# Differential Covariance: A New Class of Methods to Estimate Sparse Connectivity from Neural Recordings

## TL;DR

This paper introduces differential covariance methods for estimating neural connectivity, which outperform or match existing GLM approaches in simulations, requiring fewer data samples and applicable to various neural recording types.

## Contribution

The authors develop a novel differential covariance approach for neural connectivity estimation, expanding its application to different neural signals and demonstrating improved performance over traditional methods.

## Key findings

- Differential covariance methods outperform or match GLM in simulated data.
- The new methods require fewer data samples for accurate connectivity estimation.
- Applicable to intracellular voltage, LFP, and calcium imaging data.

## Abstract

With our ability to record more neurons simultaneously, making sense of these data is a challenge. Functional connectivity is one popular way to study the relationship between multiple neural signals. Correlation-based methods are a set of currently well-used techniques for functional connectivity estimation. However, due to explaining away and unobserved common inputs (Stevenson et al., 2008), they produce spurious connections. The general linear model (GLM), which models spikes trains as Poisson processes (Okatan et al., 2005; Truccolo et al., 2005; Pillow et al., 2008), avoids these confounds. We develop here a new class of methods by using differential signals based on simulated intracellular voltage recordings. It is equivalent to a regularized AR(2) model. We also expand the method to simulated local field potential (LFP) recordings and calcium imaging. In all of our simulated data, the differential covariance-based methods achieved better or similar performance to the GLM method and required fewer data samples. This new class of methods provides alternative ways to analyze neural signals.