Related papers: Estimating Precision Matrices for High-Dimensional…

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…

The numerical computation of the exponentiation of a real matrix has been intensively studied. The main objective of a good numerical method is to deal with round-off errors and computational cost. The situation is more complicated when…

Graphical models are commonly used to represent conditional dependence relationships between variables. There are multiple methods available for exploring them from high-dimensional data, but almost all of them rely on the assumption that…

To model modern large-scale datasets, we need efficient algorithms to infer a set of $P$ unknown model parameters from $N$ noisy measurements. What are fundamental limits on the accuracy of parameter inference, given finite signal-to-noise…

This paper deals with the time-varying high dimensional covariance matrix estimation. We propose two covariance matrix estimators corresponding with a time-varying approximate factor model and a time-varying approximate characteristic-based…

Regression models with both high-dimensional responses and covariates have attracted growing attention. Standard multivariate regression models become inadequate when the response variables depend not only on observed covariates but also on…

This paper presents a new parameter estimation algorithm for the adaptive control of a class of time-varying plants. The main feature of this algorithm is a matrix of time-varying learning rates, which enables parameter estimation error…

Calibration error is commonly adopted for evaluating the quality of uncertainty estimators in deep neural networks. In this paper, we argue that such a metric is highly beneficial for training predictive models, even when we do not…

With rapid adoption of deep learning in critical applications, the question of when and how much to trust these models often arises, which drives the need to quantify the inherent uncertainties. While identifying all sources that account…

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…

This work addresses the issue of large covariance matrix estimation in high-dimensional statistical analysis. Recently, improved iterative algorithms with positive-definite guarantee have been developed. However, these algorithms cannot be…

High-dimensional compositional data are prevalent in many applications. The simplex constraint poses intrinsic challenges to inferring the conditional dependence relationships among the components forming a composition, as encoded by a…

Latent variable models have been playing a central role in psychometrics and related fields. In many modern applications, the inference based on latent variable models involves one or several of the following features: (1) the presence of…

We study ridge estimation of the precision matrix in the high-dimensional setting where the number of variables is large relative to the sample size. We first review two archetypal ridge estimators and note that their utilized penalties do…

Gaussian graphical models are widely used to represent correlations among entities but remain vulnerable to data corruption. In this work, we introduce a modified trimmed-inner-product algorithm to robustly estimate the covariance in an…

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 estimation and inference of graphical models that characterize the dependency structure of high-dimensional tensor-valued data. To facilitate the estimation of the precision matrix corresponding to each way of the tensor, we…

Matrix valued data has become increasingly prevalent in many applications. Most of the existing clustering methods for this type of data are tailored to the mean model and do not account for the dependence structure of the features, which…

Many conventional statistical procedures are extremely sensitive to seemingly minor deviations from modeling assumptions. This problem is exacerbated in modern high-dimensional settings, where the problem dimension can grow with and…

Graphical modeling explores dependences among a collection of variables by inferring a graph that encodes pairwise conditional independences. For jointly Gaussian variables, this translates into detecting the support of the precision…