Combining tensor decomposition and time warping models for multi-neuronal spike train analysis

Abstract Recordings from large neural populations are becoming an increasingly popular and accessible method in experimental neuroscience. While the activity of individual neurons is often too stochastic to interrogate circuit function on a moment-by-moment basis, multi-neuronal recordings enable us to do so by pooling statistical power across many cells. For example, groups of neurons often exhibit correlated gain or amplitude modulation across trials, which can be statistically formalized in a tensor decomposition framework (Williams et al. 2018). Additionally, the time course of neural population dynamics can be shifted or stretched/compressed, which can be modeled by time warping methods (Williams et al. 2020). Here, I describe how these two modeling frameworks can be combined, and show some evidence that doing so can be highly advantageous for practical neural data analysis—for example, the presence of random time shifts hampers the performance and interpretability of tensor decomposition, while a time-shifted variant of this model corrects for these disruptions and uncovers ground truth structure in simulated data.