A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New algorithm for weighted low rank approximation with provable guarantees.
This paper concerns a fundamental class of convex matrix optimization problems. It presents the first algorithm that uses optimal storage and provably computes a low-rank approximation of a solution. In particular, when all solutions have low rank, the algorithm converges to a solution. This algorithm, SketchyCGM, modi…
Rank-one measurements limit feasible sets for low-rank PSD matrices.
New model reduces matrix factorization bias, yielding truly low-rank solutions.
Simplifies solving noisy SDPs for low rank matrix recovery problems.
Motivated principally by the low-rank matrix completion problem, we present an extension of the Frank-Wolfe method that is designed to induce near-optimal solutions on low-dimensional faces of the feasible region. This is accomplished by a new approach to generating ``in-face" directions at each iteration, as well as t…
In this paper, we show that the bundle method can be applied to solve semidefinite programming problems with a low rank solution without ever constructing a full matrix. To accomplish this, we use recent results from randomly sketching matrix optimization problems and from the analysis of bundle methods. Under strong d…
This work studies the linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). Searching this approximation in a data-driven approach is formalised as attempting to solve a low-rank constrained optimisation problem. This problem is non-convex and state-of-the-art algor…
CoLoRA models predict PDE solutions quickly and accurately with minimal data.
Solves weakly supervised regression using low-rank approximations and manifold regularization.
Paper studies asymmetric matrix sensing, proving gradient descent converges to low-rank solutions.
One of the popular approaches for low-rank tensor completion is to use the latent trace norm regularization. However, most existing works in this direction learn a sparse combination of tensors. In this work, we fill this gap by proposing a variant of the latent trace norm that helps in learning a non-sparse combinatio…
Sign-RIP improves robust low-rank matrix recovery by preserving norms even with corrupted measurements.
The paper reviews Hankel low-rank methods for time series analysis and forecasting.
We study the problem of prediction for evolving graph data. We formulate the problem as the minimization of a convex objective encouraging sparsity and low-rank of the solution, that reflect natural graph properties. The convex formulation allows to obtain oracle inequalities and efficient solvers. We provide empirical…
Review of algorithms for linear system approximations.
New findings show DNC is not optimal for deep models, revealing a low-rank bias.
SGD with mini-batches can solve convex low-rank matrix problems efficiently.
New framework solves low-rank optimization problems to certifiable optimality.
Paper tackles low-rank matrix recovery with column -norm regularization.
CMF is a technique for simultaneously learning low-rank representations based on a collection of matrices with shared entities. A typical example is the joint modeling of user-item, item-property, and user-feature matrices in a recommender system. The key idea in CMF is that the embeddings are shared across the matrice…
The problem of low rank matrix completion is considered in this paper. To exploit the underlying low-rank structure of the data matrix, we propose a hierarchical Gaussian prior model, where columns of the low-rank matrix are assumed to follow a Gaussian distribution with zero mean and a common precision matrix, and a W…
CP degeneracy affects tensor regression solutions, especially in high dimensions.
Semidefinite programs (SDP) are important in learning and combinatorial optimization with numerous applications. In pursuit of low-rank solutions and low complexity algorithms, we consider the Burer--Monteiro factorization approach for solving SDPs. We show that all approximate local optima are global optima for the pe…
A low-rank tensor model simplifies multi-dimensional Markov chains.
Develops efficient method for updating models with small data changes.
This work provides closed-form solutions and minimum achievable errors for a large class of low-rank approximation problems in Hilbert spaces. The proposed theorem generalizes to the case of bounded linear operators the previous results obtained in the finite dimensional case for the Frobenius norm. The theorem provide…
Partial convexification improves tractability of low-rank spectral optimization problems.
This paper addresses the problem of low-rank distance matrix completion. This problem amounts to recover the missing entries of a distance matrix when the dimension of the data embedding space is possibly unknown but small compared to the number of considered data points. The focus is on high-dimensional problems. We r…
New nonconvex regularizer speeds up low-rank matrix completion.
Dynamic Mode Decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of non-linear systems from experimental datasets. Recently, several attempts have extended DMD to the context of low-rank approximations. This extension is of particular interest for reduced-order modeling in various applicative …
Paper analyzes noisy low-rank matrix optimization, improving RIP bounds and convergence rates.
Low-rank inducing unitarily invariant norms have been introduced to convexify problems with low-rank/sparsity constraint. They are the convex envelope of a unitary invariant norm and the indicator function of an upper bounding rank constraint. The most well-known member of this family is the so-called nuclear norm. To …
New method solves nonsmooth low-rank matrix optimization problems efficiently.
GD learns matrix solutions incrementally, revealing insights into generalization.
PILNO uses neural operators to solve PDEs efficiently on point clouds.
New method decomposes corrupted data matrices into sparse and low-rank components.
Gradient descent promotes low-rank solutions in tensor completion.
LR-EDNN reduces PDE solver complexity by limiting network weights to low-rank subspace.
New algorithm improves tensor completion performance.
DCCNNs reduce computational overhead and ambiguity in convolutional neural networks.
ScaledGD accelerates ill-conditioned low-rank estimation.
We consider the problem of learning a high-dimensional but low-rank matrix from a large-scale dataset distributed over several machines, where low-rankness is enforced by a convex trace norm constraint. We propose DFW-Trace, a distributed Frank-Wolfe algorithm which leverages the low-rank structure of its updates to ac…
As surrogate functions of -norm, many nonconvex penalty functions have been proposed to enhance the sparse vector recovery. It is easy to extend these nonconvex penalty functions on singular values of a matrix to enhance low-rank matrix recovery. However, different from convex optimization, solving the nonconvex l…
This work presents a general framework for solving the low rank and/or sparse matrix minimization problems, which may involve multiple non-smooth terms. The Iteratively Reweighted Least Squares (IRLS) method is a fast solver, which smooths the objective function and minimizes it by alternately updating the variables an…
Gradient descent achieves exact linear convergence rate for symmetric matrix completion.
Principal Components Analysis (PCA) is one of the most widely used dimension reduction techniques. Robust PCA (RPCA) refers to the problem of PCA when the data may be corrupted by outliers. Recent work by Cand{è}s, Wright, Li, and Ma defined RPCA as a problem of decomposing a given data matrix into the sum of a low-ran…
Improved iterative hard thresholding for faster, sparser solutions.