We will often use variational optimization. When the variational family is not made explicit it means that the optimization is over all functions with the correct domain and codomain, e.g.

Our results extend recent developments in nonlinear ICA, and in fact, they lead to an important generalization of ICA models.

In medical imaging, for example, experts will often disagree about the exact location of object boundaries.

Here we summarize the properties of dependent rounding, see Gandhi et al. [2006] for full details.

We also address the problem of "metric membership", where group membership has a notion of order and distance.