Random forests, nonparametric and screening methods

数据的数量和复杂性都在增加，需要新的统计方法来处理越来越复杂的情况。本文的研究计划分为三个部分：1)复杂问题的随机森林，2)多变量数据的非参数推理，3)高维变量筛选。****随机森林是最流行的，准确和通用的预测和建模方法。随机森林的一大优点是，它们可以自动检测交互，而无需指定参数形式。在如今的大数据时代，它们甚至更有意义，因为它们非常适合并行计算。本研究计划的第一部分建议将随机森林扩展到复杂的问题，如带有审查的生存数据建模，以及对观测依赖的纵向数据的处理。****经典推理方法的有效性依赖于一定的分布假设，许多方法在未经验证时是非鲁棒的。本研究计划的第二部分将提出非参数方法，用于具有多变量响应的各种问题，如聚类数据，混合类型的响应和片面选择。还将开发全球新颖性检测方法。****超高维变量的筛选旨在快速降低维数，从而可以应用其他变量选择方法。本研究计划的第三部分将开发快速稳健的筛选方法，以数据驱动的方式选择要保留的变量数量，在不同的建模情况下。***本提案中研究的一个主要影响是对方法的用户，因为我们将传播本研究计划中开发的方法的计算机代码。* * * * * * * *

Data are increasing both in quantity and complexity and new statistical methods that can handle more and more complex situations are required. The research program of this proposal is divided into three parts: 1) Random forests for complex problems, 2) Nonparametric inference for multivariate data, 3) High-dimensional variable screening.****Random forests are among the most popular, accurate and versatile prediction and modeling methods. One big advantage of random forests is that they can automatically detect interactions without the need to specify a parametric form. They are even more pertinent nowadays, in the big data era, since they are well adapted for parallel computations. The first part of this research program proposes to extend random forests to complex problems, like the modeling of survival data with censoring, and the treatment of longitudinal data where the observations are dependent.****The validity of classical inference methods rely on certain distributional assumptions and many are non-robust when they are not verified. The second part of this research program will propose nonparametric methods for various problems with multivariate responses, like clustered data, mixed types of responses, and one-sided alternatives. Methods for global novelty detection will also be developed. ****The screening of variables in ultrahigh dimension aims at quickly reducing the dimensionality so other variable selection methods can be applied. The third part of this research program will develop fast robust screening methods with a data-driven way to select the number of variables to retain, in different modeling situations. ***One major impact of the research in this proposal is for the users of the methods since we will disseminate computer code for the methods developed in this research program. ********