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Abstract Robust estimation is an important problem in statistics which aims at providing a reasonable estimator when the data-generating distribution lies within an appropriately defined ball around an uncontaminated distribution. Although minimax rates of estimation have been established in recent years, many existing robust estimators with provably optimal convergence rates are also computationally intractable. In this paper, we study several estimation problems under a Wasserstein contamination model and present computationally tractable estimators motivated by generative adversarial networks (GANs). Specifically, we analyze the properties of Wasserstein GAN-based estimators for location estimation, covariance matrix estimation and linear regression and show that our proposed estimators are minimax optimal in many scenarios. Finally, we present numerical results which demonstrate the effectiveness of our estimators.
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High‐Dimensional Covariance Estimation From a Small Number of Samples
Abstract We synthesize knowledge from numerical weather prediction, inverse theory, and statistics to address the problem of estimating a high‐dimensional covariance matrix from a small number of samples. This problem is fundamental in statistics, machine learning/artificial intelligence, and in modern Earth science. We create several new adaptive methods for high‐dimensional covariance estimation, but one method, which we call Noise‐Informed Covariance Estimation (NICE), stands out because it has three important properties: (a) NICE is conceptually simple and computationally efficient; (b) NICE guarantees symmetric positive semi‐definite covariance estimates; and (c) NICE is largely tuning‐free. We illustrate the use of NICE on a large set of Earth science–inspired numerical examples, including cycling data assimilation, inversion of geophysical field data, and training of feed‐forward neural networks with time‐averaged data from a chaotic dynamical system. Our theory, heuristics and numerical tests suggest that NICE may indeed be a viable option for high‐dimensional covariance estimation in many Earth science problems.
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- Award ID(s):
- 2202991
- PAR ID:
- 10554436
- Publisher / Repository:
- DOI PREFIX: 10.1029
- Date Published:
- Journal Name:
- Journal of Advances in Modeling Earth Systems
- Volume:
- 16
- Issue:
- 9
- ISSN:
- 1942-2466
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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