Harnessing the Power of Stein Discrepancies in Bayesian Computation

统计学、机器学习和人工智能中一些最重要的应用目前都是由可用于将模型拟合到数据集的计算技术控制的。事实上，随着研究人员更好地理解感兴趣的现象，可以建立越来越复杂的现象模型；例如，对物理定律的详细微分方程描述，或定制的基于主体的动物运动模型。然而，与这些模型相关联的相应的更大的计算需求对模型可以被询问的次数施加了实际限制。这反过来又在尝试将模型拟合到数据集时提出了一个主要挑战，因为只有通过在不同的输入参数下评估模型才能识别与数据集兼容的那些参数。因此，在许多重要的应用中，目前不可能在严格的统计框架内使用最合适或最准确的模型。该项目旨在通过开发比当前最先进的计算方法更有效的新型计算方法来加速模型与数据的拟合过程。这将在贝叶斯框架中实现，其中使用“后验”概率分布来描述哪些参数最能代表数据集。支持这项研究的主要技术进步是“斯坦因差异”，它使以优化为中心的观点能够对后验分布的数值近似进行优化，从而可以采用强大的优化技术。如果成功，这些方法将减少所需模型评估的数量，使更合适和更复杂的模型能够适应数据集。反过来，这将在使用计算模型及其产生的推论和预测的各种应用领域中增加价值。审议了两项这样的申请；开发针对患者的人类心脏多物理模型，以实现个性化治疗，并预测使用新技术和新材料构建的结构的机械性能。

Some of the most important applications in statistics, machine learning and artificial intelligence are currently gated by the computational technologies available to fit models to a dataset. Indeed, as researchers better understand a phenomenon of interest, increasingly sophisticated models for the phenomenon can be built; for example, detailed differential equation descriptions of physical laws, or bespoke agent-based models of animal movement. However, the correspondingly larger computational demand associated with these models imposes a practical limit on the number of times a model can be interrogated. This in turn presents a major challenge when attempting to fit a model to a dataset, since only by evaluating the model at different input parameters can those parameters that are compatible with a dataset be identified. As a result, in many important applications it is currently not possible to use the most suitable or most accurate model within a rigorous statistical framework.This project aims to accelerate the process of fitting models to data, by developing novel computational methodology that is more efficient than the current state-of-the-art. This will be achieved in the Bayesian framework, in which a "posterior" probability distribution is used to describe which parameters best represent the dataset. The major technical advance that underpins this research is "Stein discrepancy", which enables an optimisation-centric perspective on numerical approximation of the posterior distribution, to which powerful optimisation techniques can be employed. If successful, these methods will reduce the number of model evaluations required, enabling more appropriate and sophisticated models to be fitted to a dataset. This will, in turn, add value in the diverse application domains in which computational models, and the inferences and predictions that they produce, are employed. Two such applications are considered; developing patient-specific multi-physics models of the human heart, with a view to personalised treatment, and predicting the mechanical properties of structures built using novel techniques and novel materials.