Unveiling Scaling Laws of Parameter Identifiability and Uncertainty Quantification in Data-Driven Biological Modeling

Area of Science:

• Computational Biology
• Systems Biology
• Mathematical Modeling

Background:

• Integrating high-dimensional biological data into mechanistic models requires robust practical identifiability for reliable interpretation and generalizability.
• Current coordinate identifiability analyses face numerical instabilities near singular local minimizers, hindering accurate modeling.

Purpose of the Study:

• To develop a computational framework for uncovering scaling laws in practical identifiability using asymptotic analysis.
• To provide a hierarchical approach for quantifying coordinate identifiability and managing uncertainty in non-identifiable subspaces.

Main Methods:

• Synthesizing Fisher information with perturbed Hessian matrices.
• Employing asymptotic analysis to establish fundamental scaling laws for identifiability.
• Validating the framework on synthetic and real-world biological data.

Main Results:

• The framework successfully quantifies coordinate identifiability and informs uncertainty quantification across different orders.
• Demonstrated efficiency in analyzing HIV-host dynamics and spatiotemporal amyloid-beta propagation.
• Identified critical mechanisms for HIV diagnostics and Alzheimer's disease progression.

Conclusions:

• The developed framework offers essential scaling laws for parameter identifiability and uncertainty in data-driven mechanistic modeling.
• Ensures data-driven inferences are grounded in verifiable biological reality, crucial for large-scale mechanistic digital twins.