Conformal outlier detection for multivariate functional data

Detecting outliers in multivariate functional data is crucial in a range of applications, including biomedical signal analysis and environmental monitoring. Existing methods primarily focus on identifying outliers within a given dataset but lack a principled approach for determining whether newly observed functional data deviate from a reference population. To address this limitation, we extend the conformal outlier detection framework of Bates et al. (2023) to the multivariate functional setting. A key challenge in this extension is defining appropriate nonconformity scores that effectively capture the structure of multivariate functional observations. We propose a novel nonconformity score based on the multivariate functional depth measure, which assess the centrality of an observation within a functional data distribution. This approach ensures the false discovery rate (FDR) control while offering a flexible, distribution-free method for functional outlier detection. We further introduce two practical enhancements: (i) leveraging curve transformations to improve the detection of shape outliers, and (ii) developing a two-step procedure to handle mixed training sets where the reference data may already contain outliers. The effectiveness of the proposed method is demonstrated through simulation studies and a real-data application using fMRI signals from the ADHD-200 dataset.