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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.09844 |
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| _version_ | 1866912398583005184 |
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| author | Teh, Anzo Jabbour, Mark Polyanskiy, Yury |
| author_facet | Teh, Anzo Jabbour, Mark Polyanskiy, Yury |
| contents | This work applies modern AI tools (transformers) to solving one of the oldest statistical problems: Poisson means under empirical Bayes (Poisson-EB) setting. In Poisson-EB a high-dimensional mean vector $θ$ (with iid coordinates sampled from an unknown prior $π$) is estimated on the basis of $X=\mathrm{Poisson}(θ)$. A transformer model is pre-trained on a set of synthetically generated pairs $(X,θ)$ and learns to do in-context learning (ICL) by adapting to unknown $π$. Theoretically, we show that a sufficiently wide transformer can achieve vanishing regret with respect to an oracle estimator who knows $π$ as dimension grows to infinity. Practically, we discover that already very small models (100k parameters) are able to outperform the best classical algorithm (non-parametric maximum likelihood, or NPMLE) both in runtime and validation loss, which we compute on out-of-distribution synthetic data as well as real-world datasets (NHL hockey, MLB baseball, BookCorpusOpen). Finally, by using linear probes, we confirm that the transformer's EB estimator appears to internally work differently from either NPMLE or Robbins' estimators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09844 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Solving Empirical Bayes via Transformers Teh, Anzo Jabbour, Mark Polyanskiy, Yury Machine Learning This work applies modern AI tools (transformers) to solving one of the oldest statistical problems: Poisson means under empirical Bayes (Poisson-EB) setting. In Poisson-EB a high-dimensional mean vector $θ$ (with iid coordinates sampled from an unknown prior $π$) is estimated on the basis of $X=\mathrm{Poisson}(θ)$. A transformer model is pre-trained on a set of synthetically generated pairs $(X,θ)$ and learns to do in-context learning (ICL) by adapting to unknown $π$. Theoretically, we show that a sufficiently wide transformer can achieve vanishing regret with respect to an oracle estimator who knows $π$ as dimension grows to infinity. Practically, we discover that already very small models (100k parameters) are able to outperform the best classical algorithm (non-parametric maximum likelihood, or NPMLE) both in runtime and validation loss, which we compute on out-of-distribution synthetic data as well as real-world datasets (NHL hockey, MLB baseball, BookCorpusOpen). Finally, by using linear probes, we confirm that the transformer's EB estimator appears to internally work differently from either NPMLE or Robbins' estimators. |
| title | Solving Empirical Bayes via Transformers |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2502.09844 |