# Semi-supervised Vector-valued Learning: Improved Bounds and Algorithms

arXiv: https://arxiv.org/abs/1909.04883 · HTML: https://mlsanity.com/paper/1909.04883/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Sep 2019.

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

- [Adversarially robust generalization theory via Jacobian regularization for deep neural networks](https://mlsanity.com/paper/2412.12449/) (2024)
- [Sharper Risk Bound for Multi-Task Learning with Multi-Graph Dependent Data](https://mlsanity.com/paper/2502.18167/) (2025)
- [Theoretical Analysis of Measure Consistency Regularization for Partially Observed Data](https://mlsanity.com/paper/2602.01437/) (2026)

## Abstract (arXiv)

Vector-valued learning, where the output space admits a vector-valued structure, is an important problem that covers a broad family of important domains, e.g. multi-task learning and transfer learning. Using local Rademacher complexity and unlabeled data, we derive novel semi-supervised excess risk bounds for general vector-valued learning from both kernel perspective and linear perspective. The derived bounds are much sharper than existing ones and the convergence rates are improved from the square root of labeled sample size to the square root of total sample size or directly dependent on labeled sample size. Motivated by our theoretical analysis, we propose a general semi-supervised algorithm for efficiently learning vector-valued functions, incorporating both local Rademacher complexity and Laplacian regularization. Extensive experimental results illustrate the proposed algorithm significantly outperforms the compared methods, which coincides with our theoretical findings.