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December 2018 Exact spike train inference via $\ell_{0}$ optimization
Sean Jewell, Daniela Witten
Ann. Appl. Stat. 12(4): 2457-2482 (December 2018). DOI: 10.1214/18-AOAS1162

Abstract

In recent years new technologies in neuroscience have made it possible to measure the activities of large numbers of neurons simultaneously in behaving animals. For each neuron a fluorescence trace is measured; this can be seen as a first-order approximation of the neuron’s activity over time. Determining the exact time at which a neuron spikes on the basis of its fluorescence trace is an important open problem in the field of computational neuroscience.

Recently, a convex optimization problem involving an $\ell_{1}$ penalty was proposed for this task. In this paper we slightly modify that recent proposal by replacing the $\ell_{1}$ penalty with an $\ell_{0}$ penalty. In stark contrast to the conventional wisdom that $\ell_{0}$ optimization problems are computationally intractable, we show that the resulting optimization problem can be efficiently solved for the global optimum using an extremely simple and efficient dynamic programming algorithm. Our R-language implementation of the proposed algorithm runs in a few minutes on fluorescence traces of 100,000 timesteps. Furthermore, our proposal leads to substantial improvements over the previous $\ell_{1}$ proposal, in simulations as well as on two calcium imaging datasets.

R-language software for our proposal is available on CRAN in the package LZeroSpikeInference. Instructions for running this software in python can be found at https://github.com/jewellsean/LZeroSpikeInference.

Citation

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Sean Jewell. Daniela Witten. "Exact spike train inference via $\ell_{0}$ optimization." Ann. Appl. Stat. 12 (4) 2457 - 2482, December 2018. https://doi.org/10.1214/18-AOAS1162

Information

Received: 1 November 2017; Published: December 2018
First available in Project Euclid: 13 November 2018

zbMATH: 07029462
MathSciNet: MR3875708
Digital Object Identifier: 10.1214/18-AOAS1162

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.12 • No. 4 • December 2018
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