# LRSVRG-IMC: An SVRG-Based Algorithm for LowRank Inductive Matrix Completion

arXiv: https://arxiv.org/abs/2201.08516 · HTML: https://mlsanity.com/paper/2201.08516/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 15 references that are in the map.
- First posted on arXiv 21 Jan 2022.

## Builds on (most cited first, 7 of 7)

- [Stochastic Variance Reduction for Nonconvex Optimization](https://mlsanity.com/paper/1603.06160/) (2016)
- [Variance Reduction for Faster Non-Convex Optimization](https://mlsanity.com/paper/1603.05643/) (2016)
- [Provable Inductive Matrix Completion](https://mlsanity.com/paper/1306.0626/) (2013)
- [Fast and Sample Efficient Inductive Matrix Completion via Multi-Phase Procrustes Flow](https://mlsanity.com/paper/1803.01233/) (2018)
- [Noisy Inductive Matrix Completion Under Sparse Factor Models](https://mlsanity.com/paper/1609.03958/) (2016)
- [Doubly Accelerated Stochastic Variance Reduced Dual Averaging Method for Regularized Empirical Risk Minimization](https://mlsanity.com/paper/1703.00439/) (2017)
- [Fast Stochastic Variance Reduced Gradient Method with Momentum Acceleration for Machine Learning](https://mlsanity.com/paper/1703.07948/) (2017)

## Abstract (arXiv)

Low-rank inductive matrix completion (IMC) is currently widely used in IoT data completion, recommendation systems, and so on, as the side information in IMC has demonstrated great potential in reducing sample point remains a major obstacle for the convergence of the nonconvex solutions to IMC. What's more, carefully choosing the initial solution alone does not usually help remove the saddle points. To address this problem, we propose a stocastic variance reduction gradient-based algorithm called LRSVRG-IMC. LRSVRG-IMC can escape from the saddle points under various low-rank and sparse conditions with a properly chosen initial input. We also prove that LRSVVRG-IMC achieves both a linear convergence rate and a near-optimal sample complexity. The superiority and applicability of LRSVRG-IMC are verified via experiments on synthetic datasets.