Evidential Copula Concept Embedding Models

Concept Embedding Models (CEMs) advance interpretable AI by extending Concept Bottleneck Models (CBMs) through semantic concept embeddings, providing an important solution in high-stakes domains such as medical diagnosis where accuracy and interpretability are critical. However, a fundamental limitation persists: existing CEMs inherently assume concept independence, critically overlooking the highly complex dependencies among concepts. To address this, we propose an Evidential Copula Concept Embedding Model (EC-CEM) that redefines the joint distribution over concepts, capturing inter-concept dependencies while maintaining a flexible structure that decouples the marginal concept distributions from their dependency structure. In particular, EC-CEM relaxes the concept independence assumption and uniquely integrates Copula theory with evidential deep learning to define a joint distribution over concepts. The proposed EC-CEM also develops two training objectives that aim at classification and concept modeling simultaneously. We provide theoretical justification via variational inference and demonstrate empirical superiority through extensive experiments.

AI models that reason through human-understandable concepts before making predictions offer a promising path toward interpretable AI. However, existing Concept Embedding Models assume concepts are independent — ignoring the fact that concepts naturally co-occur and influence one another. Prior work attempting to model concept dependencies faces a structural problem: concept uncertainty and correlation become entangled in the same mathematical object. We propose EC-CEM, which resolves this tension by combining two theoretical tools. First, Evidential Deep Learning gives each concept its own principled uncertainty estimate. Second, Copula theory captures how concepts depend on each other — entirely separately from those individual uncertainty estimates. Crucially, we derive a variational inference objective that binds these two components together into a single end-to-end training framework, allowing the model to simultaneously learn concept uncertainty, inter-concept dependencies, and the final classification task. The result is a more expressive and theoretically grounded model, with better empirical gains especially when only a sparse set of concepts is available.