  Non-equilibrium systems lack an explicit characterisation of their steady
state like the Boltzmann distribution for equilibrium systems. This has drastic
consequences for the inference of parameters of a model when its dynamics lacks
detailed balance. Such non-equilibrium systems occur naturally in applications
like neural networks or gene regulatory networks. Here, we focus on the
paradigmatic asymmetric Ising model and show that we can learn its parameters
from independent samples of the non-equilibrium steady state. We present both
an exact inference algorithm and a computationally more efficient, approximate
algorithm for weak interactions based on a systematic expansion around
mean-field theory. Obtaining expressions for magnetisations, two- and
three-point spin correlations, we establish that these observables are
sufficient to infer the model parameters. Further, we discuss the symmetries
characterising the different orders of the expansion around the mean field and
show how different types of dynamics can be distinguished on the basis of
samples from the non-equilibrium steady state.
