Related papers: Optimal rates of convergence for covariance matrix…
Missing data occur frequently in a wide range of applications. In this paper, we consider estimation of high-dimensional covariance matrices in the presence of missing observations under a general missing completely at random model in the…
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…
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…
We consider estimation of the covariance matrix of a multivariate random vector under the constraint that certain covariances are zero. We first present an algorithm, which we call Iterative Conditional Fitting, for computing the maximum…
We consider the problem of link prediction, based on partial observation of a large network, and on side information associated to its vertices. The generative model is formulated as a matrix logistic regression. The performance of the…
Precision matrix is of significant importance in a wide range of applications in multivariate analysis. This paper considers adaptive minimax estimation of sparse precision matrices in the high dimensional setting. Optimal rates of…
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…
Stochastic processes are often used to model complex scientific problems in fields ranging from biology and finance to engineering and physical science. This paper investigates rate-optimal estimation of the volatility matrix of a…
We consider in this paper the problem of noisy 1-bit matrix completion under a general non-uniform sampling distribution using the max-norm as a convex relaxation for the rank. A max-norm constrained maximum likelihood estimate is…
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…
Obtaining an accurate estimate of the underlying covariance matrix from finite sample size data is challenging due to sample size noise. In recent years, sophisticated covariance-cleaning techniques based on random matrix theory have been…
Covariance matrix estimation is one of the most important problems in statistics. To accommodate the complexity of modern datasets, it is desired to have estimation procedures that not only can incorporate the structural assumptions of…
In the high-dimensional data setting, the sample covariance matrix is singular. In order to get a numerically stable and positive definite modification of the sample covariance matrix in the high-dimensional data setting, in this paper we…
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…
A common data analysis task is the reduced-rank regression problem: $$\min_{\textrm{rank-}k \ X} \|AX-B\|,$$ where $A \in \mathbb{R}^{n \times c}$ and $B \in \mathbb{R}^{n \times d}$ are given large matrices and $\|\cdot\|$ is some norm.…
Estimation of convex functions finds broad applications in engineering and science, while convex shape constraint gives rise to numerous challenges in asymptotic performance analysis. This paper is devoted to minimax optimal estimation of…
Covariate shift occurs when the distribution of input features differs between the training and testing phases. In covariate shift, estimating an unknown function's moment is a classical problem that remains under-explored, despite its…
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…
High-dimensional statistical tests often ignore correlations to gain simplicity and stability leading to null distributions that depend on functionals of correlation matrices such as their Frobenius norm and other $\ell_r$ norms. Motivated…
Operator convex functions defined on the positive half-line play a prominent role in the theory of quantum information, where they are used to define quantum $f$-divergences. Such functions admit integral representations in terms of…