Tractable inference for statistical network models with local dependence

该项目涉及分析由大量链接对象组成的系统中的数据。这种数据在科学的广泛应用中很常见。这些链接可能是通过网络的存在而产生的，网络包含对象之间的显式连接（例如网站之间的链接），或者仅仅是通过较弱的关联（例如，我们预计在大多数图像中，大多数像素将具有与附近像素相似的颜色）。应用领域：物理学（磁性）;生物学（遗传学、蛋白质设计、神经模型）、计算机科学（人工智能、计算机视觉）、社会科学（社交网络）、经济学（网络效应）和工程学（目标跟踪）都具有共同的基本特征。在许多情况下，应用程序可以简化为理解生成网络的过程，并使用这些知识来预测未来的事件。例如，人们可以设想从已知恐怖分子之间联系的先前例子中学习，推断出将他们标记为恐怖分子的通信模式。这种模式的知识然后可以用于从通信网络中识别恐怖分子细胞。在存在不确定性的情况下（分析真实的数据时总是如此）做出这样的推断是统计领域的一个问题。为了获得准确的结果，通常需要使用称为贝叶斯推理的技术。贝叶斯推理通常通过称为蒙特卡罗方法的迭代算法来实现。然而，使用蒙特卡罗方法在大型网络模型中执行推理的计算成本非常高：该算法可以运行数天，数周或数月而不会产生有用的结果。这意味着，在实践中，这些方法无法使用，因此，大型网络无法使用“基于模型”的统计技术进行分析。该项目关注的是计算效率更高的算法的开发，目的是将计算时间减少到更易于管理的水平。这些算法建立在统计学和机器学习的一些最新发展基础上。

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.