  Robust low-rank matrix estimation is a topic of increasing interest, with
promising applications in a variety of fields, from computer vision to data
mining and recommender systems. Recent theoretical results establish the
ability of such data models to recover the true underlying low-rank matrix when
a large portion of the measured matrix is either missing or arbitrarily
corrupted. However, if low rank is not a hypothesis about the true nature of
the data, but a device for extracting regularity from it, no current guidelines
exist for choosing the rank of the estimated matrix. In this work we address
this problem by means of the Minimum Description Length (MDL) principle -- a
well established information-theoretic approach to statistical inference -- as
a guideline for selecting a model for the data at hand. We demonstrate the
practical usefulness of our formal approach with results for complex background
extraction in video sequences.
