Online learning of neural network structure from spike trains

Cascading series of events are a salient feature of neural networks, where neuron spikes may stimulate or inhibit spike activity in other neurons. Only individual spike times associated with each neuron are observed, usually without knowledge of the underlying relationships among neurons. This paper addresses the challenge of tracking how spikes within such networks stimulate or influence future events. The proposed approach is an online learning framework well-suited to streaming data, using a multivariate Hawkes point process model to encapsulate autoregressive features of observed events within the network. Recent work on online learning in dynamic environments is leveraged not only to exploit the dynamics within the underlying network, but also to track that network structure as it evolves. Regret bounds and experimental results demonstrate that the proposed method performs nearly as well as an oracle or batch algorithm.