LearningLowRankMatrices

Software supplement for the paper "Predictive Low Rank Matrix Learning under Partial Observations: Mixed-Projection ADMM" by Dimitris Bertsimas and Nicholas A. G. Johnson, for which a preprint is available here.

Introduction

The software in this package is designed to provide high quality feasible solutions to the predictive low rank matrix learning problem under partial observations given by

min_{X, \alpha} \sum_{(i, j) \in \Omega}(X_{ij}-A_{ij})^2 + \lambda * ||Y - X * \alpha||_2^2 + \frac{\gamma}||X||_\star

s.t. rank(X) <= k

using the Mixed-Projection ADMM algorithm described in the paper "Predictive Low Rank Matrix Learning under Partial Observations: Mixed-Projection ADMM" by Dimitris Bertsimas and Nicholas A. G. Johnson. We provide a multithreaded implementation of the algorithm.

Installation and set up (TODO)

In order to run this software, you must install a recent version of Julia from http://julialang.org/downloads/. This code was developed using Julia 1.7.3.

Several packages must be installed in Julia before the code can be run. These packages can be found in "lowRankMatrixLearning.jl". The code was last tested using the following package versions:

• Distributions v0.25.70
• LowRankApprox v0.5.2
• MatrixImpute v0.3.2
• PyCall v1.94.1
• TSVD v0.4.3

Use of the admm() function

The key method in this package is admm(). This method accepts four required arguments: A, k, Y, lambda, as well as several optional arguments which are described in the function docstring. The four required arguments correspond to the input data to the optimization problem.

Citing lowRankMatrixLearning.jl

If you use lowRankMatrixLearning.jl, we ask that you please cite the following paper:

@article{bertsimas2024predictive,
  title={Predictive Low Rank Matrix Learning under Partial Observations: Mixed-Projection ADMM},
  author={Bertsimas, Dimitris and Johnson, Nicholas AG},
  journal={arXiv preprint arXiv:2407.13731},
  year={2024}
}

Thank you

Thank you for your interest in lowRankMatrixLearning. Please let us know if you encounter any issues using this code, or have comments or questions. Feel free to email us anytime.

Dimitris Bertsimas dbertsim@mit.edu

Nicholas A. G. Johnson nagj@mit.edu