Prediction and outlier detection in classification problems

作者：Leying Guan, R. Tibshirani · 发表于：Journal of The Royal Statistical Society Series B-statistical Methodology · 年份：2019 · DOI：10.1111/rssb.12443 · 被引用次数：89 · 研究领域：Mathematics、Medicine

We consider the multi‐class classification problem when the training data and the out‐of‐sample test data may have different distributions and propose a method called BCOPS (balanced and conformal optimized prediction sets). BCOPS constructs a prediction set C(x) as a subset of class labels, possibly empty. It tries to optimize the out‐of‐sample performance, aiming to include the correct class and to detect outliers x as often as possible. BCOPS returns no prediction (corresponding to C(x) equal to the empty set) if it infers x to be an outlier. The proposed method combines supervised learning algorithms with conformal prediction to minimize a misclassification loss averaged over the out‐of‐sample distribution. The constructed prediction sets have a finite sample coverage guarantee without distributional assumptions. We also propose a method to estimate the outlier detection rate of a given procedure. We prove asymptotic consistency and optimality of our proposals under suitable assumptions and illustrate our methods on real data examples.