# Formal Bayesian Transfer Learning via the Total Risk Prior

arXiv: https://arxiv.org/abs/2507.23768 · HTML: https://mlsanity.com/paper/2507.23768/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 50 references that are in the map.
- First posted on arXiv 31 Jul 2025.

## Builds on (most cited first, 15 of 15)

- [A Comprehensive Survey on Transfer Learning](https://mlsanity.com/paper/1911.02685/) (2019)
- [A Survey on Multi-Task Learning](https://mlsanity.com/paper/1707.08114/) (2017)
- [A Survey on Negative Transfer](https://mlsanity.com/paper/2009.00909/) (2020)
- [Transfer Learning for High-dimensional Linear Regression: Prediction, Estimation, and Minimax Optimality](https://mlsanity.com/paper/2006.10593/) (2020)
- [Transfer Learning under High-dimensional Generalized Linear Models](https://mlsanity.com/paper/2105.14328/) (2021)
- [Transfer Learning in Large-scale Gaussian Graphical Models with False Discovery Rate Control](https://mlsanity.com/paper/2010.11037/) (2020)
- [Targeting Underrepresented Populations in Precision Medicine: A Federated Transfer Learning Approach](https://mlsanity.com/paper/2108.12112/) (2021)
- [Hierarchical Bayesian Modelling for Knowledge Transfer Across Engineering Fleets via Multitask Learning](https://mlsanity.com/paper/2204.12404/) (2022)
- [Bayesian multi-domain learning for cancer subtype discovery from next-generation sequencing count data](https://mlsanity.com/paper/1810.09433/) (2018)
- [Transfer Learning with Uncertainty Quantification: Random Effect Calibration of Source to Target (RECaST)](https://mlsanity.com/paper/2211.16557/) (2022)
- [Modeling Structure and Country-specific Heterogeneity in Misclassification Matrices of Verbal Autopsy-based Cause of Death Classifiers](https://mlsanity.com/paper/2312.03192/) (2023)
- [Bayesian Transfer Learning](https://mlsanity.com/paper/2312.13484/) (2023)
- [A Bayesian shrinkage estimator for transfer learning](https://mlsanity.com/paper/2403.17321/) (2024)
- [Covariate-Elaborated Robust Partial Information Transfer with Conditional Spike-and-Slab Prior](https://mlsanity.com/paper/2404.03764/) (2024)
- [Sampling the Bayesian Elastic Net](https://mlsanity.com/paper/2501.00594/) (2024)

## Abstract (arXiv)

Existing methods for transfer learning struggle to deal with situations where the source datasets are limited and not guaranteed to be well-aligned with the target dataset. A typical strategy is to use the empirical loss minimizer on the source data as a prior mean for the target parameters. We propose using a risk minimizer conditional on source parameters instead. This allows us to construct a joint posterior for all parameters from the source and target datasets. As a consequence, we benefit from full Bayesian uncertainty quantification and can perform model averaging via Gibbs sampling over indicator variables governing the inclusion of each source dataset. We show how a particular instantiation of our prior leads to a Bayesian Lasso in a transformed coordinate system and describe connections between the Maximum a Posteriori estimate associated with our approach and the Trans-Lasso method. We find that the MAP estimator MSE-dominates the Trans-Lasso in the normal means setting when there is no regularization on the source datasets. Finally, we perform numerical experiments finding that our approach provides superior predictive performance relative to frequentist and Bayesian baselines on a genetics application, particularly when the source data are limited.