Lingxiao Wang

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We propose a unified framework for estimating low-rank matrices through nonconvex optimization based on gradient descent algorithm. Our framework is quite general and can be applied to both noisy and noiseless observations. In the general case with noisy observations, we show that our algorithm is guaranteed to linearly converge to the unknown low-rank(More)
An interactive Multilingual Access Gateway (iMAG) dedicated to a website S (iMAG-S) is a good tool to make S accessible in many languages immediately and without editorial responsibility. Visitors of S as well as paid or unpaid posteditors and moderators contribute to the continuous and incremental improvement of the most important textual segments, and(More)
We study the problem of estimating low-rank matrices from linear measurements (a.k.a., matrix sensing) through nonconvex optimization. We propose an efficient stochastic variance reduced gradient descent algorithm to solve a nonconvex optimization problem of matrix sensing. Our algorithm is applicable to both noisy and noiseless settings. In the case with(More)
We present a new estimator for precision matrix in high dimensional Gaussian graphical models. At the core of the proposed estimator is a collection of node-wise linear regression with nonconvex penalty. In contrast to existing estimators for Gaussian graphical models with O(s √ log d/n) estimation error bound in terms of spectral norm, where s is the(More)
During a course of human immunodeficiency virus (HIV-1) infection, the viral load usually increases sharply to a peak following infection and then drops rapidly to a steady state, where it remains until progression to AIDS. This steady state is often referred to as the viral set point. It is believed that the HIV viral set point results from an equilibrium(More)
With the advancement of wireless networks and cloud computing, people are becoming increasingly surrounded by a variety of displays — rich electronic devices: TV, Phone, Pad, Notebook and other portable or wearable devices. These electronic products put high demands on the quality of the visual interface. Paper-like displays are reflective and do not(More)
We consider the phase retrieval problem of recovering the unknown signal from the magnitudeonly measurements, where the measurements can be contaminated by both sparse arbitrary corruption and bounded random noise. We propose a new nonconvex algorithm for robust phase retrieval, namely Robust Wirtinger Flow, to jointly estimate the unknown signal and the(More)
We propose a generic framework based on a new stochastic variance-reduced gradient descent algorithm for accelerating nonconvex low-rank matrix recovery. Starting from an appropriate initial estimator, our proposed algorithm performs projected gradient descent based on a novel semi-stochastic gradient specifically designed for low-rank matrix recovery.(More)
We propose a generic framework based on a new stochastic variance-reduced gradient descent algorithm for accelerating nonconvex low-rank matrix recovery. Starting from an appropriate initial estimator, our proposed algorithm performs projected gradient descent based on a novel semi-stochastic gradient specifically designed for low-rank matrix recovery.(More)