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.
Incorporates matrix exponential into generative flows for improved performance.
Consider a movie recommendation system where apart from the ratings information, side information such as user's age or movie's genre is also available. Unlike standard matrix completion, in this setting one should be able to predict inductively on new users/movies. In this paper, we study the problem of inductive matr…
Generalised matrix-matrix multiplication forms the kernel of many mathematical algorithms. A faster matrix-matrix multiply immediately benefits these algorithms. In this paper we implement efficient matrix multiplication for large matrices using the floating point Intel Pentium SIMD (Single Instruction Multiple Data) a…
CoreFlow models matrix-valued distributions efficiently, preserving shared low-rank structure.
Characterizes the OU matrix for up to 5 strands in braids.
Flat minima lead to better generalization in low-rank matrix recovery models.
We consider the matrix completion problem of recovering a structured matrix from noisy and partial measurements. Recent works have proposed tractable estimators with strong statistical guarantees for the case where the underlying matrix is low--rank, and the measurements consist of a subset, either of the exact individ…
Fast matrix algorithms have become the fundamental tools of machine learning in big data era. The generalized matrix regression problem is widely used in the matrix approximation such as CUR decomposition, kernel matrix approximation, and stream singular value decomposition (SVD), etc. In this paper, we propose a fast …
Effective Gram matrix predicts deep network generalization.
Paper presents a new framework for covariance matrix estimation with geometric insights.
Paper proposes a generalized precision matrix for t-Student distributions to improve portfolio optimization.
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…
Study shows generative priors improve rank-one matrix recovery with optimal sample complexity.
The paper proposes methods for predicting missing values in mixed data matrices.
Matrix formulas for super Teichmüller spaces generalize previous work and yield super λ-lengths.
Matrix completion aims to predict missing elements in a partially observed data matrix which in typical applications, such as collaborative filtering, is large and extremely sparsely observed. A standard solution is matrix factorization, which predicts unobserved entries as linear combinations of latent variables. We g…
Paper derives matrix formulae and proves skein relations for non-orientable surfaces in quasi-cluster algebras.
Study generalizes matrix completion with side info in low noise settings.
Generalized matrix-fractional (GMF) functions are a class of matrix support functions introduced by Burke and Hoheisel as a tool for unifying a range of seemingly divergent matrix optimization problems associated with inverse problems, regularization and learning. In this paper we dramatically simplify the support func…
The paper analyzes data augmentation for precision matrix estimation in high dimensions.
Random matrix theory predicts neural representations generalize well.
Classifies contravariant matrix-valued valuations on polytopes without continuity assumptions.
Recommender systems are widely used to recommend the most appealing items to users. These recommendations can be generated by applying collaborative filtering methods. The low-rank matrix completion method is the state-of-the-art collaborative filtering method. In this work, we show that the skewed distribution of rati…
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…
Study exact limits of matrix reconstruction from noisy projections.
A new NMF model for co-clustering and data approximation.
Formula for sectional curvatures on matrix groups.
In this paper, we present a unified analysis of matrix completion under general low-dimensional structural constraints induced by {\em any} norm regularization. We consider two estimators for the general problem of structured matrix completion, and provide unified upper bounds on the sample complexity and the estimatio…
Matrix SMD converges to unique solution minimizing Bregman divergence.
Researchers developed a new Riemannian manifold for SPD matrix-valued optimal transport problems.
Paper studies asymmetric matrix sensing, proving gradient descent converges to low-rank solutions.
Gradient descent proves global convergence for 4-layer matrix factorization.
This paper proposes robust matrix variate regression models with rank constraints and vector regularization.
Harer-Zagier formulas generalized to knot matrix models.
When response variables are nominal and populations are cross-classified with respect to multiple polytomies, questions often arise about the degree of association of the responses with explanatory variables. When populations are known, we introduce a nominal association vector and matrix to evaluate the dependence of …
We study the following generalized matrix rank estimation problem: given an matrix and a constant , estimate the number of eigenvalues that are greater than . In the distributed setting, the matrix of interest is the sum of matrices held by separate machines. We show that any deterministic…
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…
Derives adjoint formulas for matrix operations and applies them to specific cases.
A checkerboard graph of a special diagram of an oriented link is made a directed, edge-weighted graph in a natural way so that a principal minor of its Laplacian matrix is a Seifert matrix of the link. Doubling and weighting the edges of the graph produces a second Laplacian matrix such that a principal minor is an Ale…
Simplified matrix generator resolves credit migration model calibration issues.
Latent Dirichlet allocation (LDA) is useful in document analysis, image processing, and many information systems; however, its generalization performance has been left unknown because it is a singular learning machine to which regular statistical theory can not be applied. Stochastic matrix factorization (SMF) is a res…
Optimization problems with rank constraints arise in many applications, including matrix regression, structured PCA, matrix completion and matrix decomposition problems. An attractive heuristic for solving such problems is to factorize the low-rank matrix, and to run projected gradient descent on the nonconvex factoriz…
Study improves fractional posterior for 1-bit matrix completion.
We extend Kyle's model to include stochastic liquidity and multiple assets.
New algorithms improve on bandit feedback in matrix games with unknown payoff matrices.
New method predicts binary matrix entries using empirical Bayes and low-rank structure.
Inductive Matrix Completion (IMC) is an important class of matrix completion problems that allows direct inclusion of available features to enhance estimation capabilities. These models have found applications in personalized recommendation systems, multilabel learning, dictionary learning, etc. This paper examines a g…
We consider a generalization of low-rank matrix completion to the case where the data belongs to an algebraic variety, i.e. each data point is a solution to a system of polynomial equations. In this case the original matrix is possibly high-rank, but it becomes low-rank after mapping each column to a higher dimensional…