  Sparse sequences of neural spikes are posited to underlie aspects of working
memory, motor production, and learning. Discovering these sequences in an
unsupervised manner is a longstanding problem in statistical neuroscience.
Promising recent work utilized a convolutive nonnegative matrix factorization
model to tackle this challenge. However, this model requires spike times to be
discretized, utilizes a sub-optimal least-squares criterion, and does not
provide uncertainty estimates for model predictions or estimated parameters. We
address each of these shortcomings by developing a point process model that
characterizes fine-scale sequences at the level of individual spikes and
represents sequence occurrences as a small number of marked events in
continuous time. This ultra-sparse representation of sequence events opens new
possibilities for spike train modeling. For example, we introduce learnable
time warping parameters to model sequences of varying duration, which have been
experimentally observed in neural circuits. We demonstrate these advantages on
experimental recordings from songbird higher vocal center and rodent
hippocampus.
