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Rank-Sparsity Incoherence for Matrix Decomposition
This paper decomposes a matrix formed by adding an unknown sparse matrix to an unknown low-rank matrix into its sparse and low- rank components.
Robust PCA via Outlier Pursuit
- Huan Xu, C. Caramanis, S. Sanghavi
- Computer ScienceIEEE Transactions on Information Theory
- 20 October 2010
This work presents an efficient convex optimization-based algorithm that it calls outlier pursuit, which under some mild assumptions on the uncorrupted points recovers the exact optimal low-dimensional subspace and identifies the corrupted points.
Low-rank matrix completion using alternating minimization
This paper presents one of the first theoretical analyses of the performance of alternating minimization for matrix completion, and the related problem of matrix sensing, and shows that alternating minimizations guarantees faster convergence to the true matrix, while allowing a significantly simpler analysis.
Phase Retrieval Using Alternating Minimization
- Praneeth Netrapalli, Prateek Jain, S. Sanghavi
- Computer Science, MathematicsIEEE Transactions on Signal Processing
- 1 June 2013
This work represents the first theoretical guarantee for alternating minimization (albeit with resampling) for any variant of phase retrieval problems in the non-convex setting.
Non-convex Robust PCA
- Praneeth Netrapalli, U. Niranjan, S. Sanghavi, Anima Anandkumar, Prateek Jain
- Computer ScienceNIPS
- 28 October 2014
A new provable method for robust PCA, where the task is to recover a low-rank matrix, which is corrupted with sparse perturbations, which represents one of the few instances of global convergence guarantees for non-convex methods.
A Dirty Model for Multi-task Learning
We consider multi-task learning in the setting of multiple linear regression, and where some relevant features could be shared across the tasks. Recent research has studied the use of l1/lq norm…
Dropping Convexity for Faster Semi-definite Optimization
- Srinadh Bhojanapalli, Anastasios Kyrillidis, S. Sanghavi
- Mathematics, Computer ScienceCOLT
- 14 September 2015
This is the first paper to provide precise convergence rate guarantees for general convex functions under standard convex assumptions and to provide a procedure to initialize FGD for (restricted) strongly convex objectives and when one only has access to f via a first-order oracle.
MAX‐DOAS O4 measurements: A new technique to derive information on atmospheric aerosols—Principles and information content
 Multi AXis Differential Optical Absorption Spectroscopy (MAX-DOAS) observations of the oxygen dimer O4 which can serve as a new method for the determination of atmospheric aerosol properties are…
Learning the graph of epidemic cascades
This work analytically establishes sufficient conditions on the number of epidemics for both the global maximum-likelihood (ML) estimator, and a natural greedy algorithm to succeed with high probability in finding the graph on which an epidemic spreads, given only the times when each node gets infected.
Greedy Subspace Clustering
The statistical analysis shows that the algorithms are guaranteed exact (perfect) clustering performance under certain conditions on the number of points and the affinity between subspaces, which are weaker than those considered in the standard statistical literature.