# A Novel Approach to Quantized Matrix Completion Using Huber Loss Measure

arXiv: https://arxiv.org/abs/1810.12460 · HTML: https://mlsanity.com/paper/1810.12460/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Oct 2018.

## Built on by (most cited first, 4 of 4)

- [PanoFormer: Panorama Transformer for Indoor 360 Depth Estimation](https://mlsanity.com/paper/2203.09283/) (2022)
- [Error Loss Networks](https://mlsanity.com/paper/2106.03722/) (2021)
- [Generative Model Adversarial Training for Deep Compressed Sensing](https://mlsanity.com/paper/2106.10696/) (2021)
- [PAGCNet: A Pose-Aware and Geometry Constrained Framework for Panoramic Depth Estimation](https://mlsanity.com/paper/2510.07817/) (2025)

## Abstract (arXiv)

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.