  Recent works have demonstrated that the convergence rate of a nonparametric
density estimator can be greatly improved by using a low-rank estimator when
the target density is a convex combination of separable probability densities
with Lipschitz continuous marginals, i.e. a multiview model. However, this
assumption is very restrictive and it is not clear to what degree these
findings can be extended to general pdfs. This work answers this question by
introducing a new way of characterizing a pdf's complexity, the non-negative
Lipschitz spectrum (NL-spectrum), which, unlike smoothness properties, can be
used to characterize virtually any pdf. Finite sample bounds are presented that
are dependent on the target density's NL-spectrum. From this
dimension-independent rates of convergence are derived that characterize when
an NL-spectrum allows for a fast rate of convergence.
