Linear dynamical neural population models through nonlinear embeddings

TL;DR

This paper introduces fLDS, a flexible nonlinear neural population model that captures complex neural variability using a low-dimensional latent space and variational inference, outperforming existing linear models.

Contribution

The paper presents fLDS, a novel nonlinear generative model for neural activity that allows arbitrary smooth functions of latent states and introduces a new inference method.

Findings

fLDS captures more neural variability with fewer latent dimensions

It achieves superior predictive performance compared to linear models

The model offers better interpretability of neural data

Abstract

A body of recent work in modeling neural activity focuses on recovering low-dimensional latent features that capture the statistical structure of large-scale neural populations. Most such approaches have focused on linear generative models, where inference is computationally tractable. Here, we propose fLDS, a general class of nonlinear generative models that permits the firing rate of each neuron to vary as an arbitrary smooth function of a latent, linear dynamical state. This extra flexibility allows the model to capture a richer set of neural variability than a purely linear model, but retains an easily visualizable low-dimensional latent space. To fit this class of non-conjugate models we propose a variational inference scheme, along with a novel approximate posterior capable of capturing rich temporal correlations across time. We show that our techniques permit inference in a wide class of generative models.We also show in application to two neural datasets that, compared to state-of-the-art neural population models, fLDS captures a much larger proportion of neural variability with a small number of latent dimensions, providing superior predictive performance and interpretability.