  Cyber-physical systems (CPS) like autonomous vehicles, that utilize learning
components, are often sensitive to noise and out-of-distribution (OOD)
instances encountered during runtime. As such, safety critical tasks depend
upon OOD detection subsystems in order to restore the CPS to a known state or
interrupt execution to prevent safety from being compromised. However, it is
difficult to guarantee the performance of OOD detectors as it is difficult to
characterize the OOD aspect of an instance, especially in high-dimensional
unstructured data.
  To distinguish between OOD data and data known to the learning component
through the training process, an emerging technique is to incorporate
variational autoencoders (VAE) within systems and apply classification or
anomaly detection techniques on their latent spaces. The rationale for doing so
is the reduction of the data domain size through the encoding process, which
benefits real-time systems through decreased processing requirements,
facilitates feature analysis for unstructured data and allows more explainable
techniques to be implemented.
  This study places probably approximately correct (PAC) based guarantees on
OOD detection using the encoding process within VAEs to quantify image features
and apply conformal constraints over them. This is used to bound the detection
error on unfamiliar instances with user-defined confidence. The approach used
in this study is to empirically establish these bounds by sampling the latent
probability distribution and evaluating the error with respect to the
constraint violations that are encountered. The guarantee is then verified
using data generated from CARLA, an open-source driving simulator.
