A Note on Simulation-Based Inference by Matching Random Features

TL;DR

This paper proposes a simulation-based inference method that matches randomly chosen features of simulation outputs to data, leveraging ideas from nonlinear dynamics and machine learning to efficiently identify model parameters.

Contribution

It introduces a novel inference approach using random features for model identification, combining concepts from nonlinear dynamics and machine learning.

Findings

Matching random features can identify model parameters effectively.

Using only 2d+1 features suffices for models with d-dimensional parameters.

Preliminary numerical results support the method's potential.

Abstract

We can, and should, do statistical inference on simulation models by adjusting the parameters in the simulation so that the values of {\em randomly chosen} functions of the simulation output match the values of those same functions calculated on the data. Results from the "state-space reconstruction" or "geometry from a time series'' literature in nonlinear dynamics indicate that just $2d+1$ such functions will typically suffice to identify a model with a $d$-dimensional parameter space. Results from the "random features" literature in machine learning suggest that using random functions of the data can be an efficient replacement for using optimal functions. In this preliminary, proof-of-concept note, I sketch some of the key results, and present numerical evidence about the new method's properties. A separate, forthcoming manuscript will elaborate on theoretical and numerical details.