Simulation-based inference for efficient identification of generative models in computational connectomics
Authors: Boelts Jan , Harth Philipp , Gao Richard , Udvary Daniel , Yáñez Felipe , Baum Daniel , Hege Hans-Christian , Oberlaender Marcel , Macke Jakob H. 
Published: February 2023

Recent advances in connectomics research enable the acquisition of increasing amounts of data about the connectivity patterns of neurons. How can we use this wealth of data to efficiently derive and test hypotheses about the principles underlying these patterns? A common approach is to simulate neuronal networks using a hypothesized wiring rule in a generative model and to compare the resulting synthetic data with empirical data. However, most wiring rules have at least some free parameters, and identifying parameters that reproduce empirical data can be challenging as it often requires manual parameter tuning. Here, we propose to use simulation-based Bayesian inference (SBI) to address this challenge. Rather than optimizing a fixed wiring rule to fit the empirical data, SBI considers many parametrizations of a rule and performs Bayesian inference to identify the parameters that are compatible with the data. It uses simulated data from multiple candidate wiring rule parameters and relies on machine learning methods to estimate a probability distribution (the ‘posterior distribution over parameters conditioned on the data’) that characterizes all data-compatible parameters. We demonstrate how to apply SBI in computational connectomics by inferring the parameters of wiring rules in anin silicomodel of the rat barrel cortex, givenin vivoconnectivity measurements. SBI identifies a wide range of wiring rule parameters that reproduce the measurements. We show how access to the posterior distribution over all data-compatible parameters allows us to analyze their relationship, revealing biologically plausible parameter interactions and enabling experimentally testable predictions. We further show how SBI can be applied to wiring rules at different spatial scales to quantitatively rule out invalid wiring hypotheses. Our approach is applicable to a wide range of generative models used in connectomics, providing a quantitative and efficient way to constrain model parameters with empirical connectivity data.

Author summary

The brain is composed of an intricately connected network of cells—what are the principles that contribute to constructing these patterns of connectivity, and how? To answer these questions, amassing connectivity data alone is not enough. We must also be able to efficiently develop and test our ideas about the underlying connectivity principles. For example, we could simulate a hypothetical wiring rule like “neurons near each other are more likely to form connections” in a computational model and generate corresponding synthetic data. If the synthetic, simulated data resembles the real, measured data, then we have some confidence that our hypotheses might be correct. However, the proposed wiring rules usually have unknown parameters that we need to “tune” such that simulated data matches the measurements. The central challenge thus lies in finding all the potential parametrizations of a wiring rule that can reproduce the measured data, as this process is often idiosyncratic and labor-intensive. To tackle this challenge, we introduce an approach combining computational modeling in connectomics, deep learning, and Bayesian statistical inference to automatically infer a probability distribution over the model parameters likely to explain the data. We demonstrate our approach by inferring the parameters of a wiring rule in a detailed model of the rat barrel cortex and find that the inferred distribution identifies multiple data-compatible model parameters, reveals biologically plausible parameter interactions, and allows us to make experimentally testable predictions.