Directional variance adjustment: bias reduction in covariance matrices based on factor analysis with an application to portfolio optimization.

Robust and reliable covariance estimates play a decisive role in financial and many other applications. An important class of estimators is based on factor models. Here, we show by extensive Monte Carlo simulations that covariance matrices derived from the statistical Factor Analysis model exhibit a systematic error, which is similar to the well-known systematic error of the spectrum of the sample covariance matrix.

Introduction to machine learning for brain imaging.

Machine learning and pattern recognition algorithms have in the past years developed to become a working horse in brain imaging and the computational neurosciences, as they are instrumental for mining vast amounts of neural data of ever increasing measurement precision and detecting minuscule signals from an overwhelming noise floor. They provide the means to decode and characterize task relevant brain states and to distinguish them from non-informative brain signals. While undoubtedly this machinery has helped to gain novel biological insights, it also holds the danger of potential unintentional abuse.

Single-trial analysis and classification of ERP components--a tutorial.

Analyzing brain states that correspond to event related potentials (ERPs) on a single trial basis is a hard problem due to the high trial-to-trial variability and the unfavorable ratio between signal (ERP) and noise (artifacts and neural background activity). In this tutorial, we provide a comprehensive framework for decoding ERPs, elaborating on linear concepts, namely spatio-temporal patterns and filters as well as linear ERP classification. However, the bottleneck of these techniques is that they require an accurate covariance matrix estimation in high dimensional sensor spaces which is a highly intricate problem.

A generalized framework for quantifying the dynamics of EEG event-related desynchronization.

Brains were built by evolution to react swiftly to environmental challenges. Thus, sensory stimuli must be processed ad hoc, i.e.

A novel mechanism for evoked responses in the human brain.

Magnetoencephalographic and electroencephalographic evoked responses are primary real-time objective measures of cognitive and perceptual processes in the human brain. Two mechanisms (additive activity and phase reset) have been debated and considered as the only possible explanations for evoked responses. Here we present theoretical and empirical evidence of a third mechanism contributing to the generation of evoked responses.

Now you feel it--now you don't: ERP correlates of somatosensory awareness.

We investigated correlates of somatosensory awareness for supra theshold stimuli using event-related potentials in a masking paradigm: Conscious perception of a weak, but suprathreshold "target" stimulus was suppressed in a significant number of trials when followed by a higher-intensity "mask" stimulus. ERPs were compared for trials with perceived versus unperceived target stimuli. Early ERPs (P60, N80), generated in the contralateral S1, were found independent of stimulus perception.

Enhancing the signal-to-noise ratio of ICA-based extracted ERPs.

When decomposing single trial electroencephalography it is a challenge to incorporate prior physiological knowledge. Here, we develop a method that uses prior information about the phase-locking property of event-related potentials in a regularization framework to bias a blind source separation algorithm toward an improved separation of single-trial phase-locked responses in terms of an increased signal-to-noise ratio. In particular, we suggest a transformation of the data, using weighted average of the single trial and trial-averaged response, that redirects the focus of source separation methods onto the subspace of event-related potentials.

Spatio-spectral filters for improving the classification of single trial EEG.

Data recorded in electroencephalogram (EEG)-based brain-computer interface experiments is generally very noisy, non-stationary, and contaminated with artifacts that can deteriorate discrimination/classification methods. In this paper, we extend the common spatial pattern (CSP) algorithm with the aim to alleviate these adverse effects. In particular, we suggest an extension of CSP to the state space, which utilizes the method of time delay embedding.

BCI Competition 2003--Data set III: probabilistic modeling of sensorimotor mu rhythms for classification of imaginary hand movements.

Brain-computer interfaces require effective online processing of electroencephalogram (EEG) measurements, e.g., as a part of feedback systems.