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

A nonstationary nonparametric Bayesian approach to dynamically modeling effective connectivity in functional magnetic resonance imaging experiments

Effective connectivity analysis provides an understanding of the functional organization of the brain by studying how activated regions influence one other. We propose a nonparametric Bayesian approach to model effective connectivity assuming a dynamic nonstationary neuronal system. Our approach uses the Dirichlet process to specify an appropriate (most plausible according to our prior beliefs) dynamic model as the "expectation" of a set of plausible models upon which we assign a probability distribution. This addresses model uncertainty associated with dynamic effective connectivity. We derive a Gibbs sampling approach to sample from the joint (and marginal) posterior distributions of the unknowns. Results on simulation experiments demonstrate our model to be flexible and a better candidate in many situations. We also used our approach to analyzing functional Magnetic Resonance Imaging (fMRI) data on a Stroop task: our analysis provided new insight into the mechanism by which an individual brain distinguishes and learns about shapes of objects.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS470 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Disentangling causal webs in the brain using functional Magnetic Resonance Imaging: A review of current approaches

In the past two decades, functional Magnetic Resonance Imaging has been used to relate neuronal network activity to cognitive processing and behaviour. Recently this approach has been augmented by algorithms that allow us to infer causal links between component populations of neuronal networks. Multiple inference procedures have been proposed to approach this research question but so far, each method has limitations when it comes to establishing whole-brain connectivity patterns. In this work, we discuss eight ways to infer causality in fMRI research: Bayesian Nets, Dynamical Causal Modelling, Granger Causality, Likelihood Ratios, LiNGAM, Patel's Tau, Structural Equation Modelling, and Transfer Entropy. We finish with formulating some recommendations for the future directions in this area

Fast joint detection-estimation of evoked brain activity in event-related fMRI using a variational approach

In standard clinical within-subject analyses of event-related fMRI data, two steps are usually performed separately: detection of brain activity and estimation of the hemodynamic response. Because these two steps are inherently linked, we adopt the so-called region-based Joint Detection-Estimation (JDE) framework that addresses this joint issue using a multivariate inference for detection and estimation. JDE is built by making use of a regional bilinear generative model of the BOLD response and constraining the parameter estimation by physiological priors using temporal and spatial information in a Markovian modeling. In contrast to previous works that use Markov Chain Monte Carlo (MCMC) techniques to approximate the resulting intractable posterior distribution, we recast the JDE into a missing data framework and derive a Variational Expectation-Maximization (VEM) algorithm for its inference. A variational approximation is used to approximate the Markovian model in the unsupervised spatially adaptive JDE inference, which allows fine automatic tuning of spatial regularisation parameters. It follows a new algorithm that exhibits interesting properties compared to the previously used MCMC-based approach. Experiments on artificial and real data show that VEM-JDE is robust to model mis-specification and provides computational gain while maintaining good performance in terms of activation detection and hemodynamic shape recovery

Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience

This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet still unresolved issues of the detailed relationships among power law scaling, self-similarity, and self-organized criticality. As regards criticality, I will document that it has become a pivotal reference point in Neurodynamics. Furthermore, I will emphasize the not yet fully appreciated significance of allometric control processes. For dynamic fractals, I will assemble reasons for attributing to them the capacity to adapt task execution to contextual changes across a range of scales. The final Section consists of general reflections on the implications of the reviewed data, and identifies what appear to be issues of fundamental importance for future research in the rapidly evolving topic of this review

Fast spatial inference in the homogeneous Ising model

The Ising model is important in statistical modeling and inference in many applications, however its normalizing constant, mean number of active vertices and mean spin interaction are intractable. We provide accurate approximations that make it possible to calculate these quantities numerically. Simulation studies indicate good performance when compared to Markov Chain Monte Carlo methods and at a tiny fraction of the time. The methodology is also used to perform Bayesian inference in a functional Magnetic Resonance Imaging activation detection experiment.Comment: 18 pages, 1 figure, 3 table

Human Dorsal Striatal Activity during Choice Discriminates Reinforcement Learning Behavior from the Gambler’s Fallacy

Reinforcement learning theory has generated substantial interest in neurobiology, particularly because of the resemblance between phasic dopamine and reward prediction errors. Actor–critic theories have been adapted to account for the functions of the striatum, with parts of the dorsal striatum equated to the actor. Here, we specifically test whether the human dorsal striatum—as predicted by an actor–critic instantiation—is used on a trial-to-trial basis at the time of choice to choose in accordance with reinforcement learning theory, as opposed to a competing strategy: the gambler's fallacy. Using a partial-brain functional magnetic resonance imaging scanning protocol focused on the striatum and other ventral brain areas, we found that the dorsal striatum is more active when choosing consistent with reinforcement learning compared with the competing strategy. Moreover, an overlapping area of dorsal striatum along with the ventral striatum was found to be correlated with reward prediction errors at the time of outcome, as predicted by the actor–critic framework. These findings suggest that the same region of dorsal striatum involved in learning stimulus–response associations may contribute to the control of behavior during choice, thereby using those learned associations. Intriguingly, neither reinforcement learning nor the gambler's fallacy conformed to the optimal choice strategy on the specific decision-making task we used. Thus, the dorsal striatum may contribute to the control of behavior according to reinforcement learning even when the prescriptions of such an algorithm are suboptimal in terms of maximizing future rewards

Deciding when to decide : time-variant sequential sampling models explain the emergence of value-based decisions in the human brain

The cognitive and neuronal mechanisms of perceptual decision making have been successfully linked to sequential sampling models. These models describe the decision process as a gradual accumulation of sensory evidence over time. The temporal evolution of economic choices, however, remains largely unexplored. We tested whether sequential sampling models help to understand the formation of value-based decisions in terms of behavior and brain responses. We used functional magnetic resonance imaging (fMRI) to measure brain activity while human participants performed a buying task in which they freely decided upon how and when to choose. Behavior was accurately predicted by a time-variant sequential sampling model that uses a decreasing rather than fixed decision threshold to estimate the time point of the decision. Presupplementary motor area, caudate nucleus, and anterior insula activation was associated with the accumulation of evidence over time. Furthermore, at the beginning of the decision process the fMRI signal in these regions accounted for trial-by-trial deviations from behavioral model predictions: relatively high activation preceded relatively early responses. The updating of value information was correlated with signals in the ventromedial prefrontal cortex, left and right orbitofrontal cortex, and ventral striatum but also in the primary motor cortex well before the response itself. Our results support a view of value-based decisions as emerging from sequential sampling of evidence and suggest a close link between the accumulation process and activity in the motor system when people are free to respond at any time