The exact equivalence of distance and kernel methods in hypothesis testing
By Cencheng Shen, Joshua T. Vogelstein. 2018
50 citations recorded by the source corpus.
Distance correlation and Hilbert-Schmidt independence criterion are widely used for independence testing, two-sample testing, and many inference tasks in statistics and machine learning. These two methods are tightly related, yet are treated as two different entities in the majority of existing literature. In this paper, we propose a simple and elegant bijection between metric and kernel. The bijective transformation better preserves the similarity structure, allows distance correlation and Hilbert-Schmidt independence criterion to be always the same for hypothesis testing, streamlines the code base for implementation, and enables a rich literature of distance-based and kernel-based methodologies to directly communicate with each other.
Subfields: Statistics and Probability
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In Statistics and Probability
- Jasper Snoek
- Zhaoxi Mu
- Xinyu Yang
- Nal Kalchbrenner
- Tim Salimans
- Yizhuo Dong
- Rianne van den Berg
- Michalis K. Titsias
Citations in the corpus
- A Spectral Energy Distance for Parallel Speech Synthesis (2020, positive): “To address these limitations we propose a new training method based on the generalized energy distance [10, 32, 33], which enables the learning of implicit density models without the use of adversarial training or requiring a tractable likelihood.”
- Review of end-to-end speech synthesis technology based on deep learning (2021, methodology): “The main difference from other spectrogram-based losses is that, in addition to the attractive term between the generated data and the actual data, GED also adds a repulsive term between generated data to the training loss to avoid generated samples collapsing to a single point, thus capturing the f”