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 a data-enhanced localized conformal p-value, constructed by recalibrating an enhanced conditional distribution estimator. This estimator efficiently captures conditional information by incorporating both calibration and test data into its kernel estimation. We show that our p-values are valid in finite samples and can improve detection efficiency. Based on this p-value, we then develop a novel conditional novelty detection algorithm, along with a data-driven bandwidth selection method that ensures finite-sample false discovery rate control while enhancing detection power. Both simulated and real data experiments demonstrate the advantages of our proposed approach.

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