# Optimal Bayesian Transfer Learning

arXiv: https://arxiv.org/abs/1801.00857 · HTML: https://mlsanity.com/paper/1801.00857/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jan 2018.

## Built on by (most cited first, 17 of 17)

- [Pre-Train Your Loss: Easy Bayesian Transfer Learning with Informative Priors](https://mlsanity.com/paper/2205.10279/) (2022)
- [BR-SNIS: Bias Reduced Self-Normalized Importance Sampling](https://mlsanity.com/paper/2207.06364/) (2022)
- [Differentially Private Transferrable Deep Learning with Membership-Mappings](https://mlsanity.com/paper/2105.04615/) (2021)
- [Discriminative Noise Robust Sparse Orthogonal Label Regression-based Domain Adaptation](https://mlsanity.com/paper/2101.04563/) (2021)
- [From Multi-label Learning to Cross-Domain Transfer: A Model-Agnostic Approach](https://mlsanity.com/paper/2207.11742/) (2022)
- [Bayesian Transfer Learning](https://mlsanity.com/paper/2312.13484/) (2023)
- [Synthetic Model Combination: An Instance-wise Approach to Unsupervised Ensemble Learning](https://mlsanity.com/paper/2210.05320/) (2022)
- [Covariate-Elaborated Robust Partial Information Transfer with Conditional Spike-and-Slab Prior](https://mlsanity.com/paper/2404.03764/) (2024)
- [Geometrically Inspired Kernel Machines for Collaborative Learning Beyond Gradient Descent](https://mlsanity.com/paper/2407.04335/) (2024)
- [Robust Importance Sampling for Error Estimation in the Context of Optimal Bayesian Transfer Learning](https://mlsanity.com/paper/2109.02150/) (2021)
- [Information Theoretic Evaluation of Privacy-Leakage, Interpretability, and Transferability for Trustworthy AI](https://mlsanity.com/paper/2106.06046/) (2021)
- [Fully probabilistic design for knowledge fusion between Bayesian filters under uniform disturbances](https://mlsanity.com/paper/2109.10596/) (2021)
- [Cross-Domain Label Propagation for Domain Adaptation with Discriminative Graph Self-Learning](https://mlsanity.com/paper/2302.08710/) (2023)
- [Decision Boundary Optimization-Informed Domain Adaptation](https://mlsanity.com/paper/2502.06498/) (2025)
- [On Quantification of Borrowing of Information in Hierarchical Bayesian Models](https://mlsanity.com/paper/2509.17301/) (2025)
- [Transfer learning for nonparametric Bayesian networks](https://mlsanity.com/paper/2604.01021/) (2026)
- [Bridging Data Gaps in Structural Fragility Modeling through Transfer Learning: Methodology and Case Studies](https://mlsanity.com/paper/2606.18567/) (2026)

## Abstract (arXiv)

Transfer learning has recently attracted significant research attention, as it simultaneously learns from different source domains, which have plenty of labeled data, and transfers the relevant knowledge to the target domain with limited labeled data to improve the prediction performance. We propose a Bayesian transfer learning framework where the source and target domains are related through the joint prior density of the model parameters. The modeling of joint prior densities enables better understanding of the "transferability" between domains. We define a joint Wishart density for the precision matrices of the Gaussian feature-label distributions in the source and target domains to act like a bridge that transfers the useful information of the source domain to help classification in the target domain by improving the target posteriors. Using several theorems in multivariate statistics, the posteriors and posterior predictive densities are derived in closed forms with hypergeometric functions of matrix argument, leading to our novel closed-form and fast Optimal Bayesian Transfer Learning (OBTL) classifier. Experimental results on both synthetic and real-world benchmark data confirm the superb performance of the OBTL compared to the other state-of-the-art transfer learning and domain adaptation methods.