  Concept Bottleneck Models (CBMs) have emerged as a promising interpretable
method whose final prediction is based on intermediate, human-understandable
concepts rather than the raw input. Through time-consuming manual
interventions, a user can correct wrongly predicted concept values to enhance
the model's downstream performance. We propose Stochastic Concept Bottleneck
Models (SCBMs), a novel approach that models concept dependencies. In SCBMs, a
single-concept intervention affects all correlated concepts, thereby improving
intervention effectiveness. Unlike previous approaches that model the concept
relations via an autoregressive structure, we introduce an explicit,
distributional parameterization that allows SCBMs to retain the CBMs' efficient
training and inference procedure. Additionally, we leverage the
parameterization to derive an effective intervention strategy based on the
confidence region. We show empirically on synthetic tabular and natural image
datasets that our approach improves intervention effectiveness significantly.
Notably, we showcase the versatility and usability of SCBMs by examining a
setting with CLIP-inferred concepts, alleviating the need for manual concept
annotations.
