It is common in modern prediction problems for many predictor variables to be counts of rarely occurring events. This leads to design matrices in which many columns are highly sparse. The challenge posed by such “rare features” has received little attention despite its prevalence in diverse areas, ranging from natural language processing (e.g., rare words) to biology (e.g., rare species). We show, both theoretically and empirically, that not explicitly accounting for the rareness of features can greatly reduce the effectiveness of an analysis. We next propose a framework for aggregating rare features into denser features in a flexible manner that creates better predictors of the response. Our strategy leverages side information in the form of a tree that encodes feature similarity. We apply our method to data from TripAdvisor, in which we predict the numerical rating of a hotel based on the text of the associated review. Our method achieves high accuracy by making effective use of rare words; by contrast, the lasso is unable to identify highly predictive words if they are too rare. A companion R package, called rare, implements our new estimator, using the alternating direction method of multipliers.

在现代预测问题中，许多预测变量通常是很少发生的事件的计数。这导致其中许多列高度稀疏的设计矩阵。尽管从自然语言处理（例如稀有词）到生物学（例如稀有物种）等各个领域都盛行，但这种“稀有特征”带来的挑战却很少受到关注。我们从理论和经验上都表明，不明确考虑特征的稀缺性会大大降低分析的有效性。接下来，我们提出一个框架，以灵活的方式将稀有特征聚合为更密集的特征，从而创建更好的响应预测器。我们的策略以树的形式利用辅助信息，该信息对特征相似度进行编码。我们将方法应用于TripAdvisor的数据，其中，我们会根据相关评论的文字来预测酒店的数字评分。我们的方法通过有效地使用稀有词来实现高精度；相比之下，套索如果太少则无法识别高预测性的单词。一个称为R的伴随R包使用乘数的交替方向方法实现了我们的新估算器。