Random forests, nonparametric and screening methods

随机森林、非参数和筛选方法

• 批准号: RGPIN-2016-05702
• 负责人: Larocque, Denis
• 金额: $ 2.4万
• 依托单位: HEC Montréal
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=760906
• 关键词: Random; forests; nonparametric; screening; methods

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.

数据的数量和复杂性都在增加，需要能够处理越来越复杂情况的新的统计方法。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断，3）高维变量筛选。随机森林是目前最流行、最准确、最通用的预测和建模方法之一。随机森林的一大优势是，它们可以自动检测交互，而无需指定参数形式。 如今，在大数据时代，它们甚至更加相关，因为它们非常适合并行计算。本研究计划的第一部分提出将随机森林扩展到复杂的问题，如删失生存数据的建模，以及观察依赖的纵向数据的处理。经典推理方法的有效性依赖于某些分布假设，并且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为具有多变量响应的各种问题提出非参数方法，如聚类数据，混合类型的响应和单侧替代方案。还将开发全球新奇检测方法。 在第二个维度上筛选变量的目的是快速降维，以便其他变量选择方法可以应用。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在不同建模情况下保留的变量数量。本提案中的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。