Tractable inference for statistical network models with local dependence

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This project concerns the analysis of data from systems consisting of large numbers of linked objects. Such data is commonly found in a wide range of applications in science. The links may arise through the existence of networks, which contain explicit connections between objects (such as links between websites), or simply through weaker associations (e.g. we expect that in most images, most pixels will be of a similar colour to nearby pixels).Examples of such data arise in many different fields. Applications in: physics (magnetism); biology (genetics, protein design, neural models); computer science (artificial intelligence, computer vision); social science (social networks); economics (the network effect); and engineering (target tracking), all share common underlying characteristics. In many cases, the application can be reduced to understanding the process by which a network is generated and to use this knowledge to predict future events. For example, one can envisage learning from previous examples of contact between known terrorists, inferring patterns of communication that mark them out as such. Knowledge of this pattern may then be used to identify terrorist cells from communication networks. Making such an inference in the presence of uncertainty (which is always the case when analysing real data) is a problem that lies in the realm of statistics. In order to obtain accurate results, the use of a technique known as Bayesian inference is usually necessary. Bayesian inference is usually implemented by means of an iterative algorithm known as a Monte Carlo method.However, using Monte Carlo methods to perform inference in models of large networks can be extremely computationally expensive: the algorithm can run for days, weeks or months without producing a useful result. This means that in practice these methods cannot be used, so that large networks cannot be analysed using "model based" statistical techniques. This project is concerned with the development of algorithms that are much more computationally efficient, with the aim of reducing computational time to more manageable levels. These algorithms build on some of the most recent developments in statistics and machine learning.