BayesSum: Bayesian Quadrature in Discrete Spaces
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866917153421131776 |
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| author | Kang, Sophia Seulkee Briol, François-Xavier Karvonen, Toni Chen, Zonghao |
| author_facet | Kang, Sophia Seulkee Briol, François-Xavier Karvonen, Toni Chen, Zonghao |
| contents | This paper addresses the challenging computational problem of estimating intractable expectations over discrete domains. Existing approaches, including Monte Carlo and Russian Roulette estimators, are consistent but often require a large number of samples to achieve accurate results. We propose a novel estimator, \emph{BayesSum}, which is an extension of Bayesian quadrature to discrete domains. It is more sample efficient than alternatives due to its ability to make use of prior information about the integrand through a Gaussian process. We show this through theory, deriving a convergence rate significantly faster than Monte Carlo in a broad range of settings. We also demonstrate empirically that our proposed method does indeed require fewer samples on several synthetic settings as well as for parameter estimation for Conway-Maxwell-Poisson and Potts models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_16105 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | BayesSum: Bayesian Quadrature in Discrete Spaces Kang, Sophia Seulkee Briol, François-Xavier Karvonen, Toni Chen, Zonghao Machine Learning This paper addresses the challenging computational problem of estimating intractable expectations over discrete domains. Existing approaches, including Monte Carlo and Russian Roulette estimators, are consistent but often require a large number of samples to achieve accurate results. We propose a novel estimator, \emph{BayesSum}, which is an extension of Bayesian quadrature to discrete domains. It is more sample efficient than alternatives due to its ability to make use of prior information about the integrand through a Gaussian process. We show this through theory, deriving a convergence rate significantly faster than Monte Carlo in a broad range of settings. We also demonstrate empirically that our proposed method does indeed require fewer samples on several synthetic settings as well as for parameter estimation for Conway-Maxwell-Poisson and Potts models. |
| title | BayesSum: Bayesian Quadrature in Discrete Spaces |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2512.16105 |