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Calcium imaging permits optical measurement of neural activity. Sinceintracellular calcium concentration is an indirect measurement of neuralactivity, computational tools are necessary to infer the true underlyingspiking activity from fluorescence measurements. Bayesian model inversion canbe used to solve this problem, but typically requires either computationallyexpensive MCMC sampling, or faster but approximate maximum-a-posteriorioptimization. Here, we introduce a flexible algorithmic framework for fast,efficient and accurate extraction of neural spikes from imaging data. Using theframework of variational autoencoders, we propose to amortize inference bytraining a deep neural network to perform model inversion efficiently. Therecognition network is trained to produce samples from the posteriordistribution over spike trains. Once trained, performing inference amounts to afast single forward pass through the network, without the need for iterativeoptimization or sampling. We show that amortization can be applied flexibly toa wide range of nonlinear generative models and significantly improves upon thestate of the art in computation time, while achieving competitive accuracy. Ourframework is also able to represent posterior distributions over spike-trains.We demonstrate the generality of our method by proposing the firstprobabilistic approach for separating backpropagating action potentials fromputative synaptic inputs in calcium imaging of dendritic spines.

Fast amortized inference of neural activity from calcium imaging data with variational autoencoders