Out-of-Distribution Detection in Dependent Data for Cyber-Physical Systems with Conformal Guarantees

Abstract

Uncertainty in the predictions of learning-enabled components hinders their deployment in safety-critical cyber-physical systems (CPS). A shift from the training distribution of a learning-enabled component (LEC) is one source of uncertainty in the LEC’s predictions. Detection of this shift or out-of-distribution (OOD) detection on individual datapoints has therefore gained attention recently. But in many applications, inputs to CPS form a temporal sequence. Existing techniques for OOD detection in time-series data for CPS either do not exploit temporal relationships in the sequence or do not provide any guarantees on detection. We propose using deviation from the in-distribution temporal equivariance as the non-conformity measure in conformal anomaly detection framework for OOD detection in time-series data for CPS. Computing independent predictions from multiple conformal detectors based on the proposed measure and combining these predictions by Fisher’s method leads to the proposed detector CODiT with bounded false alarms. CODiT performs OOD detection on fixed-length windows of consecutive time-series datapoints by using Fisher value of the input window. We further propose performing OOD detection on real-time time-series traces of variable lengths with bounded false alarms. This can be done by using CODiT to compute Fisher values of the sliding windows in the input trace and combining these values by a merging function. Merging functions such as Harmonic Mean, Arithmetic Mean, Geometric Mean, and Bonferroni Method, etc. can be used to combine Fisher values of the sliding windows in the input trace, and the combined value can be used for OOD detection on the trace with bounded false alarm rate guarantees. We illustrate the efficacy of CODiT by achieving state-of-the-art results in two case studies for OOD detection on fixed-length windows. The first one is on an autonomous driving system with perception (or vision) LEC. The second case study is on a medical CPS for walking pattern or GAIT analysis where physiological (non-vision) data is collected with force-sensitive resistors attached to the subject’s body. For OOD detection on variable length traces, we consider the same case studies on the autonomous driving system and medical CPS for GAIT analysis. We report our results with four merging functions on the Fisher values computed by CODiT on the sliding windows of the input trace. We also compare the false alarm rate guarantees by these four merging functions in the autonomous driving system case study. Code, data, and trained models are available at https://github.com/kaustubhsridhar/time-series-OOD.