Related papers: Robust Covariance and Scatter Matrix Estimation un…
It is of importance to develop statistical techniques to analyze high-dimensional data in the presence of both complex dependence and possible outliers in real-world applications such as imaging data analyses. We propose a new robust…
Cellwise outliers are likely to occur together with casewise outliers in modern data sets with relatively large dimension. Recent work has shown that traditional robust regression methods may fail for data sets in this paradigm. The…
Algorithmic robust statistics has traditionally focused on the contamination model where a small fraction of the samples are arbitrarily corrupted. We consider a recent contamination model that combines two kinds of corruptions: (i) small…
Accurate platform localization is an integral component of most robotic systems. As these robotic systems become more ubiquitous, it is necessary to develop robust state estimation algorithms that are able to withstand novel and…
Big data can easily be contaminated by outliers or contain variables with heavy-tailed distributions, which makes many conventional methods inadequate. To address this challenge, we propose the adaptive Huber regression for robust…
This paper investigates the theoretical underpinnings of two fundamental statistical inference problems, the construction of confidence sets and large-scale simultaneous hypothesis testing, in the presence of heavy-tailed data. With…
We revisit the problem of computing submatrices of the Cram\'er-Rao bound (CRB), which lower bounds the variance of any unbiased estimator of a vector parameter $\vth$. We explore iterative methods that avoid direct inversion of the Fisher…
This paper studies low-rank matrix completion in the presence of heavy-tailed and possibly asymmetric noise, where we aim to estimate an underlying low-rank matrix given a set of highly incomplete noisy entries. Though the matrix completion…
We study the Gaussian and robust covariance estimation, assuming the true covariance matrix to be a Kronecker product of two lower dimensional square matrices. In both settings we define the estimators as solutions to the constrained…
We introduce a covariance matrix estimator that both takes into account the heteroskedasticity of financial returns (by using an exponentially weighted moving average) and reduces the effective dimensionality of the estimation (and hence…
A cumbersome operation in numerical analysis and linear algebra, optimization, machine learning and engineering algorithms; is inverting large full-rank matrices which appears in various processes and applications. This has both numerical…
The determination of the covariance matrix and its inverse, the precision matrix, is critical in the statistical analysis of cosmological measurements. The covariance matrix is typically estimated with a limited number of simulations at…
Network experiments are powerful tools for studying spillover effects, which avoid endogeneity by randomly assigning treatments to units over networks. However, it is non-trivial to analyze network experiments properly without imposing…
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…
A constrained L1 minimization method is proposed for estimating a sparse inverse covariance matrix based on a sample of $n$ iid $p$-variate random variables. The resulting estimator is shown to enjoy a number of desirable properties. In…
In practice, observations are often contaminated by noise, making the resulting sample covariance matrix to be an information-plus-noise-type covariance matrix. Aiming to make inferences about the spectra of the underlying true covariance…
Modern network data analysis often involves analyzing network structures alongside covariate features to gain deeper insights into underlying patterns. However, traditional covariate-assisted statistical network models may not adequately…
In this self-contained chapter, we revisit a fundamental problem of multivariate statistics: estimating covariance matrices from finitely many independent samples. Based on massive Multiple-Input Multiple-Output (MIMO) systems we illustrate…
We address one of the important problems in Big Data, namely how to combine estimators from different subsamples by robust fusion procedures, when we are unable to deal with the whole sample. We propose a general framework based on the…
In this paper, we introduce a novel and robust approach to Quantized Matrix Completion (QMC). First, we propose a rank minimization problem with constraints induced by quantization bounds. Next, we form an unconstrained optimization problem…