English
Related papers

Related papers: Robust Online Covariance and Sparse Precision Esti…

200 papers

We propose a novel approach to estimating the precision matrix of multivariate Gaussian data that relies on decomposing them into a low-rank and a diagonal component. Such decompositions are very popular for modeling large covariance…

Methodology · Statistics 2022-08-18 Noirrit Kiran Chandra , Peter Mueller , Abhra Sarkar

The computational cost for inference and prediction of statistical models based on Gaussian processes with Mat\'ern covariance functions scales cubicly with the number of observations, limiting their applicability to large data sets. The…

Statistics Theory · Mathematics 2025-03-04 David Bolin , Vaibhav Mehandiratta , Alexandre B. Simas

Estimation of the precision matrix (or inverse covariance matrix) is of great importance in statistical data analysis and machine learning. However, as the number of parameters scales quadratically with the dimension $p$, computation…

Computation · Statistics 2022-11-02 Qian LI , Binyan Jiang , Defeng Sun

This paper examines a general class of noisy matrix completion tasks where the goal is to estimate a matrix from observations obtained at a subset of its entries, each of which is subject to random noise or corruption. Our specific focus is…

Machine Learning · Statistics 2016-11-18 Akshay Soni , Swayambhoo Jain , Jarvis Haupt , Stefano Gonella

We analyze the statistical consistency of robust estimators for precision matrices in high dimensions. We focus on a contamination mechanism acting cellwise on the data matrix. The estimators we analyze are formed by plugging appropriately…

Statistics Theory · Mathematics 2015-09-25 Po-Ling Loh , Xin Lu Tan

The problem of identifying change points in high-dimensional Gaussian graphical models (GGMs) in an online fashion is of interest, due to new applications in biology, economics and social sciences. The offline version of the problem, where…

Statistics Theory · Mathematics 2020-03-18 Hossein Keshavarz , George Michailidis

Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…

Machine Learning · Statistics 2014-10-01 Yarin Gal , Mark van der Wilk , Carl E. Rasmussen

We develop a new estimator of the inverse covariance matrix for high-dimensional multivariate normal data using the horseshoe prior. The proposed graphical horseshoe estimator has attractive properties compared to other popular estimators,…

Methodology · Statistics 2019-01-08 Yunfan Li , Bruce A. Craig , Anindya Bhadra

We study high-dimensional sparse estimation tasks in a robust setting where a constant fraction of the dataset is adversarially corrupted. Specifically, we focus on the fundamental problems of robust sparse mean estimation and robust sparse…

Data Structures and Algorithms · Computer Science 2019-11-20 Ilias Diakonikolas , Sushrut Karmalkar , Daniel Kane , Eric Price , Alistair Stewart

Undirected graphs are often used to describe high dimensional distributions. Under sparsity conditions, the graph can be estimated using $\ell_1$-penalization methods. We propose and study the following method. We combine a multiple…

Machine Learning · Statistics 2012-01-11 Shuheng Zhou , Philipp Rutimann , Min Xu , Peter Buhlmann

The sparse inverse covariance estimation problem is commonly solved using an $\ell_{1}$-regularized Gaussian maximum likelihood estimator known as "graphical lasso", but its computational cost becomes prohibitive for large data sets. A…

Machine Learning · Statistics 2018-06-08 Richard Y. Zhang , Salar Fattahi , Somayeh Sojoudi

Sparse networks can be found in a wide range of applications, such as biological and communication networks. Inference of such networks from data has been receiving considerable attention lately, mainly driven by the need to understand and…

Systems and Control · Electrical Eng. & Systems 2024-12-20 Junyang Jin , Ye Yuan , Jorge Goncalves

This paper proposes a new algorithm for multiple sparse regression in high dimensions, where the task is to estimate the support and values of several (typically related) sparse vectors from a few noisy linear measurements. Our algorithm is…

Machine Learning · Statistics 2012-06-08 Ali Jalali , Sujay Sanghavi

We propose an l1-regularized likelihood method for estimating the inverse covariance matrix in the high-dimensional multivariate normal model in presence of missing data. Our method is based on the assumption that the data are missing at…

Methodology · Statistics 2012-02-28 Nicolas Städler , Peter Bühlmann

This paper proposes using a sparse-structured multivariate Gaussian to provide a closed-form approximator for the output of probabilistic ensemble models used for dense image prediction tasks. This is achieved through a convolutional neural…

Computer Vision and Pattern Recognition · Computer Science 2022-03-30 Ivor J. A. Simpson , Sara Vicente , Neill D. F. Campbell

The Gaussian process (GP) is a Bayesian nonparametric paradigm that is widely adopted for uncertainty quantification (UQ) in a number of safety-critical applications, including robotics, healthcare, as well as surveillance. The consistency…

Machine Learning · Computer Science 2024-10-10 Jinwen Xu , Qin Lu , Georgios B. Giannakis

We consider the robust estimation of the parameters of multivariate Gaussian linear regression models. To this aim we consider robust version of the usual (Mahalanobis) least-square criterion, with or without Ridge regularization. We…

Statistics Theory · Mathematics 2025-10-13 Antoine Godichon-Baggioni , Stephane S. Robin , Laure Sansonnet

Motivated by the construction of tractable robust estimators via convex relaxations, we present conditions on the sample size which guarantee an augmented notion of Restricted Eigenvalue-type condition for Gaussian designs. Such a notion is…

Statistics Theory · Mathematics 2018-12-04 Philip Thompson , Arnak S. Dalalyan

In this paper, we study the problem where a group of agents aim to collaboratively learn a common static latent function through streaming data. We propose a lightweight distributed Gaussian process regression (GPR) algorithm that is…

Machine Learning · Computer Science 2023-07-11 Zhenyuan Yuan , Minghui Zhu

The time-evolving precision matrix of a piecewise-constant Gaussian graphical model encodes the dynamic conditional dependency structure of a multivariate time-series. Traditionally, graphical models are estimated under the assumption that…

Methodology · Statistics 2017-11-01 Alexander J. Gibberd , James D. B. Nelson