Author name cluster

Stefan Haufe

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28 papers

2 author rows

AIIM Journal 2026 Journal Article

GHOSTS: Validated generation of synthetic hospital time series

Rustam Zhumagambetov
Niklas Giesa
Sebastian D. Boie
Stefan Haufe

Machine learning (ML) holds great promise to support, improve, and automatize clinical decision-making in hospitals. Model training on abundantly available routine data, however, is hindered by data protection regulations. Generative models can comply with privacy laws by learning to synthesize hospital data from a target population while ensuring data privacy. Clinical time series acquired during intensive care are, however, difficult to model using established techniques, especially due to uneven sampling intervals. Here, we introduce GHOSTS (Generator of Hospital Time Series), a novel method that is capable of generating realistic heterogeneous patient trajectories in hospitals including time series with uneven sampling intervals and static patient attributes. To achieve this, GHOSTS introduces novel regularizers and a postprocessing module leveraging low-dimensional summary statistics. We further present a suite of novel benchmarks for synthetic hospital time series, GHOSTS-Bench. We train GHOSTS on a large cohort of patient data from the MIMIC-IV and eICU critical care datasets. Along with measuring the quality of the generated data in terms of how faithfully the distributions of the real data as well as their spatio-temporal dynamics are preserved, we also measure how well ML models trained on the generated data can solve a clinical prediction task on the real data. We observe that GHOSTS outperforms two state-of-the-art approaches, DoppelGANger and HALO, with respect to these criteria. We make the GHOSTS model, a corpus of synthetic data as well as Python codes implementing GHOSTS and GHOSTS-Bench publicly available. These resources will become instrumental in the future development of powerful predictive models for intensive and perioperative care. • This study presents novel generative adversarial network with structured sparsity constrains. • It is used for generation of uneven and heterogeneous time series and static attributes. • Synthetic ICU data were used to train classifier to distinguish between low and high SOFA scores. • Experiments on MIMIC-IV and eICU datasets validated our method’s results.

NeurIPS Conference 2025 Conference Paper

Correcting misinterpretations of additive models

Benedict Clark
Rick Wilming
Hjalmar Schulz
Rustam Zhumagambetov
Danny Panknin
Stefan Haufe

Correct model interpretation in high-stakes settings is critical, yet both post-hoc feature attribution methods and so-called intrinsically interpretable models can systematically attribute false-positive importance to non-informative features such as suppressor variables. Specifically, both linear models and their powerful non-linear generalisation such as General Additive Models (GAMs) are susceptible to spurious attributions to suppressors. We present a principled generalisation of activation patterns - originally developed to make linear models interpretable - to additive models, correctly rejecting suppressor effects for non-linear features. This yields PatternGAM, an importance attribution method based on univariate generative surrogate models for the broad family of additive models, and PatternQLR for polynomial models. Empirical evaluations on the XAI-TRIS benchmark with a novel false-negative invariant formulation of the earth mover's distance accuracy metric demonstrates significant improvements over popular feature attribution methods and the traditional interpretation of additive models. Finally, real-world case studies on the COMPAS and MIMIC-IV datasets provide new insights into the role of specific features by disentangling genuine target-related information from suppression effects that would mislead conventional GAM interpretations.

NeurIPS Conference 2025 Conference Paper

Minimizing False-Positive Attributions in Explanations of Non-Linear Models

Anders Gjølbye
Stefan Haufe
Lars Kai Hansen

Suppressor variables can influence model predictions without being dependent on the target outcome, and they pose a significant challenge for Explainable AI (XAI) methods. These variables may cause false-positive feature attributions, undermining the utility of explanations. Although effective remedies exist for linear models, their extension to non-linear models and instance-based explanations has remained limited. We introduce PatternLocal, a novel XAI technique that addresses this gap. PatternLocal begins with a locally linear surrogate, e. g. , LIME, KernelSHAP, or gradient-based methods, and transforms the resulting discriminative model weights into a generative representation, thereby suppressing the influence of suppressor variables while preserving local fidelity. In extensive hyperparameter optimization on the XAI-TRIS benchmark, PatternLocal consistently outperformed other XAI methods and reduced false-positive attributions when explaining non-linear tasks, thereby enabling more reliable and actionable insights. We further evaluate PatternLocal on an EEG motor imagery dataset, demonstrating physiologically plausible explanations.

YNIMG Journal 2023 Journal Article

Alterations in rhythmic and non‐rhythmic resting‐state EEG activity and their link to cognition in older age

Elena Cesnaite
Paul Steinfath
Mina Jamshidi Idaji
Tilman Stephani
Deniz Kumral
Stefan Haufe
Christian Sander
Tilman Hensch

While many structural and biochemical changes in the brain have previously been associated with older age, findings concerning functional properties of neuronal networks, as reflected in their electrophysiological signatures, remain rather controversial. These discrepancies might arise due to several reasons, including diverse factors determining general spectral slowing in the alpha frequency range as well as amplitude mixing between the rhythmic and non-rhythmic parameters. We used a large dataset (N = 1703, mean age 70) to comprehensively investigate age-related alterations in multiple EEG biomarkers taking into account rhythmic and non-rhythmic activity and their individual contributions to cognitive performance. While we found strong evidence for an individual alpha peak frequency (IAF) decline in older age, we did not observe a significant relationship between theta power and age while controlling for IAF. Not only did IAF decline with age, but it was also positively associated with interference resolution in a working memory task primarily in the right and left temporal lobes suggesting its functional role in information sampling. Critically, we did not detect a significant relationship between alpha power and age when controlling for the 1/f spectral slope, while the latter one showed age-related alterations. These findings thus suggest that the entanglement of IAF slowing and power in the theta frequency range, as well as 1/f slope and alpha power measures, might explain inconsistencies reported previously in the literature. Finally, despite the absence of age-related alterations, alpha power was negatively associated with the speed of processing in the right frontal lobe while 1/f slope showed no consistent relationship to cognitive performance. Our results thus demonstrate that multiple electrophysiological features, as well as their interplay, should be considered for the comprehensive assessment of association between age, neuronal activity, and cognitive performance.

YNIMG Journal 2023 Journal Article

Identifying good practices for detecting inter-regional linear functional connectivity from EEG

Franziska Pellegrini
Arnaud Delorme
Vadim Nikulin
Stefan Haufe

Aggregating voxel-level statistical dependencies between multivariate time series is an important intermediate step when characterising functional connectivity (FC) between larger brain regions. However, there are numerous ways in which voxel-level data can be aggregated into inter-regional FC, and the advantages of each of these approaches are currently unclear. In this study we generate ground-truth data and compare the performances of various pipelines that estimate directed and undirected linear phase-to-phase FC between regions. We test the ability of several existing and novel FC analysis pipelines to identify the true regions within which connectivity was simulated. We test various inverse modelling algorithms, strategies to aggregate time series within regions, and connectivity metrics. Furthermore, we investigate the influence of the number of interactions, the signal-to-noise ratio, the noise mix, the interaction time delay, and the number of active sources per region on the ability of detecting phase-to-phase FC. Throughout all simulated scenarios, lowest performance is obtained with pipelines involving the absolute value of coherency. Further, the combination of dynamic imaging of coherent sources (DICS) beamforming with directed FC metrics that aggregate information across multiple frequencies leads to unsatisfactory results. Pipelines that show promising results with our simulated pseudo-EEG data involve the following steps: (1) Source projection using the linearly-constrained minimum variance (LCMV) beamformer. (2) Principal component analysis (PCA) using the same fixed number of components within every region. (3) Calculation of the multivariate interaction measure (MIM) for every region pair to assess undirected phase-to-phase FC, or calculation of time-reversed Granger Causality (TRGC) to assess directed phase-to-phase FC. We formulate recommendations based on these results that may increase the validity of future experimental connectivity studies. We further introduce the free ROIconnect plugin for the EEGLAB toolbox that includes the recommended methods and pipelines that are presented here. We show an exemplary application of the best performing pipeline to the analysis of EEG data recorded during motor imagery.

ICML Conference 2023 Conference Paper

Theoretical Behavior of XAI Methods in the Presence of Suppressor Variables

Rick Wilming
Leo Kieslich
Benedict Clark
Stefan Haufe

In recent years, the community of ’explainable artificial intelligence’ (XAI) has created a vast body of methods to bridge a perceived gap between model ’complexity’ and ’interpretability’. However, a concrete problem to be solved by XAI methods has not yet been formally stated. As a result, XAI methods are lacking theoretical and empirical evidence for the ’correctness’ of their explanations, limiting their potential use for quality-control and transparency purposes. At the same time, Haufe et al. (2014) showed, using simple toy examples, that even standard interpretations of linear models can be highly misleading. Specifically, high importance may be attributed to so-called suppressor variables lacking any statistical relation to the prediction target. This behavior has been confirmed empirically for a large array of XAI methods in Wilming et al. (2022). Here, we go one step further by deriving analytical expressions for the behavior of a variety of popular XAI methods on a simple two-dimensional binary classification problem involving Gaussian class-conditional distributions. We show that the majority of the studied approaches will attribute non-zero importance to a non-class-related suppressor feature in the presence of correlated noise. This poses important limitations on the interpretations and conclusions that the outputs of these XAI methods can afford.

YNIMG Journal 2022 Journal Article

A benchmark for prediction of psychiatric multimorbidity from resting EEG data in a large pediatric sample

Nicolas Langer
Martyna Beata Plomecka
Marius Tröndle
Anuja Negi
Tzvetan Popov
Michael Milham
Stefan Haufe

Psychiatric disorders are among the most common and debilitating illnesses across the lifespan and begin usually during childhood and adolescence, which emphasizes the importance of studying the developing brain. Most of the previous pediatric neuroimaging studies employed traditional univariate statistics on relatively small samples. Multivariate machine learning approaches have a great potential to overcome the limitations of these approaches. On the other hand, the vast majority of existing multivariate machine learning studies have focused on differentiating between children with an isolated psychiatric disorder and typically developing children. However, this line of research does not reflect the real-life situation as the majority of children with a clinical diagnosis have multiple psychiatric disorders (multimorbidity), and consequently, a clinician has the task to choose between different diagnoses and/or the combination of multiple diagnoses. Thus, the goal of the present benchmark is to predict psychiatric multimorbidity in children and adolescents. For this purpose, we implemented two kinds of machine learning benchmark challenges: The first challenge targets the prediction of the seven most prevalent DSM-V psychiatric diagnoses for the available data set, of which each individual can exhibit multiple ones concurrently (i.e. multi-task multi-label classification). Based on behavioral and cognitive measures, a second challenge focuses on predicting psychiatric symptom severity on a dimensional level (i.e. multiple regression task). For the present benchmark challenges, we will leverage existing and future data from the biobank of the Healthy Brain Network (HBN) initiative, which offers a unique large-sample dataset (N = 2042) that provides a wide array of different psychiatric developmental disorders and true hidden data sets. Due to limited real-world practicability and economic viability of MRI measurements, the present challenge will permit only resting state EEG data and demographic information to derive predictive models. We believe that a community driven effort to derive predictive markers from these data using advanced machine learning algorithms can help to improve the diagnosis of psychiatric developmental disorders.

YNIMG Journal 2022 Journal Article

Empirical Bayesian localization of event-related time-frequency neural activity dynamics

Chang Cai
Leighton Hinkley
Yijing Gao
Ali Hashemi
Stefan Haufe
Kensuke Sekihara
Srikantan S. Nagarajan

Accurate reconstruction of the spatio-temporal dynamics of event-related cortical oscillations across human brain regions is an important problem in functional brain imaging and human cognitive neuroscience with magnetoencephalography (MEG) and electroencephalography (EEG). The problem is challenging not only in terms of localization of complex source configurations from sensor measurements with unknown noise and interference but also for reconstruction of transient event-related time-frequency dynamics of cortical oscillations. We recently proposed a robust empirical Bayesian algorithm for simultaneous reconstruction of complex brain source activity and noise covariance, in the context of evoked and resting-state data. In this paper, we expand upon this empirical Bayesian framework for optimal reconstruction of event-related time-frequency dynamics of regional cortical oscillations, referred to as time-frequency Champagne (TFC). This framework enables imaging of five-dimensional (space, time, and frequency) event-related brain activity from M/EEG data, and can be viewed as a time-frequency optimized adaptive Bayesian beamformer. We evaluate TFC in both simulations and several real datasets, with comparisons to benchmark standards - variants of time-frequency optimized adaptive beamformers (TFBF) as well as the sLORETA algorithm. In simulations, we demonstrate several advantages in estimating time-frequency cortical oscillatory dynamics compared to benchmarks. With real MEG data, we demonstrate across many datasets that the proposed approach is robust to highly correlated brain activity and low SNR data, and is able to accurately reconstruct cortical dynamics with data from just a few epochs.

NeurIPS Conference 2021 Conference Paper

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

Several problems in neuroimaging and beyond require inference on the parameters of multi-task sparse hierarchical regression models. Examples include M/EEG inverse problems, neural encoding models for task-based fMRI analyses, and climate science. In these domains, both the model parameters to be inferred and the measurement noise may exhibit a complex spatio-temporal structure. Existing work either neglects the temporal structure or leads to computationally demanding inference schemes. Overcoming these limitations, we devise a novel flexible hierarchical Bayesian framework within which the spatio-temporal dynamics of model parameters and noise are modeled to have Kronecker product covariance structure. Inference in our framework is based on majorization-minimization optimization and has guaranteed convergence properties. Our highly efficient algorithms exploit the intrinsic Riemannian geometry of temporal autocovariance matrices. For stationary dynamics described by Toeplitz matrices, the theory of circulant embeddings is employed. We prove convex bounding properties and derive update rules of the resulting algorithms. On both synthetic and real neural data from M/EEG, we demonstrate that our methods lead to improved performance.

YNIMG Journal 2021 Journal Article

Robust estimation of noise for electromagnetic brain imaging with the champagne algorithm

Chang Cai
Ali Hashemi
Mithun Diwakar
Stefan Haufe
Kensuke Sekihara
Srikantan S. Nagarajan

Robust estimation of the number, location, and activity of multiple correlated brain sources has long been a challenging task in electromagnetic brain imaging from M/EEG data, one that is significantly impacted by interference from spontaneous brain activity, sensor noise, and other sources of artifacts. Recently, we introduced the Champagne algorithm, a novel Bayesian inference algorithm that has shown tremendous success in M/EEG source reconstruction. Inherent to Champagne and most other related Bayesian reconstruction algorithms is the assumption that the noise covariance in sensor data can be estimated from "baseline" or "control" measurements. However, in many scenarios, such baseline data is not available, or is unreliable, and it is unclear how best to estimate the noise covariance. In this technical note, we propose several robust methods to estimate the contributions to sensors from noise arising from outside the brain without the need for additional baseline measurements. The incorporation of these methods for diagonal noise covariance estimation improves the robust reconstruction of complex brain source activity under high levels of noise and interference, while maintaining the performance features of Champagne. Specifically, we show that the resulting algorithm, Champagne with noise learning, is quite robust to initialization and is computationally efficient. In simulations, performance of the proposed noise learning algorithm is consistently superior to Champagne without noise learning. We also demonstrate that, even without the use of any baseline data, Champagne with noise learning is able to reconstruct complex brain activity with just a few trials or even a single trial, demonstrating significant improvements in source reconstruction for electromagnetic brain imaging.

YNIMG Journal 2021 Journal Article

Unification of sparse Bayesian learning algorithms for electromagnetic brain imaging with the majorization minimization framework

Ali Hashemi
Chang Cai
Gitta Kutyniok
Klaus-Robert Müller
Srikantan S. Nagarajan
Stefan Haufe

Methods for electro- or magnetoencephalography (EEG/MEG) based brain source imaging (BSI) using sparse Bayesian learning (SBL) have been demonstrated to achieve excellent performance in situations with low numbers of distinct active sources, such as event-related designs. This paper extends the theory and practice of SBL in three important ways. First, we reformulate three existing SBL algorithms under the majorization-minimization (MM) framework. This unification perspective not only provides a useful theoretical framework for comparing different algorithms in terms of their convergence behavior, but also provides a principled recipe for constructing novel algorithms with specific properties by designing appropriate bounds of the Bayesian marginal likelihood function. Second, building on the MM principle, we propose a novel method called LowSNR-BSI that achieves favorable source reconstruction performance in low signal-to-noise-ratio (SNR) settings. Third, precise knowledge of the noise level is a crucial requirement for accurate source reconstruction. Here we present a novel principled technique to accurately learn the noise variance from the data either jointly within the source reconstruction procedure or using one of two proposed cross-validation strategies. Empirically, we could show that the monotonous convergence behavior predicted from MM theory is confirmed in numerical experiments. Using simulations, we further demonstrate the advantage of LowSNR-BSI over conventional SBL in low-SNR regimes, and the advantage of learned noise levels over estimates derived from baseline data. To demonstrate the usefulness of our novel approach, we show neurophysiologically plausible source reconstructions on averaged auditory evoked potential data.

YNIMG Journal 2020 Journal Article

Functional connectivity of EEG is subject-specific, associated with phenotype, and different from fMRI

Maximilian Nentwich
Lei Ai
Jens Madsen
Qawi K. Telesford
Stefan Haufe
Michael P. Milham
Lucas C. Parra

A variety of psychiatric, behavioral and cognitive phenotypes have been linked to brain ‘’functional connectivity’’ -- the pattern of correlation observed between different brain regions. Most commonly assessed using functional magnetic resonance imaging (fMRI), here, we investigate the connectivity-phenotype associations with functional connectivity measured with electroencephalography (EEG), using phase-coupling. We analyzed data from the publicly available Healthy Brain Network Biobank. This database compiles a growing sample of children and adolescents, currently encompassing 1657 individuals. Among a variety of assessment instruments we focus on ten phenotypic and additional demographic measures that capture most of the variance in this sample. The largest effect sizes are found for age and sex for both fMRI and EEG. We replicate previous findings of an association of Intelligence Quotient (IQ) and Attention Deficit Hyperactivity Disorder (ADHD) with the pattern of fMRI functional connectivity. We also find an association with socioeconomic status, anxiety and the Child Behavior Checklist Score. For EEG we find a significant connectivity-phenotype relationship with IQ. The actual spatial patterns of functional connectivity are quite different between fMRI and source-space EEG. However, within EEG we observe clusters of functional connectivity that are consistent across frequency bands. Additionally we analyzed reproducibility of functional connectivity. We compare connectivity obtained with different tasks, including resting state, a video and a visual flicker task. For both EEG and fMRI the variation between tasks was smaller than the variability observed between subjects. We also found an increase of reliability with increasing frequency of the EEG, and increased sampling duration. We conclude that, while the patterns of functional connectivity are distinct between fMRI and phase-coupling of EEG, they are nonetheless similar in their robustness to the task, and similar in that idiosyncratic patterns of connectivity predict individual phenotypes.

NeurIPS Conference 2019 Conference Paper

A state-space model for inferring effective connectivity of latent neural dynamics from simultaneous EEG/fMRI

Tao Tu
John Paisley
Stefan Haufe
Paul Sajda

Inferring effective connectivity between spatially segregated brain regions is important for understanding human brain dynamics in health and disease. Non-invasive neuroimaging modalities, such as electroencephalography (EEG) and functional magnetic resonance imaging (fMRI), are often used to make measurements and infer connectivity. However most studies do not consider integrating the two modalities even though each is an indirect measure of the latent neural dynamics and each has its own spatial and/or temporal limitations. In this study, we develop a linear state-space model to infer the effective connectivity in a distributed brain network based on simultaneously recorded EEG and fMRI data. Our method first identifies task-dependent and subject-dependent regions of interest (ROI) based on the analysis of fMRI data. Directed influences between the latent neural states at these ROIs are then modeled as a multivariate autogressive (MVAR) process driven by various exogenous inputs. The latent neural dynamics give rise to the observed scalp EEG measurements via a biophysically informed linear EEG forward model. We use a mean-field variational Bayesian approach to infer the posterior distribution of latent states and model parameters. The performance of the model was evaluated on two sets of simulations. Our results emphasize the importance of obtaining accurate spatial localization of ROIs from fMRI. Finally, we applied the model to simultaneously recorded EEG-fMRI data from 10 subjects during a Face-Car-House visual categorization task and compared the change in connectivity induced by different stimulus categories.

YNIMG Journal 2018 Journal Article

Elucidating relations between fMRI, ECoG, and EEG through a common natural stimulus

Stefan Haufe
Paul DeGuzman
Simon Henin
Michael Arcaro
Christopher J. Honey
Uri Hasson
Lucas C. Parra

Human brain mapping relies heavily on fMRI, ECoG and EEG, which capture different physiological signals. Relationships between these signals have been established in the context of specific tasks or during resting state, often using spatially confined concurrent recordings in animals. But it is not certain whether these correlations generalize to other contexts relevant for human cognitive neuroscience. Here, we address the case of complex naturalistic stimuli and ask two basic questions. First, how reliable are the responses evoked by a naturalistic audio-visual stimulus in each of these imaging methods, and second, how similar are stimulus-related responses across methods? To this end, we investigated a wide range of brain regions and frequency bands. We presented the same movie clip twice to three different cohorts of subjects (NEEG = 45, NfMRI = 11, NECoG = 5) and assessed stimulus-driven correlations across viewings and between imaging methods, thereby ruling out task-irrelevant confounds. All three imaging methods had similar repeat-reliability across viewings when fMRI and EEG data were averaged across subjects, highlighting the potential to achieve large signal-to-noise ratio by leveraging large sample sizes. The fMRI signal correlated positively with high-frequency ECoG power across multiple task-related cortical structures but positively with low-frequency EEG and ECoG power. In contrast to previous studies, these correlations were as strong for low-frequency as for high frequency ECoG. We also observed links between fMRI and infra-slow EEG voltage fluctuations. These results extend previous findings to the case of natural stimulus processing.

YNIMG Journal 2017 Journal Article

Consistency of EEG source localization and connectivity estimates

Keyvan Mahjoory
Vadim V. Nikulin
Loïc Botrel
Klaus Linkenkaer-Hansen
Marco M. Fato
Stefan Haufe

As the EEG inverse problem does not have a unique solution, the sources reconstructed from EEG and their connectivity properties depend on forward and inverse modeling parameters such as the choice of an anatomical template and electrical model, prior assumptions on the sources, and further implementational details. In order to use source connectivity analysis as a reliable research tool, there is a need for stability across a wider range of standard estimation routines. Using resting state EEG recordings of N=65 participants acquired within two studies, we present the first comprehensive assessment of the consistency of EEG source localization and functional/effective connectivity metrics across two anatomical templates (ICBM152 and Colin27), three electrical models (BEM, FEM and spherical harmonics expansions), three inverse methods (WMNE, eLORETA and LCMV), and three software implementations (Brainstorm, Fieldtrip and our own toolbox). Source localizations were found to be more stable across reconstruction pipelines than subsequent estimations of functional connectivity, while effective connectivity estimates where the least consistent. All results were relatively unaffected by the choice of the electrical head model, while the choice of the inverse method and source imaging package induced a considerable variability. In particular, a relatively strong difference was found between LCMV beamformer solutions on one hand and eLORETA/WMNE distributed inverse solutions on the other hand. We also observed a gradual decrease of consistency when results are compared between studies, within individual participants, and between individual participants. In order to provide reliable findings in the face of the observed variability, additional simulations involving interacting brain sources are required. Meanwhile, we encourage verification of the obtained results using more than one source imaging procedure.

YNIMG Journal 2016 Journal Article

The New York Head—A precise standardized volume conductor model for EEG source localization and tES targeting

Yu Huang
Lucas C. Parra
Stefan Haufe

In source localization of electroencephalograpic (EEG) signals, as well as in targeted transcranial electric current stimulation (tES), a volume conductor model is required to describe the flow of electric currents in the head. Boundary element models (BEM) can be readily computed to represent major tissue compartments, but cannot encode detailed anatomical information within compartments. Finite element models (FEM) can capture more tissue types and intricate anatomical structures, but with the higher precision also comes the need for semi-automated segmentation, and a higher computational cost. In either case, adjusting to the individual human anatomy requires costly magnetic resonance imaging (MRI), and thus head modeling is often based on the anatomy of an ‘arbitrary’ individual (e. g. Colin27). Additionally, existing reference models for the human head often do not include the cerebro-spinal fluid (CSF), and their field of view excludes portions of the head and neck—two factors that demonstrably affect current-flow patterns. Here we present a highly detailed FEM, which we call ICBM-NY, or "New York Head". It is based on the ICBM152 anatomical template (a non-linear average of the MRI of 152 adult human brains) defined in MNI coordinates, for which we extended the field of view to the neck and performed a detailed segmentation of six tissue types (scalp, skull, CSF, gray matter, white matter, air cavities) at 0. 5mm 3 resolution. The model was solved for 231 electrode locations. To evaluate its performance, additional FEMs and BEMs were constructed for four individual subjects. Each of the four individual FEMs (regarded as the ‘ground truth’) is compared to its BEM counterpart, the ICBM-NY, a BEM of the ICBM anatomy, an ‘individualized’ BEM of the ICBM anatomy warped to the individual head surface, and FEMs of the other individuals. Performance is measured in terms of EEG source localization and tES targeting errors. Results show that the ICBM-NY outperforms FEMs of mismatched individual anatomies as well as the BEM of the ICBM anatomy according to both criteria. We therefore propose the New York Head as a new standard head model to be used in future EEG and tES studies whenever an individual MRI is not available. We release all model data online at neuralengr. com/nyhead/ to facilitate broad adoption.

YNIMG Journal 2015 Journal Article

Identifying Granger causal relationships between neural power dynamics and variables of interest

Irene Winkler
Stefan Haufe
Anne K. Porbadnigk
Klaus-Robert Müller
Sven Dähne

Power modulations of oscillations in electro- and magnetoencephalographic (EEG/MEG) signals have been linked to a wide range of brain functions. To date, most of the evidence is obtained by correlating bandpower fluctuations to specific target variables such as reaction times or task ratings, while the causal links between oscillatory activity and behavior remain less clear. Here, we propose to identify causal relationships by the statistical concept of Granger causality, and we investigate which methods are bests suited to reveal Granger causal links between the power of brain oscillations and experimental variables. As an alternative to testing such causal links on the sensor level, we propose to linearly combine the information contained in each sensor in order to create virtual channels, corresponding to estimates of underlying brain oscillations, the Granger-causal relations of which may be assessed. Such linear combinations of sensor can be given by source separation methods such as, for example, Independent Component Analysis (ICA) or by the recently developed Source Power Correlation (SPoC) method. Here we compare Granger causal analysis on power dynamics obtained from i) sensor directly, ii) spatial filtering methods that do not optimize for Granger causality (ICA and SPoC), and iii) a method that directly optimizes spatial filters to extract sources the power dynamics of which maximally Granger causes a given target variable. We refer to this method as Granger Causal Power Analysis (GrangerCPA). Using both simulated and real EEG recordings, we find that computing Granger causality on channel-wise spectral power suffers from a poor signal-to-noise ratio due to volume conduction, while all three multivariate approaches alleviate this issue. In real EEG recordings from subjects performing self-paced foot movements, all three multivariate methods identify neural oscillations with motor-related patterns at a similar performance level. In an auditory perception task, the application of GrangerCPA reveals significant Granger-causal links between alpha oscillations and reaction times in more subjects compared to conventional methods.

YNIMG Journal 2015 Journal Article

Solving the EEG inverse problem based on space–time–frequency structured sparsity constraints

Sebastián Castaño-Candamil
Johannes Höhne
Juan-David Martínez-Vargas
Xing-Wei An
German Castellanos-Domínguez
Stefan Haufe

We introduce STOUT (spatio-temporal unifying tomography), a novel method for the source analysis of electroencephalograpic (EEG) recordings, which is based on a physiologically-motivated source representation. Our method assumes that only a small number of brain sources are active throughout a measurement, where each of the sources exhibits focal (smooth but localized) characteristics in space, time and frequency. This structure is enforced through an expansion of the source current density into appropriate spatio-temporal basis functions in combination with sparsity constraints. This approach combines the main strengths of two existing methods, namely Sparse Basis Field Expansions (Haufe et al. , 2011) and Time–Frequency Mixed-Norm Estimates (Gramfort et al. , 2013). By adjusting the ratio between two regularization terms, STOUT is capable of trading temporal for spatial reconstruction accuracy and vice versa, depending on the requirements of specific analyses and the provided data. Due to allowing for non-stationary source activations, STOUT is particularly suited for the localization of event-related potentials (ERP) and other evoked brain activity. We demonstrate its performance on simulated ERP data for varying signal-to-noise ratios and numbers of active sources. Our analysis of the generators of visual and auditory evoked N200 potentials reveals that the most active sources originate in the temporal and occipital lobes, in line with the literature on sensory processing.

YNIMG Journal 2014 Journal Article

Dimensionality reduction for the analysis of brain oscillations

Stefan Haufe
Sven Dähne
Vadim V. Nikulin

Neuronal oscillations have been shown to be associated with perceptual, motor and cognitive brain operations. While complex spatio-temporal dynamics are a hallmark of neuronal oscillations, they also represent a formidable challenge for the proper extraction and quantification of oscillatory activity with non-invasive recording techniques such as EEG and MEG. In order to facilitate the study of neuronal oscillations we present a general-purpose pre-processing approach, which can be applied for a wide range of analyses including but not restricted to inverse modeling and multivariate single-trial classification. The idea is to use dimensionality reduction with spatio-spectral decomposition (SSD) instead of the commonly and almost exclusively used principal component analysis (PCA). The key advantage of SSD lies in selecting components explaining oscillations-related variance instead of just any variance as in the case of PCA. For the validation of SSD pre-processing we performed extensive simulations with different inverse modeling algorithms and signal-to-noise ratios. In all these simulations SSD invariably outperformed PCA often by a large margin. Moreover, using a database of multichannel EEG recordings from 80 subjects we show that pre-processing with SSD significantly increases the performance of single-trial classification of imagined movements, compared to the classification with PCA pre-processing or without any dimensionality reduction. Our simulations and analysis of real EEG experiments show that, while not being supervised, the SSD algorithm is capable of extracting components primarily relating to the signal of interest often using as little as 20% of the data variance, instead of > 90% variance as in case of PCA. Given its ease of use, absence of supervision, and capability to efficiently reduce the dimensionality of multivariate EEG/MEG data, we advocate the application of SSD pre-processing for the analysis of spontaneous and induced neuronal oscillations in normal subjects and patients.

YNIMG Journal 2014 Journal Article

Finding brain oscillations with power dependencies in neuroimaging data

Sven Dähne
Vadim V. Nikulin
David Ramírez
Peter J. Schreier
Klaus-Robert Müller
Stefan Haufe

Phase synchronization among neuronal oscillations within the same frequency band has been hypothesized to be a major mechanism for communication between different brain areas. On the other hand, cross-frequency communications are more flexible allowing interactions between oscillations with different frequencies. Among such cross-frequency interactions amplitude-to-amplitude interactions are of a special interest as they show how the strength of spatial synchronization in different neuronal populations relates to each other during a given task. While, previously, amplitude-to-amplitude correlations were studied primarily on the sensor level, we present a source separation approach using spatial filters which maximize the correlation between the envelopes of brain oscillations recorded with electro-/magnetoencephalography (EEG/MEG) or intracranial multichannel recordings. Our approach, which is called canonical source power correlation analysis (cSPoC), is thereby capable of extracting genuine brain oscillations solely based on their assumed coupling behavior even when the signal-to-noise ratio of the signals is low. In addition to using cSPoC for the analysis of cross-frequency interactions in the same subject, we show that it can also be utilized for studying amplitude dynamics of neuronal oscillations across subjects. We assess the performance of cSPoC in simulations as well as in three distinctively different analysis scenarios of real EEG data, each involving several subjects. In the simulations, cSPoC outperforms unsupervised state-of-the-art approaches. In the analysis of real EEG recordings, we demonstrate excellent unsupervised discovery of meaningful power-to-power couplings, within as well as across subjects and frequency bands.

YNIMG Journal 2014 Journal Article

On the interpretation of weight vectors of linear models in multivariate neuroimaging

Stefan Haufe
Frank Meinecke
Kai Görgen
Sven Dähne
John-Dylan Haynes
Benjamin Blankertz
Felix Bießmann

The increase in spatiotemporal resolution of neuroimaging devices is accompanied by a trend towards more powerful multivariate analysis methods. Often it is desired to interpret the outcome of these methods with respect to the cognitive processes under study. Here we discuss which methods allow for such interpretations, and provide guidelines for choosing an appropriate analysis for a given experimental goal: For a surgeon who needs to decide where to remove brain tissue it is most important to determine the origin of cognitive functions and associated neural processes. In contrast, when communicating with paralyzed or comatose patients via brain–computer interfaces, it is most important to accurately extract the neural processes specific to a certain mental state. These equally important but complementary objectives require different analysis methods. Determining the origin of neural processes in time or space from the parameters of a data-driven model requires what we call a forward model of the data; such a model explains how the measured data was generated from the neural sources. Examples are general linear models (GLMs). Methods for the extraction of neural information from data can be considered as backward models, as they attempt to reverse the data generating process. Examples are multivariate classifiers. Here we demonstrate that the parameters of forward models are neurophysiologically interpretable in the sense that significant nonzero weights are only observed at channels the activity of which is related to the brain process under study. In contrast, the interpretation of backward model parameters can lead to wrong conclusions regarding the spatial or temporal origin of the neural signals of interest, since significant nonzero weights may also be observed at channels the activity of which is statistically independent of the brain process under study. As a remedy for the linear case, we propose a procedure for transforming backward models into forward models. This procedure enables the neurophysiological interpretation of the parameters of linear backward models. We hope that this work raises awareness for an often encountered problem and provides a theoretical basis for conducting better interpretable multivariate neuroimaging analyses.

YNIMG Journal 2014 Journal Article

SPoC: A novel framework for relating the amplitude of neuronal oscillations to behaviorally relevant parameters

Sven Dähne
Frank C. Meinecke
Stefan Haufe
Johannes Höhne
Michael Tangermann
Klaus-Robert Müller
Vadim V. Nikulin

Previously, modulations in power of neuronal oscillations have been functionally linked to sensory, motor and cognitive operations. Such links are commonly established by relating the power modulations to specific target variables such as reaction times or task ratings. Consequently, the resulting spatio-spectral representation is subjected to neurophysiological interpretation. As an alternative, independent component analysis (ICA) or alternative decomposition methods can be applied and the power of the components may be related to the target variable. In this paper we show that these standard approaches are suboptimal as the first does not take into account the superposition of many sources due to volume conduction, while the second is unable to exploit available information about the target variable. To improve upon these approaches we introduce a novel (supervised) source separation framework called Source Power Comodulation (SPoC). SPoC makes use of the target variable in the decomposition process in order to give preference to components whose power comodulates with the target variable. We present two algorithms that implement the SPoC approach. Using simulations with a realistic head model, we show that the SPoC algorithms are able extract neuronal components exhibiting high correlation of power with the target variable. In this task, the SPoC algorithms outperform other commonly used techniques that are based on the sensor data or ICA approaches. Furthermore, using real electroencephalography (EEG) recordings during an auditory steady state paradigm, we demonstrate the utility of the SPoC algorithms by extracting neuronal components exhibiting high correlation of power with the intensity of the auditory input. Taking into account the results of the simulations and real EEG recordings, we conclude that SPoC represents an adequate approach for the optimal extraction of neuronal components showing coupling of power with continuously changing behaviorally relevant parameters.

YNIMG Journal 2014 Journal Article

The effect of linear mixing in the EEG on Hurst exponent estimation

Duncan A.J. Blythe
Stefan Haufe
Klaus-Robert Müller
Vadim V. Nikulin

Although the long-range temporal correlation (LRTC) of the amplitude fluctuations of neuronal EEG/MEG oscillations is widely acknowledged, the majority of studies to date have been performed in sensor space, disregarding the mixing effects implied by volume conduction and confounding noise. While the effect of mixing on the evaluation of evoked responses and connectivity measures has been extensively studied, there are, to date, no studies reporting on the differences in the values of the estimated Hurst exponents when moving between sensor and source space representations of the multivariate data or on the effect of noise. Such differences, if not duly acknowledged, may lead to erroneous data interpretations. We show in simulations and in theory that measuring Hurst exponents in sensor space may lead to an incomplete picture of the LRTC properties of the underlying data and that noise may significantly bias the estimate of the Hurst exponent of the underlying signal. Moreover, these predictions are confirmed in real data, where we analyze the amplitude dynamics of neuronal oscillations in the resting state from EEG data. By moving either to an independent components representation or to a source representation which maximizes the signal to noise ratio in the alpha frequency range, we observe greater variance, skewness and kurtosis over measured Hurst exponents than in sensor space. We confirm the suitability of conventional source separation methodology by introducing a novel algorithm HeMax which obtains a source maximizing the Hurst exponent in the amplitude dynamics of narrow band oscillations. Our findings imply that the long-range correlative properties of the EEG should be studied in source space, in such a way that the SNR is maximized, or at least with spatial decomposition techniques approximating source activities, rather than in sensor space.

YNIMG Journal 2013 Journal Article

A critical assessment of connectivity measures for EEG data: A simulation study

Stefan Haufe
Vadim V. Nikulin
Klaus-Robert Müller
Guido Nolte

Information flow between brain areas is difficult to estimate from EEG measurements due to the presence of noise as well as due to volume conduction. We here test the ability of popular measures of effective connectivity to detect an underlying neuronal interaction from simulated EEG data, as well as the ability of commonly used inverse source reconstruction techniques to improve the connectivity estimation. We find that volume conduction severely limits the neurophysiological interpretability of sensor-space connectivity analyses. Moreover, it may generally lead to conflicting results depending on the connectivity measure and statistical testing approach used. In particular, we note that the application of Granger-causal (GC) measures combined with standard significance testing leads to the detection of spurious connectivity regardless of whether the analysis is performed on sensor-space data or on sources estimated using three different established inverse methods. This empirical result follows from the definition of GC. The phase-slope index (PSI) does not suffer from this theoretical limitation and therefore performs well on our simulated data. We develop a theoretical framework to characterize artifacts of volume conduction, which may still be present even in reconstructed source time series as zero-lag correlations, and to distinguish their time-delayed brain interaction. Based on this theory we derive a procedure which suppresses the influence of volume conduction, but preserves effects related to time-lagged brain interaction in connectivity estimates. This is achieved by using time-reversed data as surrogates for statistical testing. We demonstrate that this robustification makes Granger-causal connectivity measures applicable to EEG data, achieving similar results as PSI. Integrating the insights of our study, we provide a guidance for measuring brain interaction from EEG data. Software for generating benchmark data is made available.

YNIMG Journal 2011 Journal Article

Large-scale EEG/MEG source localization with spatial flexibility

Stefan Haufe
Ryota Tomioka
Thorsten Dickhaus
Claudia Sannelli
Benjamin Blankertz
Guido Nolte
Klaus-Robert Müller

We propose a novel approach to solving the electro-/magnetoencephalographic (EEG/MEG) inverse problem which is based upon a decomposition of the current density into a small number of spatial basis fields. It is designed to recover multiple sources of possibly different extent and depth, while being invariant with respect to phase angles and rotations of the coordinate system. We demonstrate the method's ability to reconstruct simulated sources of random shape and show that the accuracy of the recovered sources can be increased, when interrelated field patterns are co-localized. Technically, this leads to large-scale mathematical problems, which are solved using recent advances in convex optimization. We apply our method for localizing brain areas involved in different types of motor imagery using real data from Brain–Computer Interface (BCI) sessions. Our approach based on single-trial localization of complex Fourier coefficients yields class-specific focal sources in the sensorimotor cortices.

YNIMG Journal 2011 Journal Article

Single-trial analysis and classification of ERP components — A tutorial

Benjamin Blankertz
Steven Lemm
Matthias Treder
Stefan Haufe
Klaus-Robert Müller

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. As a remedy, we propose to use shrinkage estimators and show that appropriate regularization of linear discriminant analysis (LDA) by shrinkage yields excellent results for single-trial ERP classification that are far superior to classical LDA classification. Furthermore, we give practical hints on the interpretation of what classifiers learned from the data and demonstrate in particular that the trade-off between goodness-of-fit and model complexity in regularized LDA relates to a morphing between a difference pattern of ERPs and a spatial filter which cancels non task-related brain activity.

YNIMG Journal 2008 Journal Article

Combining sparsity and rotational invariance in EEG/MEG source reconstruction

Stefan Haufe
Vadim V. Nikulin
Andreas Ziehe
Klaus-Robert Müller
Guido Nolte

We introduce Focal Vector Field Reconstruction (FVR), a novel technique for the inverse imaging of vector fields. The method was designed to simultaneously achieve two goals: a) invariance with respect to the orientation of the coordinate system, and b) a preference for sparsity of the solutions and their spatial derivatives. This was achieved by defining the regulating penalty function, which renders the solutions unique, as a global ℓ 1-norm of local ℓ 2-norms. We show that the method can be successfully used for solving the EEG inverse problem. In the joint localization of 2–3 simulated dipoles, FVR always reliably recovers the true sources. The competing methods have limitations in distinguishing close sources because their estimates are either too smooth (LORETA, Minimum ℓ 1 -norm) or too scattered (Minimum ℓ 2 -norm). In both noiseless and noisy simulations, FVR has the smallest localization error according to the Earth Mover's Distance (EMD), which is introduced here as a meaningful measure to compare arbitrary source distributions. We also apply the method to the simultaneous localization of left and right somatosensory N20 generators from real EEG recordings. Compared to its peers FVR was the only method that delivered correct location of the source in the somatosensory area of each hemisphere in accordance with neurophysiological prior knowledge.

NeurIPS Conference 2008 Conference Paper

Estimating vector fields using sparse basis field expansions

Stefan Haufe
Vadim Nikulin
Andreas Ziehe
Klaus-Robert Müller
Guido Nolte

We introduce a novel framework for estimating vector fields using sparse basis field expansions (S-FLEX). The notion of basis fields, which are an extension of scalar basis functions, arises naturally in our framework from a rotational invariance requirement. We consider a regression setting as well as inverse problems. All variants discussed lead to second-order cone programming formulations. While our framework is generally applicable to any type of vector field, we focus in this paper on applying it to solving the EEG/MEG inverse problem. It is shown that significantly more precise and neurophysiologically more plausible location and shape estimates of cerebral current sources from EEG/MEG measurements become possible with our method when comparing to the state-of-the-art.