Estimating anatomical trajectories with Bayesian mixed-effects modeling.

We introduce a mass-univariate framework for the analysis of whole-brain structural trajectories using longitudinal Voxel-Based Morphometry data and Bayesian inference. Our approach to developmental and aging longitudinal studies characterizes heterogeneous structural growth/decline between and within groups. In particular, we propose a probabilistic generative model that parameterizes individual and ensemble average changes in brain structure using linear mixed-effects models of age and subject-specific covariates. Model inversion uses Expectation Maximization (EM), while voxelwise (empirical) priors on the size of individual differences are estimated from the data. Bayesian inference on individual and group trajectories is realized using Posterior Probability Maps (PPM). In addition to parameter inference, the framework affords comparisons of models with varying combinations of model order for fixed and random effects using model evidence. We validate the model in simulations and real MRI data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) project. We further demonstrate how subject specific characteristics contribute to individual differences in longitudinal volume changes in healthy subjects, Mild Cognitive Impairment (MCI), and Alzheimer's Disease (AD).

Dynamic causal modelling for functional near-infrared spectroscopy.

Functional near-infrared spectroscopy (fNIRS) is an emerging technique for measuring changes in cerebral hemoglobin concentration via optical absorption changes. Although there is great interest in using fNIRS to study brain connectivity, current methods are unable to infer the directionality of neuronal connections. In this paper, we apply Dynamic Causal Modelling (DCM) to fNIRS data. Specifically, we present a generative model of how observed fNIRS data are caused by interactions among hidden neuronal states. Inversion of this generative model, using an established Bayesian framework (variational Laplace), then enables inference about changes in directed connectivity at the neuronal level. Using experimental data acquired during motor imagery and motor execution tasks, we show that directed (i.e., effective) connectivity from the supplementary motor area to the primary motor cortex is negatively modulated by motor imagery, and this suppressive influence causes reduced activity in the primary motor cortex during motor imagery. These results are consistent with findings of previous functional magnetic resonance imaging (fMRI) studies, suggesting that the proposed method enables one to infer directed interactions in the brain mediated by neuronal dynamics from measurements of optical density changes.

Efficient gradient computation for dynamical models.

Data assimilation is a fundamental issue that arises across many scales in neuroscience - ranging from the study of single neurons using single electrode recordings to the interaction of thousands of neurons using fMRI. Data assimilation involves inverting a generative model that can not only explain observed data but also generate predictions. Typically, the model is inverted or fitted using conventional tools of (convex) optimization that invariably extremise some functional - norms, minimum descriptive length, variational free energy, etc. Generally, optimisation rests on evaluating the local gradients of the functional to be optimized. In this paper, we compare three different gradient estimation techniques that could be used for extremising any functional in time - (i) finite differences, (ii) forward sensitivities and a method based on (iii) the adjoint of the dynamical system. We demonstrate that the first-order gradients of a dynamical system, linear or non-linear, can be computed most efficiently using the adjoint method. This is particularly true for systems where the number of parameters is greater than the number of states. For such systems, integrating several sensitivity equations - as required with forward sensitivities - proves to be most expensive, while finite-difference approximations have an intermediate efficiency. In the context of neuroimaging, adjoint based inversion of dynamical causal models (DCMs) can, in principle, enable the study of models with large numbers of nodes and parameters.

Comparing dynamic causal models using AIC, BIC and free energy.

In neuroimaging it is now becoming standard practise to fit multiple models to data and compare them using a model selection criterion. This is especially prevalent in the analysis of brain connectivity. This paper describes a simulation study which compares the relative merits of three model selection criteria (i) Akaike's Information Criterion (AIC), (ii) the Bayesian Information Criterion (BIC) and (iii) the variational Free Energy. Differences in performance are examined in the context of General Linear Models (GLMs) and Dynamic Causal Models (DCMs). We find that the Free Energy has the best model selection ability and recommend it be used for comparison of DCMs.

A general Bayesian treatment for MEG source reconstruction incorporating lead field uncertainty.

There is uncertainty introduced when a cortical surface based model derived from an anatomical MRI is used to reconstruct neural activity with MEG data. This is a specific case of a problem with uncertainty in parameters on which M/EEG lead fields depend non-linearly. Here we present a general mathematical treatment of any such problem with a particular focus on co-registration. We use a Metropolis search followed by Bayesian Model Averaging over multiple sparse prior source inversions with different headlocation/orientation parameters. Based on MEG data alone we can locate the cortex to within 4mm at empirically realistic signal to noise ratios. We also show that this process gives improved posterior distributions on the estimated current distributions, and can be extended to make inference on the locations of local maxima by providing confidence intervals for each source.

Ten simple rules for dynamic causal modeling.

Dynamic causal modeling (DCM) is a generic Bayesian framework for inferring hidden neuronal states from measurements of brain activity. It provides posterior estimates of neurobiologically interpretable quantities such as the effective strength of synaptic connections among neuronal populations and their context-dependent modulation. DCM is increasingly used in the analysis of a wide range of neuroimaging and electrophysiological data. Given the relative complexity of DCM, compared to conventional analysis techniques, a good knowledge of its theoretical foundations is needed to avoid pitfalls in its application and interpretation of results. By providing good practice recommendations for DCM, in the form of ten simple rules, we hope that this article serves as a helpful tutorial for the growing community of DCM users.

Testing for nested oscillation.

Nested oscillation occurs when the amplitude of a faster rhythm is coupled to the phase of a slower rhythm. It has been proposed to underlie the discrete nature of perception and the capacity of working memory and is a phenomenon observable in human brain imaging data. This paper compares three published methods for detecting nested oscillation and a fourth method proposed in this paper. These are: (i) the modulation index, (ii) the phase-locking value (PLV), (iii) the envelope-to-signal correlation (ESC) and (iv) a general linear model (GLM) measure derived from ESC. We applied the methods to electrocorticographic (ECoG) data recorded during a working-memory task and to data from a simulated hippocampal interneuron network. Further simulations were then made to address the dependence of each measure on signal to noise level, coupling phase, epoch length, sample rate, signal nonstationarity, and multi-phasic coupling. Our overall conclusion is that the GLM measure is the best all-round approach for detecting nested oscillation.

A validation of dynamic causal modelling for 7T fMRI.

BACKGROUND: There is growing interest in ultra-high field magnetic resonance imaging (MRI) in cognitive and clinical neuroscience studies. However, the benefits offered by higher field strength have not been evaluated in terms of effective connectivity and dynamic causal modelling (DCM). NEW METHOD: In this study, we address the validity of DCM for 7T functional MRI data at two levels. First, we evaluate the predictive validity of DCM estimates based upon 3T and 7T in terms of reproducibility. Second, we assess improvements in the efficiency of DCM estimates at 7T, in terms of the entropy of the posterior distribution over model parameters (i.e., information gain). RESULTS: Using empirical data recorded during fist-closing movements with 3T and 7T fMRI, we found a high reproducibility of average connectivity and condition-specific changes in connectivity - as quantified by the intra-class correlation coefficient (ICC = 0.862 and 0.936, respectively). Furthermore, we found that the posterior entropy of 7T parameter estimates was substantially less than that of 3T parameter estimates; suggesting the 7T data are more informative - and furnish more efficient estimates. COMPARED WITH EXISTING METHODS: In the framework of DCM, we treated field-dependent parameters for the BOLD signal model as free parameters, to accommodate fMRI data at 3T and 7T. In addition, we made the resting blood volume fraction a free parameter, because different brain regions can differ in their vascularization. CONCLUSIONS: In this paper, we showed DCM enables one to infer changes in effective connectivity from 7T data reliably and efficiently.

Sensor space group analysis for fNIRS data.

BACKGROUND: Functional near-infrared spectroscopy (fNIRS) is a method for monitoring hemoglobin responses using optical probes placed on the scalp. fNIRS spatial resolution is limited by the distance between channels defined as a pair of source and detector, and channel positions are often inconsistent across subjects. These challenges can lead to less accurate estimate of group level effects from channel-specific measurements. NEW METHOD: This paper addresses this shortcoming by applying random-effects analysis using summary statistics to interpolated fNIRS topographic images. Specifically, we generate individual contrast images containing the experimental effects of interest in a canonical scalp surface. Random-effects analysis then allows for making inference about the regionally specific effects induced by (potentially) multiple experimental factors in a population. RESULTS: We illustrate the approach using experimental data acquired during a colour-word matching Stroop task, and show that left frontopolar regions are significantly activated in a population during Stroop effects. This result agrees with previous neuroimaging findings. COMPARED WITH EXISTING METHODS: The proposed methods (i) address potential misalignment of sensor locations between subjects using spatial interpolation; (ii) produce experimental effects of interest either on a 2D regular grid or on a 3D triangular mesh, both representations of a canonical scalp surface; and (iii) enables one to infer population effects from fNIRS data using a computationally efficient summary statistic approach (random-effects analysis). Significance of regional effects is assessed using random field theory. CONCLUSIONS: In this paper, we have shown how fNIRS data from multiple subjects can be analysed in sensor space using random-effects analysis.

Generalization in multi-layer networks of Sigma-pi units.

This paper investigates a method for predicting the generalization error that a multi-layer network of Sigma-pi units will, on average, exhibit. Theoretical values are compared with those obtained by the computer simulation of small networks learning parity and contiguity functions.

Real-time brain-computer interfacing: a preliminary study using Bayesian learning.

Preliminary results from real-time 'brain-computer interface' experiments are presented. The analysis is based on autoregressive modelling of a single EEG channel coupled with classification and temporal smoothing under a Bayesian paradigm. It is shown that uncertainty in decisions is taken into account under such a formalism and that this may be used to reject uncertain samples, thus dramatically improving system performance. Using the strictest rejection method, a classification performance of 86.5 +/- 6.9% is achieved over a set of seven subjects in two-way cursor movement experiments.

Decoding oscillatory representations and mechanisms in memory.

A fundamental goal in memory research is to understand how information is represented in distributed brain networks and what mechanisms enable its reactivation. It is evident that progress towards this goal will greatly benefit from multivariate pattern classification (MVPC) techniques that can decode representations in brain activity with high temporal resolution. Recently, progress along these lines has been achieved by applying MVPC to neural oscillations recorded with electroencephalography (EEG) and magnetoencephalography (MEG). We highlight two examples of methodological approaches for MVPC of EEG and MEG data that can be used to study memory function. The first example aims at understanding the dynamic neural mechanisms that enable reactivation of memory representations, i.e., memory replay; we discuss how MVPC can help uncover the physiological mechanisms underlying memory replay during working memory maintenance and episodic memory. The second example aims at understanding representational differences between various types of memory, such as perceptual priming and conscious recognition memory. We also highlight the conceptual and methodological differences between these two examples. Finally, we discuss potential future applications for MVPC of EEG/MEG data in studies of memory. We conclude that despite its infancy and existing methodological challenges, MVPC of EEG and MEG data is a powerful tool with which to assess mechanistic models of memory.

A dynamical pattern recognition model of γ activity in auditory cortex.

This paper describes a dynamical process which serves both as a model of temporal pattern recognition in the brain and as a forward model of neuroimaging data. This process is considered at two separate levels of analysis: the algorithmic and implementation levels. At an algorithmic level, recognition is based on the use of Occurrence Time features. Using a speech digit database we show that for noisy recognition environments, these features rival standard cepstral coefficient features. At an implementation level, the model is defined using a Weakly Coupled Oscillator (WCO) framework and uses a transient synchronization mechanism to signal a recognition event. In a second set of experiments, we use the strength of the synchronization event to predict the high gamma (75-150 Hz) activity produced by the brain in response to word versus non-word stimuli. Quantitative model fits allow us to make inferences about parameters governing pattern recognition dynamics in the brain.

Dynamic Causal Models for phase coupling.

This paper presents an extension of the Dynamic Causal Modelling (DCM) framework to the analysis of phase-coupled data. A weakly coupled oscillator approach is used to describe dynamic phase changes in a network of oscillators. The use of Bayesian model comparison allows one to infer the mechanisms underlying synchronization processes in the brain. For example, whether activity is driven by master-slave versus mutual entrainment mechanisms. Results are presented on synthetic data from physiological models and on MEG data from a study of visual working memory.

Robust Bayesian General Linear Models.

We describe a Bayesian learning algorithm for Robust General Linear Models (RGLMs). 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 a robust estimation of regression coefficients. A variational inference framework is used to prevent overfitting and provides a model order selection criterion for noise model order. This allows the RGLM to default to the usual GLM when robustness is not required. The method is compared to other robust regression methods and applied to synthetic data and fMRI.

Bayesian neural networks for classification: how useful is the evidence framework?

This paper presents an empirical assessment of the Bayesian evidence framework for neural networks using four synthetic and four real-world classification problems. We focus on three issues; model selection, automatic relevance determination (ARD) and the use of committees. Model selection using the evidence criterion is only tenable if the number of training examples exceeds the number of network weights by a factor of five or ten. With this number of available examples, however, cross-validation is a viable alternative. The ARD feature selection scheme is only useful in networks with many hidden units and for data sets containing many irrelevant variables. ARD is also useful as a hard feature selection method. Results on applying the evidence framework to the real-world data sets showed that committees of Bayesian networks achieved classification accuracies similar to the best alternative methods. Importantly, this was achievable with a minimum of human intervention.

Dynamic models for nonstationary signal segmentation.

This paper investigates Hidden Markov Models (HMMs) in which the observations are generated from an autoregressive (AR) model. The overall model performs nonstationary spectral analysis and automatically segments a time series into discrete dynamic regimes. Because learning in HMMs is sensitive to initial conditions, we initialize the HMM model with parameters derived from a cluster analysis of Kalman filter coefficients. An important aspect of the Kalman filter implementation is that the state noise is estimated on-line. This allows for an initial estimation of AR parameters for each of the different dynamic regimes. These estimates are then fine-tuned with the HMM model. The method is demonstrated on a number of synthetic problems and on electroencephalogram data.

Neural network modeling of the level of observation decision in an acute psychiatric ward.

Patients in an acute psychiatric ward need to be observed with varying levels of closeness. We report a series of experiments in which neural networks were trained to model this "level of observation" decision. One hundred eighty-seven such clinical decisions were used to train and test the networks which were evaluated by a multitrial v-fold cross-validation procedure. One neural network modeling approach was to break down the decision process into four subproblems, each of which was solved by a perceptron unit. This resulted in a hierarchical perceptron network having a structure that was equivalent to a sparsely connected two-layer perceptron. Neural network approaches were compared with nearest neighbor, linear regression, and naive Bayes classifiers. The hierarchical and sparse neural networks were the most accurate classifiers. This shows that the decision process is nonlinear, that neural nets can be more accurate than other statistical approaches, and that hierarchical decomposition is a useful methodology for neural network design.

An empirical evaluation of Bayesian sampling with hybrid Monte Carlo for training neural network classifiers.

This article gives a concise overview of Bayesian sampling for neural networks, and then presents an extensive evaluation on a set of various benchmark classification problems. The main objective is to study the sensitivity of this scheme to changes in the prior distribution of the parameters and hyperparameters, and to evaluate the efficiency of the so-called automatic relevance determination (ARD) method. The article concludes with a comparison of the achieved classification results with those obtained with (i) the evidence scheme and (ii) with non-Bayesian methods.