# Parameter estimation for biochemical reaction networks using Wasserstein distances

## TL;DR

This paper introduces a novel parameter estimation method for stochastic biochemical reaction networks that leverages Wasserstein distances, Gaussian process modeling, and Bayesian optimization to accurately fit steady-state distributions.

## Contribution

It combines Wasserstein distance-based fitting with Gaussian process and Bayesian optimization, enabling effective parameter estimation for complex stochastic models.

## Key findings

- Successfully applied to gene expression and feedback loop models
- Outperforms moment-based methods in challenging scenarios
- Applicable to various stochastic simulation models

## Abstract

We present a method for estimating parameters in stochastic models of biochemical reaction networks by fitting steady-state distributions using Wasserstein distances. We simulate a reaction network at different parameter settings and train a Gaussian process to learn the Wasserstein distance between observations and the simulator output for all parameters. We then use Bayesian optimization to find parameters minimizing this distance based on the trained Gaussian process. The effectiveness of our method is demonstrated on the three-stage model of gene expression and a genetic feedback loop for which moment-based methods are known to perform poorly. Our method is applicable to any simulator model of stochastic reaction networks, including Brownian Dynamics.