Scene Construction, Visual Foraging, and Active Inference

This paper describes an active inference scheme for visual searches and the perceptual synthesis entailed by scene construction. Active inference assumes that perception and action minimize variational free energy, where actions are selected to minimize the free energy expected in the future. This assumption generalizes risk-sensitive control and expected utility theory to include epistemic value; namely, the value (or salience) of information inherent in resolving uncertainty about the causes of ambiguous cues or outcomes. Here, we apply active inference to saccadic searches of a visual scene. We consider the (difficult) problem of categorizing a scene, based on the spatial relationship among visual objects where, crucially, visual cues are sampled myopically through a sequence of saccadic eye movements. This means that evidence for competing hypotheses about the scene has to be accumulated sequentially, calling upon both prediction (planning) and postdiction (memory). Our aim is to highlight some simple but fundamental aspects of the requisite functional anatomy; namely, the link between approximate Bayesian inference under mean field assumptions and functional segregation in the visual cortex. This link rests upon the (neurobiologically plausible) process theory that accompanies the normative formulation of active inference for Markov decision processes. In future work, we hope to use this scheme to model empirical saccadic searches and identify the prior beliefs that underwrite intersubject variability in the way people forage for information in visual scenes (e.g., in schizophrenia). Copyright © 2016 Mirza, Adams, Mathys, Friston

Attractor-like dynamics in belief updating in schizophrenia

Subjects with a diagnosis of schizophrenia (Scz) overweight unexpected evidence in probabilistic inference: such evidence becomes 'aberrantly salient'. A neurobiological explanation for this effect is that diminished synaptic gain (e.g. hypofunction of cortical N-methyl-D-aspartate receptors) in Scz destabilizes quasi-stable neuronal network states (or 'attractors'). This attractor instability account predicts that i) Scz would overweight unexpected evidence but underweight consistent evidence, ii) belief updating would be more vulnerable to stochastic fluctuations in neural activity, and iii) these effects would correlate.Hierarchical Bayesian belief updating models were tested in two independent datasets (n=80 and n=167, male and female) comprising human subjects with schizophrenia, and both clinical and non-clinical controls (some tested when unwell and on recovery) performing the 'probability estimates' version of the beads task (a probabilistic inference task). Models with a standard learning rate, or including a parameter increasing updating to 'disconfirmatory evidence', or a parameter encoding belief instability were formally compared.The 'belief instability' model (based on the principles of attractor dynamics) had most evidence in all groups in both datasets. Two of four parameters differed between Scz and non-clinical controls in each dataset: belief instability and response stochasticity. These parameters correlated in both datasets. Furthermore, the clinical controls showed similar parameter distributions to Scz when unwell, but were no different to controls once recovered.These findings are consistent with the hypothesis that attractor network instability contributes to belief updating abnormalities in Scz, and suggest that similar changes may exist during acute illness in other psychiatric conditions.SIGNIFICANCE STATEMENTSubjects with a diagnosis of schizophrenia (Scz) make large adjustments to their beliefs following unexpected evidence, but also smaller adjustments than controls following consistent evidence. This has previously been construed as a bias towards 'disconfirmatory' information, but a more mechanistic explanation may be that in Scz, neural firing patterns ('attractor states') are less stable and hence easily altered in response to both new evidence and stochastic neural firing. We model belief updating in Scz and controls in two independent datasets using a hierarchical Bayesian model, and show that all subjects are best fit by a model containing a belief instability parameter. Both this and a response stochasticity parameter are consistently altered in Scz, as the unstable attractor hypothesis predicts

Spatial attention, precision, and Bayesian inference: a study of saccadic response speed

Inferring the environment's statistical structure and adapting behavior accordingly is a fundamental modus operandi of the brain. A simple form of this faculty based on spatial attentional orienting can be studied with Posner's location-cueing paradigm in which a cue indicates the target location with a known probability. The present study focuses on a more complex version of this task, where probabilistic context (percentage of cue validity) changes unpredictably over time, thereby creating a volatile environment. Saccadic response speed (RS) was recorded in 15 subjects and used to estimate subject-specific parameters of a Bayesian learning scheme modeling the subjects' trial-by-trial updates of beliefs. Different response models-specifying how computational states translate into observable behavior-were compared using Bayesian model selection. Saccadic RS was most plausibly explained as a function of the precision of the belief about the causes of sensory input. This finding is in accordance with current Bayesian theories of brain function, and specifically with the proposal that spatial attention is mediated by a precision-dependent gain modulation of sensory input. Our results provide empirical support for precision-dependent changes in beliefs about saccade target locations and motivate future neuroimaging and neuropharmacological studies of how Bayesian inference may determine spatial attention. © The Author 2013. Published by Oxford University Pres

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

Bayesian mixed-effects inference on classification performance in hierarchical data sets

Classification algorithms are frequently used on data with a natural hierarchical structure. For instance, classifiers are often trained and tested on trial-wise measurements, separately for each subject within a group. One important question is how classification outcomes observed in individual subjects can be generalized to the population from which the group was sampled. To address this question, this paper introduces novel statistical models that are guided by three desiderata. First, all models explicitly respect the hierarchical nature of the data, that is, they are mixed-effects models that simultaneously account for within-subjects (fixed-effects) and across-subjects (random-effects) variance components. Second, maximum-likelihood estimation is replaced by full Bayesian inference in order to enable natural regularization of the estimation problem and to afford conclusions in terms of posterior probability statements. Third, inference on classification accuracy is complemented by inference on the balanced accuracy, which avoids inflated accuracy estimates for imbalanced data sets. We introduce hierarchical models that satisfy these criteria and demonstrate their advantages over conventional methods usingMCMC implementations for model inversion and model selection on both synthetic and empirical data. We envisage that our approach will improve the sensitivity and validity of statistical inference in future hierarchical classification studies. © 2012

Inferring on the intentions of others by hierarchical Bayesian learning

Inferring on others' (potentially time-varying) intentions is a fundamental problem during many social transactions. To investigate the underlying mechanisms, we applied computational modeling to behavioral data from an economic game in which 16 pairs of volunteers (randomly assigned to "player" or "adviser" roles) interacted. The player performed a probabilistic reinforcement learning task, receiving information about a binary lottery from a visual pie chart. The adviser, who received more predictive information, issued an additional recommendation. Critically, the game was structured such that the adviser's incentives to provide helpful or misleading information varied in time. Using a meta-Bayesian modeling framework, we found that the players' behavior was best explained by the deployment of hierarchical learning: they inferred upon the volatility of the advisers' intentions in order to optimize their predictions about the validity of their advice. Beyond learning, volatility estimates also affected the trial-by-trial variability of decisions: participants were more likely to rely on their estimates of advice accuracy for making choices when they believed that the adviser's intentions were presently stable. Finally, our model of the players' inference predicted the players' interpersonal reactivity index (IRI) scores, explicit ratings of the advisers' helpfulness and the advisers' self-reports on their chosen strategy. Overall, our results suggest that humans (i) employ hierarchical generative models to infer on the changing intentions of others, (ii) use volatility estimates to inform decision-making in social interactions, and (iii) integrate estimates of advice accuracy with non-social sources of information. The Bayesian framework presented here can quantify individual differences in these mechanisms from simple behavioral readouts and may prove useful in future clinical studies of maladaptive social cognition

Allostatic self-efficacy: a metacognitive theory of dyshomeostasis-induced fatigue and depression

This paper outlines a hierarchical Bayesian framework for interoception, homeostatic/allostatic control, and meta-cognition that connects fatigue and depression to the experience of chronic dyshomeostasis. Specifically, viewing interoception as the inversion of a generative model of viscerosensory inputs allows for a formal definition of dyshomeostasis (as chronically enhanced surprise about bodily signals, or, equivalently, low evidence for the brain's model of bodily states) and allostasis (as a change in prior beliefs or predictions which define setpoints for homeostatic reflex arcs). Critically, we propose that the performance of interoceptive-allostatic circuitry is monitored by a metacognitive layer that updates beliefs about the brain's capacity to successfully regulate bodily states (allostatic self-efficacy). In this framework, fatigue and depression can be understood as sequential responses to the interoceptive experience of dyshomeostasis and the ensuing metacognitive diagnosis of low allostatic self-efficacy. While fatigue might represent an early response with adaptive value (cf. sickness behavior), the experience of chronic dyshomeostasis may trigger a generalized belief of low self-efficacy and lack of control (cf. learned helplessness), resulting in depression. This perspective implies alternative pathophysiological mechanisms that are reflected by differential abnormalities in the effective connectivity of circuits for interoception and allostasis. We discuss suitably extended models of effective connectivity that could distinguish these connectivity patterns in individual patients and may help inform differential diagnosis of fatigue and depression in the future

Energy Estimation of Cosmic Rays with the Engineering Radio Array of the Pierre Auger Observatory

The Auger Engineering Radio Array (AERA) is part of the Pierre Auger Observatory and is used to detect the radio emission of cosmic-ray air showers. These observations are compared to the data of the surface detector stations of the Observatory, which provide well-calibrated information on the cosmic-ray energies and arrival directions. The response of the radio stations in the 30 to 80 MHz regime has been thoroughly calibrated to enable the reconstruction of the incoming electric field. For the latter, the energy deposit per area is determined from the radio pulses at each observer position and is interpolated using a two-dimensional function that takes into account signal asymmetries due to interference between the geomagnetic and charge-excess emission components. The spatial integral over the signal distribution gives a direct measurement of the energy transferred from the primary cosmic ray into radio emission in the AERA frequency range. We measure 15.8 MeV of radiation energy for a 1 EeV air shower arriving perpendicularly to the geomagnetic field. This radiation energy -- corrected for geometrical effects -- is used as a cosmic-ray energy estimator. Performing an absolute energy calibration against the surface-detector information, we observe that this radio-energy estimator scales quadratically with the cosmic-ray energy as expected for coherent emission. We find an energy resolution of the radio reconstruction of 22% for the data set and 17% for a high-quality subset containing only events with at least five radio stations with signal.Comment: Replaced with published version. Added journal reference and DO

Measurement of the Radiation Energy in the Radio Signal of Extensive Air Showers as a Universal Estimator of Cosmic-Ray Energy

We measure the energy emitted by extensive air showers in the form of radio emission in the frequency range from 30 to 80 MHz. Exploiting the accurate energy scale of the Pierre Auger Observatory, we obtain a radiation energy of 15.8 \pm 0.7 (stat) \pm 6.7 (sys) MeV for cosmic rays with an energy of 1 EeV arriving perpendicularly to a geomagnetic field of 0.24 G, scaling quadratically with the cosmic-ray energy. A comparison with predictions from state-of-the-art first-principle calculations shows agreement with our measurement. The radiation energy provides direct access to the calorimetric energy in the electromagnetic cascade of extensive air showers. Comparison with our result thus allows the direct calibration of any cosmic-ray radio detector against the well-established energy scale of the Pierre Auger Observatory.Comment: Replaced with published version. Added journal reference and DOI. Supplemental material in the ancillary file

How could we get nosology from computation?

Psychiatry has found it difficult to develop a nosology that allows for the targeted treatment of disorders of the mind. The historic inability of the field to agree on a nosology based on clinical experience has led it to retreat to diagnoses based on symptom checklists as laid down in the Diagnostic and Statistical Manual of Mental Disorders (DSM). While this has increased the reliability of diagnoses, hopes that biological findings would lead to the emergence of mechanistically founded diagnostic entities have not been realized despite considerable advances in neurobiology. This article sets out a possible way forward: harnessing systems theory to provide the conceptual constraints needed to link clinical phenomena with neurobiology. This approach builds on the insight that the mind is a system which, to regulate its environment, needs to have a model of that environment and needs to update predictions about it using the rules of inductive logic (i.e., Bayesian inference). The application of the rules of inductive logic is called Bayesian inference because Bayes\u2019s theorem is the most important consequence of these rules, prescribing how beliefs need to be updated in response to new information. Importantly, while Bayesian inference is by definition consistent with the rules of inductive logic, it can still be false (to the point of being pathological), in the sense of leading to false predictions, because the model underlying the inference is inadequate. Further, it can be shown that Bayesian inference can be reduced to updating beliefs based on precision-weighted prediction errors, where a prediction error is the difference between actual and predicted input, and precision is the confidence associated with the input prediction. Precision weighting of prediction errors entails that a given discrepancy between outcome and prediction means more, and leads to greater belief updates, the more confidently the prediction was made. This provides a conceptual framework linking clinical experience with the pathophysiology underlying disorders of the mind. Limitations of this approach are discussed and ways to work around them illustrated with examples. Finally, initial steps and possible future directions toward a nosology based on failures of precision weighting are discussed. Copyright MIT & Frankfurt Institute of Advaced Studies