# Bayesian Semi-supervised Inference via a Debiased Modeling Approach

arXiv: https://arxiv.org/abs/2509.17385 · HTML: https://mlsanity.com/paper/2509.17385/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 44 references that are in the map.
- First posted on arXiv 22 Sep 2025.

## Builds on (most cited first, 13 of 13)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Deep Neural Networks for Estimation and Inference](https://mlsanity.com/paper/1809.09953/) (2018)
- [Semi-supervised Inference: General Theory and Estimation of Means](https://mlsanity.com/paper/1606.07268/) (2016)
- [Efficient and Adaptive Linear Regression in Semi-Supervised Settings](https://mlsanity.com/paper/1701.04889/) (2017)
- [Semi-supervised Inference for Explained Variance in High-dimensional Linear Regression and Its Applications](https://mlsanity.com/paper/1806.06179/) (2018)
- [High-dimensional semi-supervised learning: in search for optimal inference of the mean](https://mlsanity.com/paper/1902.00772/) (2019)
- [Nonparametric inverse probability weighted estimators based on the highly adaptive lasso](https://mlsanity.com/paper/2005.11303/) (2020)
- [Bayesian Indirect Inference Using a Parametric Auxiliary Model](https://mlsanity.com/paper/1505.03372/) (2015)
- [Debiased Bayesian inference for average treatment effects](https://mlsanity.com/paper/1909.12078/) (2019)
- [Bayesian Restricted Likelihood Methods: Conditioning on Insufficient Statistics in Bayesian Regression](https://mlsanity.com/paper/1812.07736/) (2018)
- [Double Robust Semi-Supervised Inference for the Mean: Selection Bias under MAR Labeling with Decaying Overlap](https://mlsanity.com/paper/2104.06667/) (2021)
- [Double Robust Bayesian Inference on Average Treatment Effects](https://mlsanity.com/paper/2211.16298/) (2022)
- [Semiparametric posterior corrections](https://mlsanity.com/paper/2306.06059/) (2023)

## Built on by (most cited first, 1 of 1)

- [Bayesian Semiparametric Causal Inference: Targeted Doubly Robust Estimation of Treatment Effects](https://mlsanity.com/paper/2511.15904/) (2025)

## Abstract (arXiv)

Inference in semi-supervised (SS) settings has gained substantial attention in recent years due to increased relevance in modern big-data problems. In a typical SS setting, there is a much larger-sized unlabeled data, containing only observations of predictors, and a moderately sized labeled data containing observations for both an outcome and the set of predictors. Such data naturally arises when the outcome, unlike the predictors, is costly or difficult to obtain. One of the primary statistical objectives in SS settings is to explore whether parameter estimation can be improved by exploiting the unlabeled data. We propose a novel Bayesian method for estimating the population mean in SS settings. The approach yields estimators that are both efficient and optimal for estimation and inference. The method itself has several interesting artifacts. The central idea behind the method is to model certain summary statistics of the data in a targeted manner, rather than the entire raw data itself, along with a novel Bayesian notion of debiasing. Specifying appropriate summary statistics crucially relies on a debiased representation of the population mean that incorporates unlabeled data through a flexible nuisance function while also learning its estimation bias. Combined with careful usage of sample splitting, this debiasing approach mitigates the effect of bias due to slow rates or misspecification of the nuisance parameter from the posterior of the final parameter of interest, ensuring its robustness and efficiency. Concrete theoretical results, via Bernstein--von Mises theorems, are established, validating all claims, and are further supported through extensive numerical studies. To our knowledge, this is possibly the first work on Bayesian inference in SS settings, and its central ideas also apply more broadly to other Bayesian semi-parametric inference problems.