Bayesian Gaussian Process Models: PAC-Bayesian Generalisation Error Bounds and Sparse Approximations

Non-parametric models and techniques enjoy a growing popularity in the field of machine learning, and among these Bayesian inference for Gaussian process (GP) models has recently received significant attention. We feel that GP priors should be part of the standard toolbox for constructing models relevant to machine learning in the same way as parametric linear models are, and the results in this thesis help to remove some obstacles on the way towards this goal. In the first main chapter, we provide a distribution-free finite sample bound on the difference between generalisation and empirical (training) error for GP classification methods. While the general theorem (the PAC-Bayesian bound) is not new, we give a much simplified and somewhat generalised derivation and point out the underlying core technique (convex duality) explicitly. Furthermore, the application to GP models is novel (to our knowledge). A central feature of this bound is that its quality depends crucially on task knowledge being encoded faithfully in the model and prior distributions, so there is a mutual benefit between a sharp theoretical guarantee and empirically well-established statistical practices. Extensive simulations on real-world classification tasks indicate an impressive tightness of the bound, in spite of the fact that many previous bounds for related kernel machines fail to give non-trivial guarantees in this practically relevant regime. In the second main chapter, sparse approximations are developed to address the problem of the unfavourable scaling of most GP techniques with large training sets. Due to its high importance in practice, this problem has received a lot of attention recently. We demonstrate the tractability and usefulness of simple greedy forward selection with information-theoretic criteria previously used in active learning (or sequential design) and develop generic schemes for automatic model selection with many (hyper)parameters. We suggest two new generic schemes and evaluate some of their variants on large real-world classification and regression tasks. These schemes and their underlying principles (which are clearly stated and analysed) can be applied to obtain sparse approximations for a wide regime of GP models far beyond the special cases we studied here

Target classification in multimodal video

The presented thesis focuses on enhancing scene segmentation and target recognition methodologies via the mobilisation of contextual information. The algorithms developed to achieve this goal utilise multi-modal sensor information collected across varying scenarios, from controlled indoor sequences to challenging rural locations. Sensors are chiefly colour band and long wave infrared (LWIR), enabling persistent surveillance capabilities across all environments. In the drive to develop effectual algorithms towards the outlined goals, key obstacles are identified and examined: the recovery of background scene structure from foreground object ’clutter’, employing contextual foreground knowledge to circumvent training a classifier when labeled data is not readily available, creating a labeled LWIR dataset to train a convolutional neural network (CNN) based object classifier and the viability of spatial context to address long range target classification when big data solutions are not enough. For an environment displaying frequent foreground clutter, such as a busy train station, we propose an algorithm exploiting foreground object presence to segment underlying scene structure that is not often visible. If such a location is outdoors and surveyed by an infra-red (IR) and visible band camera set-up, scene context and contextual knowledge transfer allows reasonable class predictions for thermal signatures within the scene to be determined. Furthermore, a labeled LWIR image corpus is created to train an infrared object classifier, using a CNN approach. The trained network demonstrates effective classification accuracy of 95% over 6 object classes. However, performance is not sustainable for IR targets acquired at long range due to low signal quality and classification accuracy drops. This is addressed by mobilising spatial context to affect network class scores, restoring robust classification capability