Causal Neural Probabilistic Circuits

2026-03-01

AI Summary

This work proposes Causal Neural Probabilistic Circuits (CNPC), a novel approach that integrates causal probabilistic circuits into concept bottleneck models to address the limitation of ignoring causal dependencies among concepts during interventions. By combining neural attribute predictors with causal probabilistic circuits compiled from a causal graph, and fusing the predicted distribution with the marginal distribution under causal intervention via a product-of-experts mechanism, CNPC enables interpretable predictions that respect the underlying causal structure. The method supports exact and tractable causal intervention inference and includes a theoretical analysis of compositional intervention error. Experiments on five benchmark datasets demonstrate that CNPC significantly outperforms five baseline models under both in-distribution and out-of-distribution settings, achieving notably higher task accuracy in multi-attribute intervention scenarios.

Technology Category

• Machine Learning: Probabilistic Circuits and Graphical Models
• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Concept Bottleneck Models (CBMs) enhance the interpretability of end-to-end neural networks by introducing a layer of concepts and predicting the class label from the concept predictions. A key property of CBMs is that they support interventions, i.e., domain experts can correct mispredicted concept values at test time to improve the final accuracy. However, typical CBMs apply interventions by overwriting only the corrected concept while leaving other concept predictions unchanged, which ignores causal dependencies among concepts. To address this, we propose the Causal Neural Probabilistic Circuit (CNPC), which combines a neural attribute predictor with a causal probabilistic circuit compiled from a causal graph. This circuit supports exact, tractable causal inference that inherently respects causal dependencies. Under interventions, CNPC models the class distribution based on a Product of Experts (PoE) that fuses the attribute predictor's predictive distribution with the interventional marginals computed by the circuit. We theoretically characterize the compositional interventional error of CNPC w.r.t. its modules and identify conditions under which CNPC closely matches the ground-truth interventional class distribution. Experiments on five benchmark datasets in both in-distribution and out-of-distribution settings show that, compared with five baseline models, CNPC achieves higher task accuracy across different numbers of intervened attributes.

Problem

• Concept Bottleneck Models
• causal dependencies
• interventions
• causal inference
• interpretability

Innovation

• Causal Neural Probabilistic Circuit
• Concept Bottleneck Models
• Causal Inference
• Intervention
• Product of Experts