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Exact spike train inference via \(\ell_{0}\) optimization. (English) Zbl 1412.62159

Summary: 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.

MSC:

62P10 Applications of statistics to biology and medical sciences; meta analysis
62J07 Ridge regression; shrinkage estimators (Lasso)
62H12 Estimation in multivariate analysis
68T05 Learning and adaptive systems in artificial intelligence
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