# TabMGP: Martingale Posterior with TabPFN

arXiv: https://arxiv.org/abs/2510.25154 · HTML: https://mlsanity.com/paper/2510.25154/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 41 references that are in the map.
- First posted on arXiv 29 Oct 2025.

## Builds on (most cited first, 20 of 20)

- [TabPFN: A Transformer That Solves Small Tabular Classification Problems in a Second](https://mlsanity.com/paper/2207.01848/) (2022)
- [Transformers Can Do Bayesian Inference](https://mlsanity.com/paper/2112.10510/) (2021)
- [A General Framework for Updating Belief Distributions](https://mlsanity.com/paper/1306.6430/) (2013)
- [Is In-Context Learning in Large Language Models Bayesian? A Martingale Perspective](https://mlsanity.com/paper/2406.00793/) (2024)
- [Martingale posterior distributions](https://mlsanity.com/paper/2103.15671/) (2021)
- [Robust Bayesian Inference for Simulator-based Models via the MMD Posterior Bootstrap](https://mlsanity.com/paper/2202.04744/) (2022)
- [A Rigorous Link between Deep Ensembles and (Variational) Bayesian Methods](https://mlsanity.com/paper/2305.15027/) (2023)
- [A comparison of learning rate selection methods in generalized Bayesian inference](https://mlsanity.com/paper/2012.11349/) (2020)
- [Martingale Posterior Neural Processes](https://mlsanity.com/paper/2304.09431/) (2023)
- [Prediction-Centric Uncertainty Quantification via MMD](https://mlsanity.com/paper/2410.11637/) (2024)
- [On recursive Bayesian predictive distributions](https://mlsanity.com/paper/1508.07448/) (2015)
- [Exchangeable Sequence Models Quantify Uncertainty Over Latent Concepts](https://mlsanity.com/paper/2408.03307/) (2024)
- [Quasi-Bayes properties of a recursive procedure for mixtures](https://mlsanity.com/paper/1902.10708/) (2019)
- [Quasi-Bayes meets Vines](https://mlsanity.com/paper/2406.12764/) (2024)
- [Uncertainty Quantification for Prior-Data Fitted Networks using Martingale Posteriors](https://mlsanity.com/paper/2505.11325/) (2025)
- [Bayesian Predictive Inference Beyond Martingales](https://mlsanity.com/paper/2507.21874/) (2025)
- [Quasi-Bayesian Nonparametric Density Estimation via Autoregressive Predictive Updates](https://mlsanity.com/paper/2206.06462/) (2022)
- [Bayesian Quantile Estimation and Regression with Martingale Posteriors](https://mlsanity.com/paper/2406.03358/) (2024)
- [Martingale Posterior Distributions for Log-concave Density Functions](https://mlsanity.com/paper/2401.14515/) (2024)
- [Asymptotics for parametric martingale posteriors](https://mlsanity.com/paper/2410.17692/) (2024)

## Built on by (most cited first, 9 of 9)

- [TabPFN-3: Technical Report](https://mlsanity.com/paper/2605.13986/) (2026)
- [PFN-TS: Thompson Sampling for Contextual Bandits via Prior-Data Fitted Networks](https://mlsanity.com/paper/2605.10137/) (2026)
- [On Bayesian Softmax-Gated Mixture-of-Experts Models](https://mlsanity.com/paper/2604.20551/) (2026)
- [Concentration and Calibration in Predictive Bayesian Inference](https://mlsanity.com/paper/2605.00455/) (2026)
- [Variational predictive resampling](https://mlsanity.com/paper/2605.11168/) (2026)
- [Score-Based Martingale Posteriors for Deep Neural Networks](https://mlsanity.com/paper/2606.15725/) (2026)
- [Elicitation without Backpropagation: Steering Model Behavior by Optimizing the Latent Posterior](https://mlsanity.com/paper/2607.18804/) (2026)
- [Can Tabular Foundation Models Amortize Statistical Inference?](https://mlsanity.com/paper/2609.33114/) (2026)
- [Characterizing the Separability Gap in Prior-Data Fitted Networks](https://mlsanity.com/paper/2610.14989/) (2026)

## 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.