用于精确SDE建模的时变归一化流
Time-changed normalizing flows for accurate SDE modeling
AI总结：
本文提出时变归一化流TCNF，通过对Brown运动作时间形变来建模传统动态归一化流无法表示的SDE，并推广已有方法、提升推断与预测性能。
摘要：
生成范式在机器学习和深度学习模型中已变得愈发重要。常用的生成模型包括归一化流，它通过微分同胚变换对基础分布进行变换，从而实现精确的似然估计。将归一化流框架扩展以处理带时间索引的流，产生了动态归一化流，这是建模时间序列、随机过程和神经随机微分方程（SDE）的强大工具。在本工作中，我们提出了动态归一化流的一种新型变体，即时变归一化流（Time Changed Normalizing Flow，TCNF），其基础是对Brown运动进行时间形变；Brown运动构成了一个通用且广泛的Gaussian过程族。该方法使我们能够有效建模某些以其他方式无法建模的SDE，包括诸如著名的Ornstein-Uhlenbeck过程之类的标准SDE，并且推广了以往的方法，从而带来改进的结果以及更好的推断和预测能力。
英文摘要：
The generative paradigm has become increasingly important in machine learning and deep learning models. Among popular generative models are normalizing flows, which enable exact likelihood estimation by transforming a base distribution through diffeomorphic transformations. Extending the normalizing flow framework to handle time-indexed flows gave dynamic normalizing flows, a powerful tool to model time series, stochastic processes, and neural stochastic differential equations (SDEs). In this work, we propose a novel variant of dynamic normalizing flows, a Time Changed Normalizing Flow (TCNF), based on time deformation of a Brownian motion which constitutes a versatile and extensive family of Gaussian processes. This approach enables us to effectively model some SDEs, that cannot be modeled otherwise, including standard ones such as the well-known Ornstein-Uhlenbeck process, and generalizes prior methodologies, leading to improved results and better inference and prediction capability.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
