Title: Novelty Detection with Augmented Localized Conformal $p$-values
Primary area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
Keywords: Conformal inference, False discovery rate, Kernel estimation, Localized conformal inference, Novelty detection

Abstract: Novelty detection is an important area of research in both statistics and machine learning.
In this paper, we focus on the conditional novelty detection problem, where novelties arise from the relationship between different variables. We first adopt the conformal inference framework and propose the Augmented Localized Conformal $p$-values (ALCP), constructed by recalibrating an augmented conditional distribution estimator. This estimator efficiently captures conditional information by incorporating both calibration and test data into its kernel estimation. We show that the resulting $p$-values are valid in finite samples and can improve detection efficiency. Based on ALCP, we then develop a novel conditional novelty detection algorithm, along with a data-driven bandwidth selection method that ensures finite-sample false discovery rate (FDR) control while enhancing detection power. Both simulated and real data experiments demonstrate the advantages of the proposed ALCP approach.