GNMR: A provable one-line algorithm for low rank matrix recovery
This work addresses low rank matrix recovery problems that appear in broad applications, offering a provable and efficient solution with improved empirical results, though it is incremental as it builds on existing methods.
The authors tackled the problem of low rank matrix recovery in matrix completion and sensing by introducing GNMR, a simple iterative algorithm based on Gauss-Newton linearization, which achieved better performance than several popular methods, especially with very few observations near the information limit.
Low rank matrix recovery problems, including matrix completion and matrix sensing, appear in a broad range of applications. In this work we present GNMR -- an extremely simple iterative algorithm for low rank matrix recovery, based on a Gauss-Newton linearization. On the theoretical front, we derive recovery guarantees for GNMR in both the matrix sensing and matrix completion settings. Some of these results improve upon the best currently known for other methods. A key property of GNMR is that it implicitly keeps the factor matrices approximately balanced throughout its iterations. On the empirical front, we show that for matrix completion with uniform sampling, GNMR performs better than several popular methods, especially when given very few observations close to the information limit.