Matrix Completion Under Interval Uncertainty: Highlights
We present an overview of inequality-constrained matrix completion, with a particular focus on alternating least-squares (ALS) methods. The simple and seemingly obvious addition of inequality constraints to matrix completion seems to improve the statistical performance of matrix completion in a number of applications, such as collaborative filtering under interval uncertainty, robust statistics, event detection, and background modelling in computer vision. An ALS algorithm MACO by Marecek et al. outperforms others, including Sparkler, the implementation of Li et al. Code related to this paper is available at: http://optml.github.io/ac-dc/.
The work of JM received funding from the European Union’s Horizon 2020 Programme (Horizon2020/2014-2020) under grant agreement No. 688380. The work of MT was partially supported by the U.S. National Science Foundation, under award numbers NSF:CCF:1618717, NSF:CMMI:1663256, and NSF:CCF:1740796. PR acknowledges support from KAUST Faculty Baseline Research Funding Program.
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