Hilbert space embeddings of independence tests of several variables with radial basis functions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913423213723648 |
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| author | Guella, Jean Carlo |
| author_facet | Guella, Jean Carlo |
| contents | In this paper, we characterize several classes of continuous radial basis functions that can be employed to determine whether a interaction of a probability is zero or not. These functions encompass standard independence tests but also the Lancaster/Streitberg interactions, and are multivariate extensions of Bernstein functions. Addressing a gap in these two probability contexts of interactions, we introduce an indexed measure of independence that generalizes the Lancaster interaction. We present several examples of these functions derived from high-order completely monotone functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_06854 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hilbert space embeddings of independence tests of several variables with radial basis functions Guella, Jean Carlo Classical Analysis and ODEs Probability 42A82, 43A35, 44A10, 46E22, 62H15 In this paper, we characterize several classes of continuous radial basis functions that can be employed to determine whether a interaction of a probability is zero or not. These functions encompass standard independence tests but also the Lancaster/Streitberg interactions, and are multivariate extensions of Bernstein functions. Addressing a gap in these two probability contexts of interactions, we introduce an indexed measure of independence that generalizes the Lancaster interaction. We present several examples of these functions derived from high-order completely monotone functions. |
| title | Hilbert space embeddings of independence tests of several variables with radial basis functions |
| topic | Classical Analysis and ODEs Probability 42A82, 43A35, 44A10, 46E22, 62H15 |
| url | https://arxiv.org/abs/2407.06854 |