Simultaneous clustering and estimation of additive shape invariant models for recurrent event data

Technological advancements have enabled the recording of spiking activities from large neuron ensembles, presenting an exciting yet challenging opportunity for statistical analysis. This project considers the challenges from a common type of neuroscience experiments, where randomized interventions are applied over the course of each trial. The objective is to identify groups of neurons with unique stimulation responses and estimate these responses. The observed data, however, comprise superpositions of neural responses to all stimuli, which is further complicated by varying response latencies across neurons. We introduce a novel additive shape invariant model that is capable of simultaneously accommodating multiple clusters, additive components, and unknown time-shifts. We establish conditions for the identifiability of model parameters, offering guidance for the design of future experiments. We examine the properties of the proposed algorithm through simulation studies, and apply the proposed method on neural data collected in mice.