  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.
