Matrix Completion With Data-Dependent Missingness Probabilities

The problem of completing a large matrix with lots missing entries has received widespread attention in the last couple decades. Two popular approaches to completion are based on singular value thresholding and nuclear norm minimization. Most past works this subject assume that there is single number $p$ such each entry available independently probability otherwise. This assumption may not be realistic for many applications. In work, we replace it an unknown function notation="LaTeX">$f$ itself. For example, if rating given movie by viewer, then seems plausible high have greater being than low entries. We propose two new estimators, minimization, recover under assumption. estimators involve no tuning parameters, shown consistent rank also provide estimator .