  As a problem in data science the inverse Ising (or Potts) problem is to infer
the parameters of a Gibbs-Boltzmann distributions of an Ising (or Potts) model
from samples drawn from that distribution. The algorithmic and computational
interest stems from the fact that this inference task cannot be done
efficiently by the maximum likelihood criterion, since the normalizing constant
of the distribution (the partition function) can not be calculated exactly and
efficiently. The practical interest on the other hand flows from several
outstanding applications, of which the most well known has been predicting
spatial contacts in protein structures from tables of homologous protein
sequences. Most applications to date have been to data that has been produced
by a dynamical process which, as far as it is known, cannot be expected to
satisfy detailed balance. There is therefore no a priori reason to expect the
distribution to be of the Gibbs-Boltzmann type, and no a priori reason to
expect that inverse Ising (or Potts) techniques should yield useful
information. In this review we discuss two types of problems where progress
nevertheless can be made. We find that depending on model parameters there are
phases where, in fact, the distribution is close to Gibbs-Boltzmann
distribution, a non-equilibrium nature of the under-lying dynamics
notwithstanding. We also discuss the relation between inferred Ising model
parameters and parameters of the underlying dynamics.
