Intrinsic Dimension Estimation Using Wasserstein Distance
Intrinsic Dimension Estimation Using Wasserstein Distance
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发表时间：
2021-06
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通讯作者：
A. Block;Zeyu Jia;Yury Polyanskiy;A. Rakhlin
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作者：
A. Block;Zeyu Jia;Yury Polyanskiy;A. Rakhlin
长期以来，人们认为许多实际机器学习任务中遇到的高维数据具有低维结构，即流形假设成立。因此，一个自然的问题是从有限样本中估计给定总体分布的内在维度。我们引入了一种新的内在维数估计器，并提供有限样本、非渐近保证。然后，我们应用我们的技术来获取生成对抗网络（GAN）的新样本复杂性界限，仅取决于数据的内在维度。
It has long been thought that high-dimensional data encountered in many practical machine learning tasks have low-dimensional structure, i.e., the manifold hypothesis holds. A natural question, thus, is to estimate the intrinsic dimension of a given population distribution from a finite sample. We introduce a new estimator of the intrinsic dimension and provide finite sample, non-asymptotic guarantees. We then apply our techniques to get new sample complexity bounds for Generative Adversarial Networks (GANs) depending only on the intrinsic dimension of the data.