mlsanityData to 7 Oct 2026

TabMGP: Martingale Posterior with TabPFN

arXiv 2510.25154 ↗First posted 29 Oct 2025stat.ME stat.CO stat.MLcited by 6

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Abstract (arXiv)

Bayesian inference provides principled uncertainty quantification but is often limited by the challenges of prior and likelihood elicitation. The martingale posterior (MGP) (Fong et al., 2023) offers an alternative by replacing these requirements with a predictive rule. In addition, the MGP focuses inference on parameters defined through a loss function. This framework is especially resonant in the era of foundation transformers; practitioners increasingly leverage models like TabPFN for their state-of-the-art capabilities, yet often require epistemic uncertainty for a scientific estimand θ that need not parameterise the implicit latent model. The MGP provides a mechanism to recover these posterior distributions. We introduce TabMGP, an MGP built on TabPFN for tabular data. TabMGP produces credible sets with near-nominal coverage and often outperforms both handcrafted MGP constructions and standard Bayesian baselines.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 20 of its 41 references that are in the map. First posted on arXiv 29 Oct 2025.

Builds on

20 of 41 references.

References · 20

  1. 2022TabPFN: A Transformer That Solves Small Tabular Classification Problems in a Secondcited by 643
  2. 2021Transformers Can Do Bayesian Inferencecited by 338
  3. 2013A General Framework for Updating Belief Distributionscited by 172
  4. 2024Is In-Context Learning in Large Language Models Bayesian? A Martingale Perspectivecited by 51
  5. 2021Martingale posterior distributionscited by 43
  6. 2022Robust Bayesian Inference for Simulator-based Models via the MMD Posterior Bootstrapcited by 41
  7. 2023A Rigorous Link between Deep Ensembles and (Variational) Bayesian Methodscited by 31
  8. 2020A comparison of learning rate selection methods in generalized Bayesian inferencecited by 23
  9. 2023Martingale Posterior Neural Processescited by 15
  10. 2024Prediction-Centric Uncertainty Quantification via MMDcited by 8
  11. 2015On recursive Bayesian predictive distributionscited by 7
  12. 2024Exchangeable Sequence Models Quantify Uncertainty Over Latent Conceptscited by 7
8 more
  1. 2019Quasi-Bayes properties of a recursive procedure for mixturescited by 6
  2. 2024Quasi-Bayes meets Vinescited by 5
  3. 2025Uncertainty Quantification for Prior-Data Fitted Networks using Martingale Posteriorscited by 4
  4. 2025Bayesian Predictive Inference Beyond Martingalescited by 4
  5. 2022Quasi-Bayesian Nonparametric Density Estimation via Autoregressive Predictive Updatescited by 3
  6. 2024Bayesian Quantile Estimation and Regression with Martingale Posteriorscited by 3
  7. 2024Martingale Posterior Distributions for Log-concave Density Functionscited by 1
  8. 2024Asymptotics for parametric martingale posteriorscited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 6.

6 papers.

  1. 2026PFN-TS: Thompson Sampling for Contextual Bandits via Prior-Data Fitted Networkscited by 2
  2. 2026On Bayesian Softmax-Gated Mixture-of-Experts Modelscited by 1
  3. 2026Variational predictive resamplingcited by 0
  4. 2026Score-Based Martingale Posteriors for Deep Neural Networkscited by 0
  5. 2026Elicitation without Backpropagation: Steering Model Behavior by Optimizing the Latent Posteriorcited by 0
  6. 2026Can Tabular Foundation Models Amortize Statistical Inference?cited by 0