Flexible Tails for Normalising Flows

用于标准化流动的灵活尾部

• 批准号: 2597860
• 金额: --
• 依托单位: University of Bristol
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2597860
• 关键词: Flexible; Tails; Normalising; Flows

Principled analysis of data for decision making, whether human led or automated, requires dealing with uncertainty. The mature field of probability theory provides a wealth of theoretical support for dealing with problems of this nature. When probability is used to describe and reason about a system, the specific assumptions are referred to as probabilistic models. The central aim of probabilistic modelling is to successfully infer how the uncertainty about quantities of interest is distributed, known as probability distributions. This task is critical in many application domains that exhibit randomness, such as machine learning applications like facial recognition or the estimation of extreme values like predicting when the next flood may occur. The specification of probability distributions that are both flexible and convenient to estimate has clear value in these fields. Normalising flows (NFs) are one such mechanism for expressing probability distributions that have generated much recent research interest. Rather than standard parametric assumptions, the central idea of NFs is to represent a potentially complex target distribution as the transformation of a simpler base distribution. The structure of the resulting distribution is controlled by both the randomness expressed by the base distribution and the form of the transformation. By requiring that the transformation is smooth and invertible, one can evaluate the NF density exactly by the well known change of variable formula in addition to efficiently drawing samples from the NF. Recently, NF models have been successfully applied to challenging learning tasks. These include application to generating realistic images of faces and the modelling of complex physical processes. Despite the successes of NFs when performing density estimation directly, significant issues remain when applied to Bayesian inference, which commonly occurs when the quantity of interest is unobserved. One known issue with NFs is their inability to represent distributions with heavy tails. A current solution to this problem introduces a heavy tailed base distribution. In our work, we instead propose capturing heavy tailed distributions via a transformation of uniform base distributions. Our proposal has clear technical advantages over current approaches and can rely on existing extreme value literature for theoretical support. This direction of research has the potential to open up entirely new applications of NF models to important extreme value problems. Additionally, we will investigate whether sufficiently flexible tails could also improve Bayesian inference with NFs. Such an improvement would deliver wide ranging benefit to many important applications.

对决策数据进行原则性分析，无论是人为主导还是自动化，都需要处理不确定性。成熟的概率论领域为处理此类性质的问题提供了丰富的理论支持。当概率用于描述和推理系统时，特定的假设被称为概率模型。概率建模的中心目标是成功推断感兴趣数量的不确定性如何分布，称为概率分布。此任务在许多表现出随机性的应用领域中至关重要，例如面部识别等机器学习应用或预测下一次洪水何时可能发生等极值估计。既灵活又方便估计的概率分布规范在这些领域具有明显的价值。归一化流（NF）是一种表达概率分布的机制，最近引起了很多研究兴趣。 NF 的中心思想不是标准参数假设，而是将潜在复杂的目标分布表示为更简单的基本分布的变换。所得分布的结构由基本分布表示的随机性和变换的形式控制。通过要求变换平滑且可逆，除了从 NF 中高效地抽取样本之外，还可以通过众所周知的变量公式的变化来准确地评估 NF 密度。最近，NF 模型已成功应用于具有挑战性的学习任务。其中包括生成逼真的面部图像和复杂物理过程建模的应用。尽管 NF 在直接执行密度估计方面取得了成功，但在应用于贝叶斯推理时仍然存在重大问题，这通常发生在未观察到感兴趣的数量时。 NF 的一个已知问题是它们无法表示重尾分布。该问题的当前解决方案引入了重尾基础分布。在我们的工作中，我们建议通过均匀基分布的变换来捕获重尾分布。我们的建议比当前的方法具有明显的技术优势，并且可以依赖现有的极值文献作为理论支持。这一研究方向有可能为 NF 模型在重要的极值问题上开辟全新的应用。此外，我们将研究足够灵活的尾部是否也可以改进 NF 的贝叶斯推理。这种改进将为许多重要的应用带来广泛的好处。