Multimodal VAEs have recently gained significant attention as generative models for weakly-supervised learning with multiple heterogeneous modalities. In parallel, VAE-based methods have been explored as probabilistic approaches for clustering tasks. At the intersection of these two research directions, we propose a novel multimodal VAE model in which the latent space is extended to learn data clusters, leveraging shared information across modalities. Our experiments show that our proposed model improves generative performance over existing multimodal VAEs, particularly for unconditional generation. Furthermore, we propose a post-hoc procedure to automatically select the number of true clusters thus mitigating critical limitations of previous clustering frameworks. Notably, our method favorably compares to alternative clustering approaches, in weakly-supervised settings. Finally, we integrate recent advancements in diffusion models into the proposed method to improve generative quality for real-world images.

Recently, interpretable machine learning has re-explored concept bottleneck models (CBM). An advantage of this model class is the user's ability to intervene on predicted concept values, affecting the downstream output. In this work, we introduce a method to perform such concept-based interventions on *pretrained* neural networks, which are not interpretable by design, only given a small validation set with concept labels. Furthermore, we formalise the notion of *intervenability* as a measure of the effectiveness of concept-based interventions and leverage this definition to fine-tune black boxes. Empirically, we explore the intervenability of black-box classifiers on synthetic tabular and natural image benchmarks. We focus on backbone architectures of varying complexity, from simple, fully connected neural nets to Stable Diffusion. We demonstrate that the proposed fine-tuning improves intervention effectiveness and often yields better-calibrated predictions. To showcase the practical utility of our techniques, we apply them to deep chest X-ray classifiers and show that fine-tuned black boxes are more intervenable than CBMs. Lastly, we establish that our methods are still effective under vision-language-model-based concept annotations, alleviating the need for a human-annotated validation set.

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.