Probabilistic ML Verification via Weighted Model Integration

Abstract

In machine learning (ML) verification, the majority of procedures are non-quantitative and therefore cannot be used for verifying probabilistic models, or be applied in domains where hard guarantees are practically unachievable. The probabilistic formal verification (PFV) of ML models is in its infancy, with the existing approaches limited to specific ML models, properties, or both. This contrasts with standard formal methods techniques, whose successful adoption in real-world scenarios is also due to their support for a wide range of properties and diverse systems. We propose a unifying framework for the PFV of ML systems based on Weighted Model Integration (WMI), a relatively recent formalism for probabilistic inference with algebraic and logical constraints. Crucially, reducing the PFV of ML models to WMI enables the verification of many properties of interest over a wide range of systems, addressing multiple limitations of deterministic verification and ad-hoc algorithms. We substantiate the generality of the approach on prototypical tasks involving the verification of group fairness, monotonicity, robustness to noise, probabilistic local robustness and equivalence among predictors. We characterize the challenges related to the scalability of the approach and, through our WMI-based perspective, we show how successful scaling techniques in the ML verification literature can be generalized beyond their original scope.