The Exact Equivalence of Distance and Kernel Methods for Hypothesis Testing
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arXiv
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| Format: | Preprint |
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2018
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| _version_ | 1866914848858701824 |
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| author | Shen, Cencheng Vogelstein, Joshua T. |
| author_facet | Shen, Cencheng Vogelstein, Joshua T. |
| contents | Distance-based tests, also called "energy statistics", are leading methods for two-sample and independence tests from the statistics community. Kernel-based tests, developed from "kernel mean embeddings", are leading methods for two-sample and independence tests from the machine learning community. A fixed-point transformation was previously proposed to connect the distance methods and kernel methods for the population statistics. In this paper, we propose a new bijective transformation between metrics and kernels. It simplifies the fixed-point transformation, inherits similar theoretical properties, allows distance methods to be exactly the same as kernel methods for sample statistics and p-value, and better preserves the data structure upon transformation. Our results further advance the understanding in distance and kernel-based tests, streamline the code base for implementing these tests, and enable a rich literature of distance-based and kernel-based methodologies to directly communicate with each other. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1806_05514 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | The Exact Equivalence of Distance and Kernel Methods for Hypothesis Testing Shen, Cencheng Vogelstein, Joshua T. Machine Learning Distance-based tests, also called "energy statistics", are leading methods for two-sample and independence tests from the statistics community. Kernel-based tests, developed from "kernel mean embeddings", are leading methods for two-sample and independence tests from the machine learning community. A fixed-point transformation was previously proposed to connect the distance methods and kernel methods for the population statistics. In this paper, we propose a new bijective transformation between metrics and kernels. It simplifies the fixed-point transformation, inherits similar theoretical properties, allows distance methods to be exactly the same as kernel methods for sample statistics and p-value, and better preserves the data structure upon transformation. Our results further advance the understanding in distance and kernel-based tests, streamline the code base for implementing these tests, and enable a rich literature of distance-based and kernel-based methodologies to directly communicate with each other. |
| title | The Exact Equivalence of Distance and Kernel Methods for Hypothesis Testing |
| topic | Machine Learning |
| url | https://arxiv.org/abs/1806.05514 |