  The independence assumption is a useful tool to increase the tractability of
one's modelling framework. However, this assumption does not match reality;
failing to take dependencies into account can cause models to fail
dramatically. The field of multi-axis graphical modelling (also called
multi-way modelling, Kronecker-separable modelling) has seen growth over the
past decade, but these models require that the data have zero mean. In the
multi-axis case, inference is typically done in the single sample scenario,
making mean inference impossible.
  In this paper, we demonstrate how the zero-mean assumption can cause
egregious modelling errors, as well as propose a relaxation to the zero-mean
assumption that allows the avoidance of such errors. Specifically, we propose
the "Kronecker-sum-structured mean" assumption, which leads to models with
nonconvex-but-unimodal log-likelihoods that can be solved efficiently with
coordinate descent.
