Local intrinsic dimension (LID) estimation methods have received a lot of
attention in recent years thanks to the progress in deep neural networks and
generative modeling. In opposition to old non-parametric methods, new methods
use generative models to approximate diffused dataset density and scale the
methods to high-dimensional datasets like images. In this paper, we investigate
the recent state-of-the-art parametric LID estimation methods from the
perspective of the Wiener process. We explore how these methods behave when
their assumptions are not met. We give an extended mathematical description of
those methods and their error as a function of the probability density of the
data.

本研究调查了最近最先进的参数化局部内在维度估计方法，从维纳过程的角度探讨了这些方法在其假设不满足时的行为，并给出了这些方法的扩展数学描述以及其误差与数据的概率密度函数之间的关系。

基于维纳过程的局部内在维度估计方法视角

A Wiener process perspective on local intrinsic dimension estimation  methods

Normalizing flows transform a simple base distribution into a complex target
distribution and have proved to be powerful models for data generation and
density estimation. In this work, we propose a novel type of normalizing flow
driven by a differential deformation of the Wiener process. As a result, we
obtain a rich time series model whose observable process inherits many of the
appealing properties of its base process, such as efficient computation of
likelihoods and marginals. Furthermore, our continuous treatment provides a
natural framework for irregular time series with an independent arrival
process, including straightforward interpolation. We illustrate the desirable
properties of the proposed model on popular stochastic processes and
demonstrate its superior flexibility to variational RNN and latent ODE
baselines in a series of experiments on synthetic and real-world data.

本文提出一种新型的正则化流，其基于 Wiener 过程的微分变形，从而获得一个完整的时间序列模型，该模型继承了其基本过程的许多性质，如似然性和边缘效率。此外，我们的连续处理为有独立到达过程的不规则时间序列提供了自然框架，包括直接插值。在合成数据和真实世界数据的一系列实验中，我们证明了该模型相对于变分 RNN 和潜在 ODE 基线的优越灵活性。