Robust Covariance Estimation for Entry-wise Contaminated and Partially Observed Data via Expectation Maximization Algorithm
Abstract
Robust covariance estimation under entry-wise contamination and missing data is challenging in various signal processing applications. Under the Student-t model, observation-level reweighting induces a uniform attenuation across samples, which can lead to cumulative information loss even when most coordinates remain informative. The alternative Student-t* model enables coordinate-wise robustness, but its E-step is not available in closed form. We extend inference for the Student-t* model to incomplete observations through a stochastic approximation EM (SAEM) algorithm operating on a reduced latent space: stochastic updates of the coordinate-wise scales are combined with Rao-Blackwellized Gaussian conditional moments, which avoids explicit sampling of latent Gaussian variables while preserving a likelihood-based framework. Experiments on synthetic and real sensor data show a lower Fisher-Rao error than Gaussian, Student-t, imputation-based and detect-then-estimate estimators at moderate to high outlier rates under diffuse contamination.
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BibTeX
@misc{savidan2026robust,
title = {{Robust Covariance Estimation for Entry-wise Contaminated and Partially Observed Data via Expectation Maximization Algorithm}},
author = {Matys Savidan and Mohammed Nabil El Korso},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21709},
eprint = {2610.21709},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21709},
}
RIS
TY - UNPB
TI - Robust Covariance Estimation for Entry-wise Contaminated and Partially Observed Data via Expectation Maximization Algorithm
AU - Matys Savidan
AU - Mohammed Nabil El Korso
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.21709
UR - https://arxiv.org/abs/2610.21709
AB - Robust covariance estimation under entry-wise contamination and missing data is challenging in various signal processing applications. Under the Student-t model, observation-level reweighting induces a uniform attenuation across samples, which can lead to cumulative information loss even when most coordinates remain informative. The alternative Student-t^* model enables coordinate-wise robustness, but its E-step is not available in closed form. We extend inference for the Student-t^* model to incomplete observations through a stochastic approximation EM (SAEM) algorithm operating on a reduced latent space: stochastic updates of the coordinate-wise scales are combined with Rao-Blackwellized Gaussian conditional moments, which avoids explicit sampling of latent Gaussian variables while preserving a likelihood-based framework. Experiments on synthetic and real sensor data show a lower Fisher-Rao error than Gaussian, Student-t, imputation-based and detect-then-estimate estimators at moderate to high outlier rates under diffuse contamination.
ER -