Structure Learning in Coupled Dynamical Systems and Dynamic Causal Modelling

Identifying a coupled dynamical system out of many plausible candidates, each of which could serve as the underlying generator of some observed measurements, is a profoundly ill posed problem that commonly arises when modelling real world phenomena. In this review, we detail a set of statistical procedures for inferring the structure of nonlinear coupled dynamical systems (structure learning), which has proved useful in neuroscience research. A key focus here is the comparison of competing models of (ie, hypotheses about) network architectures and implicit coupling functions in terms of their Bayesian model evidence. These methods are collectively referred to as dynamical casual modelling (DCM). We focus on a relatively new approach that is proving remarkably useful; namely, Bayesian model reduction (BMR), which enables rapid evaluation and comparison of models that differ in their network architecture. We illustrate the usefulness of these techniques through modelling neurovascular coupling (cellular pathways linking neuronal and vascular systems), whose function is an active focus of research in neurobiology and the imaging of coupled neuronal systems

Learning Discriminative Bayesian Networks from High-dimensional Continuous Neuroimaging Data

Due to its causal semantics, Bayesian networks (BN) have been widely employed to discover the underlying data relationship in exploratory studies, such as brain research. Despite its success in modeling the probability distribution of variables, BN is naturally a generative model, which is not necessarily discriminative. This may cause the ignorance of subtle but critical network changes that are of investigation values across populations. In this paper, we propose to improve the discriminative power of BN models for continuous variables from two different perspectives. This brings two general discriminative learning frameworks for Gaussian Bayesian networks (GBN). In the first framework, we employ Fisher kernel to bridge the generative models of GBN and the discriminative classifiers of SVMs, and convert the GBN parameter learning to Fisher kernel learning via minimizing a generalization error bound of SVMs. In the second framework, we employ the max-margin criterion and build it directly upon GBN models to explicitly optimize the classification performance of the GBNs. The advantages and disadvantages of the two frameworks are discussed and experimentally compared. Both of them demonstrate strong power in learning discriminative parameters of GBNs for neuroimaging based brain network analysis, as well as maintaining reasonable representation capacity. The contributions of this paper also include a new Directed Acyclic Graph (DAG) constraint with theoretical guarantee to ensure the graph validity of GBN.Comment: 16 pages and 5 figures for the article (excluding appendix

Modeling Dynamic Functional Connectivity with Latent Factor Gaussian Processes

Dynamic functional connectivity, as measured by the time-varying covariance of neurological signals, is believed to play an important role in many aspects of cognition. While many methods have been proposed, reliably establishing the presence and characteristics of brain connectivity is challenging due to the high dimensionality and noisiness of neuroimaging data. We present a latent factor Gaussian process model which addresses these challenges by learning a parsimonious representation of connectivity dynamics. The proposed model naturally allows for inference and visualization of time-varying connectivity. As an illustration of the scientific utility of the model, application to a data set of rat local field potential activity recorded during a complex non-spatial memory task provides evidence of stimuli differentiation

Comparing families of dynamic causal models

Mathematical models of scientific data can be formally compared using Bayesian model evidence. Previous applications in the biological sciences have mainly focussed on model selection in which one first selects the model with the highest evidence and then makes inferences based on the parameters of that model. This “best model” approach is very useful but can become brittle if there are a large number of models to compare, and if different subjects use different models. To overcome this shortcoming we propose the combination of two further approaches: (i) family level inference and (ii) Bayesian model averaging within families. Family level inference removes uncertainty about aspects of model structure other than the characteristic of interest. For example: What are the inputs to the system? Is processing serial or parallel? Is it linear or nonlinear? Is it mediated by a single, crucial connection? We apply Bayesian model averaging within families to provide inferences about parameters that are independent of further assumptions about model structure. We illustrate the methods using Dynamic Causal Models of brain imaging data

Knowing what you know in brain segmentation using Bayesian deep neural networks

In this paper, we describe a Bayesian deep neural network (DNN) for predicting FreeSurfer segmentations of structural MRI volumes, in minutes rather than hours. The network was trained and evaluated on a large dataset (n = 11,480), obtained by combining data from more than a hundred different sites, and also evaluated on another completely held-out dataset (n = 418). The network was trained using a novel spike-and-slab dropout-based variational inference approach. We show that, on these datasets, the proposed Bayesian DNN outperforms previously proposed methods, in terms of the similarity between the segmentation predictions and the FreeSurfer labels, and the usefulness of the estimate uncertainty of these predictions. In particular, we demonstrated that the prediction uncertainty of this network at each voxel is a good indicator of whether the network has made an error and that the uncertainty across the whole brain can predict the manual quality control ratings of a scan. The proposed Bayesian DNN method should be applicable to any new network architecture for addressing the segmentation problem.Comment: Submitted to Frontiers in Neuroinformatic

Meta-analysis of functional neuroimaging data using Bayesian nonparametric binary regression

In this work we perform a meta-analysis of neuroimaging data, consisting of locations of peak activations identified in 162 separate studies on emotion. Neuroimaging meta-analyses are typically performed using kernel-based methods. However, these methods require the width of the kernel to be set a priori and to be constant across the brain. To address these issues, we propose a fully Bayesian nonparametric binary regression method to perform neuroimaging meta-analyses. In our method, each location (or voxel) has a probability of being a peak activation, and the corresponding probability function is based on a spatially adaptive Gaussian Markov random field (GMRF). We also include parameters in the model to robustify the procedure against miscoding of the voxel response. Posterior inference is implemented using efficient MCMC algorithms extended from those introduced in Holmes and Held [Bayesian Anal. 1 (2006) 145--168]. Our method allows the probability function to be locally adaptive with respect to the covariates, that is, to be smooth in one region of the covariate space and wiggly or even discontinuous in another. Posterior miscoding probabilities for each of the identified voxels can also be obtained, identifying voxels that may have been falsely classified as being activated. Simulation studies and application to the emotion neuroimaging data indicate that our method is superior to standard kernel-based methods.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS523 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org