Model selection: energy-based vs. alignment-based. The estimated interaction kernels for an energy-based model (
A) and an alignment-based model (
B). For each model, we compute two estimators: an energy-based interaction kernel
and an alignment-based interaction kernel
. Our estimators correctly identify the type of model in each case: The
norm of
is significantly larger than that of
(means and SDs:
vs.
) for the energy-based model, and the
norm of
is larger than that of
(means and SDs:
vs.
) for the alignment-based model. Note that the
axes are on very different scales.