementary learners can yield a predictor with superior prediction performance. One of the most successful tree ensemble learners is random forests. Random forests has met with considerable empirical success, yet much is still unknown about it. This research seeks to improve our understanding of random forests and utilize this knowledge to enhance its application in practical settings. This research focuses on cardiovascular disease, the number one cause of death in the developed world, cancer staging and prognostication for cancer patients, and identifying and developing genotype signatures for myelodsyplastic syndromes, a heterogeneous diseases of blood stem cells having no current curative medical therapy.