  Missing values challenge data analysis because many supervised and
unsupervised learning methods cannot be applied directly to incomplete data.
Matrix completion based on low-rank assumptions are very powerful solution for
dealing with missing values. However, existing methods do not consider the case
of informative missing values which are widely encountered in practice. This
paper proposes matrix completion methods to recover Missing Not At Random
(MNAR) data. Our first contribution is to suggest a model-based estimation
strategy by modelling the missing mechanism distribution. An EM algorithm is
then implemented, involving a Fast Iterative Soft-Thresholding Algorithm
(FISTA). Our second contribution is to suggest a computationally efficient
surrogate estimation by implicitly taking into account the joint distribution
of the data and the missing mechanism: the data matrix is concatenated with the
mask coding for the missing values; a low-rank structure for exponential family
is assumed on this new matrix, in order to encode links between variables and
missing mechanisms. The methodology that has the great advantage of handling
different missing value mechanisms is robust to model specification errors.The
performances of our methods are assessed on the real data collected from a
trauma registry (TraumaBase ) containing clinical information about over twenty
thousand severely traumatized patients in France. The aim is then to predict if
the doctors should administrate tranexomic acid to patients with traumatic
brain injury, that would limit excessive bleeding.
