The Annals of Applied Statistics

Exact spike train inference via $\ell_{0}$ optimization

Sean Jewell and Daniela Witten

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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

Article information

Ann. Appl. Stat., Volume 12, Number 4 (2018), 2457-2482.

Received: November 2017
First available in Project Euclid: 13 November 2018

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Zentralblatt MATH identifier

Neuroscience calcium imaging changepoint detection dynamic programming


Jewell, Sean; Witten, Daniela. Exact spike train inference via $\ell_{0}$ optimization. Ann. Appl. Stat. 12 (2018), no. 4, 2457--2482. doi:10.1214/18-AOAS1162.

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