Lingzhou Xue

Adaptive Algorithms for Robust Phase Retrieval

  • Zhong Zheng
  • Necdet Serhat Aybat
  • Shiqian Ma
  • Lingzhou Xue
    • Categories Nonsmooth Optimization, Robust Optimization Tags , , ,

    This paper considers the robust phase retrieval, which can be cast as a nonsmooth and nonconvex optimization problem. We propose two first-order algorithms with adaptive step sizes: the subgradient algorithm (AdaSubGrad) and the inexact proximal linear algorithm (AdaIPL). Our contribution lies in the novel design of adaptive step sizes based on quantiles of the absolute … Read more

    A New Inexact Proximal Linear Algorithm with Adaptive Stopping Criteria for Robust Phase Retrieval

  • Zhong Zheng
  • Shiqian Ma
  • Lingzhou Xue
    • Categories Nonlinear Optimization, Nonsmooth Optimization Tags , , , ,

    This paper considers the robust phase retrieval problem, which can be cast as a nonsmooth and nonconvex optimization problem. We propose a new inexact proximal linear algorithm with the subproblem being solved inexactly. Our contributions are two adaptive stopping criteria for the subproblem. The convergence behavior of the proposed methods is analyzed. Through experiments on … Read more

    Riemannian Stochastic Proximal Gradient Methods for Nonsmooth Optimization over the Stiefel Manifold

  • Bokun Wang
  • Shiqian Ma
  • Lingzhou Xue
    • Categories Nonlinear Optimization, Statistics

    Riemannian optimization has drawn a lot of attention due to its wide applications in practice. Riemannian stochastic first-order algorithms have been studied in the literature to solve large-scale machine learning problems over Riemannian manifolds. However, most of the existing Riemannian stochastic algorithms require the objective function to be differentiable, and they do not apply to … Read more

    Riemannian Stochastic Proximal Gradient Methods for Nonsmooth Optimization over the Stiefel Manifold

  • Shiqian Ma
  • Bokun Wang
  • Lingzhou Xue
    • Categories Nonlinear Optimization

    Riemannian optimization has drawn a lot of attention due to its wide applications in practice. Riemannian stochastic first-order algorithms have been studied in the literature to solve large-scale machine learning problems over Riemannian manifolds. However, most of the existing Riemannian stochastic algorithms require the objective function to be differentiable, and they do not apply to … Read more

    A Manifold Proximal Linear Method for Sparse Spectral Clustering with Application to Single-Cell RNA Sequencing Data Analysis

  • Shixiang Chen
  • Shiqian Ma
  • Bingyuan Liu
  • Zhongruo Wang
  • Lingzhou Xue
  • Hongyu Zhao
    • Categories Nonlinear Optimization

    Spectral clustering is one of the fundamental unsupervised learning methods widely used in data analysis. Sparse spectral clustering (SSC) imposes sparsity to the spectral clustering and it improves the interpretability of the model. This paper considers a widely adopted model for SSC, which can be formulated as an optimization problem over the Stiefel manifold with … Read more

    An Alternating Manifold Proximal Gradient Method for Sparse PCA and Sparse CCA

  • Shixiang Chen
  • Shiqian Ma
  • Lingzhou Xue
  • Hui Zou
    • Categories Constrained Nonlinear Optimization, Statistics

    Sparse principal component analysis (PCA) and sparse canonical correlation analysis (CCA) are two essential techniques from high-dimensional statistics and machine learning for analyzing large-scale data. Both problems can be formulated as an optimization problem with nonsmooth objective and nonconvex constraints. Since non-smoothness and nonconvexity bring numerical difficulties, most algorithms suggested in the literature either solve … Read more