Mixed vine copula flows for flexible modeling of neural dependencies

Abstract

Recordings of complex neural population responses provide a unique opportunity for advancing our understanding of neural information processing at multiple scales and improving performance of brain computer interfaces. However, most existing analytical techniques fall short of capturing the complexity of interactions within the concerted population activity. Vine copula-based approaches have shown to be successful at addressing complex high-order dependencies within the population, disentangled from the single-neuron statistics. However, most applications have focused on parametric copulas which bear the risk of misspecifying dependence structures. In order to avoid this risk, we adopted a fully non-parametric approach for the single-neuron margins and copulas by using Neural Spline Flows (NSF). We validated the NSF framework on simulated data of continuous and discrete types with various forms of dependency structures and with different dimensionality. Overall, NSFs performed similarly to existing non-parametric estimators, while allowing for considerably faster and more flexible sampling which also enables faster Monte Carlo estimation of copula entropy. Moreover, our framework was able to capture low and higher order heavy tail dependencies in neuronal responses recorded in the mouse primary visual cortex during a visual learning task while the animal was navigating a virtual reality environment. These findings highlight an often ignored aspect of complexity in coordinated neuronal activity which can be important for understanding and deciphering collective neural dynamics for neurotechnological applications.

Discovering Low-Dimensional Descriptions of Multineuronal Dependencies

“…As in our previous work [41], we modeled the margin and copula densities nonparametrically using Rational-Quadratic Neural Spline Flows (NSF) [42], a specific type of normalizing flow [43]. These flows are a class of generative models that can construct arbitrary probability densities using smooth and invertible transformations to and from simple probability distributions.…”

“…As previously [41], we chose the uniform distribution on [0, 1] as a base distribution for NSF so that backward and forward flow transformations for the margins approximate the probability/distributional and the quantile transform, respectively. The reason for choosing NSF [42] for modeling both margin and copula densities was that they combine the flexibility of non-affine flows while maintaining easy invertibility by approximating a quasiinverse with piecewise spline-based transformations around knot points of the mapping.…”

“…The procedure we followed for fitting the C-vine model with NSF to data was the same as in our previous work, where it is described in more detail [41]. Briefly, we decided the order of the variables for the C-vine model based on a heuristic, namely, the sum of absolute value Kendall's taus that we calculated for each neuron in relation to every other neuron.…”

“…In our previous work [41], we studied neural dependencies with NSF-based C-vine copulas in a small subset of mouse V1 layer 2/3 neurons that were recorded during a virtual navigation task [56]. Even in this small subset we identified features such as asymmetric tail dependencies that would have been ignored by conventional pairwise correlations analyses.…”

“…In our previous work [41], we followed a fully non-parametric approach for capturing single-neuron margins and copula densities by using Neural Spline Flows (NSF) [42], which is a class of normalizing flows [43]. We found that NSFs performed similarly to existing non-parametric estimators while allowing for faster and more flexible sampling.…”