Efficient Out-of-Distribution Detection Using Latent Space of $β$-VAE for Cyber-Physical Systems

Deep Neural Networks are actively being used in the design of autonomous Cyber-Physical Systems (CPSs). The advantage of these models is their ability to handle high-dimensional state-space and learn compact surrogate representations of the operational state spaces. However, the problem is that the sampled observations used for training the model may never cover the entire state space of the physical environment, and as a result, the system will likely operate in conditions that do not belong to the training distribution. These conditions that do not belong to training distribution are referred to as Out-of-Distribution (OOD). Detecting OOD conditions at runtime is critical for the safety of CPS. In addition, it is also desirable to identify the context or the feature(s) that are the source of OOD to select an appropriate control action to mitigate the consequences that may arise because of the OOD condition. In this paper, we study this problem as a multi-labeled time series OOD detection problem over images, where the OOD is defined both sequentially across short time windows (change points) as well as across the training data distribution. A common approach to solving this problem is the use of multi-chained one-class classifiers. However, this approach is expensive for CPSs that have limited computational resources and require short inference times. Our contribution is an approach to design and train a single $\beta$-Variational Autoencoder detector with a partially disentangled latent space sensitive to variations in image features. We use the feature sensitive latent variables in the latent space to detect OOD images and identify the most likely feature(s) responsible for the OOD. We demonstrate our approach using an Autonomous Vehicle in the CARLA simulator and a real-world automotive dataset called nuImages.