  Tensor decomposition methods are popular tools for learning latent variables
given only lower-order moments of the data. However, the standard assumption is
that we have sufficient data to estimate these moments to high accuracy. In
this work, we consider the case in which certain dimensions of the data are not
always observed---common in applied settings, where not all measurements may be
taken for all observations---resulting in moment estimates of varying quality.
We derive a weighted tensor decomposition approach that is computationally as
efficient as the non-weighted approach, and demonstrate that it outperforms
methods that do not appropriately leverage these less-observed dimensions.
