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Poster
Covariance shrinkage for autocorrelated data
Daniel Bartz · Klaus-Robert Müller

Tue Dec 09 04:00 PM -- 08:59 PM (PST) @ Level 2, room 210D
in Poster Session »

The accurate estimation of covariance matrices is essential for many signal processing and machine learning algorithms. In high dimensional settings the sample covariance is known to perform poorly, hence regularization strategies such as analytic shrinkage of Ledoit/Wolf are applied. In the standard setting, i.i.d. data is assumed, however, in practice, time series typically exhibit strong autocorrelation structure, which introduces a pronounced estimation bias. Recent work by Sancetta has extended the shrinkage framework beyond i.i.d. data. We contribute in this work by showing that the Sancetta estimator, while being consistent in the high-dimensional limit, suffers from a high bias in finite sample sizes. We propose an alternative estimator, which is (1) unbiased, (2) less sensitive to hyperparameter choice and (3) yields superior performance in simulations on toy data and on a real world data set from an EEG-based Brain-Computer-Interfacing experiment.

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Author Information

Daniel Bartz (TU Berlin)
Klaus-Robert Müller (TU Berlin)

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