# Nonlinear Evolution via Spatially-Dependent Linear Dynamics for Electrophysiology and Calcium Data

arXiv: https://arxiv.org/abs/1811.02459 · HTML: https://mlsanity.com/paper/1811.02459/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Nov 2018.

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

- [Variational Combinatorial Sequential Monte Carlo Methods for Bayesian Phylogenetic Inference](https://mlsanity.com/paper/2106.00075/) (2021)
- [Deep inference of latent dynamics with spatio-temporal super-resolution using selective backpropagation through time](https://mlsanity.com/paper/2111.00070/) (2021)

## Abstract (arXiv)

Latent variable models have been widely applied for the analysis of time series resulting from experimental neuroscience techniques. In these datasets, observations are relatively smooth and possibly nonlinear. We present Variational Inference for Nonlinear Dynamics (VIND), a variational inference framework that is able to uncover nonlinear, smooth latent dynamics from sequential data. The framework is a direct extension of PfLDS; including a structured approximate posterior describing spatially-dependent linear dynamics, as well as an algorithm that relies on the fixed-point iteration method to achieve convergence. We apply VIND to electrophysiology, single-cell voltage and widefield imaging datasets with state-of-the-art results in reconstruction error. In single-cell voltage data, VIND finds a 5D latent space, with variables akin to those of Hodgkin-Huxley-like models. VIND's learned dynamics are further quantified by predicting future neural activity. VIND excels in this task, in some cases substantially outperforming current methods.