Inference of Qualitative Models from Steady-State Data via Weighted MaxSMT

2026-05-08

AI Summary

This work addresses the challenge of inferring qualitative models from noisy steady-state biological data, where measurement errors often render formal specifications unsatisfiable, obscuring the distinction between genuine modeling inaccuracies and technical artifacts. To overcome this, the study introduces weighted MaxSMT for the first time in this context, encoding uncertain observations as weighted soft constraints to enable model inference even in the presence of conflicts, thereby identifying the model best aligned with the data. The approach accommodates both Boolean and multi-valued variables and supports diverse constraint types—including discretization thresholds and differential expression rankings—substantially enhancing robustness and scalability. Empirical validation demonstrates successful inference of neural cell differentiation models from prior networks spanning 200 to 1,300 genes, confirming the method’s efficacy in large-scale biological systems.

Abstract

Qualitative models provide crucial instruments for modelling complex biological systems. While advances in automated reasoning and symbolic encodings have enabled rigorous inference of these models from data, the process remains highly fragile. First, biological measurement errors inevitably propagate into formal model specifications. Second, when a specification becomes unsatisfiable, distinguishing between fundamental design flaws and minor technical errors is notoriously difficult. This uncertainty often leads to under-specification, as it is unclear which observations are still ``safe'' to incorporate. To overcome these challenges, we introduce a robust inference method based on weighted MaxSMT. By encoding uncertain biological observations as weighted soft constraints, our approach enables the solver to identify a model best reflecting the observations, even with some conflicting constraints. Our method allows for Boolean and multi-valued variable domains, alongside observations derived from discretisation (level constraints) and differential expression (ordering constraints). We show our approach can be used to successfully infer neural cell differentiation models from prior-knowledge networks with 200--1300 genes using ordering constraints on all included genes.

Problem

• qualitative models
• steady-state data
• measurement errors
• unsatisfiable specifications
• model inference

Innovation

• Weighted MaxSMT
• qualitative modeling
• soft constraints
• biological network inference
• ordering constraints