# Transfer Learning for Nonparametric Classification: Minimax Rate and Adaptive Classifier

arXiv: https://arxiv.org/abs/1906.02903 · HTML: https://mlsanity.com/paper/1906.02903/

## Key facts

- Cited by 65 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jun 2019.

## Built on by (most cited first, 30 of 65)

- [Transfer Learning under High-dimensional Generalized Linear Models](https://mlsanity.com/paper/2105.14328/) (2021)
- [Optimally tackling covariate shift in RKHS-based nonparametric regression](https://mlsanity.com/paper/2205.02986/) (2022)
- [AdaNPC: Exploring Non-Parametric Classifier for Test-Time Adaptation](https://mlsanity.com/paper/2304.12566/) (2023)
- [CARROT: A Cost Aware Rate Optimal Router](https://mlsanity.com/paper/2502.03261/) (2025)
- [Adaptive and Robust Multi-Task Learning](https://mlsanity.com/paper/2202.05250/) (2022)
- [Transfer Learning for Contextual Multi-armed Bandits](https://mlsanity.com/paper/2211.12612/) (2022)
- [Weighted Training for Cross-Task Learning](https://mlsanity.com/paper/2105.14095/) (2021)
- [Transfer Learning for Nonparametric Regression: Non-asymptotic Minimax Analysis and Adaptive Procedure](https://mlsanity.com/paper/2401.12272/) (2024)
- [Targeting Underrepresented Populations in Precision Medicine: A Federated Transfer Learning Approach](https://mlsanity.com/paper/2108.12112/) (2021)
- [Pseudo-Labeling for Kernel Ridge Regression under Covariate Shift](https://mlsanity.com/paper/2302.10160/) (2023)
- [A transfer learning framework for weak-to-strong generalization](https://mlsanity.com/paper/2405.16236/) (2024)
- [Understanding new tasks through the lens of training data via exponential tilting](https://mlsanity.com/paper/2205.13577/) (2022)
- [A Class of Geometric Structures in Transfer Learning: Minimax Bounds and Optimality](https://mlsanity.com/paper/2202.11685/) (2022)
- [Mixture Proportion Estimation Beyond Irreducibility](https://mlsanity.com/paper/2306.01253/) (2023)
- [Model-free Test Time Adaptation for Out-Of-Distribution Detection](https://mlsanity.com/paper/2311.16420/) (2023)
- [Label Noise: Ignorance Is Bliss](https://mlsanity.com/paper/2411.00079/) (2024)
- [Transfer Learning with Uncertainty Quantification: Random Effect Calibration of Source to Target (RECaST)](https://mlsanity.com/paper/2211.16557/) (2022)
- [Transfer Learning Beyond Bounded Density Ratios](https://mlsanity.com/paper/2403.11963/) (2024)
- [Efficient and Multiply Robust Risk Estimation under General Forms of Dataset Shift](https://mlsanity.com/paper/2306.16406/) (2023)
- [Minimax And Adaptive Transfer Learning for Nonparametric Classification under Distributed Differential Privacy Constraints](https://mlsanity.com/paper/2406.20088/) (2024)
- [Deep Transfer Learning: Model Framework and Error Analysis](https://mlsanity.com/paper/2410.09383/) (2024)
- [Adaptive transfer learning](https://mlsanity.com/paper/2106.04455/) (2021)
- [On Causality in Domain Adaptation and Semi-Supervised Learning: an Information-Theoretic Analysis for Parametric Models](https://mlsanity.com/paper/2205.04641/) (2022)
- [Help Me Help You: The Aggregate Value of Source and Target Data in Transfer Learning](https://mlsanity.com/paper/2408.16189/) (2024)
- [Test-time Correlation Alignment](https://mlsanity.com/paper/2505.00533/) (2025)
- [Transfer Q-learning](https://mlsanity.com/paper/2202.04709/) (2022)
- [Classification Tree Pruning Under Covariate Shift](https://mlsanity.com/paper/2305.04335/) (2023)
- [Unified Transfer Learning Models in High-Dimensional Linear Regression](https://mlsanity.com/paper/2307.00238/) (2023)
- [Transfer Learning for Kernel-based Regression](https://mlsanity.com/paper/2310.13966/) (2023)
- [Transfer Learning for Latent Variable Network Models](https://mlsanity.com/paper/2406.03437/) (2024)

## Abstract (arXiv)

Human learners have the natural ability to use knowledge gained in one setting for learning in a different but related setting. This ability to transfer knowledge from one task to another is essential for effective learning. In this paper, we study transfer learning in the context of nonparametric classification based on observations from different distributions under the posterior drift model, which is a general framework and arises in many practical problems. We first establish the minimax rate of convergence and construct a rate-optimal two-sample weighted K-NN classifier. The results characterize precisely the contribution of the observations from the source distribution to the classification task under the target distribution. A data-driven adaptive classifier is then proposed and is shown to simultaneously attain within a logarithmic factor of the optimal rate over a large collection of parameter spaces. Simulation studies and real data applications are carried out where the numerical results further illustrate the theoretical analysis. Extensions to the case of multiple source distributions are also considered.