Tom Heskes

Functional connectivity concerns the correlated activity between neuronal populations in spatially segregated regions of the brain, which may be studied using functional magnetic resonance imaging (fMRI). This coupled activity is conveniently expressed using covariance, but this measure fails to distinguish between direct and indirect effects. A popular alternative that addresses this issue is partial correlation, which regresses out the signal of potentially confounding variables, resulting in a measure that reveals only direct connections. Importantly, provided the data are normally distributed, if two variables are conditionally independent given all other variables, their respective partial correlation is zero. In this paper, we propose a probabilistic generative model that allows us to estimate functional connectivity in terms of both partial correlations and a graph representing conditional independencies. Simulation results show that this methodology is able to outperform the graphical LASSO, which is the de facto standard for estimating partial correlations. Furthermore, we apply the model to estimate functional connectivity for twenty subjects using resting-state fMRI data. Results show that our model provides a richer representation of functional connectivity as compared to considering partial correlations alone. Finally, we demonstrate how our approach can be extended in several ways, for instance to achieve data fusion by informing the conditional independence graph with data from probabilistic tractography. As our Bayesian formulation of functional connectivity provides access to the posterior distribution instead of only to point estimates, we are able to quantify the uncertainty associated with our results. This reveals that while we are able to infer a clear backbone of connectivity in our empirical results, the data are not accurately described by simply looking at the mode of the distribution over connectivity. The implication of this is that deterministic alternatives may misjudge connectivity results by drawing conclusions from noisy and limited data.

Attention-deficit/hyperactivity disorder (ADHD) is a common and highly heritable disorder affecting both children and adults. One of the candidate genes for ADHD is DAT1, encoding the dopamine transporter. In an attempt to clarify its mode of action, we assessed brain activity during the reward anticipation phase of the Monetary Incentive Delay (MID) task in a functional MRI paradigm in 87 adult participants with ADHD and 77 controls (average age 36.5 years). The MID task activates the ventral striatum, where DAT1 is most highly expressed. A previous analysis based on standard statistical techniques did not show any significant dependencies between a variant in the DAT1 gene and brain activation [Hoogman et al. (2013); Neuropsychopharm 23:469-478]. Here, we used an alternative method for analyzing the data, that is, causal modeling. The Bayesian Constraint-based Causal Discovery (BCCD) algorithm [Claassen and Heskes (2012); Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence] is able to find direct and indirect dependencies between variables, determines the strength of the dependencies, and provides a graphical visualization to interpret the results. Through BCCD one gets an opportunity to consider several variables together and to infer causal relations between them. Application of the BCCD algorithm confirmed that there is no evidence of a direct link between DAT1 genetic variability and brain activation, but suggested an indirect link mediated through inattention symptoms and diagnostic status of ADHD. Our finding of an indirect link of DAT1 with striatal activity during reward anticipation might explain existing discrepancies in the current literature. Further experiments should confirm this hypothesis. © 2015 Wiley Periodicals, Inc.

Better acquisition protocols and analysis techniques are making it possible to use fMRI to obtain highly detailed visualizations of brain processes. In particular we focus on the reconstruction of natural images from BOLD responses in visual cortex. We expand our linear Gaussian framework for percept decoding with Gaussian mixture models to better represent the prior distribution of natural images. Reconstruction of such images then boils down to probabilistic inference in a hybrid Bayesian network. In our set-up, different mixture components correspond to different character categories. Our framework can automatically infer higher-order semantic categories from lower-level brain areas. Furthermore, the framework can gate semantic information from higher-order brain areas to enforce the correct category during reconstruction. When categorical information is not available, we show that automatically learned clusters in the data give a similar improvement in reconstruction. The hybrid...

ABSTRACT We target the problem of accuracy and robustness in causal inference from finite data sets. Our aim is to combine the inherent robustness of the Bayesian approach with the theoretical strength and clarity of constraint-based methods. We use a Bayesian score to obtain probability estimates on the input statements used in a constraint-based procedure. These are subsequently processed in decreasing order of reliability, letting more reliable decisions take precedence in case of conflicts, until a single output model is obtained. Tests show that a basic implementation of the resulting Bayesian Constraint-based Causal Discovery (BCCD) algorithm already outperforms established procedures such as FCI and Conservative PC. It indicates which causal decisions in the output have high reliability and which do not. The approach is easily adapted to other application areas such as complex independence tests.

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We study the learning dynamics of neural networks from a general point of view. The environment from which the network learns is defined as a set of input stimuli. At discrete points in time, one of these stimuli is presented and an incremental learning step takes place. If the time between learning steps is drawn from a Poisson distribution, the