|Discovering Switching Autoregressive Dynamics in Neural Spike Train Recordings
|Year of Publication
|Johnson, MJ, Linderman, SW, Datta, SR, Adams, R
|Salt Lake City, UT, USA
Generalized linear models (GLM) are powerful tools for identifying dependence in spiking populations of neurons, both over time and within the population (Paninski, 2004). The GLM identifies these dependencies by modeling spiking patterns through a linear regression and an appropriately-selected link function and likelihood. This regression setup is appealing for its simplicity, the wide variety of available priors, the potential for interpretability, and its computational efficiency. However, the GLM suffers from at least three notable deficiencies. First, the model is linear up to the link function, which only allows a limited range of response maps from neural spiking histories. Second, the model’s parameters are fixed over time, while neural responses may vary due to processes that are exogenous to the population. Third, the generalized linear model presupposes a characteristic time scale for all dynamics, when there may be multiple, varying time scales of neural activity in a given population. Here we seek to address these deficiencies via a switching variant of the generalized linear model. A switching system is one that evolves through a set of discrete states over time, with each state exhibiting its own lowlevel dynamics. For example, the latent state of a hidden Markov model (HMM) can be used to determine the parameters of an autoregressive (AR) process. These HMM-AR models can be used to identify common patterns of linear dependence that vary over time. Bayesian nonparametric versions of HMM-AR models extend these ideas to allow for an infinite number of such patterns to exist a priori, and semi-Markov variants allow the different states to have idiosyncratic duration distributions. Here we develop GLM variants of these switching AR processes and specialize them for neural spiking data. In particular, we exploit recent data augmentation schemes for negative binomial likelihood functions (Pillow and Scott, 2012) to make inference tractable in HDP-HSMM-AR models with count-based observations.
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