Efficient Inference of Flexible Interaction in Spiking-neuron Networks
This work addresses the need for flexible interaction modeling in neuroscience, though it is incremental as it builds on existing nonlinear Hawkes process frameworks.
The paper tackled the problem of modeling both excitatory and inhibitory interactions in neuronal spiking activities, which the classic Hawkes process cannot handle, by developing an efficient expectation-maximization algorithm that estimates functional connectivity with interpretable results on real neural data.
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 (Pólya-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.