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.
This paper tackles fitting multilevel low rank matrices by addressing three problems.
Rank-one measurements limit feasible sets for low-rank PSD matrices.
Develops a fast algorithm for fitting multilevel factor models.
With the advent of massive data sets much of the computational science and engineering community has moved toward data-intensive approaches in regression and classification. However, these present significant challenges due to increasing size, complexity and dimensionality of the problems. In particular, covariance mat…
Matrices of (approximate) low rank are pervasive in data science, appearing in recommender systems, movie preferences, topic models, medical records, and genomics. While there is a vast literature on how to exploit low rank structure in these datasets, there is less attention on explaining why the low rank structure ap…
New algorithm learns low-rank matrices with linear number of samples.
Algorithm recovers multiple low-rank matrices from unlabeled data.
Improved Bayesian regression for large datasets using multilevel Gibbs sampling.
Model trains passing events on a bridge using multilevel Gaussian process.
New framework solves low-rank optimization problems to certifiable optimality.
New method reduces computational cost for nonnegative low rank matrix approximation.
New algorithms improve RPCA for large matrices with upper rank bounds.
Develops PRPCA for smooth image recovery combining low-rank and smoothness.
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…
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…
Weight Decay induces low-rank weight matrices in neural networks, improving generalization.
We develop latent variable models for Bayesian learning based low-rank matrix completion and reconstruction from linear measurements. For under-determined systems, the developed methods are shown to reconstruct low-rank matrices when neither the rank nor the noise power is known a-priori. We derive relations between th…
Matrix completion is a problem that arises in many data-analysis settings where the input consists of a partially-observed matrix (e.g., recommender systems, traffic matrix analysis etc.). Classical approaches to matrix completion assume that the input partially-observed matrix is low rank. The success of these methods…
The low displacement rank (LDR) framework for structured matrices represents a matrix through two displacement operators and a low-rank residual. Existing use of LDR matrices in deep learning has applied fixed displacement operators encoding forms of shift invariance akin to convolutions. We introduce a class of LDR ma…
New method corrects quantization errors in LLMs using low-rank matrices.
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…
Matrix factorization is a well-studied task in machine learning for compactly representing large, noisy data. In our approach, instead of using the traditional concept of matrix rank, we define a new notion of link-rank based on a non-linear link function used within factorization. In particular, by applying the round …
LOCUS separates brain network connectivity matrices efficiently.
In this letter, we propose an algorithm for recovery of sparse and low rank components of matrices using an iterative method with adaptive thresholding. In each iteration, the low rank and sparse components are obtained using a thresholding operator. This algorithm is fast and can be implemented easily. We compare it w…
New bound for neural networks with full-rank weights, independent of network width.
Low-rank approximations of data matrices are an important dimensionality reduction tool in machine learning and regression analysis. We consider the case of categorical variables, where it can be formulated as the problem of finding low-rank approximations to Boolean matrices. In this paper we give what is to the best …
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…
TensorGuide improves LoRA efficiency and expressivity through joint tensor-train optimization.
Algorithm compresses large matrices by approximating them as low rank and low precision factors.
Accelerates MCMC sampling for large-scale problems using machine learning.
Flora uses random projections to achieve high-rank updates with low memory usage.
Mirror descent algorithm recovers low-rank matrices in matrix sensing.
Riemannian gradient descent escapes some spurious critical points on low-rank matrix manifold.
Estimation of low-rank matrices is of significant interest in a range of contemporary applications. In this paper, we introduce a rank-one projection model for low-rank matrix recovery and propose a constrained nuclear norm minimization method for stable recovery of low-rank matrices in the noisy case. The procedure is…
Paper finds a lower bound for estimating low-rank matrices in logistic regression.
Paper proposes a new method to separate low rank and sparse matrices without bias.
This paper uncovers the low-rank structure of neural network Hessians.
Efficient algorithm for Hadamard decomposition of matrices.
New method solves nonsmooth low-rank matrix optimization problems efficiently.
ScaledGD improves gradient descent for ill-conditioned low-rank matrix estimation.
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…
Multiresolution Matrix Factorization (MMF) was recently introduced as an alternative to the dominant low-rank paradigm in order to capture structure in matrices at multiple different scales. Using ideas from multiresolution analysis (MRA), MMF teased out hierarchical structure in symmetric matrices by constructing a se…
We address the problem of minimizing a convex function over the space of large matrices with low rank. While this optimization problem is hard in general, we propose an efficient greedy algorithm and derive its formal approximation guarantees. Each iteration of the algorithm involves (approximately) finding the left an…
Matrix completion works well for smooth non-linear structures, even without low-rank assumptions.
Paper proposes a new algorithm for graph learning with covariance constraints.
Recently low displacement rank (LDR) matrices, or so-called structured matrices, have been proposed to compress large-scale neural networks. Empirical results have shown that neural networks with weight matrices of LDR matrices, referred as LDR neural networks, can achieve significant reduction in space and computation…
Low-rank structure emerges in neural networks during learning.
Robust principal component analysis (RPCA) has drawn significant attentions due to its powerful capability in recovering low-rank matrices as well as successful appplications in various real world problems. The current state-of-the-art algorithms usually need to solve singular value decomposition of large matrices, whi…