Nicholas A. G. Johnson

Predictive Low Rank Matrix Learning under Partial Observations: Mixed-Projection ADMM

  • Dimitris Bertsimas
  • Nicholas A. G. Johnson
    • Categories Data Science Algorithms, Nonlinear Optimization Tags , , ,

    We study the problem of learning a partially observed matrix under the low rank assumption in the presence of fully observed side information that depends linearly on the true underlying matrix. This problem consists of an important generalization of the Matrix Completion problem, a central problem in Statistics, Operations Research and Machine Learning, that arises … Read more

    Compressed Sensing: A Discrete Optimization Approach

  • Dimitris Bertsimas
  • Nicholas A. G. Johnson
    • Categories (Mixed) Integer Nonlinear Programming, Second-Order Cone Programming, Statistics Tags , , , ,

    We study the Compressed Sensing (CS) problem, which is the problem of finding the most sparse vector that satisfies a set of linear measurements up to some numerical tolerance. CS is a central problem in Statistics, Operations Research and Machine Learning which arises in applications such as signal processing, data compression, image reconstruction, and multi-label … Read more

    Sparse Plus Low Rank Matrix Decomposition: A Discrete Optimization Approach

  • Dimitris Bertsimas
  • Ryan Cory-Wright
  • Nicholas A. G. Johnson
    • Categories Applications - OR and Management Sciences, Data-Mining, Statistics Tags , , , ,

    We study the Sparse Plus Low-Rank decomposition problem (SLR), which is the problem of decomposing a corrupted data matrix into a sparse matrix of perturbations plus a low-rank matrix containing the ground truth. SLR is a fundamental problem in Operations Research and Machine Learning which arises in various applications, including data compression, latent semantic indexing, … Read more