While including pairwise interactions in a regression model can better approximate response surface, fitting such an interaction model is a well-known difficult problem. In particular, analyzing contemporary high-dimensional datasets often leads to extremely large-scale interaction modeling problem, where the challenge is posed to identify important interactions among millions or even billions of candidate interactions. While several methods have recently been proposed to tackle this challenge, they are mostly designed by (1) assuming the hierarchy assumption among the important interactions and (or) (2) focusing on the case in linear models with interactions and (sub)Gaussian errors. In practice, however, neither of these two building blocks has to hold. In this paper, we propose an interaction modeling framework in generalized linear models (GLMs) which is free of any assumptions on hierarchy. We develop a non-trivial extension of the reluctance interaction selection principle to the GLMs setting, where a main effect is preferred over an interaction if all else is equal. Our proposed method is easy to implement, and is highly scalable to large-scale datasets. Theoretically, we demonstrate that it possesses screening consistency under high-dimensional setting. Numerical studies on simulated datasets and a real dataset show that the proposed method does not sacrifice statistical performance in the presence of significant computational gain.
Generalized raking and stabilized weights for regression modeling in two-phase samples
University of Melbourne（墨尔本大学）；Murdoch Children’s Research Institute（默多克儿童研究所）；Vanderbilt University（范德堡大学）；Kaiser Permanente Washington Health Research Institute（凯撒永久华盛顿健康研究所）；University of Auckland（奥克兰大学）
Joint Spatial and Temporal Generalized Dissimilarity Mixed Modeling (stGDMM) for Beta Diversity
Brigham Young University（杨百翰大学）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；University of Cape Town（开普敦大学）；South African Environmental Observation Network（南非环境观测网络）；University of Connecticut（康涅狄格大学）；Duke University（杜克大学）
Distributional regression models for Extended Generalized Pareto distributions
扩展广义帕累托分布（EGPD）（Naveau et al. 2016）是一个分布族，已引入该分布族来对正随机变量的全范围进行建模，但其下尾和上尾根据阈值以上峰值方法进行分布。本文的目的是扩大EGPD的应用范围，允许分析师将协变量对模型的影响。特别是，我们介绍了一个规范，EGPD的参数可以建模为协变量，如空间或时间的加性函数。作为相关产品，我们提供了一个用R编写的附加代码，它足够灵活，可以以通用的方式实现EGPD，允许引入新的参数形式。我们展示了我们的附加模块在法国西北部地区的每小时一次的模拟上的潜力，并讨论了建模策略。
