arXiv subjects

Thomas Parr

Publications and source records attributed to Thomas Parr.

31 records · Page 2Linked to original sources

arXiv2020

Anticipation in architectural experience: a computational neurophenomenology for architecture?

The perceptual experience of architecture is enacted by the sensory and motor system. When we act, we change the perceived environment according to a set of expectations that depend on our body and the built environment. The continuous process of collecting sensory information is thus based on bodily affordances. Affordances characterize the fit between the physical structure of the body and capacities for movement in the built environment. Since little has been done regarding the role of architectural design in the emergence of perceptual experience on a neuronal level, this paper offers a first step towards the role of architectural design in perceptual experience. An approach to synthesize concepts from computational neuroscience with architectural phenomenology into a computational neurophenomenology is considered. The outcome is a framework under which studies of architecture and cognitive neuroscience can be cast.

q-bio.NC↗

arXiv2020

Active inference: demystified and compared

Active inference is a first principle account of how autonomous agents operate in dynamic, non-stationary environments. This problem is also considered in reinforcement learning (RL), but limited work exists on comparing the two approaches on the same discrete-state environments. In this paper, we provide: 1) an accessible overview of the discrete-state formulation of active inference, highlighting natural behaviors in active inference that are generally engineered in RL; 2) an explicit discrete-state comparison between active inference and RL on an OpenAI gym baseline. We begin by providing a condensed overview of the active inference literature, in particular viewing the various natural behaviors of active inference agents through the lens of RL. We show that by operating in a pure belief-based setting, active inference agents can carry out epistemic exploration, and account for uncertainty about their environment in a Bayes-optimal fashion. Furthermore, we show that the reliance on an explicit reward signal in RL is removed in active inference, where reward can simply be treated as another observation; even in the total absence of rewards, agent behaviors are learned through preference learning. We make these properties explicit by showing two scenarios in which active inference agents can infer behaviors in reward-free environments compared to both Q-learning and Bayesian model-based RL agents; by placing zero prior preferences over rewards and by learning the prior preferences over the observations corresponding to reward. We conclude by noting that this formalism can be applied to more complex settings if appropriate generative models can be formulated. In short, we aim to demystify the behavior of active inference agents by presenting an accessible discrete state-space and time formulation, and demonstrate these behaviors in a OpenAI gym environment, alongside RL agents.

cs.AI↗

arXiv2020

Dynamic causal modelling of immune heterogeneity

An interesting inference drawn by some Covid-19 epidemiological models is that there exists a proportion of the population who are not susceptible to infection -- even at the start of the current pandemic. This paper introduces a model of the immune response to a virus. This is based upon the same sort of mean-field dynamics as used in epidemiology. However, in place of the location, clinical status, and other attributes of people in an epidemiological model, we consider the state of a virus, B and T-lymphocytes, and the antibodies they generate. Our aim is to formalise some key hypotheses as to the mechanism of resistance. We present a series of simple simulations illustrating changes to the dynamics of the immune response under these hypotheses. These include attenuated viral cell entry, pre-existing cross-reactive humoral (antibody-mediated) immunity, and enhanced T-cell dependent immunity. Finally, we illustrate the potential application of this sort of model by illustrating variational inversion (using simulated data) of this model to illustrate its use in testing hypotheses. In principle, this furnishes a fast and efficient immunological assay--based on sequential serology--that provides a (i) quantitative measure of latent immunological responses and (ii) a Bayes optimal classification of the different kinds of immunological response (c.f., glucose tolerance tests used to test for insulin resistance). This may be especially useful in assessing SARS-CoV-2 vaccines.

q-bio.QM↗

arXiv2020

Parcels and particles: Markov blankets in the brain

At the inception of human brain mapping, two principles of functional anatomy underwrote most conceptions - and analyses - of distributed brain responses: namely functional segregation and integration. There are currently two main approaches to characterising functional integration. The first is a mechanistic modelling of connectomics in terms of directed effective connectivity that mediates neuronal message passing and dynamics on neuronal circuits. The second phenomenological approach usually characterises undirected functional connectivity (i.e., measurable correlations), in terms of intrinsic brain networks, self-organised criticality, dynamical instability, etc. This paper describes a treatment of effective connectivity that speaks to the emergence of intrinsic brain networks and critical dynamics. It is predicated on the notion of Markov blankets that play a fundamental role in the self-organisation of far from equilibrium systems. Using the apparatus of the renormalisation group, we show that much of the phenomenology found in network neuroscience is an emergent property of a particular partition of neuronal states, over progressively larger scales. As such, it offers a way of linking dynamics on directed graphs to the phenomenology of intrinsic brain networks.

q-bio.NC↗

arXiv2020

Effective immunity and second waves: a dynamic causal modelling study

This technical report addresses a pressing issue in the trajectory of the coronavirus outbreak; namely, the rate at which effective immunity is lost following the first wave of the pandemic. This is a crucial epidemiological parameter that speaks to both the consequences of relaxing lockdown and the propensity for a second wave of infections. Using a dynamic causal model of reported cases and deaths from multiple countries, we evaluated the evidence models of progressively longer periods of immunity. The results speak to an effective population immunity of about three months that, under the model, defers any second wave for approximately six months in most countries. This may have implications for the window of opportunity for tracking and tracing, as well as for developing vaccination programmes, and other therapeutic interventions.

q-bio.PE↗

arXiv2020

Sophisticated Inference

Active inference offers a first principle account of sentient behaviour, from which special and important cases can be derived, e.g., reinforcement learning, active learning, Bayes optimal inference, Bayes optimal design, etc. Active inference resolves the exploitation-exploration dilemma in relation to prior preferences, by placing information gain on the same footing as reward or value. In brief, active inference replaces value functions with functionals of (Bayesian) beliefs, in the form of an expected (variational) free energy. In this paper, we consider a sophisticated kind of active inference, using a recursive form of expected free energy. Sophistication describes the degree to which an agent has beliefs about beliefs. We consider agents with beliefs about the counterfactual consequences of action for states of affairs and beliefs about those latent states. In other words, we move from simply considering beliefs about 'what would happen if I did that' to 'what would I believe about what would happen if I did that'. The recursive form of the free energy functional effectively implements a deep tree search over actions and outcomes in the future. Crucially, this search is over sequences of belief states, as opposed to states per se. We illustrate the competence of this scheme, using numerical simulations of deep decision problems.

q-bio.NC↗

arXiv2020

Markov Blankets in the Brain

Recent characterisations of self-organising systems depend upon the presence of a Markov blanket: a statistical boundary that mediates the interactions between what is inside of and outside of a system. We leverage this idea to provide an analysis of partitions in neuronal systems. This is applicable to brain architectures at multiple scales, enabling partitions into single neurons, brain regions, and brain-wide networks. This treatment is based upon the canonical micro-circuitry used in empirical studies of effective connectivity, so as to speak directly to practical applications. This depends upon the dynamic coupling between functional units, whose form recapitulates that of a Markov blanket at each level. The nuance afforded by partitioning neural systems in this way highlights certain limitations of modular perspectives of brain function that only consider a single level of description.

q-bio.NC↗

arXiv2020

Tracking and tracing in the UK: a dynamic causal modelling study

By equipping a previously reported dynamic causal model of COVID-19 with an isolation state, we modelled the effects of self-isolation consequent on tracking and tracing. Specifically, we included a quarantine or isolation state occupied by people who believe they might be infected but are asymptomatic, and only leave if they test negative. We recovered maximum posteriori estimates of the model parameters using time series of new cases, daily deaths, and tests for the UK. These parameters were used to simulate the trajectory of the outbreak in the UK over an 18-month period. Several clear-cut conclusions emerged from these simulations. For example, under plausible (graded) relaxations of social distancing, a rebound of infections within weeks is unlikely. The emergence of a later second wave depends almost exclusively on the rate at which we lose immunity, inherited from the first wave. There exists no testing strategy that can attenuate mortality rates, other than by deferring or delaying a second wave. A sufficiently powerful tracking and tracing policy--implemented at the time of writing (10th May 2020)--will defer any second wave beyond a time horizon of 18 months. Crucially, this deferment is within current testing capabilities (requiring an efficacy of tracing and tracking of about 20% of asymptomatic infected cases, with less than 50,000 tests per day). These conclusions are based upon a dynamic causal model for which we provide some construct and face validation, using a comparative analysis of the United Kingdom and Germany, supplemented with recent serological studies.

q-bio.QM↗

arXiv2020

Second waves, social distancing, and the spread of COVID-19 across America

We recently described a dynamic causal model of a COVID-19 outbreak within a single region. Here, we combine several of these (epidemic) models to create a (pandemic) model of viral spread among regions. Our focus is on a second wave of new cases that may result from loss of immunity--and the exchange of people between regions--and how mortality rates can be ameliorated under different strategic responses. In particular, we consider hard or soft social distancing strategies predicated on national (Federal) or regional (State) estimates of the prevalence of infection in the population. The modelling is demonstrated using timeseries of new cases and deaths from the United States to estimate the parameters of a factorial (compartmental) epidemiological model of each State and, crucially, coupling between States. Using Bayesian model reduction, we identify the effective connectivity between States that best explains the initial phases of the outbreak in the United States. Using the ensuing posterior parameter estimates, we then evaluate the likely outcomes of different policies in terms of mortality, working days lost due to lockdown and demands upon critical care. The provisional results of this modelling suggest that social distancing and loss of immunity are the two key factors that underwrite a return to endemic equilibrium.

q-bio.PE↗

arXiv2020

Dynamic causal modelling of COVID-19

This technical report describes a dynamic causal model of the spread of coronavirus through a population. The model is based upon ensemble or population dynamics that generate outcomes, like new cases and deaths over time. The purpose of this model is to quantify the uncertainty that attends predictions of relevant outcomes. By assuming suitable conditional dependencies, one can model the effects of interventions (e.g., social distancing) and differences among populations (e.g., herd immunity) to predict what might happen in different circumstances. Technically, this model leverages state-of-the-art variational (Bayesian) model inversion and comparison procedures, originally developed to characterise the responses of neuronal ensembles to perturbations. Here, this modelling is applied to epidemiological populations to illustrate the kind of inferences that are supported and how the model per se can be optimised given timeseries data. Although the purpose of this paper is to describe a modelling protocol, the results illustrate some interesting perspectives on the current pandemic; for example, the nonlinear effects of herd immunity that speak to a self-organised mitigation process.

q-bio.PE↗

arXiv2020

Active inference on discrete state-spaces: a synthesis

Active inference is a normative principle underwriting perception, action, planning, decision-making and learning in biological or artificial agents. From its inception, its associated process theory has grown to incorporate complex generative models, enabling simulation of a wide range of complex behaviours. Due to successive developments in active inference, it is often difficult to see how its underlying principle relates to process theories and practical implementation. In this paper, we try to bridge this gap by providing a complete mathematical synthesis of active inference on discrete state-space models. This technical summary provides an overview of the theory, derives neuronal dynamics from first principles and relates this dynamics to biological processes. Furthermore, this paper provides a fundamental building block needed to understand active inference for mixed generative models; allowing continuous sensations to inform discrete representations. This paper may be used as follows: to guide research towards outstanding challenges, a practical guide on how to implement active inference to simulate experimental behaviour, or a pointer towards various in-silico neurophysiological responses that may be used to make empirical predictions.

q-bio.NC↗

arXiv2020

Some interesting observations on the free energy principle

Biehl et al (2020) present some interesting observations on an early formulation of the free energy principle in (Friston, 2013). We use these observations to scaffold a discussion of the technical arguments that underwrite the free energy principle. This discussion focuses on solenoidal coupling between various (subsets of) states in sparsely coupled systems that possess a Markov blanket - and the distinction between exact and approximate Bayesian inference, implied by the ensuing Bayesian mechanics.

q-bio.NC↗

arXiv2019

Bayesian model reduction

This paper reviews recent developments in statistical structure learning; namely, Bayesian model reduction. Bayesian model reduction is a method for rapidly computing the evidence and parameters of probabilistic models that differ only in their priors. In the setting of variational Bayes this has an analytical solution, which finesses the problem of scoring large model spaces in model comparison or structure learning. In this technical note, we review Bayesian model reduction and provide the relevant equations for several discrete and continuous probability distributions. We provide worked examples in the context of multivariate linear regression, Gaussian mixture models and dynamical systems (dynamic causal modelling). These examples are accompanied by the Matlab scripts necessary to reproduce the results. Finally, we briefly review recent applications in the fields of neuroimaging and neuroscience. Specifically, we consider structure learning and hierarchical or empirical Bayes that can be regarded as a metaphor for neurobiological processes like abductive reasoning.

stat.ME↗