Gradient estimators for parameter inference in discrete stochastic kinetic models
This work addresses parameter inference for researchers in physics and computational biology using stochastic models, offering incremental improvements by adapting existing gradient estimators.
The authors tackled the challenge of inferring parameters in discrete stochastic kinetic models, which are non-differentiable, by applying three gradient estimators from machine learning to the Gillespie algorithm, finding that the GS-ST estimator often works well but can fail in difficult regimes, while others provide more robust gradients.
Stochastic kinetic models are ubiquitous in physics, yet inferring their parameters from experimental data remains challenging. In deterministic models, parameter inference often relies on gradients, as they can be obtained efficiently through automatic differentiation. However, these tools cannot be directly applied to stochastic simulation algorithms (SSA) such as the Gillespie algorithm, since sampling from a discrete set of reactions introduces non-differentiable operations. In this work, we adopt three gradient estimators from machine learning for the Gillespie SSA: the Gumbel-Softmax Straight-Through (GS-ST) estimator, the Score Function estimator, and the Alternative Path estimator. We compare the properties of all estimators in two representative systems exhibiting relaxation or oscillatory dynamics, where the latter requires gradient estimation of time-dependent objective functions. We find that the GS-ST estimator mostly yields well-behaved gradient estimates, but exhibits diverging variance in challenging parameter regimes, resulting in unsuccessful parameter inference. In these cases, the other estimators provide more robust, lower variance gradients. Our results demonstrate that gradient-based parameter inference can be integrated effectively with the Gillespie SSA, with different estimators offering complementary advantages.