Efficient Inference for Dynamic Flexible Interactions of Neural Populations

Publication Type:
Journal Article
Journal of Machine Learning Research, 2022, 23, (-)
Issue Date:
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Hawkes process provides an effective statistical framework for analyzing the interactions of neural spiking activities Although utilized in many real applications the classic Hawkes process is incapable of modeling inhibitory interactions among neural population Instead the nonlinear Hawkes process allows for modeling a more flexible influence pattern with excitatory or inhibitory interactions This work proposes a flexible nonlinear Hawkes process variant based on sigmoid nonlinearity To ease inference three sets of auxiliary latent variables P lya Gamma variables latent marked Poisson processes and sparsity variables are augmented to make functional connection weights appear in a Gaussian form which enables simple iterative algorithms with analytical updates As a result the efficient Gibbs sampler expectation maximization EM algorithm and mean field MF approximation are derived to estimate the interactions among neural populations Furthermore to reconcile with time varying neural systems the proposed time invariant model is extended to a dynamic version by introducing a Markov state process Similarly three analytical iterative inference algorithms Gibbs sampler EM algorithm and mean field approximation are derived We compare the accuracy and efficiency of these inference algorithms on synthetic data and further experiment on real neural recordings to demonstrate that the developed models achieve superior performance over the state of the art competitors 2022 Feng Zhou Quyu Kong Zhijie Deng Jichao Kan Yixuan Zhang Cheng Feng and Jun Zhu
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