A Bayesian perspective on stochastic neurocontrol

Control design for stochastic uncertain nonlinear systems is traditionally based on minimizing the expected value of a suitably chosen loss function. Moreover, most control methods usually assume the certainty equivalence principle to simplify the problem and make it computationally tractable. We offer an improved probabilistic framework which is not constrained by these previous assumptions, and provides a more natural framework for incorporating and dealing with uncertainty. The focus of this paper is on developing this framework to obtain an optimal control law strategy using a fully probabilistic approach for information extraction from process data, which does not require detailed knowledge of system dynamics. Moreover, the proposed control method framework allows handling the problem of input-dependent noise. A basic paradigm is proposed and the resulting algorithm is discussed. The proposed probabilistic control method is for the general nonlinear class of discrete-time systems. It is demonstrated theoretically on the affine class. A nonlinear simulation example is also provided to validate theoretical development.

Experiments in time:exploring the components of motor timing behaviour in dyslexia

This investigation aimed to pinpoint the elements of motor timing control that are responsible for the increased variability commonly found in children with developmental dyslexia on paced or unpaced motor timing tasks (Chapter 3). Such temporal processing abilities are thought to be important for developing the appropriate phonological representations required for the development of literacy skills. Similar temporal processing difficulties arise in other developmental disorders such as Attention Deficit Hyperactivity Disorder (ADHD). Motor timing behaviour in developmental populations was examined in the context of models of typical human timing behaviour, in particular the Wing-Kristofferson model, allowing estimation of the contribution of different timing control systems, namely timekeeper and implementation systems (Chapter 2 and Methods Chapters 4 and 5). Research examining timing in populations with dyslexia and ADHD has been inconsistent in the application of stimulus parameters and so the first investigation compared motor timing behaviour across different stimulus conditions (Chapter 6). The results question the suitability of visual timing tasks which produced greater performance variability than auditory or bimodal tasks. Following an examination of the validity of the Wing-Kristofferson model (Chapter 7) the model was applied to time series data from an auditory timing task completed by children with reading difficulties and matched control groups (Chapter 8). Expected group differences in timing performance were not found, however, associations between performance and measures of literacy and attention were present. Results also indicated that measures of attention and literacy dissociated in their relationships with components of timing, with literacy ability being correlated with timekeeper variance and attentional control with implementation variance. It is proposed that these timing deficits associated with reading difficulties are attributable to central timekeeping processes and so the contribution of error correction to timing performance was also investigated (Chapter 9). Children with lower scores on measures of literacy and attention were found to have a slower or failed correction response to phase errors in timing behaviour. Results from the series of studies suggest that the motor timing difficulty in poor reading children may stem from failures in the judgement of synchrony due to greater tolerance of uncertainty in the temporal processing system.

Stability of multi-agent systems

This work attempts to shed light to the fundamental concepts behind the stability of Multi-Agent Systems. We view the system as a discrete time Markov chain with a potentially unknown transitional probability distribution. The system will be considered to be stable when its state has converged to an equilibrium distribution. Faced with the non-trivial task of establishing the convergence to such a distribution, we propose a hypothesis testing approach according to which we test whether the convergence of a particular system metric has occurred. We describe some artificial multi-agent ecosystems that were developed and we present results based on these systems which confirm that this approach qualitatively agrees with our intuition.

Variational mean-field algorithm for efficient inference in large systems of stochastic differential equations

This work introduces a Gaussian variational mean-field approximation for inference in dynamical systems which can be modeled by ordinary stochastic differential equations. This new approach allows one to express the variational free energy as a functional of the marginal moments of the approximating Gaussian process. A restriction of the moment equations to piecewise polynomial functions, over time, dramatically reduces the complexity of approximate inference for stochastic differential equation models and makes it comparable to that of discrete time hidden Markov models. The algorithm is demonstrated on state and parameter estimation for nonlinear problems with up to 1000 dimensional state vectors and compares the results empirically with various well-known inference methodologies.