Kavli Affiliate: Eric Miller
| First 5 Authors: Michael T. Wojnowicz, Kaitlin Gili, Preetish Rath, Eric Miller, Jeffrey Miller
| Summary:
We seek a computationally efficient model for a collection of time series
arising from multiple interacting entities (a.k.a. "agents"). Recent models of
spatiotemporal patterns across individuals fail to incorporate explicit
system-level collective behavior that can influence the trajectories of
individual entities. To address this gap in the literature, we present a new
hierarchical switching-state model that can be trained in an unsupervised
fashion to simultaneously learn both system-level and individual-level
dynamics. We employ a latent system-level discrete state Markov chain that
provides top-down influence on latent entity-level chains which in turn govern
the emission of each observed time series. Recurrent feedback from the
observations to the latent chains at both entity and system levels allows
recent situational context to inform how dynamics unfold at all levels in
bottom-up fashion. We hypothesize that including both top-down and bottom-up
influences on group dynamics will improve interpretability of the learned
dynamics and reduce error when forecasting. Our hierarchical switching
recurrent dynamical model can be learned via closed-form variational coordinate
ascent updates to all latent chains that scale linearly in the number of
entities. This is asymptotically no more costly than fitting a separate model
for each entity. Analysis of both synthetic data and real basketball team
movements suggests our lean parametric model can achieve competitive forecasts
compared to larger neural network models that require far more computational
resources. Further experiments on soldier data as well as a synthetic task with
64 cooperating entities show how our approach can yield interpretable insights
about team dynamics over time.
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