Parametric Copula-GP model for analyzing multidimensional neuronal and behavioral relationships

Abstract

One of the main goals of current systems neuroscience is to understand how neuronal populations integrate sensory information to inform behavior. However, estimating stimulus or behavioral information that is encoded in high-dimensional neuronal populations is challenging. We propose a method based on parametric copulas which allows modeling joint distributions of neuronal and behavioral variables characterized by different statistics and timescales. To account for temporal or spatial changes in dependencies between variables, we model varying copula parameters by means of Gaussian Processes (GP). We validate the resulting Copula-GP framework on synthetic data and on neuronal and behavioral recordings obtained in awake mice. We show that the use of a parametric description of the high-dimensional dependence structure in our method provides better accuracy in mutual information estimation in higher dimensions compared to other non-parametric methods. Moreover, by quantifying the redundancy between neuronal and behavioral variables, our model exposed the location of the reward zone in an unsupervised manner (i.e., without using any explicit cues about the task structure). These results demonstrate that the Copula-GP framework is particularly useful for the analysis of complex multidimensional relationships between neuronal, sensory and behavioral variables.

Mixed vine copula flows for flexible modeling of neural dependencies

“…Having validated the vine flow copula framework with artificial data, we subsequently focused on spiking activity from a subset of 5 V1 layer 2/3 neurons while the animal was navigating a virtual reality corridor (Figure 6A) (Henschke et al, 2020). A parametric vine copula framework with Gaussian processes (Kudryashova et al, 2022) was recently applied to calcium transients from the same V1 layer 2/3 neurons (Henschke et al, 2020). In the present study, we focused instead on modeling the deconvolved spiking activity with flow-based vine copulas.…”

“…First of all, real spike counts are characterized by discrete distributions and they exhibit a positive skew instead of a symmetric shape (Onken et al, 2009). Also, spike data do not usually display elliptical dependence as in the normal distribution but tend to be heavy tailed (Kudryashova et al, 2022), which geometrically translates to having probability mass concentrated on one of the corners. Finally, although the multivariate normal distribution is characterized by only second-order correlations, recent studies have indicated that higher order correlations are substantially present in local cortical populations and have a significant effect on the informational content of encoding (Pillow et al, 2008;Ohiorhenuan et al, 2010;Yu et al, 2011;Shimazaki et al, 2012;Montangie and Montani, 2017) as well as on the performance of decoding models (Michel and Jacobs, 2006).…”