Fast maximum likelihood estimation using continuous-time neural point process models
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10827_2015_Article_551.pdf
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Author(s)
Lepage, Kyle Q.
MacDonald, Christopher J
Date Issued
March 2015
Journal
Journal of Computational Neuroscience
Publisher
Springer Science+Business Media
Citation
Lepage, Kyle Q., and Christopher J. MacDonald. “Fast Maximum Likelihood Estimation Using Continuous-Time Neural Point Process Models.” J Comput Neurosci 38, no. 3 (March 20, 2015): 499–519.
Version
Author's final manuscript
Abstract
A recent report estimates that the number of simultaneously recorded neurons is growing exponentially. A commonly employed statistical paradigm using discrete-time point process models of neural activity involves the computation of a maximum-likelihood estimate. The time to computate this estimate, per neuron, is proportional to the number of bins in a finely spaced discretization of time. By using continuous-time models of neural activity and the optimally efficient Gaussian quadrature, memory requirements and computation times are dramatically decreased in the commonly encountered situation where the number of parameters p is much less than the number of time-bins n. In this regime, with q equal to the quadrature order, memory requirements are decreased from O(np) to O(qp), and the number of floating-point operations are decreased from O(np2) to O(qp2). Accuracy of the proposed estimates is assessed based upon physiological consideration, error bounds, and mathematical results describing the relation between numerical integration error and numerical error affecting both parameter estimates and the observed Fisher information. A check is provided which is used to adapt the order of numerical integration. The procedure is verified in simulation and for hippocampal recordings. It is found that in 95 % of hippocampal recordings a q of 60 yields numerical error negligible with respect to parameter estimate standard error. Statistical inference using the proposed methodology is a fast and convenient alternative to statistical inference performed using a discrete-time point process model of neural activity. It enables the employment of the statistical methodology available with discrete-time inference, but is faster, uses less memory, and avoids any error due to discretization.
MIT Department
Picower Institute for Learning and Memory
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s10827-015-0551-y
