Empirical vine copula modeling to study multivariate neural representations during complex behaviors

An important goal is to understand how neural activity relates to specific parameters in the external world and behavioral outputs. However, in many cases, it is difficult to isolate the contributions of single behavioral, external, or internal variates to neural activity, especially as the behaviors studied increase in complexity and focus on internal, cognitive variables. Behavior and experiment variables often have complex statistical dependencies, and generating a correct model of the relationships between neural activity and these variables requires understanding the dependency structure between all these variables. State-of-the-art approaches to model neural activity in terms of individual task or stimulus components, such as GLMs or deep neural networks, either make strong assumptions about the dependency structure or do not expose the dependencies explicitly, which makes the analysis and interpretation of how neural activity relates to behavior and experiment variables challenging. We propose a new approach for the modeling of neural activity that accounts for any general statistical dependency structure, regardless of its complexity and without making any parametric assumptions. We developed an analytical kernel vine copula to estimate the joint density function between neural activity patterns and all the dimensions of interest for the behavioral task or sensory stimulus. The copula structure captures the dependency structure of the multivariate density function and gives an empirical representation of the full statistical dependencies between all the variables, including neural activity. Using the vine decomposition allows us to estimate the density function regardless of the dimensionality. The density function can be used generatively to produce realistic samples, with similar dependency structure to the data, and can utilize mutual information tools to investigate neural coding. We used vine copula modeling to study the mouse posterior parietal cortex during a navigation-based choice task and to distinguish representations of movement-related actions and task-related choice signals.