Low-rank approximation
View article: Code and data for "Generalizing Reduced Rank Extrapolation to Low-Rank Matrix Sequences"
Code and data for "Generalizing Reduced Rank Extrapolation to Low-Rank Matrix Sequences" Open
Please read the contained README.md for further information on the files included and their particular licenses. This version of rre.zip contains a small set of new experiments, defined by code/run_all_appendix.m. We did not re-run all our…
View article: Speeding up the Goemans-Williamson randomized procedure by difference-of-convex optimization
Speeding up the Goemans-Williamson randomized procedure by difference-of-convex optimization Open
We present a novel approach to accelerate the Goemans-Williamson (GW) randomized rounding procedure for quadratic unconstrained binary optimization (QUBO) problems. Instead of solving the conventional semi-definite programming (SDP) relaxa…
View article: Speeding up the Goemans-Williamson randomized procedure by difference-of-convex optimization
Speeding up the Goemans-Williamson randomized procedure by difference-of-convex optimization Open
We present a novel approach to accelerate the Goemans-Williamson (GW) randomized rounding procedure for quadratic unconstrained binary optimization (QUBO) problems. Instead of solving the conventional semi-definite programming (SDP) relaxa…
View article: Matrix approximations of operators
Matrix approximations of operators Open
The approximate representation of operators by finite matrices is analysed in terms of accuracy and convergence. The identity operator, for example, can be reconstructed using a basis of harmonic oscillator states leading to a narrow peak …
View article: Matrix approximations of operators
Matrix approximations of operators Open
The approximate representation of operators by finite matrices is analysed in terms of accuracy and convergence. The identity operator, for example, can be reconstructed using a basis of harmonic oscillator states leading to a narrow peak …
View article: Structured Approximation of Toeplitz Matrices and Subspaces
Structured Approximation of Toeplitz Matrices and Subspaces Open
This paper studies two structured approximation problems: (1) Recovering a corrupted low-rank Toeplitz matrix and (2) recovering the range of a Fourier matrix from a single observation. Both problems are computationally challenging because…
View article: Structured Approximation of Toeplitz Matrices and Subspaces
Structured Approximation of Toeplitz Matrices and Subspaces Open
This paper studies two structured approximation problems: (1) Recovering a corrupted low-rank Toeplitz matrix and (2) recovering the range of a Fourier matrix from a single observation. Both problems are computationally challenging because…
View article: FairLRF: Achieving Fairness through Sparse Low Rank Factorization
FairLRF: Achieving Fairness through Sparse Low Rank Factorization Open
As deep learning (DL) techniques become integral to various applications, ensuring model fairness while maintaining high performance has become increasingly critical, particularly in sensitive fields such as medical diagnosis. Although a v…
View article: FairLRF: Achieving Fairness through Sparse Low Rank Factorization
FairLRF: Achieving Fairness through Sparse Low Rank Factorization Open
As deep learning (DL) techniques become integral to various applications, ensuring model fairness while maintaining high performance has become increasingly critical, particularly in sensitive fields such as medical diagnosis. Although a v…
View article: RLS Framework with Segmentation of the Forgetting Profile and Low Rank Updates
RLS Framework with Segmentation of the Forgetting Profile and Low Rank Updates Open
This report describes a new regularization approach based on segmentation of the forgetting profile in sliding window least squares estimation. Each segment is designed to enforce specific desirable properties of the estimator such as rapi…
View article: Generalization Bounds for Semi-supervised Matrix Completion with Distributional Side Information
Generalization Bounds for Semi-supervised Matrix Completion with Distributional Side Information Open
We study a matrix completion problem where both the ground truth $R$ matrix and the unknown sampling distribution $P$ over observed entries are low-rank matrices, and \textit{share a common subspace}. We assume that a large amount $M$ of \…
View article: Generalization Bounds for Semi-supervised Matrix Completion with Distributional Side Information
Generalization Bounds for Semi-supervised Matrix Completion with Distributional Side Information Open
We study a matrix completion problem where both the ground truth $R$ matrix and the unknown sampling distribution $P$ over observed entries are low-rank matrices, and \textit{share a common subspace}. We assume that a large amount $M$ of \…
View article: Faster MAX-CUT on Bounded Threshold Rank Graphs
Faster MAX-CUT on Bounded Threshold Rank Graphs Open
We design new algorithms for approximating 2CSPs on graphs with bounded threshold rank, that is, whose normalized adjacency matrix has few eigenvalues larger than $\varepsilon$, smaller than $-\varepsilon$, or both. Unlike on worst-case gr…
View article: Sparse integer-preserving Gram–Schmidt orthogonalization for REF QR factorization
Sparse integer-preserving Gram–Schmidt orthogonalization for REF QR factorization Open
QR factorization is foundational for mathematics, computer science, and operations research. Typically, QR factorizations are computed in floating-point precision, which, though appropriate for the majority of applications, have been shown…
View article: Extended-Krylov-subspace methods for trust-region and norm-regularization subproblems
Extended-Krylov-subspace methods for trust-region and norm-regularization subproblems Open
We consider an effective new method for solving trust-region and norm-regularization problems that arise as subproblems in many optimization applications. We show that the solutions to such subproblems lie on a manifold of approximately ve…
View article: Improved Differentially Private Algorithms for Rank Aggregation
Improved Differentially Private Algorithms for Rank Aggregation Open
Rank aggregation is a task of combining the rankings of items from multiple users into a single ranking that best represents the users' rankings. Alabi et al. (AAAI'22) presents differentially-private (DP) polynomial-time approximation sch…
View article: Improved Differentially Private Algorithms for Rank Aggregation
Improved Differentially Private Algorithms for Rank Aggregation Open
Rank aggregation is a task of combining the rankings of items from multiple users into a single ranking that best represents the users' rankings. Alabi et al. (AAAI'22) presents differentially-private (DP) polynomial-time approximation sch…
View article: Faster MAX-CUT on Bounded Threshold Rank Graphs
Faster MAX-CUT on Bounded Threshold Rank Graphs Open
We design new algorithms for approximating 2CSPs on graphs with bounded threshold rank, that is, whose normalized adjacency matrix has few eigenvalues larger than $\varepsilon$, smaller than $-\varepsilon$, or both. Unlike on worst-case gr…
View article: Extended-Krylov-subspace methods for trust-region and norm-regularization subproblems
Extended-Krylov-subspace methods for trust-region and norm-regularization subproblems Open
We consider an effective new method for solving trust-region and norm-regularization problems that arise as subproblems in many optimization applications. We show that the solutions to such subproblems lie on a manifold of approximately ve…
View article: Fast Neural Tangent Kernel Alignment, Norm and Effective Rank via Trace Estimation
Fast Neural Tangent Kernel Alignment, Norm and Effective Rank via Trace Estimation Open
The Neural Tangent Kernel (NTK) characterizes how a model's state evolves over Gradient Descent. Computing the full NTK matrix is often infeasible, especially for recurrent architectures. Here, we introduce a matrix-free perspective, using…
View article: Faster Algorithms for Structured Matrix Multiplication via Flip Graph Search
Faster Algorithms for Structured Matrix Multiplication via Flip Graph Search Open
We give explicit low-rank bilinear non-commutative schemes for multiplying structured $n \times n$ matrices with $2 \leq n \leq 5$, which serve as building blocks for recursive algorithms with improved multiplicative factors in asymptotic …
View article: Faster Algorithms for Structured Matrix Multiplication via Flip Graph Search
Faster Algorithms for Structured Matrix Multiplication via Flip Graph Search Open
We give explicit low-rank bilinear non-commutative schemes for multiplying structured $n \times n$ matrices with $2 \leq n \leq 5$, which serve as building blocks for recursive algorithms with improved multiplicative factors in asymptotic …
View article: A proximal alternative directional method of multipliers for a class of low rank matrix recovery problems
A proximal alternative directional method of multipliers for a class of low rank matrix recovery problems Open
View article: Fast Neural Tangent Kernel Alignment, Norm and Effective Rank via Trace Estimation
Fast Neural Tangent Kernel Alignment, Norm and Effective Rank via Trace Estimation Open
The Neural Tangent Kernel (NTK) characterizes how a model's state evolves over Gradient Descent. Computing the full NTK matrix is often infeasible, especially for recurrent architectures. Here, we introduce a matrix-free perspective, using…
View article: New perturbation bounds for low rank approximation of matrices via contour analysis
New perturbation bounds for low rank approximation of matrices via contour analysis Open
Let $A$ be an $m \times n$ matrix with rank $r$ and spectral decomposition $A = \sum _{i=1}^r σ_i u_i v_i^\top, $ where $σ_i$ are its singular values, ordered decreasingly, and $u_i, v_i$ are the corresponding left and right singular vecto…
View article: New perturbation bounds for low rank approximation of matrices via contour analysis
New perturbation bounds for low rank approximation of matrices via contour analysis Open
Let $A$ be an $m \times n$ matrix with rank $r$ and spectral decomposition $A = \sum _{i=1}^r σ_i u_i v_i^\top, $ where $σ_i$ are its singular values, ordered decreasingly, and $u_i, v_i$ are the corresponding left and right singular vecto…
View article: Fast Time-Varying mmWave MIMO Channel Estimation and Reconstruction: An Efficient Rank-Aware Matrix Completion Method
Fast Time-Varying mmWave MIMO Channel Estimation and Reconstruction: An Efficient Rank-Aware Matrix Completion Method Open
We address the problem of fast time-varying channel estimation in millimeter-wave (mmWave) MIMO systems with imperfect channel state information (CSI) and facilitate efficient channel reconstruction. Specifically, leveraging the low-rank a…
View article: Fast Time-Varying mmWave MIMO Channel Estimation and Reconstruction: An Efficient Rank-Aware Matrix Completion Method
Fast Time-Varying mmWave MIMO Channel Estimation and Reconstruction: An Efficient Rank-Aware Matrix Completion Method Open
We address the problem of fast time-varying channel estimation in millimeter-wave (mmWave) MIMO systems with imperfect channel state information (CSI) and facilitate efficient channel reconstruction. Specifically, leveraging the low-rank a…
View article: Many (most?) column subset selection criteria are NP hard
Many (most?) column subset selection criteria are NP hard Open
We consider a variety of criteria for selecting k representative columns from a real matrix A with rank(A)>=k. The criteria include the following optimization problems: absolute volume and S-optimality maximization; norm and condition mini…
View article: Accelerated Frank-Wolfe Algorithms: Complementarity Conditions and Sparsity
Accelerated Frank-Wolfe Algorithms: Complementarity Conditions and Sparsity Open
We develop new accelerated first-order algorithms in the Frank-Wolfe (FW) family for minimizing smooth convex functions over compact convex sets, with a focus on two prominent constraint classes: (1) polytopes and (2) matrix domains given …