  We address the problem of efficiently and informatively quantifying how
multiplets of variables carry information about the future of the dynamical
system they belong to. In particular we want to identify groups of variables
carrying redundant or synergistic information, and track how the size and the
composition of these multiplets changes as the collective behavior of the
system evolves. In order to afford a parsimonious expansion of shared
information, and at the same time control for lagged interactions and common
effect, we develop a dynamical, conditioned version of the O-information, a
framework recently proposed to quantify high-order interdependencies via
multivariate extension of the mutual information. We thus obtain an expansion
of the transfer entropy in which synergistic and redundant effects are
separated. We apply this framework to a dataset of spiking neurons from a
monkey performing a perceptual discrimination task. The method identifies
synergistic multiplets that include neurons previously categorized as
containing little relevant information individually.
