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Harnessing the Power of Stein Discrepancies in Bayesian Computation

利用贝叶斯计算中斯坦因差异的力量

基本信息

批准号：
EP/W019590/1
负责人：
Chris Oates
金额：
$ 89.8万
依托单位：
Newcastle University
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2022
资助国家：
英国
起止时间：
2022 至无数据
项目状态：
未结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FW019590%2F1
关键词：
Harnessing Power Stein Discrepancies Bayesian

项目摘要

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.

统计学、机器学习和人工智能中的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来控制的。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，物理定律的详细微分方程描述，或基于代理的动物运动模型。然而，与这些模型相关联的相应较大的计算需求对模型可以被询问的次数施加了实际限制。这反过来又提出了一个重大的挑战，当试图拟合一个模型的数据集，因为只有通过评估模型在不同的输入参数可以识别那些参数是兼容的数据集。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。本项目旨在通过开发比当前最先进的计算方法更有效的新计算方法来加速模型与数据拟合的过程。这将在贝叶斯框架内实现，其中使用“后验”概率分布来描述哪些参数最好地表示数据集。支持这项研究的主要技术进步是“Stein差异”，它使后验分布的数值近似能够以优化为中心，可以采用强大的优化技术。如果成功，这些方法将减少所需的模型评估数量，使更合适和复杂的模型能够拟合到数据集。这反过来又会在不同的应用领域增加价值，在这些应用领域中，采用了计算模型以及它们产生的推断和预测。考虑了两个这样的应用;开发针对患者的人类心脏多物理模型，以期进行个性化治疗，以及预测使用新技术和新材料构建的结构的机械性能。