Learning stochasticity: a nonparametric framework for intrinsic noise estimation

TL;DR

This paper introduces Trine, a nonparametric kernel-based framework for estimating state-dependent intrinsic noise from time-series data, enabling better understanding of complex dynamical systems without relying on parametric models.

Contribution

The paper presents Trine, a novel three-phase, nonparametric method that accurately infers intrinsic noise in complex systems, outperforming traditional parametric approaches.

Findings

Trine accurately estimates intrinsic noise in biological and ecological systems.

It performs comparably to an oracle in benchmark problems.

Trine uncovers hidden dynamics without predefined parametric assumptions.

Abstract

Understanding the principles that govern dynamical systems is a central challenge across many scientific domains, including biology and ecology. Incomplete knowledge of nonlinear interactions and stochastic effects often renders bottom-up modeling approaches ineffective, motivating the development of methods that can discover governing equations directly from data. In such contexts, parametric models often struggle without strong prior knowledge, especially when estimating intrinsic noise. Nonetheless, incorporating stochastic effects is often essential for understanding the dynamic behavior of complex systems such as gene regulatory networks and signaling pathways. To address these challenges, we introduce Trine (Three-phase Regression for INtrinsic noisE), a nonparametric, kernel-based framework that infers state-dependent intrinsic noise from time-series data. Trine features a three-stage algorithm that com- bines analytically solvable subproblems with a structured kernel architecture that captures both abrupt noise-driven fluctuations and smooth, state-dependent changes in variance. We validate Trine on biological and ecological systems, demonstrating its ability to uncover hidden dynamics without relying on predefined parametric assumptions. Across several benchmark problems, Trine achieves performance comparable to that of an oracle. Biologically, this oracle can be viewed as an idealized observer capable of directly tracking the random fluctuations in molecular concentrations or reaction events within a cell. The Trine framework thus opens new avenues for understanding how intrinsic noise affects the behavior of complex systems.