Hadamard-Hitchcock decompositions: identifiability and computation
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866911237573443584 |
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| author | Oneto, Alessandro Vannieuwenhoven, Nick |
| author_facet | Oneto, Alessandro Vannieuwenhoven, Nick |
| contents | A Hadamard-Hitchcock decomposition of a multidimensional array is a decomposition that expresses the latter as a Hadamard product of several tensor rank decompositions. Such decompositions can encode probability distributions that arise from statistical graphical models associated to complete bipartite graphs with one layer of observed random variables and one layer of hidden ones, usually called restricted Boltzmann machines. We establish generic identifiability of Hadamard-Hitchcock decompositions by exploiting the reshaped Kruskal criterion for tensor rank decompositions. A flexible algorithm leveraging existing decomposition algorithms for tensor rank decomposition is introduced for computing a Hadamard-Hitchcock decomposition. Numerical experiments illustrate its computational performance and numerical accuracy. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2308_06597 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hadamard-Hitchcock decompositions: identifiability and computation Oneto, Alessandro Vannieuwenhoven, Nick Algebraic Geometry Numerical Analysis Statistics Theory 15A69, 62E10, 14M99, 65Y20, 14N07 A Hadamard-Hitchcock decomposition of a multidimensional array is a decomposition that expresses the latter as a Hadamard product of several tensor rank decompositions. Such decompositions can encode probability distributions that arise from statistical graphical models associated to complete bipartite graphs with one layer of observed random variables and one layer of hidden ones, usually called restricted Boltzmann machines. We establish generic identifiability of Hadamard-Hitchcock decompositions by exploiting the reshaped Kruskal criterion for tensor rank decompositions. A flexible algorithm leveraging existing decomposition algorithms for tensor rank decomposition is introduced for computing a Hadamard-Hitchcock decomposition. Numerical experiments illustrate its computational performance and numerical accuracy. |
| title | Hadamard-Hitchcock decompositions: identifiability and computation |
| topic | Algebraic Geometry Numerical Analysis Statistics Theory 15A69, 62E10, 14M99, 65Y20, 14N07 |
| url | https://arxiv.org/abs/2308.06597 |