# Nearly Optimal Bayesian Inference for Structural Missingness

arXiv: https://arxiv.org/abs/2601.18500 · HTML: https://mlsanity.com/paper/2601.18500/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 52 references that are in the map.
- First posted on arXiv 26 Jan 2026.

## Builds on (most cited first, 28 of 28)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [TabPFN: A Transformer That Solves Small Tabular Classification Problems in a Second](https://mlsanity.com/paper/2207.01848/) (2022)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Transformers Can Do Bayesian Inference](https://mlsanity.com/paper/2112.10510/) (2021)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [TabICL: A Tabular Foundation Model for In-Context Learning on Large Data](https://mlsanity.com/paper/2502.05564/) (2025)
- [Handling Missing Data with Graph Representation Learning](https://mlsanity.com/paper/2010.16418/) (2020)
- [TabPFN-2.5: Advancing the State of the Art in Tabular Foundation Models](https://mlsanity.com/paper/2511.08667/) (2025)
- [Missing Data Imputation using Optimal Transport](https://mlsanity.com/paper/2002.03860/) (2020)
- [Minimizing Trajectory Curvature of ODE-based Generative Models](https://mlsanity.com/paper/2301.12003/) (2023)
- [HyperImpute: Generalized Iterative Imputation with Automatic Model Selection](https://mlsanity.com/paper/2206.07769/) (2022)
- [PFNs4BO: In-Context Learning for Bayesian Optimization](https://mlsanity.com/paper/2305.17535/) (2023)
- [Functional Flow Matching](https://mlsanity.com/paper/2305.17209/) (2023)
- [Generating and Imputing Tabular Data via Diffusion and Flow-based Gradient-Boosted Trees](https://mlsanity.com/paper/2309.09968/) (2023)
- [Do-PFN: In-Context Learning for Causal Effect Estimation](https://mlsanity.com/paper/2506.06039/) (2025)
- [CausalPFN: Amortized Causal Effect Estimation via In-Context Learning](https://mlsanity.com/paper/2506.07918/) (2025)
- [MCFlow: Monte Carlo Flow Models for Data Imputation](https://mlsanity.com/paper/2003.12628/) (2020)
- [ReMasker: Imputing Tabular Data with Masked Autoencoding](https://mlsanity.com/paper/2309.13793/) (2023)
- [TabPFN Unleashed: A Scalable and Effective Solution to Tabular Classification Problems](https://mlsanity.com/paper/2502.02527/) (2025)
- [Transformed Distribution Matching for Missing Value Imputation](https://mlsanity.com/paper/2302.10363/) (2023)
- [Learning from data with structured missingness](https://mlsanity.com/paper/2304.01429/) (2023)
- [Position: The Future of Bayesian Prediction Is Prior-Fitted](https://mlsanity.com/paper/2505.23947/) (2025)
- [DiffPuter: Empowering Diffusion Models for Missing Data Imputation](https://mlsanity.com/paper/2405.20690/) (2024)
- [Data Imputation with Iterative Graph Reconstruction](https://mlsanity.com/paper/2212.02810/) (2022)
- [Interpretable Machine Learning for TabPFN](https://mlsanity.com/paper/2403.10923/) (2024)
- [Optimal Transport for Structure Learning Under Missing Data](https://mlsanity.com/paper/2402.15255/) (2024)

## Abstract (arXiv)

Structural missingness breaks 'just impute and train': values can be undefined by causal or logical constraints, and the mask may depend on observed variables, unobserved variables (MNAR), and other missingness indicators. It simultaneously brings (i) a catch-22 situation with causal loop, prediction needs the missing features, yet inferring them depends on the missingness mechanism, (ii) under MNAR, the unseen are different, the missing part can come from a shifted distribution, and (iii) plug-in imputation, a single fill-in can lock in uncertainty and yield overconfident, biased decisions. In the Bayesian view, prediction via the posterior predictive distribution integrates over the full model posterior uncertainty, rather than relying on a single point estimate. This framework decouples (i) learning an in-model missing-value posterior from (ii) label prediction by optimizing the predictive posterior distribution, enabling posterior integration. This decoupling yields an in-model almost-free-lunch: once the posterior is learned, prediction is plug-and-play while preserving uncertainty propagation. It achieves SOTA on 43 classification and 15 imputation benchmarks, with finite-sample near Bayes-optimality guarantees under our SCM prior.