# Neuronal Network Inference and Membrane Potential Model using Multivariate Hawkes Processes

arXiv: https://arxiv.org/abs/2108.00758 · HTML: https://mlsanity.com/paper/2108.00758/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Aug 2021.

## Built on by (most cited first, 5 of 5)

- [PCA for Point Processes](https://mlsanity.com/paper/2404.19661/) (2024)
- [Sparklen: A Statistical Learning Toolkit for High-Dimensional Hawkes Processes in Python](https://mlsanity.com/paper/2502.18979/) (2025)
- [Causal Structure Learning in Hawkes Processes with Complex Latent Confounder Networks](https://mlsanity.com/paper/2508.11727/) (2025)
- [Chemical Reaction Networks Learn Better than Spiking Neural Networks](https://mlsanity.com/paper/2603.12060/) (2026)
- [Clinically Meaningful Explainability for NeuroAI: An ethical, technical, and clinical perspective](https://mlsanity.com/paper/2603.18028/) (2026)

## Abstract (arXiv)

In this work, we propose to catch the complexity of the membrane potential's dynamic of a motoneuron between its spikes, taking into account the spikes from other neurons around. Our approach relies on two types of data: extracellular recordings of multiple spikes trains and intracellular recordings of the membrane potential of a central neuron. Our main contribution is to provide a unified framework and a complete pipeline to analyze neuronal activity from data extraction to statistical inference. The first step of the procedure is to select a subnetwork of neurons impacting the central neuron: we use a multivariate Hawkes process to model the spike trains of all neurons and compare two sparse inference procedures to identify the connectivity graph. Then we infer a jump-diffusion dynamic in which jumps are driven from a Hawkes process, the occurrences of which correspond to the spike trains of the aforementioned subset of neurons that interact with the central neuron. We validate the Hawkes model with a goodness-of-fit test and we show that taking into account the information from the connectivity graph improves the inference of the jump-diffusion process. The entire code has been developed and is freely available on GitHub.