Scalable Bayesian Time Warping at Single-Neuron Resolution

Neuroscience analyses often require trial-averaging to determine reliable neural signals. However, trial-to-trial heterogeneity in the timing of neural dynamics often limits the efficacy of trial-averaging. In many cases, this heterogeneity may be linked to latent events, such as decision time, which lack obvious behavioral correlates. Here, we formulate a scalable Bayesian approach to time warping to resolve this challenge. We leverage newly developed methods for efficient Gaussian process regression, introduce a prior over monotonic piecewise-linear functions, and develop a parallel, blocked Hamiltonian Monte Carlo-within-Gibbs sampling approach to learn a full posterior distribution over model parameters. Moreover, we show this approach is capable of identifying warping function posteriors for individual neurons. On synthetic data, this capability can be used to identify latent subpopulation structure invisible to existing methods. On data from rat orbitofrontal cortex during a temporal wagering task, population-level fits favor more complex warps than most individual neurons require, providing evidence for heterogeneous single-neuron alignment surrounding a latent decision. Additionally, fitting to individual neurons sharpens firing patterns obscured by a shared population warp. In all, our results illustrate that Bayesian time warping is a practical tool for neural data analysis that not only mitigates trial-to-trial heterogeneity, but can leverage it to reveal previously hidden structure in single-neuron dynamics.