Prediction and outlier detection in classification problems

Leying Guan and Robert Tibshirani

Journal of the Royal Statistical Society Series B, 2022, vol. 84, issue 2, 524-546

Abstract: 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.

Date: 2022
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