Related papers: High dimensional matrix estimation through ellipti…
In this paper, we introduce a class of improved estimators for the mean parameter matrix of a multivariate normal distribution with an unknown variance-covariance matrix. In particular, the main results of [D.Ch\'etelat and M. T.…
High-dimensional data subject to heavy-tailed phenomena and heterogeneity are commonly encountered in various scientific fields and bring new challenges to the classical statistical methods. In this paper, we combine the asymmetric square…
We present new algorithms for $M$-estimators of multivariate scatter and location and for symmetrized $M$-estimators of multivariate scatter. The new algorithms are considerably faster than currently used fixed-point and related algorithms.…
The goal of this paper is to develop distributionally robust optimization (DRO) estimators, specifically for multidimensional Extreme Value Theory (EVT) statistics. EVT supports using semi-parametric models called max-stable distributions…
We offer a survey of recent results on covariance estimation for heavy-tailed distributions. By unifying ideas scattered in the literature, we propose user-friendly methods that facilitate practical implementation. Specifically, we…
We propose a novel a posteriori error estimator for conforming finite element discretizations of two- and three-dimensional Helmholtz problems. The estimator is based on an equilibrated flux that is computed by solving patchwise mixed…
Large-dimensional factor model has drawn much attention in the big-data era, in order to reduce the dimensionality and extract underlying features using a few latent common factors. Conventional methods for estimating the factor model…
Several recent publications report advances in training optimal decision trees (ODT) using mixed-integer programs (MIP), due to algorithmic advances in integer programming and a growing interest in addressing the inherent suboptimality of…
This article studies the behavior of regularized Tyler estimators (RTEs) of scatter matrices. The key advantages of these estimators are twofold. First, they guarantee by construction a good conditioning of the estimate and second, being a…
Determining the number of factors in high-dimensional factor models remains a fundamental challenge, particularly when data are incomplete. This paper introduces the concept of identifiable factors, those that can be reliably recovered…
Highly robust and efficient estimators for the generalized linear model with a dispersion parameter are proposed. The estimators are based on three steps. In the first step the maximum rank correlation estimator is used to consistently…
Stepped-wedge designs are increasingly used in randomized experiments to accommodate logistical and ethical constraints by staggering treatment roll-out over time. Despite their popularity, existing analytical methods largely rely on…
A high-dimensional $r$-factor model for an $n$-dimensional vector time series is characterised by the presence of a large eigengap (increasing with $n$) between the $r$-th and the $(r+1)$-th largest eigenvalues of the covariance matrix.…
High-dimensional covariance estimation is notoriously sensitive to outliers. While statistically optimal estimators exist for general heavy-tailed distributions, they often rely on computationally expensive techniques like semidefinite…
We propose Mixed-Panels-Transformer Encoder (MPTE), a novel framework for estimating factor models in panel datasets with mixed frequencies and nonlinear signals. Traditional factor models rely on linear signal extraction and require…
This thesis designs a prediction system based on matrix factorization to predict the classification accuracy of a specific model on a particular dataset. In this thesis, we conduct comprehensive empirical research on more than fifty…
High-dimensional and sparse (HiDS) matrices are omnipresent in a variety of big data-related applications. Latent factor analysis (LFA) is a typical representation learning method that extracts useful yet latent knowledge from HiDS matrices…
In this paper, based on the combination of tensor neural network and a posteriori error estimator, a novel type of machine learning method is proposed to solve high-dimensional boundary value problems with homogeneous and non-homogeneous…
Euclidean embedding from noisy observations containing outlier errors is an important and challenging problem in statistics and machine learning. Many existing methods would struggle with outliers due to a lack of detection ability. In this…
Asymmetry along with heteroscedasticity or contamination often occurs with the growth of data dimensionality. In ultra-high dimensional data analysis, such irregular settings are usually overlooked for both theoretical and computational…