TY - JOUR
T1 - Scaling the Poisson GLM to massive neural datasets through polynomial approximations
AU - Zoltowski, David M.
AU - Pillow, Jonathan William
N1 - Funding Information:
DMZ was supported by NIH grant T32MH065214 and JWP was supported by grants from the Simons Foundation (SCGB AWD1004351 and AWD543027), the NIH (R01EY017366, R01NS104899) and a U19 NIH-NINDS BRAIN Initiative Award (NS104648-01). The authors thank Nick Steinmetz for sharing the Neuropixels data and thank Rob Kass, Stephen Keeley, Michael Morais, Neil Spencer, Nick Steinmetz, Nicholas Roy, and the anonymous reviewers for providing helpful comments.
Publisher Copyright:
© 2018 Curran Associates Inc..All rights reserved.
PY - 2018
Y1 - 2018
N2 - Recent advances in recording technologies have allowed neuroscientists to record simultaneous spiking activity from hundreds to thousands of neurons in multiple brain regions. Such large-scale recordings pose a major challenge to existing statistical methods for neural data analysis. Here we develop highly scalable approximate inference methods for Poisson generalized linear models (GLMs) that require only a single pass over the data. Our approach relies on a recently proposed method for obtaining approximate sufficient statistics for GLMs using polynomial approximations [7], which we adapt to the Poisson GLM setting. We focus on inference using quadratic approximations to nonlinear terms in the Poisson GLM log-likelihood with Gaussian priors, for which we derive closed-form solutions to the approximate maximum likelihood and MAP estimates, posterior distribution, and marginal likelihood. We introduce an adaptive procedure to select the polynomial approximation interval and show that the resulting method allows for efficient and accurate inference and regularization of high-dimensional parameters. We use the quadratic estimator to fit a fully-coupled Poisson GLM to spike train data recorded from 831 neurons across five regions of the mouse brain for a duration of 41 minutes, binned at 1 ms resolution. Across all neurons, this model is fit to over 2 billion spike count bins and identifies fine-timescale statistical dependencies between neurons within and across cortical and subcortical areas.
AB - Recent advances in recording technologies have allowed neuroscientists to record simultaneous spiking activity from hundreds to thousands of neurons in multiple brain regions. Such large-scale recordings pose a major challenge to existing statistical methods for neural data analysis. Here we develop highly scalable approximate inference methods for Poisson generalized linear models (GLMs) that require only a single pass over the data. Our approach relies on a recently proposed method for obtaining approximate sufficient statistics for GLMs using polynomial approximations [7], which we adapt to the Poisson GLM setting. We focus on inference using quadratic approximations to nonlinear terms in the Poisson GLM log-likelihood with Gaussian priors, for which we derive closed-form solutions to the approximate maximum likelihood and MAP estimates, posterior distribution, and marginal likelihood. We introduce an adaptive procedure to select the polynomial approximation interval and show that the resulting method allows for efficient and accurate inference and regularization of high-dimensional parameters. We use the quadratic estimator to fit a fully-coupled Poisson GLM to spike train data recorded from 831 neurons across five regions of the mouse brain for a duration of 41 minutes, binned at 1 ms resolution. Across all neurons, this model is fit to over 2 billion spike count bins and identifies fine-timescale statistical dependencies between neurons within and across cortical and subcortical areas.
UR - http://www.scopus.com/inward/record.url?scp=85064203847&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85064203847&partnerID=8YFLogxK
M3 - Conference article
AN - SCOPUS:85064203847
SN - 1049-5258
VL - 2018-December
SP - 3517
EP - 3527
JO - Advances in Neural Information Processing Systems
JF - Advances in Neural Information Processing Systems
T2 - 32nd Conference on Neural Information Processing Systems, NeurIPS 2018
Y2 - 2 December 2018 through 8 December 2018
ER -