Publications

Neuroimaging produces data that are continuous in one or more dimensions. This calls for an inference framework that can handle data that approximate functions of space, for example, anatomical images, time--frequency maps and distributed source reconstructions of electromagnetic recordings over time. Statistical parametric mapping (SPM) is the standard framework for whole-brain inference in neuroimaging: SPM uses random field theory to furnish $p$-values that are adjusted to control family-wise error or false discovery rates, when making topological inferences over large volumes of space. Random field theory regards data as realizations of a continuous process in one or more dimensions. This contrasts with classical approaches like the Bonferroni correction, which consider images as collections of discrete samples with no continuity properties (i.e., the probabilistic behavior at one point in the image does not depend on other points). Here, we illustrate how random field theory can be applied to data that vary as a function of time, space or frequency. We emphasize how topological inference of this sort is invariant to the geometry of the manifolds on which data are sampled. This is particularly useful in electromagnetic studies that often deal with very smooth data on scalp or cortical meshes. This application illustrates the versatility and simplicity of random field theory and the seminal contributions of Keith Worsley (1951--2009), a key architect of topological inference.

This chapter looks at prediction from the point of view of perception; namely, the fitting or inversion of internal models of sensory data by the brain. It focuses on how neural networks could be configured to invert these models and deconvolve sensory causes from sensory input. The chapter is organized as follows. The first section introduces hierarchical dynamic models. Hierarchies induce empirical priors that provide constraints, which are exploited during inversion. The second considers model inversion in statistical terms. The third shows how this inversion can be formulated as a simple gradient ascent using neuronal networks. The final section considers how evoked brain responses might be understood in terms of inference under hierarchical dynamic models of sensory input.

This paper reviews a simple solution to the continuous-discrete Bayesian nonlinear state estimation problem that has been proposed recently. The key ideas are analytic noise processes, variational Bayes, and the formulation of the problem in terms of generalized coordinates of motion. Some of the algorithms, specifically dynamic expectation maximization and variational filtering, have been shown to outperform existing approaches like extended Kalman filtering and particle filtering. A pedagogical review of the theoretical formulation is presented, with an emphasis on concepts that are not as widely known in the filtering literature. We illustrate the appliction of these concepts using a numerical example.

Recent years have seen the emergence of an important new fundamental theory of brain function. This theory brings information-theoretic, Bayesian, neuroscientific, and machine learning approaches into a single framework whose overarching principle is the minimization of surprise (or, equivalently, the maximization of expectation). The most comprehensive such treatment is the "free-energy minimization" formulation due to Karl Friston (see e.g., Friston and Stephan, 2007; Friston, 2010a,b - see also Fiorillo, 2010; Thornton, 2010). A recurrent puzzle raised by critics of these models is that biological systems do not seem to avoid surprises. We do not simply seek a dark, unchanging chamber, and stay there. This is the "Dark-Room Problem." Here, we describe the problem and further unpack the issues to which it speaks. Using the same format as the prolog of Eddington's Space, Time, and Gravitation (Eddington, 1920) we present our discussion as a conversation between: an information theorist (Thornton), a physicist (Friston), and a philosopher (Clark).

Hermeneutics refers to interpretation and translation of text (typically ancient scriptures) but also applies to verbal and non-verbal communication. In a psychological setting it nicely frames the problem of inferring the intended content of a communication. In this paper, we offer a solution to the problem of neural hermeneutics based upon active inference. In active inference, action fulfils predictions about how we will behave (e.g., predicting we will speak). Crucially, these predictions can be used to predict both self and others – during speaking and listening respectively. Active inference mandates the suppression of prediction errors by updating an internal model that generates predictions – both at fast timescales (through perceptual inference) and slower timescales (through perceptual learning). If two agents adopt the same model, then – in principle – they can predict each other and minimise their mutual prediction errors. Heuristically, this ensures they are singing from the same hymn sheet. This paper builds upon recent work on active inference and communication to illustrate perceptual learning using simulated birdsongs. Our focus here is the neural hermeneutics implicit in learning, where communication facilitates long-term changes in generative models that are trying to predict each other. In other words, communication induces perceptual learning and enables others to (literally) change our minds and vice versa.

Abstract Perceptual awareness depends upon the way in which we engage with our sensorium. This notion is central to active inference, a theoretical framework that treats perception and action as inferential processes. This variational perspective on cognition formalizes the notion of perception as hypothesis testing and treats actions as experiments that are designed (in part) to gather evidence for or against alternative hypotheses. The common treatment of perception and action affords a useful interpretation of certain perceptual phenomena whose active component is often not acknowledged. In this article, we start by considering Troxler fading – the dissipation of a peripheral percept during maintenance of fixation, and its recovery during free (saccadic) exploration. This offers an important example of the failure to maintain a percept without actively interrogating a visual scene. We argue that this may be understood in terms of the accumulation of uncertainty about a hypothesized stimulus when free exploration is disrupted by experimental instructions or pathology. Once we take this view, we can generalize the idea of using bodily (oculomotor) action to resolve uncertainty to include the use of mental (attentional) actions for the same purpose. This affords a useful way to think about binocular rivalry paradigms, in which perceptual changes need not be associated with an overt movement.

In this critique, we review the usefulness of functional localising scans in functional MRI studies. We consider their conceptual motivations and the implications for experimental design and inference. Functional localisers can often be viewed as acquiring data from cells that have been removed from an implicit factorial design. This perspective reveals their potentially restrictive nature. We deconstruct two examples from the recent literature to highlight the key issues. We conclude that localiser scans can be unnecessary and, in some instances, lead to a biased and inappropriately constrained characterisation of functional anatomy.

This letter offers a computational account of Pavlovian conditioning in the cerebellum based on active inference and predictive coding. Using eyeblink conditioning as a canonical paradigm, we formulate a minimal generative model that can account for spontaneous blinking, startle responses, and (delay or trace) conditioning. We then establish the face validity of the model using simulated responses to unconditioned and conditioned stimuli to reproduce the sorts of behavior that are observed empirically. The scheme’s anatomical validity is then addressed by associating variables in the predictive coding scheme with nuclei and neuronal populations to match the (extrinsic and intrinsic) connectivity of the cerebellar (eyeblink conditioning) system. Finally, we try to establish predictive validity by reproducing selective failures of delay conditioning, trace conditioning, and extinction using (simulated and reversible) focal lesions. Although rather metaphorical, the ensuing scheme can account for a remarkable range of anatomical and neurophysiological aspects of cerebellar circuitry—and the specificity of lesion-deficit mappings that have been established experimentally. From a computational perspective, this work shows how conditioning or learning can be formulated in terms of minimizing variational free energy (or maximizing Bayesian model evidence) using exactly the same principles that underlie predictive coding in perception.