20 accepted papers
This work has two contributions. First, we introduce a provably secure (Byzantine-resilient) sample- and communication-efficient alternating gradient descent (GD) and minimization based algorithms for solving the federated low rank matrix completion (LRMC) problem. This involves learning a low rank…
We introduce a real-time undersampled dynamic MRI algorithm, termed FewShot-AltGDmin-MRI, that is generalizable: works for many different applications and sampling trajectories without any application-specific parameter tuning. FS-AGM-MRI operates in real-time after processing the first short mini-b…
This work introduces a Byzantine resilient solution for learning low-dimensional linear representation. Our main contribution is the development of a provably Byzantine-resilient AltGDmin algorithm for solving this problem in a federated setting. We argue that our solution is sample-efficient, fast,…
This work studies our recently developed algorithm, decentralized alternating projected gradient descent algorithm (Dec-AltGDmin), for recovering a low rank (LR) matrix from independent column-wise linear projections in a decentralized setting. This means that the observed data is spread across L ag…
We study how representation learning can improve the learning efficiency of contextual bandit problems. We study the setting where we play T linear contextual bandits with dimension simultaneously, and these T bandit tasks collectively share a common linear representation with a dimensionality of r…
This work studies our recently developed decentralized algorithm, decentralized alternating projected gradient descent algorithm, called Dec-AltProjGDmin, for solving the following low-rank (LR) matrix recovery problem: recover an LR matrix from independent column-wise linear projections (LR column-…
In recent work , we developed a fast, memory-efficient, and sample-efficient solution to the Low Rank column-wise Compressive Sensing (LRcCS) problem: recover an n × q LR matrix from m under-sampled linear projections of each of its columns. Here, undersampled means m ≪ n,q . The matrix LR model and…
In recent work we developed a fast and sample-efficient gradient descent (GD) solution to the following "Low Rank column-wise Compressive Sensing (LRcCS)": recover an n × q, rank-r matrix X <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">*</sup> from me…
Robust Subspace Tracking with missing data (RST-miss) has been extensively studied in the past decade. In this work we study RST-miss to the setting where the data is federated and when the over-air data communication modality is used for information exchange between the K peer nodes and the central…
Phaseless subspace tracking is the problem of recovering a time sequence of discrete signals from magnitude-only measurements of their linear projections, when the true signal lies in a low-dimensional subspace that can change with time. A typical assumption used in a lot of work is that the subspac…
This work proposes the first set of simple, practically useful, and provable algorithms for two inter-related problems. (i) The first is low-rank matrix recovery from magnitude-only (phaseless) linear projections of each of its columns. This finds important applications in phaseless dynamic imaging,…
Robust Matrix Completion (RMC) is the problem of estimating a low-rank matrix in the presence of missing entries and element-wise (sparse) outliers. In this work, we study the RMC problem with the extra assumption that the clean data is generated from either a fixed or a slowly-changing low-dimensio…
Robust PCA (RPCA) is the problem of separating a given data matrix into the sum of a sparse matrix and a low-rank matrix. Static RPCA is the RPCA problem in which the subspace from which the true data is generated remains fixed over time. Dynamic RPCA instead assumes that the subspace can change wit…
In this paper, we introduce a principled algorithmic approach for Fourier ptychographic imaging of dynamic, time-varying targets. To the best of our knowledge, this setting has not been explicitly addressed in the ptychography literature. We argue that such a setting is very natural, and that our me…
Robust subspace tracking (RST) can be simply understood as a dynamic (time-varying) extension of robust PCA. More precisely, it is the problem of tracking data lying in a fixed or slowly-changing low-dimensional subspace while being robust to sparse outliers. This work develops a recursive projected…
We consider the problem of super-resolution for sub-diffraction imaging. We adapt conventional Fourier ptychographic approaches, for the case where the images to be acquired have an underlying structured sparsity. We propose some sub-sampling strategies which can be easily adapted to existing ptycho…
We study the problem of recovering a low-rank matrix, X, from phaseless measurements of random linear projections of its columns. We develop a novel solution approach, called AltMinTrunc, that consists of a two-step truncated spectral initialization step, followed by a three-step alternating minimiz…
Given a matrix of observed data, Principal Components Analysis (PCA) computes a small number of orthogonal directions that contain most of its variability. Provably accurate solutions for PCA have been in use for a long time. However, to the best of our knowledge, all existing theoretical guarantees…
In this work we develop and study a novel online robust principal components’ analysis (RPCA) algorithm based on the recently introduced ReProCS framework. Our algorithm significantly improves upon the original ReProCS algorithm and it also returns even more accurate offline estimates. The key contr…
We study the problem of sequentially recovering a sparse vector x <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> and a vector from a low-dimensional subspace ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1…