# Hypothesis Transfer Learning via Transformation Functions

arXiv: https://arxiv.org/abs/1612.01020 · HTML: https://mlsanity.com/paper/1612.01020/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Dec 2016.

## Built on by (most cited first, 26 of 26)

- [Knowledge Distillation with the Reused Teacher Classifier](https://mlsanity.com/paper/2203.14001/) (2022)
- [Deep transfer operator learning for partial differential equations under conditional shift](https://mlsanity.com/paper/2204.09810/) (2022)
- [On Inductive Biases for Heterogeneous Treatment Effect Estimation](https://mlsanity.com/paper/2106.03765/) (2021)
- [On the Power of Multitask Representation Learning in Linear MDP](https://mlsanity.com/paper/2106.08053/) (2021)
- [Representation Learning Beyond Linear Prediction Functions](https://mlsanity.com/paper/2105.14989/) (2021)
- [A Scaling Law for Synthetic-to-Real Transfer: How Much Is Your Pre-training Effective?](https://mlsanity.com/paper/2108.11018/) (2021)
- [Generalized Knowledge Distillation via Relationship Matching](https://mlsanity.com/paper/2205.01915/) (2022)
- [Provable General Function Class Representation Learning in Multitask Bandits and MDPs](https://mlsanity.com/paper/2205.15701/) (2022)
- [Towards Robust Out-of-Distribution Generalization Bounds via Sharpness](https://mlsanity.com/paper/2403.06392/) (2024)
- [TransFusion: Covariate-Shift Robust Transfer Learning for High-Dimensional Regression](https://mlsanity.com/paper/2404.01153/) (2024)
- [Task Generalization With AutoRegressive Compositional Structure: Can Learning From D Tasks Generalize to DT Tasks?](https://mlsanity.com/paper/2502.08991/) (2025)
- [Smoothness Adaptive Hypothesis Transfer Learning](https://mlsanity.com/paper/2402.14966/) (2024)
- [Best-Effort Adaptation](https://mlsanity.com/paper/2305.05816/) (2023)
- [Hypothesis Transfer Learning with Surrogate Classification Losses: Generalization Bounds through Algorithmic Stability](https://mlsanity.com/paper/2305.19694/) (2023)
- [Diversity-enhancing Generative Network for Few-shot Hypothesis Adaptation](https://mlsanity.com/paper/2307.05948/) (2023)
- [Transfer learning with affine model transformation](https://mlsanity.com/paper/2210.09745/) (2022)
- [On Hypothesis Transfer Learning of Functional Linear Models](https://mlsanity.com/paper/2206.04277/) (2022)
- [Hypothesis Transfer in Bandits by Weighted Models](https://mlsanity.com/paper/2211.07387/) (2022)
- [A Prototype-Oriented Clustering for Domain Shift with Source Privacy](https://mlsanity.com/paper/2302.03807/) (2023)
- [Fixed-Gaussian Spectral Algorithms: Minimax Optimal Rates for Misspecified Learning and Transfer](https://mlsanity.com/paper/2501.10870/) (2025)
- [Towards Understanding the Benefit of Multitask Representation Learning in Decision Process](https://mlsanity.com/paper/2503.00345/) (2025)
- [Mixed-Sample SGD: an End-to-end Analysis of Supervised Transfer Learning](https://mlsanity.com/paper/2507.04194/) (2025)
- [ISTRBoost: Importance Sampling Transfer Regression using Boosting](https://mlsanity.com/paper/2204.12044/) (2022)
- [Source-free Domain Adaptation Requires Penalized Diversity](https://mlsanity.com/paper/2304.02798/) (2023)
- [Transfer Learning of Surrogate Models: Integrating Domain Warping and Affine Transformations](https://mlsanity.com/paper/2501.18344/) (2025)
- [Transfer Learning in Nonparametric Regression with Deep ReLU Networks](https://mlsanity.com/paper/2608.20255/) (2026)

## Abstract (arXiv)

We consider the Hypothesis Transfer Learning (HTL) problem where one incorporates a hypothesis trained on the source domain into the learning procedure of the target domain. Existing theoretical analysis either only studies specific algorithms or only presents upper bounds on the generalization error but not on the excess risk. In this paper, we propose a unified algorithm-dependent framework for HTL through a novel notion of transformation function, which characterizes the relation between the source and the target domains. We conduct a general risk analysis of this framework and in particular, we show for the first time, if two domains are related, HTL enjoys faster convergence rates of excess risks for Kernel Smoothing and Kernel Ridge Regression than those of the classical non-transfer learning settings. Experiments on real world data demonstrate the effectiveness of our framework.