Generalised Variational Bayesian Inference in Infinite Dimensions

无限维广义变分贝叶斯推理

• 批准号: 2444047
• 金额: --
• 依托单位: University of Oxford
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2020
• 资助国家: 英国
• 起止时间: 2020 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2444047
• 关键词: Generalised; Variational; Bayesian; Inference; Infinite

The advent of high-dimensional datasets, characterized by both their large size (number of observations) and feature space (the quantity of measurements per observation), has created a heightened demand for machine learning algorithms capable of handling such data. Notable successes, like ChatGPT, which harnessed a staggering 45 TB of text for training, exemplify the need for models that can handle large amounts of data.The past decade has witnessed remarkable advancements in instructing machine learning models to make precise predictions. Nonetheless, these models often lack awareness of their limitations. ChatGPT, for instance, may confidently assert erroneous information and cite fictitious articles to bolster its arguments. As a result, equipping predictive models with a measure of confidence has become a primary concern within the machine learning field known as uncertainty quantification.The literature offers numerous approaches to uncertainty quantification, many of which can be effectively summarized under the framework of generalised variational Bayesian inference. In this research endeavour, we propose employing tools from infinite-dimensional analysis, such as Gaussian measures in Banach spaces and the Wasserstein gradient flow, to scrutinize the generalised variational Bayesian inference problem. We are confident that contemporary mathematical techniques will enhance our comprehension of existing procedures and facilitate the development of new ones.Our approach will be grounded in fundamental principles, drawing from measure theory, functional analysis, and probability theory. Our primary objective is to furnish both a rigorous mathematical analysis and experimental exploration of any novel procedures we introduce. To maximize applicability, we will either construct new open-source software libraries or enhance existing ones. This fundamental research has the potential to impact a broad spectrum of applications, given the widespread adoption of machine learning algorithms and uncertainty quantification in the digital economy, engineering, scientific research, and healthcare.This project resides within the EPSRC Mathematical Sciences research domain, specifically in the field of statistics and applied probability.

高维数据集的出现，其特点是尺寸大（观测数量）和特征空间（每个观测的测量数量），这对能够处理此类数据的机器学习算法提出了更高的需求。 ChatGPT 等显着的成功利用了惊人的 45 TB 文本进行训练，这说明了对能够处理大量数据的模型的需求。过去十年见证了指导机器学习模型进行精确预测的显着进步。尽管如此，这些模型往往缺乏对其局限性的认识。例如，ChatGPT 可能会自信地断言错误信息并引用虚构文章来支持其论点。因此，为预测模型配备置信度已成为机器学习领域（称为不确定性量化）的主要关注点。文献提供了多种不确定性量化方法，其中许多方法可以在广义变分贝叶斯推理的框架下进行有效总结。在这项研究工作中，我们建议使用无限维分析工具，例如巴纳赫空间中的高斯测度和 Wasserstein 梯度流，来仔细研究广义变分贝叶斯推理问题。我们相信，当代数学技术将增强我们对现有程序的理解，并促进新程序的开发。我们的方法将基于基本原理，借鉴测度论、泛函分析和概率论。我们的主要目标是对我们引入的任何新颖程序提供严格的数学分析和实验探索。为了最大限度地提高适用性，我们将构建新的开源软件库或增强现有的软件库。鉴于机器学习算法和不确定性量化在数字经济、工程、科学研究和医疗保健中的广泛采用，这项基础研究有可能影响广泛的应用。该项目属于 EPSRC 数学科学研究领域，特别是统计和应用概率领域。