Search Results for author: Shiqian Ma

Found 30 papers, 2 papers with code

On the Convergence of Projected Alternating Maximization for Equitable and Optimal Transport

no code implementations29 Sep 2021 Minhui Huang, Shiqian Ma, Lifeng Lai

This paper studies the equitable and optimal transport (EOT) problem, which has many applications such as fair division problems and optimal transport with multiple agents etc.

A Riemannian smoothing steepest descent method for non-Lipschitz optimization on submanifolds

no code implementations9 Apr 2021 Chao Zhang, Xiaojun Chen, Shiqian Ma

In this paper, we propose a Riemannian smoothing steepest descent method to minimize a nonconvex and non-Lipschitz function on submanifolds.

Projection Robust Wasserstein Barycenters

no code implementations5 Feb 2021 Minhui Huang, Shiqian Ma, Lifeng Lai

One of the popular solution methods for this task is to compute the barycenter of the probability measures under the Wasserstein metric.

Riemannian optimization

A Riemannian Block Coordinate Descent Method for Computing the Projection Robust Wasserstein Distance

no code implementations9 Dec 2020 Minhui Huang, Shiqian Ma, Lifeng Lai

We show that the complexity of arithmetic operations for RBCD to obtain an $\epsilon$-stationary point is $O(\epsilon^{-3})$.

Robust Low-rank Matrix Completion via an Alternating Manifold Proximal Gradient Continuation Method

no code implementations18 Aug 2020 Minhui Huang, Shiqian Ma, Lifeng Lai

This problem aims to decompose a partially observed matrix into the superposition of a low-rank matrix and a sparse matrix, where the sparse matrix captures the grossly corrupted entries of the matrix.

Low-Rank Matrix Completion Riemannian optimization

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

no code implementations18 Jul 2020 Zhongruo Wang, Bingyuan Liu, Shixiang Chen, Shiqian Ma, Lingzhou Xue, Hongyu Zhao

This paper considers a widely adopted model for SSC, which can be formulated as an optimization problem over the Stiefel manifold with nonsmooth and nonconvex objective.

Manifold Proximal Point Algorithms for Dual Principal Component Pursuit and Orthogonal Dictionary Learning

no code implementations5 May 2020 Shixiang Chen, Zengde Deng, Shiqian Ma, Anthony Man-Cho So

Second, we propose a stochastic variant of ManPPA called StManPPA, which is well suited for large-scale computation, and establish its sublinear convergence rate.

Dictionary Learning

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

no code implementations3 May 2020 Bokun Wang, Shiqian Ma, Lingzhou Xue

In this paper, we present two Riemannian stochastic proximal gradient methods for minimizing nonsmooth function over the Stiefel manifold.

Low-Rank Matrix Completion Riemannian optimization

Stochastic Zeroth-order Riemannian Derivative Estimation and Optimization

no code implementations25 Mar 2020 Jiaxiang Li, Krishnakumar Balasubramanian, Shiqian Ma

We consider stochastic zeroth-order optimization over Riemannian submanifolds embedded in Euclidean space, where the task is to solve Riemannian optimization problem with only noisy objective function evaluations.

Riemannian optimization

Zeroth-Order Algorithms for Nonconvex Minimax Problems with Improved Complexities

no code implementations22 Jan 2020 Zhongruo Wang, Krishnakumar Balasubramanian, Shiqian Ma, Meisam Razaviyayn

We first design and analyze the Zeroth-Order Gradient Descent Ascent (\texttt{ZO-GDA}) algorithm, and provide improved results compared to existing works, in terms of oracle complexity.

Accelerated Dual-Averaging Primal-Dual Method for Composite Convex Minimization

no code implementations15 Jan 2020 Conghui Tan, Yuqiu Qian, Shiqian Ma, Tong Zhang

Dual averaging-type methods are widely used in industrial machine learning applications due to their ability to promoting solution structure (e. g., sparsity) efficiently.

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

no code implementations27 Mar 2019 Shixiang Chen, Shiqian Ma, Lingzhou Xue, Hui Zou

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.

Stochastic Primal-Dual Method for Empirical Risk Minimization with O(1) Per-Iteration Complexity

no code implementations NeurIPS 2018 Conghui Tan, Tong Zhang, Shiqian Ma, Ji Liu

Regularized empirical risk minimization problem with linear predictor appears frequently in machine learning.

Efficient Optimization Algorithms for Robust Principal Component Analysis and Its Variants

no code implementations9 Jun 2018 Shiqian Ma, Necdet Serhat Aybat

Robust PCA has drawn significant attention in the last decade due to its success in numerous application domains, ranging from bio-informatics, statistics, and machine learning to image and video processing in computer vision.

An ADMM-Based Interior-Point Method for Large-Scale Linear Programming

1 code implementation31 May 2018 Tianyi Lin, Shiqian Ma, Yinyu Ye, Shuzhong Zhang

Due its connection to Newton's method, IPM is often classified as second-order method -- a genre that is attached with stability and accuracy at the expense of scalability.

Optimization and Control

Highly accurate model for prediction of lung nodule malignancy with CT scans

no code implementations6 Feb 2018 Jason Causey, Junyu Zhang, Shiqian Ma, Bo Jiang, Jake Qualls, David G. Politte, Fred Prior, Shuzhong Zhang, Xiuzhen Huang

Here we present NoduleX, a systematic approach to predict lung nodule malignancy from CT data, based on deep learning convolutional neural networks (CNN).

Computed Tomography (CT)

Primal-Dual Optimization Algorithms over Riemannian Manifolds: an Iteration Complexity Analysis

no code implementations5 Oct 2017 Junyu Zhang, Shiqian Ma, Shuzhong Zhang

For prohibitively large-size tensor or machine learning models, we present a sampling-based stochastic algorithm with the same iteration complexity bound in expectation.

Community Detection Compressive Sensing

Geometric descent method for convex composite minimization

no code implementations NeurIPS 2017 Shixiang Chen, Shiqian Ma, Wei Liu

In this paper, we extend the geometric descent method recently proposed by Bubeck, Lee and Singh to tackle nonsmooth and strongly convex composite problems.

Stochastic Quasi-Newton Methods for Nonconvex Stochastic Optimization

no code implementations5 Jul 2016 Xiao Wang, Shiqian Ma, Donald Goldfarb, Wei Liu

In this paper we study stochastic quasi-Newton methods for nonconvex stochastic optimization, where we assume that noisy information about the gradients of the objective function is available via a stochastic first-order oracle (SFO).

General Classification Stochastic Optimization

Barzilai-Borwein Step Size for Stochastic Gradient Descent

no code implementations NeurIPS 2016 Conghui Tan, Shiqian Ma, Yu-Hong Dai, Yuqiu Qian

One of the major issues in stochastic gradient descent (SGD) methods is how to choose an appropriate step size while running the algorithm.

Stochastic Optimization

Structured Nonconvex and Nonsmooth Optimization: Algorithms and Iteration Complexity Analysis

no code implementations9 May 2016 Bo Jiang, Tianyi Lin, Shiqian Ma, Shuzhong Zhang

In particular, we consider in this paper some constrained nonconvex optimization models in block decision variables, with or without coupled affine constraints.

Global Convergence of Unmodified 3-Block ADMM for a Class of Convex Minimization Problems

no code implementations16 May 2015 Tianyi Lin, Shiqian Ma, Shuzhong Zhang

The alternating direction method of multipliers (ADMM) has been successfully applied to solve structured convex optimization problems due to its superior practical performance.

Efficient Algorithms for Robust and Stable Principal Component Pursuit Problems

no code implementations26 Sep 2013 Necdet Serhat Aybat, Donald Goldfarb, Shiqian Ma

Moreover, if the observed data matrix has also been corrupted by a dense noise matrix in addition to gross sparse error, then the stable principal component pursuit (SPCP) problem is solved to recover the low-rank matrix.

Optimization and Control

An Extragradient-Based Alternating Direction Method for Convex Minimization

no code implementations27 Jan 2013 Tianyi Lin, Shiqian Ma, Shuzhong Zhang

The classical alternating direction type methods usually assume that the two convex functions have relatively easy proximal mappings.

Fast Alternating Linearization Methods for Minimizing the Sum of Two Convex Functions

no code implementations23 Dec 2009 Donald Goldfarb, Shiqian Ma, Katya Scheinberg

We present in this paper first-order alternating linearization algorithms based on an alternating direction augmented Lagrangian approach for minimizing the sum of two convex functions.

Fixed Point and Bregman Iterative Methods for Matrix Rank Minimization

1 code implementation11 May 2009 Shiqian Ma, Donald Goldfarb, Lifeng Chen

The tightest convex relaxation of this problem is the linearly constrained nuclear norm minimization.

Optimization and Control Information Theory Information Theory

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