Exact identifiability analysis for a class of partially observed near-linear stochastic differential equation models

2025-03-25

AI Summary

Structural identifiability analysis lacks rigorous theoretical foundations and computational tools for partially observable, near-linear stochastic differential equation (SDE) models. Method: This paper introduces the first formal definition of structural identifiability for SDEs and establishes a moment-based analytical framework grounded in the dynamics of statistical moments. It derives observable moment constraints to assess exact identifiability of parameter combinations, characterizes the fundamental role of initial conditions, and extends the differential algebra approach to stochastic systems—enabling analysis of two- and higher-dimensional linear and near-linear SDEs. Symbolic computation and algebraic elimination are employed to verify identifiability. Contribution/Results: The work fills a critical theoretical gap in stochastic system identifiability, providing the first general, computationally tractable framework for structural identifiability analysis of SDEs. It yields explicit characterizations of identifiable parameter subsets across multiple model classes, thereby enabling principled stochastic modeling and parameter inference in domains such as systems biology.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Intelligent Robots: State Estimation
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Abstract

Stochasticity plays a key role in many biological systems, necessitating the calibration of stochastic mathematical models to interpret associated data. For model parameters to be estimated reliably, it is typically the case that they must be structurally identifiable. Yet, while theory underlying structural identifiability analysis for deterministic differential equation models is highly developed, there are currently no tools for the general assessment of stochastic models. In this work, we extend the well-established differential algebra framework for structural identifiability analysis to linear and a class of near-linear, two-dimensional, partially observed stochastic differential equation (SDE) models. Our framework is based on a deterministic recurrence relation that describes the dynamics of the statistical moments of the system of SDEs. From this relation, we iteratively form a series of necessarily satisfied equations involving only the observed moments, from which we are able to establish structurally identifiable parameter combinations. We demonstrate our framework for a suite of linear (two- and $n$-dimensional) and non-linear (two-dimensional) models. Most importantly, we define the notion of structural identifiability for SDE models and establish the effect of the initial condition on identifiability. We conclude with a discussion on the applicability and limitations of our approach, and potential future research directions.

Problem

• Extending identifiability analysis to stochastic differential equation models
• Developing tools for structural identifiability in partially observed SDEs
• Establishing identifiable parameter combinations using moment dynamics

Innovation

• Extends differential algebra to stochastic models
• Uses moment dynamics for identifiability analysis
• Defines structural identifiability for SDEs