Biomedical subjects

Jérémie Mattout

Publications and source records attributed to Jérémie Mattout.

8 recordsLinked to original sources

PubMed2006

Variational free energy and the Laplace approximation.

This note derives the variational free energy under the Laplace approximation, with a focus on accounting for additional model complexity induced by increasing the number of model parameters. This is relevant when using the free energy as an approximation to the log-evidence in Bayesian model averaging and selection. By setting restricted maximum likelihood (ReML) in the larger context of variational learning and expectation maximisation (EM), we show how the ReML objective function can be adjusted to provide an approximation to the log-evidence for a particular model. This means ReML can be used for model selection, specifically to select or compare models with different covariance components. This is useful in the context of hierarchical models because it enables a principled selection of priors that, under simple hyperpriors, can be used for automatic model selection and relevance determination (ARD). Deriving the ReML objective function, from basic variational principles, discloses the simple relationships among Variational Bayes, EM and ReML. Furthermore, we show that EM is formally identical to a full variational treatment when the precisions are linear in the hyperparameters. Finally, we also consider, briefly, dynamic models and how these inform the regularisation of free energy ascent schemes, like EM and ReML.

Bayes Theorem↗

PubMed2006

Dynamic causal modeling of evoked responses in EEG and MEG.

Neuronally plausible, generative or forward models are essential for understanding how event-related fields (ERFs) and potentials (ERPs) are generated. In this paper, we present a new approach to modeling event-related responses measured with EEG or MEG. This approach uses a biologically informed model to make inferences about the underlying neuronal networks generating responses. The approach can be regarded as a neurobiologically constrained source reconstruction scheme, in which the parameters of the reconstruction have an explicit neuronal interpretation. Specifically, these parameters encode, among other things, the coupling among sources and how that coupling depends upon stimulus attributes or experimental context. The basic idea is to supplement conventional electromagnetic forward models, of how sources are expressed in measurement space, with a model of how source activity is generated by neuronal dynamics. A single inversion of this extended forward model enables inference about both the spatial deployment of sources and the underlying neuronal architecture generating them. Critically, this inference covers long-range connections among well-defined neuronal subpopulations. In a previous paper, we simulated ERPs using a hierarchical neural-mass model that embodied bottom-up, top-down and lateral connections among remote regions. In this paper, we describe a Bayesian procedure to estimate the parameters of this model using empirical data. We demonstrate this procedure by characterizing the role of changes in cortico-cortical coupling, in the genesis of ERPs. In the first experiment, ERPs recorded during the perception of faces and houses were modeled as distinct cortical sources in the ventral visual pathway. Category-selectivity, as indexed by the face-selective N170, could be explained by category-specific differences in forward connections from sensory to higher areas in the ventral stream. We were able to quantify and make inferences about these effects using conditional estimates of connectivity. This allowed us to identify where, in the processing stream, category-selectivity emerged. In the second experiment, we used an auditory oddball paradigm to show that the mismatch negativity can be explained by changes in connectivity. Specifically, using Bayesian model selection, we assessed changes in backward connections, above and beyond changes in forward connections. In accord with theoretical predictions, there was strong evidence for learning-related changes in both forward and backward coupling. These examples show that category- or context-specific coupling among cortical regions can be assessed explicitly, within a mechanistic, biologically motivated inference framework.

Auditory Pathways↗

PubMed2006

Data-driven parceling and entropic inference in MEG.

In Amblard et al. [Amblard, C., Lapalme, E., Lina, J.M. 2004. Biomagnetic source detection by maximum entropy and graphical models. IEEE Trans. Biomed. Eng. 55 (3) 427--442], the authors introduced the maximum entropy on the mean (MEM) as a methodological framework for solving the magnetoencephalography (MEG) inverse problem. The main component of the MEM is a reference probability density that enables one to include all kind of prior information on the source intensity distribution to be estimated. This reference law also encompasses the definition of a model. We consider a distributed source model together with a clustering hypothesis that assumes functionally coherent dipoles. The reference probability distribution is defined as a prior parceling of the cortical surface. In this paper, we present a data-driven approach for parceling out the cortex into regions that are functionally coherent. Based on the recently developed multivariate source pre-localization (MSP) principle [Mattout, J., Pelegrini-Issac, M., Garnero, L., Benali, H. 2005. Multivariate source pre-localization (MSP): Use of functionally informed basis functions for better conditioning the MEG inverse problem. NeuroImage 26 (2) 356--373], the data-driven clustering (DDC) of the dipoles provides an efficient parceling of the sources as well as an estimate of parameters of the initial reference probability distribution. On MEG simulated data, the DDC is shown to further improve the MEM inverse approach, as evaluated considering two different iterative algorithms and using classical error metrics as well as ROC (receiver operating characteristic) curve analysis. The MEM solution is also compared to a LORETA-like inverse approach. The data-driven clustering allows to take most advantage of the MEM formalism. Its main trumps lie in the flexible probabilistic way of introducing priors and in the notion of spatial coherent regions of activation. The latter reduces the dimensionality of the problem. In so doing, it narrows down the gap between the two types of inverse methods, the popular dipolar approaches and the distributed ones.

Algorithms↗

PubMed2006

Bayesian estimation of evoked and induced responses.

We describe an extension of our empirical Bayes approach to magnetoencephalography/electroencephalography (MEG/EEG) source reconstruction that covers both evoked and induced responses. The estimation scheme is based on classical covariance component estimation using restricted maximum likelihood (ReML). We have focused previously on the estimation of spatial covariance components under simple assumptions about the temporal correlations. Here we extend the scheme, using temporal basis functions to place constraints on the temporal form of the responses. We show how the same scheme can estimate evoked responses that are phase-locked to the stimulus and induced responses that are not. For a single trial the model is exactly the same. In the context of multiple trials, however, the inherent distinction between evoked and induced responses calls for different treatments of the underlying hierarchical multitrial model. We derive the respective models and show how they can be estimated efficiently using ReML. This enables the Bayesian estimation of evoked and induced changes in power or, more generally, the energy of wavelet coefficients.

Algorithms↗

PubMed2006

Bayesian spatio-temporal approach for EEG source reconstruction: conciliating ECD and distributed models.

Characterizing the cortical activity sources of electroencephalography (EEG)/magnetoencephalography data is a critical issue since it requires solving an ill-posed inverse problem that does not admit a unique solution. Two main different and complementary source models have emerged: equivalent current dipoles (ECD) and distributed linear (DL) models. While ECD models remain highly popular since they provide an easy way to interpret the solutions, DL models (also referred to as imaging techniques) are known to be more realistic and flexible. In this paper, we show how those two representations of the brain electromagnetic activity can be cast into a common general framework yielding an optimal description and estimation of the EEG sources. From this extended source mixing model, we derive a hybrid approach whose key aspect is the separation between temporal and spatial characteristics of brain activity, which allows to dramatically reduce the number of DL model parameters. Furthermore, the spatial profile of the sources, as a temporal invariant map, is estimated using the entire time window data, allowing to significantly enhance the information available about the spatial aspect of the EEG inverse problem. A Bayesian framework is introduced to incorporate distinct temporal and spatial constraints on the solution and to estimate both parameters and hyperparameters of the model. Using simulated EEG data, the proposed inverse approach is evaluated and compared with standard distributed methods using both classical criteria and ROC curves.

Algorithms↗

PubMed2005

MEG source localization under multiple constraints: an extended Bayesian framework.

To use Electroencephalography (EEG) and Magnetoencephalography (MEG) as functional brain 3D imaging techniques, identifiable distributed source models are required. The reconstruction of EEG/MEG sources rests on inverting these models and is ill-posed because the solution does not depend continuously on the data and there is no unique solution in the absence of prior information or constraints. We have described a general framework that can account for several priors in a common inverse solution. An empirical Bayesian framework based on hierarchical linear models was proposed for the analysis of functional neuroimaging data [Friston, K., Penny, W., Phillips, C., Kiebel, S., Hinton, G., Ashburner, J., 2002. Classical and Bayesian inference in neuroimaging: theory. NeuroImage 16, 465-483] and was evaluated recently in the context of EEG [Phillips, C., Mattout, J., Rugg, M.D., Maquet, P., Friston, K., 2005. An empirical Bayesian solution to the source reconstruction problem in EEG. NeuroImage 24, 997-1011]. The approach consists of estimating the expected source distribution and its conditional variance that is constrained by an empirically determined mixture of prior variance components. Estimation uses Expectation-Maximization (EM) to give the Restricted Maximum Likelihood (ReML) estimate of the variance components (in terms of hyperparameters) and the Maximum A Posteriori (MAP) estimate of the source parameters. In this paper, we extend the framework to compare different combinations of priors, using a second level of inference based on Bayesian model selection. Using Monte-Carlo simulations, ReML is first compared to a classic Weighted Minimum Norm (WMN) solution under a single constraint. Then, the ReML estimates are evaluated using various combinations of priors. Both standard criterion and ROC-based measures were used to assess localization and detection performance. The empirical Bayes approach proved useful as: (1) ReML was significantly better than WMN for single priors; (2) valid location priors improved ReML source localization; (3) invalid location priors did not significantly impair performance. Finally, we show how model selection, using the log-evidence, can be used to select the best combination of priors. This enables a global strategy for multiple prior-based regularization of the MEG/EEG source reconstruction.

Bayes Theorem↗

PubMed2003

Localization Estimation Algorithm (LEA): a supervised prior-based approach for solving the EEG/MEG inverse problem.

Localizing and quantifying the sources of ElectroEncephaloGraphy (EEG) and MagnetoEncephaloGraphy (MEG) measurements is an ill-posed inverse problem, whose solution requires a spatial regularization involving both anatomical and functional priors. The distributed source model enables the introduction of such constraints. However, the resulting solution is unstable since the equation system one has to solve is badly conditioned and under-determined. We propose an original approach for solving the inverse problem, that allows to deal with a better-determined system and to temper the influence of priors according to their consistency with the measured EEG/MEG data. This Localization Estimation Algorithm (LEA) estimates the amplitude of a selected subset of sources, which are localized based on a prior distribution of activation probability. LEA is evaluated through numerical simulations and compared to a classical Weighted Minimum Norm estimation.

Algorithms↗

PubMed2003

Multivariate group effect analysis in functional Magnetic Resonance Imaging.

In functional MRI (fMRI), analysis of multisubject data typically involves spatially normalizing (i.e. co-registering in a common standard space) all data sets and summarizing results in a single group activation map. This widely used approach does not explicitely account for between-subject anatomo-functional variability. Therefore, we propose a group effect analysis method which makes use of a multivariate model to select the main signal variations that are common to all subjects, while allowing final statistical inference on the individual scale. The normalization step is thus avoided and individual anatomo-functional features are preserved. The approach is evaluated by using simulated data and it is shown that sensitivity is drastically improved compared to more conventional individual analysis.

Algorithms↗