Solving Empirical Bayes via Transformers

• URL: http://arxiv.org/abs/2502.09844v1
• Date: Fri, 14 Feb 2025 01:06:15 GMT
• Title: Solving Empirical Bayes via Transformers
• Authors: Anzo Teh, Mark Jabbour, Yury Polyanskiy,
• Abstract summary: This work applies modern AI tools (transformers) to solving one of the oldest statistical problems: Poisson means under empirical Bayes (Poisson-EB) setting.<n>A transformer model is pre-trained on a set of synthetically generated pairs $(X,theta)$ and learns to do in-context learning (ICL) by adapting to unknown $pi$.
• Score: 18.654470796004265
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 $\theta$ (with iid coordinates sampled from an unknown prior $\pi$) is estimated on the basis of $X=\mathrm{Poisson}(\theta)$. A transformer model is pre-trained on a set of synthetically generated pairs $(X,\theta)$ and learns to do in-context learning (ICL) by adapting to unknown $\pi$. Theoretically, we show that a sufficiently wide transformer can achieve vanishing regret with respect to an oracle estimator who knows $\pi$ 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.

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