quality of semidefinite relaxations

Statistical and Computational Guarantees of Kernel Max-Sliced Wasserstein Distances

  • Jie Wang
    • Categories Optimization in Data Science Tags , ,

    Optimal transport has been very successful for various machine learning tasks; however, it is known to suffer from the curse of dimensionality. Hence, dimensionality reduction is desirable when applied to high-dimensional data with low-dimensional structures. The kernel max-sliced (KMS) Wasserstein distance is developed for this purpose by finding an optimal nonlinear mapping that reduces data … Read more

    Sums of Random Symmetric Matrices and Applications

  • Arkadi Nemirovski
    • Categories Approximation Algorithms, Semi-definite Programming Tags , , , ,

    Let B_i be deterministic symmetric m\times m matrices, and \xi_i be independent random scalars with zero mean and “of order of one” (e.g., \xi_i are Gaussian with zero mean and unit standard deviation). We are interested in conditions for the “typical norm” of the random matrix S_N = \xi_1B_1+…+\xi_NB_N to be of order of 1. … Read more