  In this paper, we introduce a novel and robust approach to Quantized Matrix
Completion (QMC). First, we propose a rank minimization problem with
constraints induced by quantization bounds. Next, we form an unconstrained
optimization problem by regularizing the rank function with Huber loss. Huber
loss is leveraged to control the violation from quantization bounds due to two
properties: 1- It is differentiable, 2- It is less sensitive to outliers than
the quadratic loss. A Smooth Rank Approximation is utilized to endorse lower
rank on the genuine data matrix. Thus, an unconstrained optimization problem
with differentiable objective function is obtained allowing us to advantage
from Gradient Descent (GD) technique. Novel and firm theoretical analysis on
problem model and convergence of our algorithm to the global solution are
provided. Another contribution of our work is that our method does not require
projections or initial rank estimation unlike the state- of-the-art. In the
Numerical Experiments Section, the noticeable outperformance of our proposed
method in learning accuracy and computational complexity compared to those of
the state-of- the-art literature methods is illustrated as the main
contribution.
