  Interpretable models are designed to make decisions in a human-interpretable
manner. Representatively, Concept Bottleneck Models (CBM) follow a two-step
process of concept prediction and class prediction based on the predicted
concepts. CBM provides explanations with high-level concepts derived from
concept predictions; thus, reliable concept predictions are important for
trustworthiness. In this study, we address the ambiguity issue that can harm
reliability. While the existence of a concept can often be ambiguous in the
data, CBM predicts concepts deterministically without considering this
ambiguity. To provide a reliable interpretation against this ambiguity, we
propose Probabilistic Concept Bottleneck Models (ProbCBM). By leveraging
probabilistic concept embeddings, ProbCBM models uncertainty in concept
prediction and provides explanations based on the concept and its corresponding
uncertainty. This uncertainty enhances the reliability of the explanations.
Furthermore, as class uncertainty is derived from concept uncertainty in
ProbCBM, we can explain class uncertainty by means of concept uncertainty. Code
is publicly available at https://github.com/ejkim47/prob-cbm.
