Timezone: »
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.
Author Information
Daniel Bartz (TU Berlin)
Klaus-Robert Müller (TU Berlin)
More from the Same Authors
-
2022 Poster: So3krates: Equivariant attention for interactions on arbitrary length-scales in molecular systems »
Thorben Frank · Oliver Unke · Klaus-Robert Müller -
2021 Poster: Efficient hierarchical Bayesian inference for spatio-temporal regression models in neuroimaging »
Ali Hashemi · Yijing Gao · Chang Cai · Sanjay Ghosh · Klaus-Robert Müller · Srikantan Nagarajan · Stefan Haufe -
2021 Poster: SE(3)-equivariant prediction of molecular wavefunctions and electronic densities »
Oliver Unke · Mihail Bogojeski · Michael Gastegger · Mario Geiger · Tess Smidt · Klaus-Robert Müller -
2020 : Panel »
Alan Aspuru-Guzik · Jennifer Listgarten · Klaus-Robert Müller · Nadine Schneider -
2020 : Invited Talk: Klaus Robert-Müller & Kristof Schütt: Machine Learning meets Quantum Chemistry »
Klaus-Robert Müller · Kristof Schütt -
2019 Demonstration: Learning Machines can Curl - Adaptive Deep Reinforcement Learning enables the robot Curly to win against human players in an icy world »
Dong-Ok Won · Sang-Hoon Lee · Klaus-Robert Müller · Seong-Whan Lee -
2019 Poster: Explanations can be manipulated and geometry is to blame »
Ann-Kathrin Dombrowski · Maximillian Alber · Christopher Anders · Marcel Ackermann · Klaus-Robert Müller · Pan Kessel -
2018 Workshop: Machine Learning for Molecules and Materials »
José Miguel Hernández-Lobato · Klaus-Robert Müller · Brooks Paige · Matt Kusner · Stefan Chmiela · Kristof Schütt -
2017 : Opening Remarks »
Klaus-Robert Müller -
2017 Workshop: Interpreting, Explaining and Visualizing Deep Learning - Now what ? »
Klaus-Robert Müller · Andrea Vedaldi · Lars K Hansen · Wojciech Samek · Grégoire Montavon -
2017 Workshop: Machine Learning for Molecules and Materials »
Kristof Schütt · Klaus-Robert Müller · Anatole von Lilienfeld · José Miguel Hernández-Lobato · Klaus-Robert Müller · Alan Aspuru-Guzik · Bharath Ramsundar · Matt Kusner · Brooks Paige · Stefan Chmiela · Alexandre Tkatchenko · Anatole von Lilienfeld · Koji Tsuda -
2017 : Opening remarks »
Klaus-Robert Müller -
2017 Poster: SchNet: A continuous-filter convolutional neural network for modeling quantum interactions »
Kristof Schütt · Pieter-Jan Kindermans · Huziel Enoc Sauceda Felix · Stefan Chmiela · Alexandre Tkatchenko · Klaus-Robert Müller -
2017 Poster: An Empirical Study on The Properties of Random Bases for Kernel Methods »
Maximilian Alber · Pieter-Jan Kindermans · Kristof Schütt · Klaus-Robert Müller · Fei Sha -
2016 Poster: Wasserstein Training of Restricted Boltzmann Machines »
Grégoire Montavon · Klaus-Robert Müller · Marco Cuturi -
2013 Poster: Robust Spatial Filtering with Beta Divergence »
Wojciech Samek · Duncan Blythe · Klaus-Robert Müller · Motoaki Kawanabe -
2013 Poster: Generalizing Analytic Shrinkage for Arbitrary Covariance Structures »
Daniel Bartz · Klaus-Robert Müller -
2013 Spotlight: Robust Spatial Filtering with Beta Divergence »
Wojciech Samek · Duncan Blythe · Klaus-Robert Müller · Motoaki Kawanabe -
2013 Spotlight: Generalizing Analytic Shrinkage for Arbitrary Covariance Structures »
Daniel Bartz · Klaus-Robert Müller -
2012 Poster: Learning Invariant Representations of Molecules for Atomization Energy Prediction »
Grégoire Montavon · Katja Hansen · Siamac Fazli · Matthias Rupp · Franziska Biegler · Andreas Ziehe · Alexandre Tkatchenko · Anatole von Lilienfeld · Klaus-Robert Müller -
2011 Demonstration: Real-time social media analysis with TWIMPACT »
Mikio L Braun · Matthias L Jugel · Klaus-Robert Müller -
2010 Workshop: Charting Chemical Space: Challenges and Opportunities for AI and Machine Learning »
Pierre Baldi · Klaus-Robert Müller · Gisbert Schneider -
2010 Poster: Layer-wise analysis of deep networks with Gaussian kernels »
Grégoire Montavon · Mikio L Braun · Klaus-Robert Müller -
2009 Poster: Efficient and Accurate Lp-Norm Multiple Kernel Learning »
Marius Kloft · Ulf Brefeld · Soeren Sonnenburg · Pavel Laskov · Klaus-Robert Müller · Alexander Zien -
2009 Poster: Subject independent EEG-based BCI decoding »
Siamac Fazli · Cristian Grozea · Márton Danóczy · Benjamin Blankertz · Florin Popescu · Klaus-Robert Müller -
2009 Spotlight: Subject independent EEG-based BCI decoding »
Siamac Fazli · Cristian Grozea · Márton Danóczy · Benjamin Blankertz · Florin Popescu · Klaus-Robert Müller -
2008 Poster: Playing Pinball with non-invasive BCI »
Michael W Tangermann (ne Schröder) · Matthias Krauledat · Konrad Grzeska · Max Sagebaum · Benjamin Blankertz · Klaus-Robert Müller -
2008 Poster: Estimating vector fields using sparse basis field expansions »
Stefan Haufe · Vadim Nikulin · Andreas Ziehe · Klaus-Robert Müller · Guido Nolte -
2007 Spotlight: Invariant Common Spatial Patterns: Alleviating Nonstationarities in Brain-Computer Interfacing »
Benjamin Blankertz · Motoaki Kawanabe · Ryota Tomioka · Friederike Hohlefeld · Vadim Nikulin · Klaus-Robert Müller -
2007 Poster: Invariant Common Spatial Patterns: Alleviating Nonstationarities in Brain-Computer Interfacing »
Benjamin Blankertz · Motoaki Kawanabe · Ryota Tomioka · Friederike Hohlefeld · Vadim Nikulin · Klaus-Robert Müller -
2007 Poster: Heterogeneous Component Analysis »
Shigeyuki Oba · Motoaki Kawanabe · Klaus-Robert Müller · Shin Ishii -
2007 Spotlight: Heterogeneous Component Analysis »
Shigeyuki Oba · Motoaki Kawanabe · Klaus-Robert Müller · Shin Ishii -
2006 Workshop: Current Trends in Brain-Computer Interfacing »
Klaus-Robert Müller · José del R. Millán · Matthias Krauledat · Roderick Murray-Smith · Benjamin Blankertz -
2006 Poster: Logistic Regression for Single Trial EEG Classification »
Ryota Tomioka · Kazuyuki Aihara · Klaus-Robert Müller -
2006 Poster: Towards Zero-Training for Brain-Computer Interface Experiments »
Matthias Krauledat · Michael Schröder · Benjamin Blankertz · Klaus-Robert Müller -
2006 Spotlight: Logistic Regression for Single Trial EEG Classification »
Ryota Tomioka · Kazuyuki Aihara · Klaus-Robert Müller -
2006 Poster: Inducing Metric Violations in Human Similarity Judgements »
Julian Laub · Jakob H Macke · Klaus-Robert Müller · Felix A Wichmann -
2006 Poster: Denoising and Dimension Reduction in Feature Space »
Mikio L Braun · Joachim M Buhmann · Klaus-Robert Müller