Quantifying Signal-to-Noise Ratio in Neural Latent Trajectories via Fisher Information

TL;DR

This paper derives a Fisher information-based upper bound on the signal-to-noise ratio for neural latent trajectory inference, providing insights for model fitting, neural response simulation, and experiment design.

Contribution

It introduces a practical SNR bound for neural trajectory inference based on Fisher information, linking it to overdispersion and temporal regularities.

Findings

Inference methods exploiting temporal regularities achieve higher SNRs.

The SNR bound is proportional to overdispersion and Fisher information per neuron.

Results inform model fitting, neural response simulation, and experimental design.

Abstract

Spike train signals recorded from a large population of neurons often exhibit low-dimensional spatio-temporal structure and modeled as conditional Poisson observations. The low-dimensional signals that capture internal brain states are useful for building brain machine interfaces and understanding the neural computation underlying meaningful behavior. We derive a practical upper bound to the signal-to-noise ratio (SNR) of inferred neural latent trajectories using Fisher information. We show that the SNR bound is proportional to the overdispersion factor and the Fisher information per neuron. Further numerical experiments show that inference methods that exploit the temporal regularities can achieve higher SNRs that are proportional to the bound. Our results provide insights for fitting models to data, simulating neural responses, and design of experiments.