Estimating rank-one matrices with mismatched prior and noise: universality and large deviations
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866913635256762368 |
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| author | Guionnet, Alice Ko, Justin Krzakala, Florent Zdeborová, Lenka |
| author_facet | Guionnet, Alice Ko, Justin Krzakala, Florent Zdeborová, Lenka |
| contents | We prove a universality result that reduces the free energy of rank-one matrix estimation problems in the setting of mismatched prior and noise to the computation of the free energy for a modified Sherrington-Kirkpatrick spin glass. Our main result is an almost sure large deviation principle for the overlaps between the truth signal and the estimator for both the Bayes-optimal and mismatched settings. Through the large deviations principle, we recover the limit of the free energy in mismatched inference problems and the universality of the overlaps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_09283 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Estimating rank-one matrices with mismatched prior and noise: universality and large deviations Guionnet, Alice Ko, Justin Krzakala, Florent Zdeborová, Lenka Probability We prove a universality result that reduces the free energy of rank-one matrix estimation problems in the setting of mismatched prior and noise to the computation of the free energy for a modified Sherrington-Kirkpatrick spin glass. Our main result is an almost sure large deviation principle for the overlaps between the truth signal and the estimator for both the Bayes-optimal and mismatched settings. Through the large deviations principle, we recover the limit of the free energy in mismatched inference problems and the universality of the overlaps. |
| title | Estimating rank-one matrices with mismatched prior and noise: universality and large deviations |
| topic | Probability |
| url | https://arxiv.org/abs/2306.09283 |