Random function priors for exchangeable arrays with applications to graphs and relational data

A fundamental problem in the analysis of structured relational data like graphs, networks, databases, and matrices is to extract a summary of the common structure underlying relations between individual entities. Relational data are typically encoded in the form of arrays; invariance to the ordering of rows and columns corresponds to exchangeable arrays. Results in probability theory due to Aldous, Hoover and Kallenberg show that exchangeable arrays can be represented in terms of a random measurable function which constitutes the natural model parameter in a Bayesian model. We obtain a flexible yet simple Bayesian nonparametric model by placing a Gaussian process prior on the parameter function. Efficient inference utilises elliptical slice sampling combined with a random sparse approximation to the Gaussian process. We demonstrate applications of the model to network data and clarify its relation to models in the literature, several of which emerge as special cases.

Model reductions for inference: generality of pairwise, binary, and planar factor graphs.

We offer a solution to the problem of efficiently translating algorithms between different types of discrete statistical model. We investigate the expressive power of three classes of model-those with binary variables, with pairwise factors, and with planar topology-as well as their four intersections. We formalize a notion of "simple reduction" for the problem of inferring marginal probabilities and consider whether it is possible to "simply reduce" marginal inference from general discrete factor graphs to factor graphs in each of these seven subclasses. We characterize the reducibility of each class, showing in particular that the class of binary pairwise factor graphs is able to simply reduce only positive models. We also exhibit a continuous "spectral reduction" based on polynomial interpolation, which overcomes this limitation. Experiments assess the performance of standard approximate inference algorithms on the outputs of our reductions.

SLP: A zero-contact non-invasive method for pulmonary function testing

Structured Light Plethysmography (SLP) is a novel non-invasive method that uses structured light to perform pulmonary function testing that does not require physical contact with a patient. The technique produces an estimate of chest wall volume changes over time. A patient is observed continuously by two cameras and a known pattern of light (i.e. structured light) is projected onto the chest using an off-the-shelf projector. Corner features from the projected light pattern are extracted, tracked and brought into correspondence for both camera views over successive frames. A novel self calibration algorithm recovers the intrinsic and extrinsic camera parameters from these point correspondences. This information is used to reconstruct a surface approximation of the chest wall and several novel ideas for 'cleaning up' the reconstruction are used. The resulting volume and derived statistics (e.g. FVC, FEV) agree very well with data taken with a spirometer. © 2010. The copyright of this document resides with its authors.