Concept Bottleneck Models (CBMs) are interpretable models that predict the target variable through high-level human-understandable concepts, allowing users to intervene on mispredicted concepts to adjust the final output. While recent work has shown that modeling dependencies between concepts can improve CBM performance, especially under interventions, such approaches typically require retraining the entire model, which may be infeasible when access to the original data or compute is limited. In this paper, we introduce Post-hoc Stochastic Concept Bottleneck Models (PSCBMs), a lightweight method that augments any pre-trained CBM with a multivariate normal distribution over concepts by adding only a small covariance-prediction module, without retraining the backbone model. We propose two training strategies and show on real-world data that PSCBMs consistently match or improve both concept and target accuracy over standard CBMs at test time. Furthermore, we show that due to the modeling of concept dependencies, PSCBMs perform much better than CBMs under interventions, while remaining far more efficient than retraining a similar stochastic model from scratch.

翻译：概念瓶颈模型（CBM）是一种可解释模型，它通过人类可理解的高层概念来预测目标变量，允许用户对错误预测的概念进行干预以调整最终输出。尽管近期研究表明，建模概念间的依赖关系可以提升CBM的性能（尤其在干预场景下），但这类方法通常需要重新训练整个模型，当原始数据或计算资源受限时可能难以实现。本文提出后验随机概念瓶颈模型（PSCBM），这是一种轻量级方法，仅需添加一个小的协方差预测模块，即可为任何预训练的CBM注入概念上的多元正态分布，而无需重新训练主干模型。我们提出了两种训练策略，并在真实世界数据上证明，PSCBM在测试时始终能匹配或超越标准CBM在概念准确率和目标准确率上的表现。此外，由于对概念依赖关系的建模，PSCBM在干预场景下的性能显著优于CBM，同时其训练效率远高于从头训练同类随机模型。