High stakes classification refers to classification problems where erroneously predicting the wrong class is very bad, but assigning "unknown" is acceptable. We make the argument that these problems require us to give multiple unknown classes, to get the most information out of our analysis. With imperfect data we refer to covariates with a large number of missing values, large noise variance, and some errors in the data. The combination of high stakes classification and imperfect data is very common in practice, but it is very difficult to work on using current methods. We present a one-class classifier (OCC) to solve this problem, and we call it NBP. The classifier is based on Naive Bayes, simple to implement, and interpretable. We show that NBP gives both good predictive performance, and works for high stakes classification based on imperfect data. The model we present is quite simple; it is just an OCC based on density estimation. However, we have always felt a big gap between the applied classification problems we have worked on and the theory and models we use for classification, and this model closes that gap. Our main contribution is the motivation for why this model is a good approach, and we hope that this paper will inspire further development down this path.

翻译：高风险分类是指错误预测类别会带来严重后果，但允许将样本标记为“未知”的分类问题。我们论证这类问题需要设置多个未知类别，以便从分析中获取最大信息。不完美数据指协变量存在大量缺失值、噪声方差较大以及数据中存在部分错误。高风险分类与不完美数据的组合在实际中非常常见，但现有方法难以处理这一挑战。我们提出一种名为NBP的一类分类器（OCC）来解决该问题。该分类器基于朴素贝叶斯方法，易于实现且可解释性强。研究表明，NBP不仅具有良好的预测性能，还能有效处理基于不完美数据的高风险分类。我们提出的模型非常简单——仅是一个基于密度估计的一类分类器。然而，我们始终认为实际分类问题与现有分类理论及模型之间存在巨大鸿沟，而该模型恰好弥合了这一差距。本文的核心贡献在于阐释了该模型为何是一种有效方法，并期望能启发后续研究沿此方向深入发展。