Modern real world optimisation problems are increasingly becoming large scale. However, searching in high dimensional search spaces is notoriously difficult. Many methods break down as dimensionality increases and Estimation of Distribution Algorithm (EDA) is especially prone to the curse of dimensionality. In this thesis, we device new EDA variants that are capable of searching in large dimensional continuous domains. We in particular (i) investigated heavy tails search distributions, (ii) we clarify a controversy in the literature about the capabilities of Gaussian versus Cauchy search distributions, (iii) we constructed a new way of projecting a large dimensional search space to low dimensional subspaces in a way that gives us control of the size of covariance of the search distribution and we develop adaptation techniques to exploit this and (iv) we proposed a random embedding technique in EDA that takes advantage of low intrinsic dimensional structure of problems. All these developments avail us with new techniques to tackle high dimensional optimization problems.

Human studies have shown that gaze shifts are mostly driven by the task. One explanation is that fixations gather information about task relevant properties, where task relevance is signalled by reward. This thesis pursues primarily an engineering science goal to determine what mechanisms a rational decision maker could employ to select a gaze location optimally, or near optimally, given limited information and limited computation time. To do so we formulate and characterise three computational models of gaze shifting (implemented on a simulated humanoid robot), which use lookahead to imagine the informational effects of possible gaze fixations. Our first model selects the gaze that most reduces uncertainty in the scene (Unc), the second maximises expected rewards by reducing uncertainty (Rew+Unc), and the third maximises the expected gain in cumulative reward by reducing uncertainty (Rew+Unc+Gain). We also present an integrated account of a visual search process into the Rew+Unc+Gain gaze scheme. Our secondary goal is concerned with the way in which humans might select the next gaze location. We compare the hand-eye coordination timings of our models to previously published human data, and we provide evidence that only the models that incorporate both uncertainty and reward (Rew+Unc and Rew+Unc+Gain) match human data.

This thesis is concerned with deriving planning algorithms for robot manipulators. Manipulation has two effects, the robot has a physical effect on the object, and it also acquires information about the object. This thesis presents algorithms that treat both problems. First, I present an extension of the well-known piano mover’s problem where a robot pushing an object must plan its movements as well as those of the object. This requires simultaneous planning in the joint space of the robot and the configuration space of the object, in contrast to the original problem which only requires planning in the latter space. The effects of a robot action on the object configuration are determined by the non-invertible rigid body mechanics. To solve this a two-level planner is presented that coordinates planning in each space. Second, I consider planning under uncertainty and in particular planning for information effects. I consider the case where a robot has to reach and grasp an object under pose uncertainty caused by shape incompleteness. The main novel outcome is to enable tactile information gain planning for a dexterous, highdegree of freedom manipulator with non- Gaussian pose uncertainty. The method is demonstrated in trials with both simulated and real robots.

The enormous power of modern computers has made possible the statistical modelling of data with dimensionality that would have made this task inconceivable only decades ago. However, experience in such modelling has made researchers aware of many issues associated with working in high-dimensional domains, collectively known as `the curse of dimensionality', which can confound practitioners' desires to build good models of the world from these data. When the dimensionality is very large, low-dimensional methods and geometric intuition both break down in these high-dimensional spaces. To mitigate the dimensionality curse we can use low-dimensional representations of the original data that capture most of the information it contained. However, little is currently known about the effect of such dimensionality reduction on classifier performance. In this thesis we develop theory quantifying the effect of random projection - a recent, very promising, non-adaptive dimensionality reduction technique - on the classification performance of Fisher's Linear Discriminant (FLD), a successful and widely-used linear classifier. We tackle the issues associated with small sample size and high-dimensionality by using randomly projected FLD ensembles, and we develop theory explaining why our new approach performs well. Finally, we quantify the generalization error of Kernel FLD, a related non-linear projected classifier.

Kernel methods are powerful learning techniques with excellent generalization capability. This thesis develops three advanced approaches within the generic SVM framework in the application domain of time series data. The first contribution presents a new methodology for incorporating privileged information about the future evolution of time series, which is only available in the training phase. The task is prediction of the ordered categories of future time series movements. This is implemented by directly extending support vector ordinal regression with implicit constraints to leaning using privileged information paradigm. The second contribution demonstrates a novel methodology of constructing efficient kernels for time series classification problems. These kernels are constructed by representing each time series through a linear readout model from a high dimensional state space model with a fixed deterministically constructed dynamic part. Learning is then performed in the linear readout model space. Finally, in the same context, we introduce yet another novel time series kernel by co-learning the dynamic part and a global metric in the linear readout model space, encouraging time series from the same class to be represented by close model representations, while model representations of time series from different classes to be well-separated.

Strongly lensed variable quasars can serve as precise cosmological probes, provided that time delays between the image fluxes can be accurately measured. This thesis, explores in detail a new approach based on kernel regression estimates, which is able to estimate a single time delay given several data sets for the same quasar. We develop realistic artificial data sets in order to carry out controlled experiments to test the performance of this new approach. We also test our method on real data from strongly lensed quasar Q0957+561 and compare our estimates against existing results. Furthermore, we attempt to resolve the problem for smaller delays in gravitationally lensed photon streams. We test whether a more principled treatment of delay estimation in lensed photon streams, compared with the standard kernel estimation method, can have benefits of more accurate (less biased) and/or more stable (less variance) estimation. To that end, we propose a delay estimation method in which a single latent nonhomogeneous Poisson process underlying the lensed photon streams is imposed. The rate function model is formulated as a linear combination of nonlinear basis functions. Such a unifying rate function is then used in delay estimation based on the corresponding Innovation Process.

Accent is cited as an issue for speech recognition systems. Our experiments showed that the ASR word error rate is up to seven times greater for accented speech compared with standard British English. The main objective of this research is to develop Automatic Speech Recognition (ASR) techniques that are robust to accent variation. We applied different acoustic modelling techniques to compensate for the effects of regional accents on the ASR performance. For conventional GMM-HMM based ASR systems, we showed that using a small amount of data from a test speaker to choose an accent dependent model using an accent identification system, or building a model using the data from N neighbouring speakers in AID space, will result in superior performance compared to that obtained with unsupervised or supervised speaker adaptation. In addition we showed that using a DNN-HMM rather than a GMM-HMM based acoustic model would improve the recognition accuracy considerably. Even if we apply two stages of accent followed by speaker adaptation to the GMM-HMM baseline system, the GMM-HMM based system will not outperform the baseline DNN-HMM based system. For more contemporary DNN-HMM based ASR systems we investigated how adding different types of accented data to the training set can provide better recognition accuracy on accented speech. Finally, we proposed a new approach for visualisation of the AID feature space. This is helpful in analysing the AID recognition accuracies and analysing AID confusion matrices.

This thesis presents a novel market-based method, inspired by retail markets for resource allocation in fully decentralised computational systems where agents are self-interested. The posted offer mechanism used requires no central or regional coordinator or complex negotiation strategies. The stability of outcome allocations, those at equilibrium, is analysed and compared for three buyer behaviour models. The approach is scalable, robust and may be tuned to achieve a range of desired outcome resource allocations. These include a balanced load, allocations reflective of providers’ differing capabilities and those appropriate to heterogeneous buyer preferences over multiple attributes. The behaviour of the approach is studied both game theoretically and in simulation, where novel evolutionary market agents act on behalf of resource providing nodes to adaptively price their resources over time in response to market conditions. Sellers competitively co-evolve their offers online without any need for global market information. This is shown to lead the system to the game theoretically predicted outcome resource allocation when buyers’ decision functions degrade gracefully. Additionally, allocations remain stable in the presence of small changes in price and other more disruptive agents. The posted offer model therefore appears to be a useful mechanism for resource allocation in both homogeneous and heterogeneous decentralised computational systems where nodes are self-interested. Furthermore, evolutionary computation is shown to be a potential approach to realising self-interested adaptive pricing behaviour under the assumption of private information present in the posted offer model.

Peer-to-Peer (P2P) infrastructure has been used for designing many large-scale distributed systems. Structured P2P, in particular, has received a greater amount of research attention. Having trust in such the P2P environments can help mitigate many problems including security, because peers can choose to interact with the ones that are deemed trustworthy. However, there exists numerous hurdles that need to be overcome before a reliable trust system can be implemented for P2P. This thesis seeks to improve the existing reputation metrics and feedback mechanisms which are important components of the trust system. The new reputation metrics are more resilient to manipulations, and they take into account negative feedback. New protocols are also proposed as parts of the feedback mechanisms, and they allow an honest peer in a structured P2P system to securely detect if another peer has misbehaved. The new protocols make used of hardware-based security which is in the form of trusted devices: TPMs and the newly proposed trusted device called TTMs. The protocols are analyzed using formal methods and simulation. CSP is used to model and verify the properties of these protocols. The performance of these protocols is then evaluated using a new, distributed simulation platform called dPeerSim.

We begin with an introduction which describes the thesis in detail, and then a preliminary chapter in which we discuss rewriting systems, associated complexes and finiteness conditions. In particular, we recall the graph of derivations r and the 2- complex V associated to any rewriting system, and the related geometric finiteness conditions F DT and F HT. In §1.4 we give basic definitions and results about finite complete rewriting systems, that is, rewriting systems which rewrite any word in a finite number of steps to its normal form, the unique irreducible word in its congruence class. The main work of the thesis begins in Chapter 2 with some discussion of rewriting systems for groups which are confluent on the congruence class containing the empty word. In §2.1 we characterize groups admitting finite A-complete rewriting systems as those with a A-Dehn presentation, and in §2.2 we give some examples of finite rewriting systems for groups which are A-complete but not complete. For the remainder of the thesis, we study how the properties of finite complete rewriting systems which are discussed in the first chapter are mirrored in higher dimensions. In Chapter 3 we extend the 2-complex V to form a new 3-complex VP, and in Chapter 4 we define new finiteness conditions F DT2 and F HT2 based on the homotopy and homology of this complex. In §4.4 we show that if a monoid admits a finite complete rewriting system, then it is of type F DT2 • The final chapter contains a discussion of alternative ways to define such higher dimensional finiteness conditions. This leads to the introduction, in §5.2, of a variant of the Guba-Sapir homotopy reduction system which can be associated to any co~­ plete rewriting system. This is a rewriting system operating on paths in r, and is complete in the sense that it rewrites paths in a finite number of steps to a unique "normal form".