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.

翻译：在现代预测问题中，许多预测变量往往是罕见事件的发生计数。这导致设计矩阵中许多列高度稀疏。尽管在从自然语言处理（如罕见词汇）到生物学（如稀有物种）等不同领域普遍存在，这类"罕见特征"带来的挑战却鲜受关注。我们从理论和实证两方面证明，若不明确考虑特征的稀有性，会极大降低分析的有效性。接着我们提出一个框架，将罕见特征灵活聚合为更密集的特征，从而构建更优的响应变量预测因子。该策略利用编码特征相似性的树形结构作为辅助信息。我们将方法应用于TripAdvisor数据，通过评论文本预测酒店数值评分。该方法通过高效利用罕见词汇达到高精确度；相比之下，若词汇过于稀疏，Lasso无法识别具有强预测性的词汇。配套R语言包"rare"采用交替方向乘子法实现这一新估计量。