Estimating dynamic models by matching random features

2026-07-23

AI Summary

This work addresses the challenge of parameter estimation in dynamic models where the likelihood function is intractable, and existing likelihood-free methods either rely on handcrafted summary statistics or computationally expensive neural networks. To overcome these limitations, the authors propose a simulation-based inference approach leveraging random features. Their key innovation lies in introducing embedding theory from nonlinear dynamical systems into simulation-based inference, enabling identification of a p-dimensional parameter model by matching only a small number (2p+1) of random features between observed and simulated data. The method applies to both stationary and non-stationary processes and, under mild regularity conditions, yields consistent estimators. This framework establishes a new paradigm for dynamic system parameter estimation that is efficient, broadly applicable, and theoretically grounded.

Abstract

Scientists increasingly express their ideas as dynamic models of complex processes. It is often much easier to simulate these models than to calculate the probability of their generating a particular outcome, making likelihood-based estimation infeasible. Existing likelihood-free approaches rely either on manually chosen summary statistics or on representations learned by neural networks. The former is error-prone and laborious, while the latter is computationally intensive, leaving many scientists in a difficult position. We show that, for a large class of dynamic models, parameters can be estimated by matching a small number of random features of the observed and simulated data. Specifically, we adapt results from nonlinear dynamics to show that models with a $p$-dimensional parameter can generically be identified from just $2p+1$ random features. We introduce two estimators for stationary and nonstationary processes, respectively, and we establish their consistency under mild regularity conditions. More broadly, our results serve as the foundation for a new class of random feature methods for simulation-based estimation and inference.

Problem

• dynamic models
• likelihood-free estimation
• simulation-based inference
• parameter estimation
• random features

Innovation

• random features
• likelihood-free inference
• dynamic models
• simulation-based estimation
• parameter identification