Prediction and outlier detection in classification problems

TL;DR

This paper introduces BCOPS, a method combining conformal prediction and supervised learning to create prediction sets that handle distribution shifts and detect outliers in multi-class classification, with theoretical guarantees.

Contribution

The paper proposes BCOPS, a novel approach that optimizes prediction sets for out-of-sample performance and outlier detection, with proven asymptotic consistency and finite-sample coverage guarantees.

Findings

BCOPS effectively detects outliers and maintains coverage.

The method demonstrates asymptotic optimality.

Real data examples validate the approach.

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 as often as possible, but also detecting outliers $x$, for which the method returns no prediction (corresponding to $C(x)$ equal to the empty set). The proposed method combines supervised-learning algorithms with the method of 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 method. We prove asymptotic consistency and optimality of our proposals under suitable assumptions and illustrate our methods on real data examples.