  We use the general setting for contrast (potential) functions in statistical
and information geometry provided by Lie groupoids and Lie algebroids. The
contrast functions are defined on Lie groupoids and give rise to two-forms and
three-forms on the corresponding Lie algebroid. We study the case when the
two-form is degenerate and show how in sufficiently regular cases one reduces
it to a pseudometric structures. Transversal Levi-Civita connections for
Riemannian foliations are generalized to the Lie groupoid/Lie algebroid case.
