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 method solves nonsmooth low-rank matrix optimization problems efficiently.
New approach to convex hulls for low-rank problems.
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…
We introduce a new framework for optimal transport using Schatten-p regularization to recover low-rank structures.
Robust PCA is a widely used statistical procedure to recover a underlying low-rank matrix with grossly corrupted observations. This work considers the problem of robust PCA as a nonconvex optimization problem on the manifold of low-rank matrices, and proposes two algorithms (for two versions of retractions) based on ma…
New framework solves low-rank optimization problems to certifiable optimality.
A low-rank tensor model simplifies multi-dimensional Markov chains.
Equivalent formulations for low-rank matrix optimization are proven.
New method improves robust low-rank matrix completion for computer vision.
Research reveals deep networks often learn low-rank structures, leading to more efficient training and fine-tuning.
Paper improves MVSC using tensor low-rank modeling.
We study the convergence of a variant of distributed gradient descent (DGD) on a distributed low-rank matrix approximation problem wherein some optimization variables are used for consensus (as in classical DGD) and some optimization variables appear only locally at a single node in the network. We term the resulting a…
Efficiently implements MEG for low-rank matrix optimization problems.
New model enhances SPIM for solving low-rank combinatorial optimization and statistical learning problems.
The paper reviews Hankel low-rank methods for time series analysis and forecasting.
Optimizes wide low-rank neural networks for reduced parameters and cost.
Optimization problems with rank constraints appear in many diverse fields such as control, machine learning and image analysis. Since the rank constraint is non-convex, these problems are often approximately solved via convex relaxations. Nuclear norm regularization is the prevailing convexifying technique for dealing …
We propose a unified framework for estimating low-rank matrices through nonconvex optimization based on gradient descent algorithm. Our framework is quite general and can be applied to both noisy and noiseless observations. In the general case with noisy observations, we show that our algorithm is guaranteed to linearl…
New algorithm tackles low-rank constraints in optimal transport problems.
A new Riemannian framework optimizes LoRA for faster convergence and better performance.
We revisit the use of Stochastic Gradient Descent (SGD) for solving convex optimization problems that serve as highly popular convex relaxations for many important low-rank matrix recovery problems such as \textit{matrix completion}, \textit{phase retrieval}, and more. The computational limitation of applying SGD to so…
We provide new approximation guarantees for greedy low rank matrix estimation under standard assumptions of restricted strong convexity and smoothness. Our novel analysis also uncovers previously unknown connections between the low rank estimation and combinatorial optimization, so much so that our bounds are reminisce…
Composite convex optimization problems which include both a nonsmooth term and a low-rank promoting term have important applications in machine learning and signal processing, such as when one wishes to recover an unknown matrix that is simultaneously low-rank and sparse. However, such problems are highly challenging t…
New method solves matrix completion problems to certifiable optimality.
New nonconvex regularizer speeds up low-rank matrix completion.
TensorGuide improves LoRA efficiency and expressivity through joint tensor-train optimization.
Paper explores statistical and computational limits of estimating low-rank Gaussian mixtures.
New algorithm for low-rank optimal transport with improved interpretability and efficiency.
Paper develops a new weighted low-rank matrix approximation technique.
We study the problem of estimating low-rank matrices from linear measurements (a.k.a., matrix sensing) through nonconvex optimization. We propose an efficient stochastic variance reduced gradient descent algorithm to solve a nonconvex optimization problem of matrix sensing. Our algorithm is applicable to both noisy and…
Flora uses random projections to achieve high-rank updates with low memory usage.
Algorithm recovers multiple low-rank matrices from unlabeled data.
New findings show DNC is not optimal for deep models, revealing a low-rank bias.
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…
Unified approach tackles high-dimensional tensor bandits with convex optimization and weakly decomposable regularizers.
Paper proposes a new method to separate low rank and sparse matrices without bias.
This work studies low-rank approximation of a positive semidefinite matrix from partial entries via nonconvex optimization. We characterized how well local-minimum based low-rank factorization approximates a fixed positive semidefinite matrix without any assumptions on the rank-matching, the condition number or eigensp…
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…
New method for online low-rank matrix completion with improved regret.
Gradient descent with small random init mimics spectral methods for low-rank matrix recovery.
Partial convexification improves tractability of low-rank spectral optimization problems.
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…
In this paper, we propose a low-rank approximation method based on discrete least-squares for the approximation of a multivariate function from random, noisy-free observations. Sparsity inducing regularization techniques are used within classical algorithms for low-rank approximation in order to exploit the possible sp…
Paper proposes fast, robust methods for low-rank matrix recovery.
Low-rank metric learning aims to learn better discrimination of data subject to low-rank constraints. It keeps the intrinsic low-rank structure of datasets and reduces the time cost and memory usage in metric learning. However, it is still a challenge for current methods to handle datasets with both high dimensions and…
We propose a generic framework based on a new stochastic variance-reduced gradient descent algorithm for accelerating nonconvex low-rank matrix recovery. Starting from an appropriate initial estimator, our proposed algorithm performs projected gradient descent based on a novel semi-stochastic gradient specifically desi…
We investigate the sample size requirement for exact recovery of a high order tensor of low rank from a subset of its entries. In the Tucker decomposition framework, we show that the Riemannian optimization algorithm with initial value obtained from a spectral method can reconstruct a tensor of size $n\times n \times\c…