Efficient Inference of Flexible Interaction in Spiking-neuron NetworksDownload PDF

Published: 12 Jan 2021, Last Modified: 05 May 2023ICLR 2021 PosterReaders: Everyone
Keywords: neural spike train, nonlinear Hawkes process, auxiliary latent variable, conjugacy
Abstract: Hawkes process provides an effective statistical framework for analyzing the time-dependent interaction of neuronal spiking activities. Although utilized in many real applications, the classic Hawkes process is incapable of modelling inhibitory interactions among neurons. Instead, the nonlinear Hawkes process allows for a more flexible influence pattern with excitatory or inhibitory interactions. In this paper, three sets of auxiliary latent variables (Polya-Gamma variables, latent marked Poisson processes and sparsity variables) are augmented to make functional connection weights in a Gaussian form, which allows for a simple iterative algorithm with analytical updates. As a result, an efficient expectation-maximization (EM) algorithm is derived to obtain the maximum a posteriori (MAP) estimate. We demonstrate the accuracy and efficiency performance of our algorithm on synthetic and real data. For real neural recordings, we show our algorithm can estimate the temporal dynamics of interaction and reveal the interpretable functional connectivity underlying neural spike trains.
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One-sentence Summary: An efficient conjugate EM algorithm for nonlinear multivariate Hawkes processes based on auxiliary latent variables augmentation.
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