Adversarial Robust Low Rank Matrix Estimation: Compressed Sensing and Matrix Completion
This work addresses robust matrix recovery for applications like signal processing and recommendation systems, offering incremental improvements in error bounds.
The paper tackles robust low-rank matrix estimation in trace regression with adversarial output contamination, proposing a unified Huber loss and nuclear norm approach to achieve sharp error bounds for matrix compressed sensing and completion.
We consider robust low rank matrix estimation as a trace regression when outputs are contaminated by adversaries. The adversaries are allowed to add arbitrary values to arbitrary outputs. Such values can depend on any samples. We deal with matrix compressed sensing, including lasso as a partial problem, and matrix completion, and then we obtain sharp estimation error bounds. To obtain the error bounds for different models such as matrix compressed sensing and matrix completion, we propose a simple unified approach based on a combination of the Huber loss function and the nuclear norm penalization, which is a different approach from the conventional ones. Some error bounds obtained in the present paper are sharper than the past ones.