# Unlabelled Data Improves Bayesian Uncertainty Calibration under Covariate Shift

arXiv: https://arxiv.org/abs/2006.14988 · HTML: https://mlsanity.com/paper/2006.14988/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jun 2020.

## Built on by (most cited first, 21 of 21)

- [When and How Mixup Improves Calibration](https://mlsanity.com/paper/2102.06289/) (2021)
- [Bayesian Learning for Neural Networks: an algorithmic survey](https://mlsanity.com/paper/2211.11865/) (2022)
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- [An Information-theoretical Approach to Semi-supervised Learning under Covariate-shift](https://mlsanity.com/paper/2202.12123/) (2022)
- [JAWS: Auditing Predictive Uncertainty Under Covariate Shift](https://mlsanity.com/paper/2207.10716/) (2022)
- [Data-SUITE: Data-centric identification of in-distribution incongruous examples](https://mlsanity.com/paper/2202.08836/) (2022)
- [Training on Test Data with Bayesian Adaptation for Covariate Shift](https://mlsanity.com/paper/2109.12746/) (2021)
- [Conservative Prediction via Data-Driven Confidence Minimization](https://mlsanity.com/paper/2306.04974/) (2023)
- [Exploring Covariate and Concept Shift for Detection and Calibration of Out-of-Distribution Data](https://mlsanity.com/paper/2110.15231/) (2021)
- [Bayesian neural networks for predicting uncertainty in full-field material response](https://mlsanity.com/paper/2406.14838/) (2024)
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- [GeoConformal prediction: a model-agnostic framework of measuring the uncertainty of spatial prediction](https://mlsanity.com/paper/2412.08661/) (2024)
- [Stratified Learning: A General-Purpose Statistical Method for Improved Learning under Covariate Shift](https://mlsanity.com/paper/2106.11211/) (2021)
- [Adversarial Learning Networks: Source-free Unsupervised Domain Incremental Learning](https://mlsanity.com/paper/2301.12054/) (2023)
- [Probabilistic Shapley Value Modeling and Inference](https://mlsanity.com/paper/2402.04211/) (2024)
- [Bayes2IMC: In-Memory Computing for Bayesian Binary Neural Networks](https://mlsanity.com/paper/2411.07902/) (2024)
- [Efficient Learning Under Density Shift in Incremental Settings Using Cram'er-Rao-Based Regularization](https://mlsanity.com/paper/2502.12949/) (2025)
- [ClusterMine: Robust Label-Free Visual Out-Of-Distribution Detection via Concept Mining from Text Corpora](https://mlsanity.com/paper/2511.07068/) (2025)
- [From Local Geometry to Global Pseudo Labeling for Robust Positive Unlabeled Learning under Covariate Shift](https://mlsanity.com/paper/2605.31187/) (2026)
- [Cross-Dataset Transfer and Unknown-Class Detection in Imbalanced SAR Ship Classification](https://mlsanity.com/paper/2609.31658/) (2026)

## Abstract (arXiv)

Modern neural networks have proven to be powerful function approximators, providing state-of-the-art performance in a multitude of applications. They however fall short in their ability to quantify confidence in their predictions - this is crucial in high-stakes applications that involve critical decision-making. Bayesian neural networks (BNNs) aim at solving this problem by placing a prior distribution over the network's parameters, thereby inducing a posterior distribution that encapsulates predictive uncertainty. While existing variants of BNNs based on Monte Carlo dropout produce reliable (albeit approximate) uncertainty estimates over in-distribution data, they tend to exhibit over-confidence in predictions made on target data whose feature distribution differs from the training data, i.e., the covariate shift setup. In this paper, we develop an approximate Bayesian inference scheme based on posterior regularisation, wherein unlabelled target data are used as "pseudo-labels" of model confidence that are used to regularise the model's loss on labelled source data. We show that this approach significantly improves the accuracy of uncertainty quantification on covariate-shifted data sets, with minimal modification to the underlying model architecture. We demonstrate the utility of our method in the context of transferring prognostic models of prostate cancer across globally diverse populations.