A Novel Approach to Quantized Matrix Completion Using Huber Loss Measure

TL;DR

This paper presents a robust, differentiable approach to quantized matrix completion using Huber loss, enabling efficient gradient-based optimization without projections or initial rank estimation, and demonstrating superior accuracy and efficiency.

Contribution

Introduces a novel Huber loss-based regularization for quantized matrix completion, with theoretical convergence guarantees and improved performance over existing methods.

Findings

Outperforms state-of-the-art methods in accuracy

Reduces computational complexity

Does not require projections or initial rank estimation

Abstract

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.