Robust covariance estimation tackles missing and corrupted sensor data
Robust Covariance Estimation for Entry-wise Contaminated and Partially Observed Data via Expectation Maximization Algorithm
Machine Learning
Summary
Estimating relationships between data points becomes tricky when data entries are missing or corrupted by outliers. The authors address this by improving a statistical model—the Student-t star model—that treats each data coordinate individually for better robustness. They develop an algorithm that works even when some data points are missing, mixing smart approximations instead of costly sampling. Their method performs better than common alternatives when data is heavily contaminated and incomplete.
What this means in practice
- •For sensor data analysts: Improve measurement relationship estimates from sensors suffering from missing or corrupted readings by using a robust iterative algorithm.
- •For financial risk teams: Generate more reliable covariance estimates from incomplete, contaminated financial datasets for better portfolio risk evaluation.
Authors
Matys Savidan, Mohammed Nabil El Korso
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.