# A Bayesian Approach to (Online) Transfer Learning: Theory and Algorithms

arXiv: https://arxiv.org/abs/2109.01377 · HTML: https://mlsanity.com/paper/2109.01377/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 68 references that are in the map.
- First posted on arXiv 3 Sep 2021.

## Builds on (most cited first, 22 of 22)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [XLNet: Generalized Autoregressive Pretraining for Language Understanding](https://mlsanity.com/paper/1906.08237/) (2019)
- [Learning Transferable Features with Deep Adaptation Networks](https://mlsanity.com/paper/1502.02791/) (2015)
- [Adversarial Discriminative Domain Adaptation](https://mlsanity.com/paper/1702.05464/) (2017)
- [A Comprehensive Survey on Transfer Learning](https://mlsanity.com/paper/1911.02685/) (2019)
- [Deep Visual Domain Adaptation: A Survey](https://mlsanity.com/paper/1802.03601/) (2018)
- [Deep Transfer Learning with Joint Adaptation Networks](https://mlsanity.com/paper/1605.06636/) (2016)
- [Bridging Theory and Algorithm for Domain Adaptation](https://mlsanity.com/paper/1904.05801/) (2019)
- [Characterizing and Avoiding Negative Transfer](https://mlsanity.com/paper/1811.09751/) (2018)
- [An Information-Theoretic Analysis of Thompson Sampling](https://mlsanity.com/paper/1403.5341/) (2014)
- [A survey on domain adaptation theory: learning bounds and theoretical guarantees](https://mlsanity.com/paper/2004.11829/) (2020)
- [Theoretical Analysis of Domain Adaptation with Optimal Transport](https://mlsanity.com/paper/1610.04420/) (2016)
- [Visual Domain Adaptation with Manifold Embedded Distribution Alignment](https://mlsanity.com/paper/1807.07258/) (2018)
- [Continuously Indexed Domain Adaptation](https://mlsanity.com/paper/2007.01807/) (2020)
- [Joint Geometrical and Statistical Alignment for Visual Domain Adaptation](https://mlsanity.com/paper/1705.05498/) (2017)
- [Transfer Learning with Dynamic Distribution Adaptation](https://mlsanity.com/paper/1909.08531/) (2019)
- [Minimum Excess Risk in Bayesian Learning](https://mlsanity.com/paper/2012.14868/) (2020)
- [AdaGraph: Unifying Predictive and Continuous Domain Adaptation through Graphs](https://mlsanity.com/paper/1903.07062/) (2019)
- [Generalization Bounds for Domain Adaptation](https://mlsanity.com/paper/1304.1574/) (2013)
- [Information-theoretic analysis for transfer learning](https://mlsanity.com/paper/2005.08697/) (2020)
- [Online Transfer Learning in Reinforcement Learning Domains](https://mlsanity.com/paper/1507.00436/) (2015)
- [Injecting Prior Knowledge for Transfer Learning into Reinforcement Learning Algorithms using Logic Tensor Networks](https://mlsanity.com/paper/1906.06576/) (2019)

## Built on by (most cited first, 3 of 3)

- ['No' Matters: Out-of-Distribution Detection in Multimodality Long Dialogue](https://mlsanity.com/paper/2410.23883/) (2024)
- [Multivariate and Online Transfer Learning with Uncertainty Quantification](https://mlsanity.com/paper/2411.12555/) (2024)
- [Transfer learning for nonparametric Bayesian networks](https://mlsanity.com/paper/2604.01021/) (2026)

## Abstract (arXiv)

Transfer learning is a machine learning paradigm where knowledge from one problem is utilized to solve a new but related problem. While conceivable that knowledge from one task could be useful for solving a related task, if not executed properly, transfer learning algorithms can impair the learning performance instead of improving it -- commonly known as negative transfer. In this paper, we study transfer learning from a Bayesian perspective, where a parametric statistical model is used. Specifically, we study three variants of transfer learning problems, instantaneous, online, and time-variant transfer learning. For each problem, we define an appropriate objective function, and provide either exact expressions or upper bounds on the learning performance using information-theoretic quantities, which allow simple and explicit characterizations when the sample size becomes large. Furthermore, examples show that the derived bounds are accurate even for small sample sizes. The obtained bounds give valuable insights into the effect of prior knowledge for transfer learning, at least with respect to our Bayesian formulation of the transfer learning problem. In particular, we formally characterize the conditions under which negative transfer occurs. Lastly, we devise two (online) transfer learning algorithms that are amenable to practical implementations, one of which does not require the parametric assumption. We demonstrate the effectiveness of our algorithms with real data sets, focusing primarily on when the source and target data have strong similarities.