arXiv research

Unified approach for robust low rank matrix estimation with adversaries.

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

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…

Dual-T method improves transition matrix estimation in noisy label learning.

New algorithms estimate matrix norms without matrix multiplication.

New methods estimate covariance for matrix data without assuming fixed size or specific distributions.

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…

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

In this work we construct an optimal shrinkage estimator for the precision matrix in high dimensions. We consider the general asymptotics when the number of variables $p\rightarrow\infty$ and the sample size $n\rightarrow\infty$ so that $p/n\rightarrow c\in (0, +\infty)$. The precision matrix is estimated directly, wit…

SCOPE estimator improves covariance and precision matrix estimation.

Method estimates noise transition matrix from noisy labels without relying on unreliable class-posterior estimation.

New methods improve portfolio risk minimization by estimating covariance matrix more accurately.

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

New spectral methods improve matrix estimation in RL with low-rank structure.

The paper derives Cramer-Rao bounds for Laplacian matrix estimation under various constraints.

In this work we construct an optimal linear shrinkage estimator for the covariance matrix in high dimensions. The recent results from the random matrix theory allow us to find the asymptotic deterministic equivalents of the optimal shrinkage intensities and estimate them consistently. The developed distribution-free es…

Paper improves efficiency in matrix computations for Gaussian processes.

The paper proposes methods for predicting missing values in mixed data matrices.

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…

Matrix completion is a modern missing data problem where both the missing structure and the underlying parameter are high dimensional. Although missing structure is a key component to any missing data problems, existing matrix completion methods often assume a simple uniform missing mechanism. In this work, we study ma…

A new R package for high-dimensional regression and precision matrix estimation.

Study compares different covariance estimation methods for portfolio allocation.

Paper proves inequality for Green function on Kähler manifolds.

Due to the insufficient measurements in the distribution system state estimation (DSSE), full observability and redundant measurements are difficult to achieve without using the pseudo measurements. The matrix completion state estimation (MCSE) combines the matrix completion and power system model to estimate voltage b…

Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to largely outperform the sample covariance matrix estimate and to compete with state…

Matrix completion is often applied to data with entries missing not at random (MNAR). For example, consider a recommendation system where users tend to only reveal ratings for items they like. In this case, a matrix completion method that relies on entries being revealed at uniformly sampled row and column indices can …

Paper proposes diagnostics for error and variance estimation in randomized matrix computations.

Proposes a new method for selecting regularization parameters in sparse precision matrix estimation.

UA-LQE improves value function learning by selectively erasing uncertain entries in Q-matrix.

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-…

Novel method for efficient low-rank matrix estimation and bandit algorithms.

We derive an interpolation version of constrained matrix Li-Yau-Hamilton estimate on Kähler manifolds. As a result, we first get a constrained matrix Li-Yau-Hamilton estimate for heat equation on a Kähler manifold with fixed Kähler metric. Secondly, we get a corresponding estimate for forward conjugate heat equation on…

Correlation matrices play a key role in many multivariate methods (e.g., graphical model estimation and factor analysis). The current state-of-the-art in estimating large correlation matrices focuses on the use of Pearson's sample correlation matrix. Although Pearson's sample correlation matrix enjoys various good prop…

Paper improves matrix-valued data classification using nonparametric LDA.

We study the adaptive estimation of copula correlation matrix $Σ$ for the semi-parametric elliptical copula model. In this context, the correlations are connected to Kendall's tau through a sine function transformation. Hence, a natural estimate for $Σ$ is the plug-in estimator $\hatΣ$ with Kendall's tau statistic. We …

In this paper, we study the problem of precision matrix estimation when the dataset contains sensitive information. In the differential privacy framework, we develop a differentially private ridge estimator by perturbing the sample covariance matrix. Then we develop a differentially private graphical lasso estimator by…

The inverse covariance matrix provides considerable insight for understanding statistical models in the multivariate setting. In particular, when the distribution over variables is assumed to be multivariate normal, the sparsity pattern in the inverse covariance matrix, commonly referred to as the precision matrix, cor…

New algorithm improves matrix estimation with one-sided covariates.

This paper sets fundamental limits for rank-one matrix estimation with varying noise levels.

We introduce a new sparse estimator of the covariance matrix for high-dimensional models in which the variables have a known ordering. Our estimator, which is the solution to a convex optimization problem, is equivalently expressed as an estimator which tapers the sample covariance matrix by a Toeplitz, sparsely-banded…

Improved heat equation estimates without gradient curvature assumption.

Improved matrix completion for non-uniformly sampled data.

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

JME continually estimates data moments privately and accurately.

We present novel understandings of the Gamma-Poisson (GaP) model, a probabilistic matrix factorization model for count data. We show that GaP can be rewritten free of the score/activation matrix. This gives us new insights about the estimation of the topic/dictionary matrix by maximum marginal likelihood estimation. In…

The paper improves Bayesian precision matrix estimation for high-dimensional sparse data.

New framework explains why nonconvex methods work well in low-rank matrix estimation.

Study improves Hayashi-Yoshida estimator for high-dimensional stock covolatility.