Stochastic Variational Bayesian Inference for a Nonlinear Forward Model

TL;DR

This paper introduces a stochastic variational Bayesian inference method for nonlinear models, providing a flexible and computationally efficient alternative to analytical solutions, demonstrated on toy and real MRI data.

Contribution

A novel stochastic VB approach for nonlinear model inference that avoids certain approximations of the analytical method, enabling broader applicability.

Findings

Achieves comparable parameter recovery to analytical VB.

Offers competitive computational speed despite sampling.

Successfully applied to MRI perfusion data.

Abstract

Variational Bayes (VB) has been used to facilitate the calculation of the posterior distribution in the context of Bayesian inference of the parameters of nonlinear models from data. Previously an analytical formulation of VB has been derived for nonlinear model inference on data with additive gaussian noise as an alternative to nonlinear least squares. Here a stochastic solution is derived that avoids some of the approximations required of the analytical formulation, offering a solution that can be more flexibly deployed for nonlinear model inference problems. The stochastic VB solution was used for inference on a biexponential toy case and the algorithmic parameter space explored, before being deployed on real data from a magnetic resonance imaging study of perfusion. The new method was found to achieve comparable parameter recovery to the analytic solution and be competitive in terms of computational speed despite being reliant on sampling.