Title: Leveraging Gradient Estimators for Parameter Inference in Discrete Stochastic Kinetic Models

Abstract:

While stochastic kinetic models are prevalent across physics, extracting their parameters from empirical data presents significant difficulties. In the realm of deterministic modeling, parameter inference frequently depends on gradient calculations, which are efficiently derived via automatic differentiation (AD). However, direct application of AD to the Gillespie stochastic simulation algorithm (SSA) is precluded because the discrete nature of reaction sampling introduces non-differentiable operations. To address this, our study applies three machine learning-derived gradient estimators to the Gillespie SSA: the Gumbel-Softmax Straight-Through (GS-ST) estimator, the Score Function estimator, and the Alternative Path estimator. These tools were utilized to compute gradients for both time-dependent and steady-state observables, with their efficacy assessed through representative biophysical systems exhibiting either oscillatory dynamics (the repressilator) or relaxation dynamics (bimolecular association). Our analysis reveals that while the GS-ST estimator typically produces stable gradient estimates, it suffers from diverging variance in difficult parameter regimes, potentially leading to inference failures. In such scenarios, alternative estimators deliver more robust gradients with lower variance. Ultimately, our findings confirm that gradient-based parameter inference can be successfully integrated with the Gillespie SSA, as the various estimators provide complementary strengths.

Source: arXiv Generated at: 2026-06-04 00:00:00 UTC