Dynamical Systems Trees

TL;DR

Dynamical Systems Trees (DSTs) are a hierarchical probabilistic modeling framework that extends traditional dynamical models to describe interacting processes in groups, with efficient inference and broad applicability.

Contribution

The paper introduces DSTs as a novel hierarchical model for multiple interacting dynamical processes, extending existing models like Kalman filters and hidden Markov models.

Findings

Effective inference and learning algorithms for DSTs.

Successful application to gene expression data.

Modeling of group behavior in football games.

Abstract

We propose dynamical systems trees (DSTs) as a flexible class of models for describing multiple processes that interact via a hierarchy of aggregating parent chains. DSTs extend Kalman filters, hidden Markov models and nonlinear dynamical systems to an interactive group scenario. Various individual processes interact as communities and sub-communities in a tree structure that is unrolled in time. To accommodate nonlinear temporal activity, each individual leaf process is modeled as a dynamical system containing discrete and/or continuous hidden states with discrete and/or Gaussian emissions. Subsequent higher level parent processes act like hidden Markov models and mediate the interaction between leaf processes or between other parent processes in the hierarchy. Aggregator chains are parents of child processes that they combine and mediate, yielding a compact overall parameterization. We provide tractable inference and learning algorithms for arbitrary DST topologies via an efficient structured mean-field algorithm. The diverse applicability of DSTs is demonstrated by experiments on gene expression data and by modeling group behavior in the setting of an American football game.