# Binary matrix completion with nonconvex regularizers

## TL;DR

This paper introduces a novel binary matrix completion model using nonconvex regularizers, providing theoretical recovery guarantees and an accelerated algorithm, outperforming existing convex regularization methods on synthetic and real data.

## Contribution

The paper proposes a new nonconvex regularizer-based BMC model with recovery guarantees and an accelerated proximal algorithm for efficient solution.

## Key findings

- The proposed method outperforms convex regularization approaches in experiments.
- The accelerated algorithm achieves a convergence rate of 1/T.
- The model demonstrates superior recovery performance on synthetic and real datasets.

## Abstract

Many practical problems involve the recovery of a binary matrix from partial information, which makes the binary matrix completion (BMC) technique received increasing attention in machine learning. In particular, we consider a special case of BMC problem, in which only a subset of positive elements can be observed. In recent years, convex regularization based methods are the mainstream approaches for this task. However, the applications of nonconvex surrogates in standard matrix completion have demonstrated better empirical performance. Accordingly, we propose a novel BMC model with nonconvex regularizers and provide the recovery guarantee for the model. Furthermore, for solving the resultant nonconvex optimization problem, we improve the popular proximal algorithm with acceleration strategies. It can be guaranteed that the convergence rate of the algorithm is in the order of ${1/T}$, where $T$ is the number of iterations. Extensive experiments conducted on both synthetic and real-world data sets demonstrate the superiority of the proposed approach over other competing methods.