Related papers: Linear Shrinkage Estimation of Covariance Matrices…

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…

In this work, we propose a new randomized algorithm for computing a low-rank approximation to a given matrix. Taking an approach different from existing literature, our method first involves a specific biased sampling, with an element being…

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 $l_1$-norm penalty to encourage the sparsity and…

Multi-group covariance estimation for matrix-variate data with small within group sample sizes is a key part of many data analysis tasks in modern applications. To obtain accurate group-specific covariance estimates, shrinkage estimation…

In high-dimensional data analysis, regularization methods pursuing sparsity and/or low rank have received a lot of attention recently. To provide a proper amount of shrinkage, it is typical to use a grid search and a model comparison…

Estimating covariance matrices with high-dimensional complex data presents significant challenges, particularly concerning positive definiteness, sparsity, and numerical stability. Existing robust sparse estimators often fail to guarantee…

We consider the problem of simultaneous estimation of a sequence of dependent parameters that are generated from a hidden Markov model. Based on observing a noise contaminated vector of observations from such a sequence model, we consider…

We consider the problem of learning error covariance matrices for robotic state estimation. The convergence of a state estimator to the correct belief over the robot state is dependent on the proper tuning of noise models. During inference,…

With machine learning being a popular topic in current computational materials science literature, creating representations for compounds has become common place. These representations are rarely compared, as evaluating their performance -…

Recently many regularized estimators of large covariance matrices have been proposed, and the tuning parameters in these estimators are usually selected via cross-validation. However, there is no guideline on the number of folds for…

In this paper, we propose a scalable Bayesian method for sparse covariance matrix estimation by incorporating a continuous shrinkage prior with a screening procedure. In the first step of the procedure, the off-diagonal elements with small…

When shrinking a covariance matrix towards (a multiple) of the identity matrix, the trace of the covariance matrix arises naturally as the optimal scaling factor for the identity target. The trace also appears in other context, for example…

Estimating the number of signals embedded in noise is a fundamental problem in array signal processing. The classic RMT estimator based on random matrix theory (RMT) tends to under-estimate the number of signals as it does not consider the…

This letter proposes a novel sparsity-aware adaptive filtering scheme and algorithms based on an alternating optimization strategy with shrinkage. The proposed scheme employs a two-stage structure that consists of an alternating…

Randomized algorithms have proven to perform well on a large class of numerical linear algebra problems. Their theoretical analysis is critical to provide guarantees on their behaviour, and in this sense, the stochastic analysis of the…

Lasso and other regularization procedures are attractive methods for variable selection, subject to a proper choice of shrinkage parameter. Given a set of potential subsets produced by a regularization algorithm, a consistent model…

The use of sparse precision (inverse covariance) matrices has become popular because they allow for efficient algorithms for joint inference in high-dimensional models. Many applications require the computation of certain elements of the…

Shrinkage estimators have profound impacts in statistics and in scientific and engineering applications. In this article, we consider shrinkage estimation in the presence of linear predictors. We formulate two heteroscedastic hierarchical…

We describe a fast computation method for leave-one-out cross-validation (LOOCV) for $k$-nearest neighbours ($k$-NN) regression. We show that, under a tie-breaking condition for nearest neighbours, the LOOCV estimate of the mean square…

We show that in a common high-dimensional covariance model, the choice of loss function has a profound effect on optimal estimation. In an asymptotic framework based on the Spiked Covariance model and use of orthogonally invariant…