Scalable Learning from Probability Measures with Mean Measure Quantization
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911536249831424 |
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| author | Gachon, Erell Cazelles, Elsa Bigot, Jérémie |
| author_facet | Gachon, Erell Cazelles, Elsa Bigot, Jérémie |
| contents | We consider statistical learning problems in which data are observed as a set of probability measures. Optimal transport (OT) is a popular tool to compare and manipulate such objects, but its computational cost becomes prohibitive when the measures have large support. We study a quantization-based approach in which all input measures are approximated by $K$-point discrete measures sharing a common support. We establish consistency of the resulting quantized measures. We further derive convergence guarantees for several OT-based downstream tasks computed from the quantized measures. Numerical experiments on synthetic and real datasets demonstrate that the proposed approach achieves performance comparable to individual quantization while substantially reducing runtime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_04907 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scalable Learning from Probability Measures with Mean Measure Quantization Gachon, Erell Cazelles, Elsa Bigot, Jérémie Machine Learning We consider statistical learning problems in which data are observed as a set of probability measures. Optimal transport (OT) is a popular tool to compare and manipulate such objects, but its computational cost becomes prohibitive when the measures have large support. We study a quantization-based approach in which all input measures are approximated by $K$-point discrete measures sharing a common support. We establish consistency of the resulting quantized measures. We further derive convergence guarantees for several OT-based downstream tasks computed from the quantized measures. Numerical experiments on synthetic and real datasets demonstrate that the proposed approach achieves performance comparable to individual quantization while substantially reducing runtime. |
| title | Scalable Learning from Probability Measures with Mean Measure Quantization |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2502.04907 |