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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 maximum(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)
We consider the phase retrieval problem of recovering the unknown signal from the magnitude-only 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)
—The Advanced Very High Resolution Radiometer (AVHRR) series of instruments have been frequently used for land cover change and global environment studies. The availability of more than 30 years' records have made important time-series studies possible. Removing cloud effects from AVHRR images is a critical task when using the data to monitor land cover(More)
This paper describes a corpus of nearly 10K French-Chinese aligned segments, produced by post-editing machine translated computer science courseware. This corpus was built from 2013 to 2016 within the MACAU project, by native Chinese students. The quality, as judged by native speakers, is adequate for understanding (far better than by reading only the(More)
A series of poly(ADP-ribose)polymerase (PARP)-1 inhibitors containing a novel scaffold, the 1H-thieno[3,4-d]imidazole-4-carboxamide moiety, was designed and synthesized. These efforts provided some compounds with relatively good PARP-1 inhibitory activity, and among them, 16l was the most potent one. Cellular evaluations indicated that the(More)