Inference for High-Dimensional Self-Exciting Point Processes

2017 - presentpresent
In a variety of settings, our only glimpse at a network’s structure is through the lens of time series observations. For instance, in a social network, we may observe a time series of members’ activities, such as posts on social media. In electrical systems, cascading chains of power failures reveal critical information about the underlying power distribution network. During epidemics, networks among computers or a population are reflected by the time at which each node becomes infected. In biological neural networks, firing neurons can trigger or inhibit the firing of their neighbors, so that information about the network structure is embedded within spike train observations. This proposal focuses on the setting in which a network’s functional structure (modeled as directed edge weights of a graph) corresponds to the extent to which one node’s activity stimulates or inhibits activity in another node. For instance, the network structure may indicate who is influencing whom within a social network or the connectivity of neurons. The interactions between nodes are thus critical to a fundamental understanding of the underlying functional network structure and accurate predictions of likely future events. The above processes are self-exciting in that the likelihood of future events depends on past events (i.e., a particular type of autoregressive process). This temporal dependence among events can make accurate inference particularly challenging and requires the development of new theory and novel algorithms.