Justin R. Chumbley

False discovery rate revisited: FDR and topological inference using Gaussian random fields

In this note, we revisit earlier work on false discovery rate (FDR) and evaluate it in relation to topological inference in statistical parametric mapping. We note that controlling the false discovery rate of voxels is not equivalent to controlling the false discovery rate of activations. This is a problem that is unique to inference on images, in which the underlying signal is continuous (i.e., signal which does not have a compact support). In brief, inference based on conventional voxel-wise FDR procedures is not appropriate for inferences on the topological features of a statistical parametric map (SPM), such as peaks or regions of activation. We describe the nature of the problem, illustrate it with some examples and suggest a simple solution based on controlling the false discovery rate of connected excursion sets within an SPM, characterised by their volume.

Topological FDR for neuroimaging

In this technical note, we describe and validate a topological false discovery rate (FDR) procedure for statistical parametric mapping. This procedure is designed to deal with signal that is continuous and has, in principle, unbounded spatial support. We therefore infer on topological features of the signal, such as the existence of local maxima or peaks above some threshold. Using results from random field theory, we assign a p-value to each maximum in an SPM and identify an adaptive threshold that controls false discovery rate, using the Benjamini and Hochberg (BH) procedure (1995). This provides a natural complement to conventional family wise error (FWE) control on local maxima. We use simulations to contrast these procedures; both in terms of their relative number of discoveries and their spatial accuracy (via the distribution of the Euclidian distance between true and discovered activations). We also assessed two other procedures: cluster-wise and voxel-wise FDR procedures. Our results suggest that (a) FDR control of maxima or peaks is more sensitive than FWE control of peaks with minimal cost in terms of false-positives, (b) voxel-wise FDR is substantially less accurate than topological FWE or FDR control. Finally, we present an illustrative application using an fMRI study of visual attention.

Inhibition of the human two-pore domain potassium channel, TREK-1, by fluoxetine and its metabolite norfluoxetine.

1 Block of the human two‐pore domain potassium (2‐PK) channel TREK‐1 by fluoxetine (ProzacR) and its active metabolite, norfluoxetine, was investigated using whole‐cell patch‐clamp recording of currents through recombinant channels in tsA 201 cells. 2 Fluoxetine produced a concentration‐dependent inhibition of TREK‐1 current that was reversible on wash. The IC50 for block was 19 μM. Block by fluoxetine was voltage‐independent. Fluoxetine (100 μM) produced an 84% inhibition of TREK‐1 currents, but only a 31% block of currents through a related 2‐PK channel, TASK‐3. 3 Norfluoxetine was a more potent inhibitor of TREK‐1 currents with an IC50 of 9 μM. Block by norfluoxetine was also voltage‐independent. 4 Truncation of the C‐terminus of TREK‐1 (Δ89) resulted in a loss of channel function, which could be restored by intracellular acidification or the mutation E306A. The mutation E306A alone increased basal TREK‐1 current and resulted in a loss of the slow phase of TREK‐1 activation. 5 Progressive deletion of the C‐terminus of TREK‐1 had no effect on the inhibition of the channel by fluoxetine. The E306A mutation, on the other hand, reduced the magnitude of fluoxetine inhibition, with 100 μM producing only a 40% inhibition. 6 It is concluded that fluoxetine and norfluoxetine are potent inhibitors of TREK‐1. Block of TREK‐1 by fluoxetine may have important consequences when the drug is used clinically in the treatment of depression.

A Metropolis-Hastings algorithm for dynamic causal models

Dynamic causal modelling (DCM) is a modelling framework used to describe causal interactions in dynamical systems. It was developed to infer the causal architecture of networks of neuronal populations in the brain [Friston, K.J., Harrison, L, Penny, W., 2003. Dynamic causal modelling. NeuroImage. Aug; 19 (4): 1273-302]. In current formulations of DCM, the mean structure of the likelihood is a nonlinear and numerical function of the parameters, which precludes exact or analytic Bayesian inversion. To date, approximations to the posterior depend on the assumption of normality (i.e., the Laplace assumption). In particular, two arguments have been used to motivate normality of the prior and posterior distributions. First, Gaussian priors on the parameters are specified carefully to ensure that activity in the dynamic system of neuronal populations converges to a steady state (i.e., the dynamic system is dissipative). Secondly, normality of the posterior is an approximation based on general asymptotic results, regarding the form of the posterior under infinite data [Friston, K.J., Harrison, L, Penny, W., 2003. Dynamic causal modelling. NeuroImage. Aug; 19 (4): 1273-302]. Here, we provide a critique of these assumptions and evaluate them numerically. We use a Bayesian inversion scheme (the Metropolis-Hastings algorithm) that eschews both assumptions. This affords an independent route to the posterior and an external means to assess the performance of conventional schemes for DCM. It also allows us to assess the sensitivity of the posterior to different priors. First, we retain the conventional priors and compare the ensuing approximate posterior (Laplace) to the exact posterior (MCMC). Our analyses show that the Laplace approximation is appropriate for practical purposes. In a second, independent set of analyses, we compare the exact posterior under conventional priors with an exact posterior under newly defined uninformative priors. Reassuringly, we observe that the posterior is, for all practical purposes, insensitive of the choice of prior.

Variational Bayesian mixed-effects inference for classification studies

Multivariate classification algorithms are powerful tools for predicting cognitive or pathophysiological states from neuroimaging data. Assessing the utility of a classifier in application domains such as cognitive neuroscience, brain-computer interfaces, or clinical diagnostics necessitates inference on classification performance at more than one level, i.e., both in individual subjects and in the population from which these subjects were sampled. Such inference requires models that explicitly account for both fixed-effects (within-subjects) and random-effects (between-subjects) variance components. While models of this sort are standard in mass-univariate analyses of fMRI data, they have not yet received much attention in multivariate classification studies of neuroimaging data, presumably because of the high computational costs they entail. This paper extends a recently developed hierarchical model for mixed-effects inference in multivariate classification studies and introduces an efficient variational Bayes approach to inference. Using both synthetic and empirical fMRI data, we show that this approach is equally simple to use as, yet more powerful than, a conventional t-test on subject-specific sample accuracies, and computationally much more efficient than previous sampling algorithms and permutation tests. Our approach is independent of the type of underlying classifier and thus widely applicable. The present framework may help establish mixed-effects inference as a future standard for classification group analyses.

Functional lateralization of the anterior insula during feedback processing

Effective adaptive behavior rests on an appropriate understanding of how much responsibility we have over outcomes in the environment. This attribution of agency to ourselves or to an external event influences our behavioral and affective response to the outcomes. Despite its special importance to understanding human motivation and affect, the neural mechanisms involved in self‐attributed rewards and punishments remain unclear. Previous evidence implicates the anterior insula (AI) in evaluating the consequences of our own actions. However, it is unclear if the AI has a general role in feedback evaluation (positive and negative) or plays a specific role during error processing. Using functional magnetic resonance imaging and a motion prediction task, we investigate neural responses to self‐ and externally attributed monetary gains and losses. We found that attribution effects vary according to the valence of feedback: significant valence × attribution interactions in the right AI, the anterior cingulate cortex (ACC), the midbrain, and the right ventral putamen. Self‐attributed losses were associated with increased activity in the midbrain, the ACC and the right AI, and negative BOLD response in the ventral putamen. However, higher BOLD activity to self‐attributed feedback (losses and gains) was observed in the left AI, the thalamus, and the cerebellar vermis. These results suggest a functional lateralization of the AI. The right AI, together with the midbrain and the ACC, is mainly involved in processing the salience of the outcome, whereas the left is part of a cerebello‐thalamic‐cortical pathway involved in cognitive control processes important for subsequent behavioral adaptations. Hum Brain Mapp 35:4428–4439, 2014.

Learning and generalization under ambiguity: an fMRI study.

Adaptive behavior often exploits generalizations from past experience by applying them judiciously in new situations. This requires a means of quantifying the relative importance of prior experience and current information, so they can be balanced optimally. In this study, we ask whether the brain generalizes in an optimal way. Specifically, we used Bayesian learning theory and fMRI to test whether neuronal responses reflect context-sensitive changes in ambiguity or uncertainty about experience-dependent beliefs. We found that the hippocampus expresses clear ambiguity-dependent responses that are associated with an augmented rate of learning. These findings suggest candidate neuronal systems that may be involved in aberrations of generalization, such as over-confidence.

Endogenous Cortisol Predicts Decreased Loss Aversion in Young Men

Human and nonhuman animals respond asymmetrically to predicted punishments and rewards (Dayan & Seymour, 2008; Kahneman, 2011). In human decision making, for example, people pay more to avoid losses than to gain equivalent rewards. Because such loss aversion counterproductively diminishes an individual’s expected payoffs, it has become one of the most studied choice biases. It is unclear whether biological markers of punishment or stress exposure—most notably the glucocorticoid stress hormone cortisol of the hypothalamicpituitary-adrenal (HPA) axis—predict this particular form of behavioral punishment sensitivity. Acute glucocorticoid administration desensitizes subjects to threat and punishment, whereas chronic administration sensitizes them, increasing anxiety (Aerni et al., 2004; de Quervain & Margraf, 2008; Schelling et al., 2006; Soravia et al., 2006). This mirrors the mainstream view that acute stress responses are adaptive, whereas chronic exposure is detrimental (Chrousos, 2009). There is evidence that HPA-axis traits specifically undermine decision making. HPA disturbances predict addictive behavior (Koob & Kreek, 2007; Marinelli & Piazza, 2002; Putman, Antypa, Crysovergi, & van der Does, 2010; Sinha, 2008), and the relation between longterm HPA activity and pathological gambling (Wohl, Matheson, Young, & Anisman, 2008) may reflect altered punishment sensitivity. In nonclinical populations, the threat of financial loss (i.e., imminent poverty) chronically elevates cortisol (Haushofer, de Laat, & Chemin, 2012). Yet it is unknown whether chronically elevated cortisol, in turn, alters exposure to new losses by altering decision making. Such a feedback cycle might be adaptive (negative feedback) or maladaptive (positive feedback), depending on whether it limits or exacerbates financial loss. In the present study, we sidestepped the issue of causation and simply assessed whether an individual’s maladaptive loss aversion increased with chronic exposure to endogenous cortisol, which we assayed using hair samples.

Surprise Beyond Prediction Error

Surprise drives learning. Various neural “prediction error” signals are believed to underpin surprise‐based reinforcement learning. Here, we report a surprise signal that reflects reinforcement learning but is neither un/signed reward prediction error (RPE) nor un/signed state prediction error (SPE). To exclude these alternatives, we measured surprise responses in the absence of RPE and accounted for a host of potential SPE confounds. This new surprise signal was evident in ventral striatum, primary sensory cortex, frontal poles, and amygdala. We interpret these findings via a normative model of surprise. Hum Brain Mapp 35:4805–4814, 2014.

Fatal attraction: Ventral striatum predicts costly choice errors in humans

Animals approach rewards and cues associated with reward, even when this behavior is irrelevant or detrimental to the attainment of these rewards. Motivated by these findings we study the biology of financially-costly approach behavior in humans. Our subjects passively learned to predict the occurrence of erotic rewards. We show that neuronal responses in ventral striatum during this Pavlovian learning task stably predict an individuals general tendency towards financially-costly approach behavior in an active choice task several months later. Our data suggest that approach behavior may prevent some individuals from acting in their own interests.