Gaussian processes:iterative sparse approximations

In recent years there has been an increased interest in applying non-parametric methods to real-world problems. Significant research has been devoted to Gaussian processes (GPs) due to their increased flexibility when compared with parametric models. These methods use Bayesian learning, which generally leads to analytically intractable posteriors. This thesis proposes a two-step solution to construct a probabilistic approximation to the posterior. In the first step we adapt the Bayesian online learning to GPs: the final approximation to the posterior is the result of propagating the first and second moments of intermediate posteriors obtained by combining a new example with the previous approximation. The propagation of em functional forms is solved by showing the existence of a parametrisation to posterior moments that uses combinations of the kernel function at the training points, transforming the Bayesian online learning of functions into a parametric formulation. The drawback is the prohibitive quadratic scaling of the number of parameters with the size of the data, making the method inapplicable to large datasets. The second step solves the problem of the exploding parameter size and makes GPs applicable to arbitrarily large datasets. The approximation is based on a measure of distance between two GPs, the KL-divergence between GPs. This second approximation is with a constrained GP in which only a small subset of the whole training dataset is used to represent the GP. This subset is called the em Basis Vector, or BV set and the resulting GP is a sparse approximation to the true posterior. As this sparsity is based on the KL-minimisation, it is probabilistic and independent of the way the posterior approximation from the first step is obtained. We combine the sparse approximation with an extension to the Bayesian online algorithm that allows multiple iterations for each input and thus approximating a batch solution. The resulting sparse learning algorithm is a generic one: for different problems we only change the likelihood. The algorithm is applied to a variety of problems and we examine its performance both on more classical regression and classification tasks and to the data-assimilation and a simple density estimation problems.

Depth propagation and surface construction in 3-D vision

In stereo vision, regions with ambiguous or unspecified disparity can acquire perceived depth from unambiguous regions. This has been called stereo capture, depth interpolation or surface completion. We studied some striking induced depth effects suggesting that depth interpolation and surface completion are distinct stages of visual processing. An inducing texture (2-D Gaussian noise) had sinusoidal modulation of disparity, creating a smooth horizontal corrugation. The central region of this surface was replaced by various test patterns whose perceived corrugation was measured. When the test image was horizontal 1-D noise, shown to one eye or to both eyes without disparity, it appeared corrugated in much the same way as the disparity-modulated (DM) flanking regions. But when the test image was 2-D noise, or vertical 1-D noise, little or no depth was induced. This suggests that horizontal orientation was a key factor. For a horizontal sine-wave luminance grating, strong depth was induced, but for a square-wave grating, depth was induced only when its edges were aligned with the peaks and troughs of the DM flanking surface. These and related results suggest that disparity (or local depth) propagates along horizontal 1-D features, and then a 3-D surface is constructed from the depth samples acquired. The shape of the constructed surface can be different from the inducer, and so surface construction appears to operate on the results of a more local depth propagation process.

Statnote 9: The one-way analysis of variance (random effects model)

There is an alternative model of the 1-way ANOVA called the 'random effects' model or ‘nested’ design in which the objective is not to test specific effects but to estimate the degree of variation of a particular measurement and to compare different sources of variation that influence the measurement in space and/or time. The most important statistics from a random effects model are the components of variance which estimate the variance associated with each of the sources of variation influencing a measurement. The nested design is particularly useful in preliminary experiments designed to estimate different sources of variation and in the planning of appropriate sampling strategies.

Activation of the neutrophil respiratory burst by plasma from periodontitis patients is mediated by pro-inflammatory cytokines

Aim: To determine the effect of periodontitis patients' plasma on the neutrophil oxidative burst and the role of albumin, immunoglobulins (Igs) and cytokines. Materials and Methods: Plasma was collected from chronic periodontitis patients (n=11) and periodontally healthy controls (n=11) and used with/without depletion of albumin and Ig or antibody neutralization of IL-8, GM-CSF or IFN-a to prime/stimulate peripheral blood neutrophils, isolated from healthy volunteers. The respiratory burst was measured by lucigenin-dependent chemiluminescence. Plasma cytokine levels were determined by ELISA. Results: Plasmas from patients were significantly more effective in both directly stimulating neutrophil superoxide production and priming for subsequent formyl-met-leu-phe (fMLP)-stimulated superoxide production than plasmas from healthy controls (p<0.05). This difference was maintained after depletion of albumin and Ig. Plasma from patients contained higher mean levels of IL-8, GM-CSF and IFN-a. Individual neutralizing antibodies against IL-8, GM-CSF or IFN-a inhibited the direct stimulatory effect of patients' plasma, whereas the ability to prime for fMLP-stimulated superoxide production was only inhibited by neutralization of IFN-a. The stimulating and priming effects of control plasma were unaffected by antibody neutralization. Conclusions: This study demonstrates that plasma cytokines may have a role in inducing the hyperactive (IL-8, GM-CSF, IFN-a) and hyper-reactive (IFN-a) neutrophil phenotype seen in periodontitis patients.