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.

Machine Learning (stat.ML); Machine Learning (cs.LG)

arXiv:2610.21709 [stat.ML]

(or arXiv:2610.21709v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2610.21709 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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