Geometric deep learning for likelihood-free statistical inference

用于无似然统计推断的几何深度学习

• 批准号: 2720990
• 金额: --
• 依托单位: University College London
• 依托单位国家: 英国
• 项目类别: Studentship
• 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=studentship-2720990
• 关键词: Geometric; deep; learning; likelihood; free

Deep learning has been remarkably successful in the interpretation of standard (Euclidean) data, such as 1D time series data, 2D image data, and 3D video or volumetric data, now exceeding human accuracy in many cases. However, standard deep learning techniques fail catastrophically when applied to data defined on other domains, such as data defined over networks, graphs, 3D objects, or other manifolds such as the sphere. This has given rise to the field of geometric deep learning (Bronstein et al. 2017; Bronstein et al. 2021).The bedrock of much scientific analysis is statistical inference, in particular Bayesian approaches. Recently, simulation-based inference techniques (cf. likelihood-free inference) have emerged, and are rapidly evolving, for scenarios where an explicit likelihood is not available or simply to speed up inference in time-critical applications (e.g. in gravitational wave detection for rapid electromagnetic follow-up). For a brief review see Cranmer et al. 2020. These techniques build on powerful machine learning models for probability distributions (e.g. Papamakarios et al. 2021).The focus of the current project is to develop integrated geometric deep learning and simulation-based inference techniques (cf. likelihood-free inference) for data defined over complex domains, such as spherical manifolds and graphs. This will involve developing geometric emulation, imaging, and inference techniques as part of a overarching inference pipeline. A key component of such a pipeline will be geometric scattering network representations (Mallat 2012; McEwen et al. 2021). The techniques developed will have application in cosmology, medical imaging, geophysics and beyond; we will collaborate with others to apply them in the aforementioned fields.

深度学习在解释标准（欧几里得）数据（例如 1D 时间序列数据、2D 图像数据以及 3D 视频或体积数据）方面取得了巨大成功，现在在许多情况下超过了人类的准确性。然而，当应用于其他领域定义的数据（例如通过网络、图形、3D 对象或其他流形（例如球体）定义的数据）时，标准深度学习技术会发生灾难性的失败。这催生了几何深度学习领域（Bronstein et al. 2017；Bronstein et al. 2021）。许多科学分析的基础是统计推断，特别是贝叶斯方法。最近，基于模拟的推理技术（参见无似然推理）已经出现，并且正在迅速发展，适用于无法获得明确似然的场景，或者只是为了加快时间关键型应用中的推理速度（例如，在引力波探测中）快速电磁跟踪）。简要回顾请参见 Cranmer 等人。 2020。这些技术建立在强大的概率分布机器学习模型的基础上（例如 Papamakarios 等人，2021）。当前项目的重点是开发集成的几何深度学习和基于模拟的推理技术（参见无似然推理）在复杂域（例如球面流形和图）上定义的数据。这将涉及开发几何仿真、成像和推理技术，作为总体推理流程的一部分。这种管道的一个关键组成部分将是几何散射网络表示（Mallat 2012；McEwen 等人 2021）。开发的技术将应用于宇宙学、医学成像、地球物理学等领域；我们将与其他人合作，将它们应用到上述领域。