arXiv research

Proposes a robust factor analysis for matrix data.

Paper analyzes robust matrix completion with efficient nonconvex method and leave-one-out analysis.

New matrix reveals cluster info in sparse directed graphs.

Efficient private matrix analysis algorithms for recent variants.

A new method clusters rows of a matrix of point processes.

This note gives a simple analysis of a randomized approximation scheme for matrix multiplication proposed by Sarlos (2006) based on a random rotation followed by uniform column sampling. The result follows from a matrix version of Bernstein's inequality and a tail inequality for quadratic forms in subgaussian random ve…

This work analyzes self-attention matrices using random matrix theory.

In this paper, we formulate the Canonical Correlation Analysis (CCA) problem on matrix manifolds. This framework provides a natural way for dealing with matrix constraints and tools for building efficient algorithms even in an adaptive setting. Finally, an adaptive CCA algorithm is proposed and applied to a change dete…

Paper improves matrix-valued data classification using nonparametric LDA.

Study shows generative priors improve rank-one matrix recovery with optimal sample complexity.

In this paper the exact linear relation between the leading eigenvectors of the modularity matrix and the singular vectors of an uncentered data matrix is developed. Based on this analysis the concept of a modularity component is defined, and its properties are developed. It is shown that modularity component analysis …

In this paper we consider the low-rank matrix completion problem with specific application to forecasting in time series analysis. Briefly, the low-rank matrix completion problem is the problem of imputing missing values of a matrix under a rank constraint. We consider a matrix completion problem for Hankel matrices an…

We propose an algorithm to impute and forecast a time series by transforming the observed time series into a matrix, utilizing matrix estimation to recover missing values and de-noise observed entries, and performing linear regression to make predictions. At the core of our analysis is a representation result, which st…

In this paper we give definitions of matrix rates of return which do not depend on the choice of basis describing baskets. We give their economic interpretation. The matrix rate of return describes baskets of arbitrary type and extends portfolio analysis to the complex variable domain. This allows us for simultaneous a…

We introduce RSE to measure robustness in estimation problems.

An ADRC-incorporated SGD algorithm improves latent factor analysis speed and accuracy.

Paper presents a new framework for covariance matrix estimation with geometric insights.

Gradient descent achieves exact linear convergence rate for symmetric matrix completion.

New method for factor analysis using nuclear and $\ell_0$ norms.

In this paper, we develop a relative error bound for nuclear norm regularized matrix completion, with the focus on the completion of full-rank matrices. Under the assumption that the top eigenspaces of the target matrix are incoherent, we derive a relative upper bound for recovering the best low-rank approximation of t…

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…

UPCA solves data matrix completion with permuted columns.

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…

A new method uses Gram matrix for efficient multivariate functional principal components.

We analyse the matrix factorization problem. Given a noisy measurement of a product of two matrices, the problem is to estimate back the original matrices. It arises in many applications such as dictionary learning, blind matrix calibration, sparse principal component analysis, blind source separation, low rank matrix …

PSMM method optimizes matrix sufficient dimension reduction.

GD learns matrix solutions incrementally, revealing insights into generalization.

Matrix factorization is a popular approach to solving matrix estimation problems based on partial observations. Existing matrix factorization is based on least squares and aims to yield a low-rank matrix to interpret the conditional sample means given the observations. However, in many real applications with skewed and…

Unified error analysis for low-rank approximation improves data assimilation performance.

Matrix factorization methods are extensively employed to understand complex data. In this paper, we introduce the cross-product penalized component analysis (XCAN), a sparse matrix factorization based on the optimization of a loss function that allows a trade-off between variance maximization and structural preservatio…

Many tasks require finding groups of elements in a matrix of numbers, symbols or class likelihoods. One approach is to use efficient bi- or tri-linear factorization techniques including PCA, ICA, sparse matrix factorization and plaid analysis. These techniques are not appropriate when addition and multiplication of mat…

Paper proposes a novel method to improve matrix completion with median loss for large datasets.

Paper analyzes singular subspace estimation in noisy matrix models.

Gradient descent solves rank-one matrix estimation problem with detailed time evolution analysis.

A very simple interpretation of matrix completion problem is introduced based on statistical models. Combined with the well-known results from missing data analysis, such interpretation indicates that matrix completion is still a valid and principled estimation procedure even without the missing completely at random (M…

A representative model in integrative analysis of two high-dimensional correlated datasets is to decompose each data matrix into a low-rank common matrix generated by latent factors shared across datasets, a low-rank distinctive matrix corresponding to each dataset, and an additive noise matrix. Existing decomposition …

We consider the problem of approximately reconstructing a partially-observed, approximately low-rank matrix. This problem has received much attention lately, mostly using the trace-norm as a surrogate to the rank. Here we study low-rank matrix reconstruction using both the trace-norm, as well as the less-studied max-no…

Global stability bounds for matrix frames in phase retrieval problems.

We provide a unified analysis of the predictive risk of ridge regression and regularized discriminant analysis in a dense random effects model. We work in a high-dimensional asymptotic regime where $p, n \to \infty$ and $p/n \to γ\in (0, \, \infty)$, and allow for arbitrary covariance among the features. For both metho…

We provide a method to prepare covariance matrices for quantum datasets.

Due to challenging applications such as collaborative filtering, the matrix completion problem has been widely studied in the past few years. Different approaches rely on different structure assumptions on the matrix in hand. Here, we focus on the completion of a (possibly) low-rank matrix with binary entries, the so-c…

The paper analyzes data augmentation for precision matrix estimation in high dimensions.

In (exploratory) factor analysis, the loading matrix is identified only up to orthogonal rotation. For identifiability, one thus often takes the loading matrix to be lower triangular with positive diagonal entries. In Bayesian inference, a standard practice is then to specify a prior under which the loadings are indepe…

Advances neural tri-factorization for clustering and discordance analysis of multi-typed data.

ScaledGD improves gradient descent for ill-conditioned low-rank matrix estimation.

This paper proposes robust matrix variate regression models with rank constraints and vector regularization.

Low-rank matrix approximations are often used to help scale standard machine learning algorithms to large-scale problems. Recently, matrix coherence has been used to characterize the ability to extract global information from a subset of matrix entries in the context of these low-rank approximations and other sampling-…

A new GNN architecture called coVariance neural network (VNN) improves stability and transferability of covariance matrix analysis.