nils-herrmann/clean_scirepeval huggingface dataset:
Cognitive tasks for driving a brain-computer interfacing system: a pilot study

Different cognitive tasks were investigated for use with a brain-computer interface (BCI). The main aim was to evaluate which two of several candidate tasks lead to patterns of electroencephalographic (EEG) activity that could be differentiated most reliably and, therefore, produce the highest communication rate. An optimal signal processing method was also sought to enhance differentiation of EEG profiles across tasks. In ten normal subjects (five male), aged 29-54 years, EEG activity was recorded from four channels during cognitive tasks grouped in pairs, and performed alternately. Four imagery tasks were: spatial navigation around a familiar environment; auditory imagery of a familiar tune; and right and left motor imagery of opening and closing the hand. Signal processing methodology included autoregressive (AR) modeling and classification based on logistic regression and a nonlinear generative classifier. The highest communication rate was found using the navigation and auditory imagery tasks. In terms of classification performance and, hence, possible communication rate, these results were significantly better (p<0.05) than those obtained with the classical pairing of motor tasks involving imaginary movements of the left and right hands. In terms of EEG data analysis, a nonlinear classification model provided more robust results than a linear model (p/spl Lt/0.01), and a lower AR model order than those used in previous work was found to be effective. These findings have implications for establishing appropriate methods to operate BCI systems, particularly for disabled people who may experience difficulty with motor tasks, even motor imagery.
Mixtures of general linear models for functional neuroimaging

We set out a new general framework for making inferences from neuroimaging data, which includes a standard approach to neuroimaging analysis, statistical parametric mapping (SPM), as a special case. The model offers numerous conceptual and statistical advantages that derive from analyzing data at the "cluster level" rather than the "voxel level" and from explicit modeling of the shape and position of clusters of activation. This provides a natural and principled way to pool data from nearby voxels for parameter and variance-component estimation. The model can also be viewed as performing a spatio-temporal cluster analysis. The parameters of the model are estimated using an expectation maximization (EM) algorithm.
Hierarchical Models

Hierarchical models are central to many current analyses of functional imaging data including random effects analysis, models using fMRI as priors for EEG source localization and spatiotemporal Bayesian modelling of imaging data . These hierarchical models posit linear relations between variables with error terms that are Gaussian. The General Linear Model (GLM), which to date has been so central to the analysis of functional imaging data, is a special case of these hierarchical models consisting of just a single layer. Model fitting and statistical inference for hierarchical models can be implemented using a Parametric Empirical Bayes (PEB) algorithm described in Chapter 17 and in . The algorithm is sufficiently general to accomodate multiple levels in the hierarchy and allows for the error covariances to take on arbitrary form. This generality is particularly appealing as it renders the method applicable to a wide variety of modelling scenarios. Because of this generality, however, and the complexity of scenarios in which the method is applied, readers wishing to learn about PEB for the first time are advised to read this chapter first. We provide an introduction to hierarchical models and focus on some relatively simple examples. Each model and PEB algorithm we present is a special case of that described in . Whilst there are a number of tutorials on hierarchical modelling [9],[2] what we describe here has been tailored for functional imaging applications. We also note that a tutorial on hierarchical models is, to our minds, also a tutorial on Bayesian inference as higher levels act as priors for parameters in lower levels. Readers are therefore encouraged to also consult background texts on Bayesian inference, such as . We restrict our attention to two-level models and show, in section 2, how one computes the posterior distributions over the firstand second-level parameters. These are derived, initially, for completely general design and error covariance matrices. We then consider two special cases (i) models with equal error variances and (ii) separable models. In section 3 of the chapter we show how the parameters and covariance components can be estimated using PEB. In section 4 we show how a two-level hierarchical model can be used for Random-Effects Analysis. For equal subject error variances at the first level and the same first-level design matrices (ie. balanced designs) we show that
Bayesian nonstationary autoregressive models for biomedical signal analysis

We describe a variational Bayesian algorithm for the estimation of a multivariate autoregressive model with time-varying coefficients that adapt according to a linear dynamical system. The algorithm allows for time and frequency domain characterization of nonstationary multivariate signals and is especially suited to the analysis of event-related data. Results are presented on synthetic data and real electroencephalogram data recorded in event-related desynchronization and photic synchronization scenarios.
Variational Bayes for generalized autoregressive models

We describe a variational Bayes (VB) learning algorithm for generalized autoregressive (GAR) models. The noise is modeled as a mixture of Gaussians rather than the usual single Gaussian. This allows different data points to be associated with different noise levels and effectively provides robust estimation of AR coefficients. The VB framework is used to prevent overfitting and provides model-order selection criteria both for AR order and noise model order. We show that for the special case of Gaussian noise and uninformative priors on the noise and weight precisions, the VB framework reduces to the Bayesian evidence framework. The algorithm is applied to synthetic and real data with encouraging results.
Bayesian multivariate autoregressive models with structured priors

A variational Bayesian (VB) learning algorithm for parameter estimation and model-order selection in multivariate autoregressive (MAR) models is described. The use of structured priors in which subsets of coefficients are grouped together and constrained to be of a similar magnitude is explored. This allows MAR models to be more readily applied to high-dimensional data and to data with greater temporal complexity. The VB model order selection criterion is compared with the minimum description length approach. Results are presented on synthetic and electroencephalogram data.
An EM algorithm for Gaussian Markov Random Fields

Lavine [7] has shown how 1-dimensional Linear Dynamical Systems (LDS’s) can be used for exact inference in 2(or higher) dimensional Gaussian Markov Random Fields (GMRFs). His trick is to relate the row of an image to the state of the LDS and introduce pseudoobservations (which turn out to be zero) such that the evolution equation implements vertical neighbour contstraints and the observation equation implements horizontal neighbour constraints. Thus, exact inference can take place using Kalman smoothing. In this report we show how nonstationary smoothness parameters can be estimated using the M-step of the EM algorithm for LDS’s.
Random-Effects Analysis

Neuroimaging data from multiple subjects can be analysed using fixedeffects (FFX) or random-effects (RFX) analysis. FFX analysis is used for reporting case studies and RFX is used to make inferences about the population from which subjects are drawn. We demonstrate both methods on data from a multiple subject PET study and describe the mathematical basis of the two approaches. Finally, in neuroimaging, RFX is implemented using the computationally efficient ‘summary-statistic’ approach. We show that this is mathematically equivalent to the more computationally demanding maximum likelihood procedure.
Effective Connectivity and Intersubject Variability: Using a Multisubject Network to Test Differences and Commonalities

This article is about intersubject variability in the functional integration of activity in different brain regions. Previous studies of functional and effective connectivity have dealt with intersubject variability by analyzing data from different subjects separately or pretending the data came from the same subject. These approaches do not allow one to test for differences among subjects. The aim of this work was to illustrate how differences in connectivity among subjects can be addressed explicitly using structural equation modeling. This is enabled by constructing a multisubject network that comprises m regions of interest for each of the n subjects studied, resulting in a total of m x n nodes. Constructing a network of regions from different subjects may seem counterintuitive but embodies two key advantages. First, it allows one to test directly for differences among subjects by comparing models that do and do not allow a particular connectivity parameter to vary over subjects. Second, a multisubject network provides additional degrees of freedom to estimate the model's free parameters. Any neurobiological hypothesis normally addressed by single-subject or group analyses can still be tested, but with greater sensitivity. The common influence of experimental variables is modeled by connecting a virtual node, whose time course reflects stimulus onsets, to the sensory or "input" region in all subjects. Further experimental changes in task or cognitive set enter through modulation of the connections. This approach allows one to model both endogenous (or intrinsic) variance and exogenous effects induced by experimental design. We present a functional magnetic resonance imaging study that uses a multisubject network to investigate intersubject variability in functional integration in the context of single word and pseudoword reading. We tested whether the effect of word type on the reading-related coupling differed significantly among subjects. Our results showed that a number of forward and backward connections were stronger for reading pseudowords than words, and, in one case, connectivity showed significant intersubject variability. The discussion focuses on the implications of our findings and on further applications of the multisubject network analysis.
Variational Bayes for Generalized

We describe a variational Bayes (VB) learning algo- rithm for generalized autoregressive (GAR) models. The noise is modeled as a mixture of Gaussians rather than the usual single Gaussian. This allows different data points to be associated with different noise levels and effectively provides robust estimation of AR coefficients. The VB framework is used to prevent overfitting and provides model-order selection criteria both for AR order and noise model order. We show that for the special case of Gaussian noise and uninformative priors on the noise and weight precisions, the VB framework reduces to the Bayesian evidence framework. The algorithm is applied to synthetic and real data with encour- aging results.
Bayesian inference and posterior probability maps

This paper describes the construction of posterior probability maps that enable conditional or Bayesian inferences about regionally-specific effects in neuroimaging. Posterior probability maps are images of the probability or confidence that an activation or effect exceeds some specified threshold, given the data. Posterior probability maps (PPMs) represent a complementary alternative to statistical parametric maps (SPMs) that are used to make classical inferences. However, a key problem in Bayesian inference is the specification of appropriate priors. This problem can be eschewed by using empirical Bayes in which prior variances are estimated from the data, under some simple assumptions about their form. Empirical Bayes requires a hierarchical observation model, in which higher levels can be regarded as providing prior constraints on lower levels. In neuroimaging observations of the same effect over voxels provides a natural, two-level hierarchy that enables an empirical Bayesian approach. We present a brief motivation and the operational details of a simple empirical Bayesian method for computing posterior probability maps. We then compare Bayesian and classical inference through the equivalent PPMs and SPMs testing for the same effects in the same data.
Wavelet smoothing of fMRI activation images

Images from functional imaging experiments are subject to a data processing stream involving motion correction and spatial normalization. The next step is then to smooth the images using a Gaussian kernel. One reason for the smoothing step is to render activation information amenable to classical statistical inference via Random Field Theory. This requires that the residual fields have a smoothness, measured by the Full Width at Half Maximum (FWHM) of a Gaussian kernel, that is of the order of three times the voxel edge size. If one were to abandon the classical inference framework in favour of Bayesian inference however, see eg. , then the above motivation for smoothing disappears. This then leaves the second reason for smoothing which derives from the fact that a point mass of neural activity gives rise to a spatially extended hemodynamic response, the relation being defined by the spatial hemodynamic Point Response Function (PRF). If one assumes that the PRF is Gaussian with a known FWHM, then one can increase the Signal-to-Noise Ratio (SNR) in functional images by smoothing with that kernel. Overor under specification of the FWHM, however, will lead to suboptimal increase in SNR. Further, if the PRF is non-stationary then smoothing with a fixed size Gaussian kernel is clearly sub-optimal. This provides the motivation for smoothing with other methods such as wavelets.
Classical and Bayesian Inference in Neuroimaging: Theory

This paper reviews hierarchical observation models, used in functional neuroimaging, in a Bayesian light. It emphasizes the common ground shared by classical and Bayesian methods to show that conventional analyses of neuroimaging data can be usefully extended within an empirical Bayesian framework. In particular we formulate the procedures used in conventional data analysis in terms of hierarchical linear models and establish a connection between classical inference and parametric empirical Bayes (PEB) through covariance component estimation. This estimation is based on an expectation maximization or EM algorithm. The key point is that hierarchical models not only provide for appropriate inference at the highest level but that one can revisit lower levels suitably equipped to make Bayesian inferences. Bayesian inferences eschew many of the difficulties encountered with classical inference and characterize brain responses in a way that is more directly predicated on what one is interested in. The motivation for Bayesian approaches is reviewed and the theoretical background is presented in a way that relates to conventional methods, in particular restricted maximum likelihood (ReML). This paper is a technical and theoretical prelude to subsequent papers that deal with applications of the theory to a range of important issues in neuroimaging. These issues include; (i) Estimating nonsphericity or variance components in fMRI time-series that can arise from serial correlations within subject, or are induced by multisubject (i.e., hierarchical) studies. (ii) Spatiotemporal Bayesian models for imaging data, in which voxels-specific effects are constrained by responses in other voxels. (iii) Bayesian estimation of nonlinear models of hemodynamic responses and (iv) principled ways of mixing structural and functional priors in EEG source reconstruction. Although diverse, all these estimation problems are accommodated by the PEB framework described in this paper.
Mixtures of Independent Component Analysers

Gaussian Mixture Models (GMMs) are widely used throughout the fields of machine learning and statistics. Despite their popularity, however, GMMs suffer from two serious drawbacks. The first is that, as the dimensionality d of the problem space increases, the size of each covariance matrix, d 2, becomes prohibitively large. This can be dealt with by assuming isotropic Gaussians (ie.ignoring the covariance structure) but this greatly reduces the flexibility of the model class. This problem has been solved by Tipping and Bishop  who replaced each Gaussian with a probabilistic Principal Component Analysis (PCA) model. This allowed the dimensionality of each covariance to be effectively reduced whilst maintaining the richness of the model class. The second problem with GMMs is that each component is a Gaussian, an assumption which is often violated in many natural clustering problems [5]. It is this second problem which we address in this paper. A solution is reached by extending the mixtures of probabilistic PCA model to a mixtures of Independent Component Analysis (ICA) model.
ICA: model order selection and dynamic source models

In this chapter we investigate ICA models in which the number of sources, M , may be less than the number of sensors, N ; so-called non-square mixing. The 'extra' sensor observations are explained as observation noise. This general approach may be called Probabilistic Independent Component Analysis (PICA) by analogy with the Probabilistic Principal Component Analysis (PPCA) model of (11); ICA and PCA don't have observation noise, PICA and PPCA do. Non-square ICA models give rise to a likelihood model for the data involving an integral which is intractable. In this chapter we build on previous work in which the integral is estimated using a Laplace approximation. By making the further assumption that the unmixing matrix lies on the decorrelating manifold we are able to make a number of simplifications. Firstly, the observation noise can be estimated using PCA methods, and, secondly, optimisation takes place in a space having a much reduced dimensionality; having order M 2 parameters rather than M × N. Again, building on previous work, we derive a model order selection criterion for selecting the appropriate number of sources. This is based on the Laplace approximation as applied to the decorrelating manifold and is compared with PCA model order selection methods. Standard ICA, if there is such a thing, is not a proper time series model, as each source is considered to be Independent and Identically Distributed (IID). But with dynamic source models, temporal information is used and, as we show, this can lead to much improved source estimation. The second part of this chapter looks at the use of such dynamic source models, where the sources are modelled using a generalised autoregressive (GAR) process. This is the usual autoregressive process 1
Variational Bayes for non-Gaussian autoregressive models

We describe a variational Bayesian (VB) learning algorithm for Non-Gaussian Autoregressive (AR) models. The noise is modelled as a mixture of Gaussians rather than the usual single Gaussian. This allows different data points to be associated with different noise levels and effectively provides a robust estimation of AR coefficients. The VB framework is used to prevent overfitting and provides model order selection criteria both for AR order and noise model order. The algorithm is applied to synthetic data and to EEG.
An ensemble learning approach to independent component analysis

Independent Component Analysis (ICA) is an important tool for extracting structure from data. ICA is traditionally performed under a maximum likelihood scheme in a latent variable model and in the absence of noise. Although extensively utilised maximum likelihood estimation has well known drawbacks such as overfitting and sensitivity to local-maxima. We propose a Bayesian learning scheme, Variational Bayes or Ensemble Learning, for both latent variables and parameters in the model.
Hidden Markov independent components for biosignal analysis

Much research in unsupervised learning builds on the idea of using generative models for modelling the probability distribution over a set of observations. These approaches suggest that powerful new data analysis tools may be derived by combining existing models using a probabilistic generative framework. We follow this approach and combine hidden Markov models (HMMs), independent component analysis (ICA) and generalised autoregressive models (GAR) into a single generative model for the analysis of nonstationary multivariate time series. Our motivation for this work derives from our desire to analyse biomedical signals which are known to be highly non-stationary. Moreover, in signals such as the electroencephalogram (EEG), for example, we have a number of sensors (electrodes) which detect signals emanating from a number of cortical sources via an unknown mixing process. This naturally fits an ICA approach which is further enhanced by noting that the sources themselves are characterised by their dynamic content. This leads us to the use of generalised autoregressive (GAR) processes to model the sources.
Bayesian methods for autoregressive models

We describe a variational Bayesian (VB) learning algorithm for parameter estimation and model order selection in antoregressive (AR) models. With uninformative priors on the precisions of the coefficient and noise distributions the VB framework is shown to be identical to the Bayesian evidence framework. The VB model order selection criterion is compared with the minimum description length (MDL) criterion on synthetic data and on EEG.
The Bayesian Paradigm: Second Generation Neural Computing

When reasoning in the presence of uncertainty there is a unique and self-consistent set of rules for induction and model selection – Bayesian inference. Recent advances in neural networks have been fuelled by the adoption of this Bayesian framework, either implicitly, for example through the use of committees, or explicitly through Bayesian evidence and sampling frameworks. In this chapter, we show how this ‘second generation’ of neural network techniques can be applied to biomedical data and focus on the networks’ ability to provide assessments of the confidence associated with its predictions. This is an essential requirement for any automatic biomedical pattern recognition system. It allows low confidence decisions to be highlighted and deferred, possibly to a human expert, and falls naturally out of the Bayesian framework.
Hidden Markov Independent Component Analysis

We propose a generative model for the analysis of non-stationary multivariate time series. The model uses a hidden Markov process to switch between independent component models where the components themselves are modelled as generalised autoregressive processes. The model is demonstrated on synthetic problems and EEG data. Much recent research in unsupervised learning [17,20] builds on the idea of using generative models  for modelling the probability distribution over a set of observations. These approaches suggest that powerful new data analysis tools may be derived by combining existing models using a probabilistic ‘generative’ framework. In this paper, we follow this approach and combine hidden Markov models (HMM), Independent Component Analysis (ICA) and generalised autoregressive models (GAR) into a single generative model for the analysis of non-stationary multivariate time series.