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Found 23 papers, 11 papers with code
A Fast Algorithm for Low Rank + Sparse column-wise Compressive Sensing
We aim to recover an $n \times q$ matrix, $\X^* =[ \x_1^*, \x_2^*, \cdots , \x_q^*]$ from $m$ independent linear projections of each of its $q$ columns, given by $\y_k :=\A_k\x_k^*$, $k \in [q]$.
Byzantine-Resilient Federated PCA and Low Rank Matrix Recovery
We also study the most natural solution for this problem, a geometric median based modification of the federated power method, and explain why it is not useful.
Fast Low Rank column-wise Compressive Sensing for Accelerated Dynamic MRI
This claim is based on comparisons on 8 different retrospectively under sampled multi-coil dynamic MRI applications, sampled using either 1D Cartesian or 2D pseudo radial under sampling, at multiple sampling rates.
Detection and Mitigation of Byzantine Attacks in Distributed Training
For strong attacks, we demonstrate a reduction in the fraction of distorted gradients ranging from 16%-99% as compared to the prior state-of-the-art.
Fast Low Rank column-wise Compressive Sensing for Accelerated Dynamic MRI
By general, we mean that our algorithm can be used for multiple accelerated dynamic MRI applications and multiple sampling rates (acceleration rates) and patterns with a single choice of parameters (no parameter tuning).
Fast and Sample-Efficient Federated Low Rank Matrix Recovery from column-wise Linear and Quadratic Projections
Finally, it can also be efficiently federated with a communication cost of only $nr$ per node, instead of $nq$ for projected GD.
Information Theory Information Theory
Non-Convex Structured Phase Retrieval
Phase retrieval (PR), also sometimes referred to as quadratic sensing, is a problem that occurs in numerous signal and image acquisition domains ranging from optics, X-ray crystallography, Fourier ptychography, sub-diffraction imaging, and astronomy.
Fast Robust Subspace Tracking via PCA in Sparse Data-Dependent Noise
An important setting where this is useful is for linearly data dependent noise that is sparse with support that changes enough over time.
Federated Over-Air Subspace Tracking from Incomplete and Corrupted Data
In this work we study the problem of Subspace Tracking with missing data (ST-miss) and outliers (Robust ST-miss).
Random Convolutional Coding for Robust and Straggler Resilient Distributed Matrix Computation
Distributed matrix computations (matrix-vector and matrix-matrix multiplications) are at the heart of several tasks within the machine learning pipeline.
Information Theory Information Theory
Provable Low Rank Phase Retrieval
We study the Low Rank Phase Retrieval (LRPR) problem defined as follows: recover an $n \times q$ matrix $X^*$ of rank $r$ from a different and independent set of $m$ phaseless (magnitude-only) linear projections of each of its columns.
Provable Subspace Tracking from Missing Data and Matrix Completion
In this work, we show that a simple modification of our robust ST solution also provably solves ST-miss and robust ST-miss.
Phaseless Subspace Tracking
This work takes the first steps towards solving the "phaseless subspace tracking" (PST) problem.
Static and Dynamic Robust PCA and Matrix Completion: A Review
Robust PCA (RPCA) refers to the problem of PCA when the data may be corrupted by outliers.
Nearly Optimal Robust Subspace Tracking
We prove that NORST solves both the RST and the dynamic RPCA problems under weakened standard RPCA assumptions, two simple extra assumptions (slow subspace change and most outlier magnitudes lower bounded), and a few minor assumptions.
Robust Subspace Learning: Robust PCA, Robust Subspace Tracking, and Robust Subspace Recovery
The problem of subspace learning or PCA in the presence of outliers is called robust subspace learning or robust PCA (RPCA).
Video Denoising and Enhancement via Dynamic Video Layering
Video denoising refers to the problem of removing "noise" from a video sequence.
Finite Sample Guarantees for PCA in Non-Isotropic and Data-Dependent Noise
This work obtains novel finite sample guarantees for Principal Component Analysis (PCA).
Provable Dynamic Robust PCA or Robust Subspace Tracking
Dynamic robust PCA refers to the dynamic (time-varying) extension of robust PCA (RPCA).
PCA in Data-Dependent Noise (Correlated-PCA): Nearly Optimal Finite Sample Guarantees
We study Principal Component Analysis (PCA) in a setting where a part of the corrupting noise is data-dependent and, as a result, the noise and the true data are correlated.
Correlated-PCA: Principal Components' Analysis when Data and Noise are Correlated
We obtain a correctness result for the standard eigenvalue decomposition (EVD) based solution to PCA under simple assumptions on the data-noise correlation.
Correlated-PCA: Principal Components' Analysis when Data and Noise are Correlated
We obtain a correctness result for the standard eigenvalue decomposition (EVD) based solution to PCA under simple assumptions on the data-noise correlation.
Online Matrix Completion and Online Robust PCA
In this work, we develop a practical modification of our recently proposed algorithm to solve both the online RPCA and online MC problems.
