Exact Spike Train Inference Via 0 Optimization

Abstract: In recent years, new technologies in neuroscience have made it possible to measure the activities of large numbers of neurons 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 `1 penalty was proposed for this task. In this paper, we slightly modify that recent proposal by replacing the `1 penalty with an `0 penalty. In stark contrast to the conventional wisdom that `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 substantially better results than the previous `1 proposal, on synthetic data as well as on two calcium imaging data sets. R-language software for our proposal is now available at https://github.com/ jewellsean/LZeroSpikeInference and will be available soon on CRAN in the package LZeroSpikeInference.