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.
Paper studies asymmetric matrix sensing, proving gradient descent converges to low-rank solutions.
We present a unified framework for low-rank matrix estimation with nonconvex penalties. We first prove that the proposed estimator attains a faster statistical rate than the traditional low-rank matrix estimator with nuclear norm penalty. Moreover, we rigorously show that under a certain condition on the magnitude of t…
New nonconvex regularizer speeds up low-rank matrix completion.
Sign-RIP improves robust low-rank matrix recovery by preserving norms even with corrupted measurements.
Paper develops methods for non-quadratic loss low-rank matrix recovery.
Nonnegative low-rank matrix recovery can have spurious local minima.
Survey of structured low-rank algorithms for MR signal recovery.
Gradient descent solves asymmetric low-rank matrix sensing without balancing.
We address some theoretical guarantees for Schatten- quasi-norm minimization () in recovering low-rank matrices from compressed linear measurements. Firstly, using null space properties of the measurement operator, we provide a sufficient condition for exact recovery of low-rank matrices. This condition…
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…
This paper uncovers the low-rank structure of neural network Hessians.
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…
The problem of low-rank matrix estimation recently received a lot of attention due to challenging applications. A lot of work has been done on rank-penalized methods and convex relaxation, both on the theoretical and applied sides. However, only a few papers considered Bayesian estimation. In this paper, we review the …
FedLoRU improves FL efficiency by using low-rank updates.
New method improves matrix completion accuracy, especially in noisy data.
New method fits low-rank models for egocentrically sampled networks.
We accelerate the power method for strong low-rank approximation using fast sketching.
New model-free algorithms learn representations for low-rank MDPs efficiently.
New algorithms estimate Jacobian matrices for large-scale machine learning.
Paper analyzes noisy low-rank matrix optimization, improving RIP bounds and convergence rates.
This paper tackles fitting multilevel low rank matrices by addressing three problems.
Many applications require recovering a ground truth low-rank matrix from noisy observations of the entries, which in practice is typically formulated as a weighted low-rank approximation problem and solved by non-convex optimization heuristics such as alternating minimization. In this paper, we provide provable recover…
Given the superposition of a low-rank matrix plus the product of a known fat compression matrix times a sparse matrix, the goal of this paper is to establish deterministic conditions under which exact recovery of the low-rank and sparse components becomes possible. This fundamental identifiability issue arises with tra…
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…
Sparse PCA is a widely used technique for high-dimensional data analysis. In this paper, we propose a new method called low-rank principal eigenmatrix analysis. Different from sparse PCA, the dominant eigenvectors are allowed to be dense but are assumed to have a low-rank structure when matricized appropriately. Such a…
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…
The paper connects neural collapse and low-rank bias in networks with L2 regularization.
Paper proposes fast, robust methods for low-rank matrix recovery.
New method improves tensor completion for weakly-dependent spatiotemporal data.
ScaledGD accelerates ill-conditioned low-rank estimation.
ScaledGD improves gradient descent for ill-conditioned low-rank matrix estimation.
In the paper, we consider the problem of link prediction in time-evolving graphs. We assume that certain graph features, such as the node degree, follow a vector autoregressive (VAR) model and we propose to use this information to improve the accuracy of prediction. Our strategy involves a joint optimization procedure …
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…
Most recent results in matrix completion assume that the matrix under consideration is low-rank or that the columns are in a union of low-rank subspaces. In real-world settings, however, the linear structure underlying these models is distorted by a (typically unknown) nonlinear transformation. This paper addresses the…
The paper analyzes conditions for solving low-rank matrix recovery problems with noisy measurements.
Low-rank modeling plays a pivotal role in signal processing and machine learning, with applications ranging from collaborative filtering, video surveillance, medical imaging, to dimensionality reduction and adaptive filtering. Many modern high-dimensional data and interactions thereof can be modeled as lying approximat…
Unified error analysis for low-rank approximation improves data assimilation performance.
The paper reveals low-rank structure in neural network gradients, influenced by data and model parameters.
Proposes a new model for image restoration combining deep learning and total variation.
LOT improves optimal transport for large datasets.
New method avoids spurious critical points for low-rank matrix recovery.
We establish a "low rank property" for Sobolev mappings that pointwise solve a first order nonlinear system of PDEs, whose smooth solutions have the so-called "contact property". As a consequence, Sobolev mappings from an open set of the plane, taking values in the first Heisenberg group and that have almost everywhere…
This paper aims at achieving a simultaneously sparse and low-rank estimator from the semidefinite population covariance matrices. We first benefit from a convex optimization which develops -norm penalty to encourage the sparsity and nuclear norm to favor the low-rank property. For the proposed estimator, we then p…
This work tackles sparse coding in DLRA for interpretable multiway data.
ScaledGD algorithm estimates low-rank tensors efficiently from corrupted data.
Equivalent formulations for low-rank matrix optimization are proven.
Recently, there has been an abundance of works on designing Deep Neural Networks (DNNs) that are robust to adversarial examples. In particular, a central question is which features of DNNs influence adversarial robustness and, therefore, can be to used to design robust DNNs. In this work, this problem is studied throug…