Including pairwise interactions between the predictors of a regression model can produce better predicting models. However, to fit such interaction models on typical data sets in biology and other fields can often require solving enormous variable selection problems with billions of interactions. The scale of such problems demands methods that are computationally cheap (both in time and memory) yet still have sound statistical properties. Motivated by these large-scale problem sizes, we adopt a very simple guiding principle: One should prefer main effects over interactions if all else is equal. This "reluctance" to interactions, while reminiscent of the hierarchy principle for interactions, is much less restrictive. We design a computationally efficient method built upon this principle and provide theoretical results indicating favorable statistical properties. Empirical results show dramatic computational improvement without sacrificing statistical properties. For example, the proposed method can solve a problem with 10 billion interactions with 5-fold cross-validation in under 7 hours on a single CPU.

翻译：在回归模型中纳入预测变量之间的两两交互作用可产生预测性能更优的模型。然而，针对生物学及其他领域的典型数据集拟合此类交互模型，往往需要解决涉及数十亿交互项的庞大变量选择问题。此类问题的规模要求方法必须兼具计算经济性（包括时间与内存）与良好的统计性质。受大规模问题场景驱动，我们采用极其简洁的指导原则：在其他条件相同时，应优先选择主效应而非交互效应。这种对交互作用的"勉强性"虽与交互作用的层次原则相似，但约束性弱得多。基于该原则，我们设计了一种高效计算方法，并提供了表明其具有优越统计性质的理论结果。实验结果表明，该方法在保持统计性质的同时，实现了计算效率的显著提升。例如，在单个CPU上，所提方法可在7小时内解决包含5折交叉验证的100亿交互项问题。