# A Unified and Stable Risk Minimization Framework for Weakly Supervised Learning with Theoretical Guarantees

arXiv: https://arxiv.org/abs/2511.22823 · HTML: https://mlsanity.com/paper/2511.22823/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 51 references that are in the map.
- First posted on arXiv 28 Nov 2025.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels](https://mlsanity.com/paper/1805.07836/) (2018)
- [Confident Learning: Estimating Uncertainty in Dataset Labels](https://mlsanity.com/paper/1911.00068/) (2019)
- [How does Disagreement Help Generalization against Label Corruption?](https://mlsanity.com/paper/1901.04215/) (2019)
- [Positive-Unlabeled Learning with Non-Negative Risk Estimator](https://mlsanity.com/paper/1703.00593/) (2017)
- [Learning from positive and unlabeled data: a survey](https://mlsanity.com/paper/1811.04820/) (2018)
- [Progressive Identification of True Labels for Partial-Label Learning](https://mlsanity.com/paper/2002.08053/) (2020)
- [Learning from Complementary Labels](https://mlsanity.com/paper/1705.07541/) (2017)
- [Do We Need Zero Training Loss After Achieving Zero Training Error?](https://mlsanity.com/paper/2002.08709/) (2020)
- [Class-prior Estimation for Learning from Positive and Unlabeled Data](https://mlsanity.com/paper/1611.01586/) (2016)
- [On the Minimal Supervision for Training Any Binary Classifier from Only Unlabeled Data](https://mlsanity.com/paper/1808.10585/) (2018)
- [Dist-PU: Positive-Unlabeled Learning from a Label Distribution Perspective](https://mlsanity.com/paper/2212.02801/) (2022)
- [Classification from Pairwise Similarity and Unlabeled Data](https://mlsanity.com/paper/1802.04381/) (2018)
- [Mitigating Overfitting in Supervised Classification from Two Unlabeled Datasets: A Consistent Risk Correction Approach](https://mlsanity.com/paper/1910.08974/) (2019)
- [Classification from Pairwise Similarities/Dissimilarities and Unlabeled Data via Empirical Risk Minimization](https://mlsanity.com/paper/1904.11717/) (2019)
- [Text Compression-aided Transformer Encoding](https://mlsanity.com/paper/2102.05951/) (2021)
- [Learning with Proper Partial Labels](https://mlsanity.com/paper/2112.12303/) (2021)
- [Multi-class Classification from Multiple Unlabeled Datasets with Partial Risk Regularization](https://mlsanity.com/paper/2207.01555/) (2022)
- [Auxiliary Tasks Enhanced Dual-affinity Learning for Weakly Supervised Semantic Segmentation](https://mlsanity.com/paper/2403.01156/) (2024)
- [Defect detection using weakly supervised learning](https://mlsanity.com/paper/2303.15092/) (2023)
- [Sentinel-1 SAR Based Weakly Supervised Learning For Tropical Forest Mapping](https://mlsanity.com/paper/2408.00107/) (2024)

## Abstract (arXiv)

Weakly supervised learning has emerged as a practical alternative to fully supervised learning when complete and accurate labels are costly or infeasible to acquire. However, many existing methods are tailored to specific supervision patterns -- such as positive-unlabeled (PU), unlabeled-unlabeled (UU), complementary-label (CLL), partial-label (PLL), or similarity-unlabeled annotations -- and rely on post-hoc corrections to mitigate instability induced by indirect supervision. We propose a principled, unified framework that bypasses such post-hoc adjustments by directly formulating a stable surrogate risk grounded in the structure of weakly supervised data. The formulation naturally subsumes diverse settings -- including PU, UU, CLL, PLL, multi-class unlabeled, and tuple-based learning -- under a single optimization objective. We further establish a non-asymptotic generalization bound via Rademacher complexity that clarifies how supervision structure, model capacity, and sample size jointly govern performance. Beyond this, we analyze the effect of class-prior misspecification on the bound, deriving explicit terms that quantify its impact, and we study identifiability, giving sufficient conditions -- most notably via supervision stratification across groups -- under which the target risk is recoverable. Extensive experiments show consistent gains across class priors, dataset scales, and class counts -- without heuristic stabilization -- while exhibiting robustness to overfitting.