Stochastic Concept Bottleneck Models

TL;DR

This work proposes Stochastic Concept Bottleneck Models (SCBMs), a novel approach that models concept dependencies and introduces an explicit, distributional parameterization that allows SCBMs to retain the CBMs' efficient training and inference procedure.

Abstract

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.

Figures (9)

• Figure 1: Overview of the proposed method for the CUB dataset. (a) A user intervenes on the concept of 'primary color: yellow'. Unlike CBMs, our method then uses this information to adjust the predicted probability of correlated concepts, thereby affecting the target prediction. (b) Schematic overview of the intervention procedure. A user's intervention ${\bm{c}}'_{\mathcal{S}}$ is used to infer the logits $\boldsymbol{\eta}_{\setminus \mathcal{S}}$ of the remaining concepts. (c) Visualization of the learned global dependency structure as a correlation matrix for the 112 concepts of CUB wah2011caltech. Characterization of concepts on the left.
• Figure 2: Performance after intervening on concepts in the order of highest predicted uncertainty. Concept and target accuracy (%) are shown in the first and second rows, respectively. Results are reported as averages and standard deviations of model performance across ten seeds.
• Figure 3: Test-set calibration (%) of concept predictions. Results are reported as averages and standard deviations of model performance across ten seeds. For each dataset and metric, the best-performing method is bolded and the runner-up is underlined. Lower is better.
• Figure 4: Performance after intervening on concepts in the order of highest predicted uncertainty in CIFAR-100 with 892 concepts. Concept and target accuracy (%) are shown in the first and second rows, respectively. Results are reported as averages and standard deviations of model performance across 3 seeds.
• Figure 5: Intervention performance in the order of highest predicted uncertainty in CUB. Concept and target accuracy (%) are shown in the first and second rows, respectively. Results are reported as averages and standard deviations of model performance across 3 seeds.