# Inverting brain grey matter models with likelihood-free inference: a tool for trustable cytoarchitecture measurements

arXiv: https://arxiv.org/abs/2111.08693 · HTML: https://mlsanity.com/paper/2111.08693/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 60 references that are in the map.
- First posted on arXiv 15 Nov 2021.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [Automatic Posterior Transformation for Likelihood-Free Inference](https://mlsanity.com/paper/1905.07488/) (2019)
- [Fast ε-free Inference of Simulation Models with Bayesian Conditional Density Estimation](https://mlsanity.com/paper/1605.06376/) (2016)
- [Rotationally-invariant mapping of scalar and orientational metrics of neuronal microstructure with diffusion MRI](https://mlsanity.com/paper/1609.09144/) (2016)

## Built on by (most cited first, 2 of 2)

- [L-C2ST: Local Diagnostics for Posterior Approximations in Simulation-Based Inference](https://mlsanity.com/paper/2306.03580/) (2023)
- [μGUIDE: a framework for quantitative imaging via generalized uncertainty-driven inference using deep learning](https://mlsanity.com/paper/2312.17293/) (2023)

## Abstract (arXiv)

Effective characterisation of the brain grey matter cytoarchitecture with quantitative sensitivity to soma density and volume remains an unsolved challenge in diffusion MRI (dMRI). Solving the problem of relating the dMRI signal with cytoarchitectural characteristics calls for the definition of a mathematical model that describes brain tissue via a handful of physiologically-relevant parameters and an algorithm for inverting the model. To address this issue, we propose a new forward model, specifically a new system of equations, requiring a few relatively sparse b-shells. We then apply modern tools from Bayesian analysis known as likelihood-free inference (LFI) to invert our proposed model. As opposed to other approaches from the literature, our algorithm yields not only an estimation of the parameter vector θ that best describes a given observed data point x0, but also a full posterior distribution p(θ|x0) over the parameter space. This enables a richer description of the model inversion, providing indicators such as credible intervals for the estimated parameters and a complete characterization of the parameter regions where the model may present indeterminacies. We approximate the posterior distribution using deep neural density estimators, known as normalizing flows, and fit them using a set of repeated simulations from the forward model. We validate our approach on simulations using dmipy and then apply the whole pipeline on two publicly available datasets.