1 research outputs found
Efficient Inference of Flexible Interaction in Spiking-neuron Networks
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
(P\'{o}lya-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