Learning from label proportions (LLP) is a weakly supervised setting where training data are grouped into bags with only bag-level label proportions observed, and the goal is to learn a classifier that predicts labels for individual instances. Recently, a large body of methods has emerged; however, most of them rely on the assumption that instance-label pairs are sampled i.i.d. and randomly assembled into bags, an assumption often violated in real-world scenarios. Our experimental results indicate that these methods perform suboptimally under non-random settings. In this work, we adopt a more realistic assumption: bags are sampled i.i.d., and instance labels are conditionally independent given the instances. Under this setting, we show that the label counts follow a Poisson multinomial distribution. Motivated by this observation, we propose LLP via moment matching (LLP-MM), a simple yet effective approach which leverages multi-order factorial moments as training objectives, encouraging the classifier predictions to match these moments and thereby more fully exploit the underlying statistical structure of the data. Extensive experiments on benchmark datasets under various bag construction strategies demonstrate the effectiveness of our approach while maintaining high computational efficiency. Our code is available at https://github.com/TianhaoMa5/LLP-MM.
Figures & tables
Figure 1: An illustration of structured bag construction based on instance features. A common example of a structured-bag assumption is to group instances with similar feature patterns into the same bag; for example, as shown in the figure, instances sharing the same shape feature are assigned to one bag.
Dataset
Method
16
32
64
128
Average
Rank
Random Bag
CIFAR-10
PM
93.51 ± 0.11
90.05 ± 0.22
75.23 ± 0.70
60.02 ± 0.33
79.70
4
DSQ
93.52 ± 0.15
91.39 ± 0.16
79.86 ± 0.77
61.90 ± 1.35
81.67
3
LLP-PVC
91.95 ± 0.07
90.55 ± 0.08
83.79 ± 0.57
64.44 ± 1.45
82.68
2
LLP-FC
75.29 ± 0.72
61.06 ± 0.87
53.89 ± 0.61
60.01 ± 0.24
62.56
7
ROT
93.21 ± 0.09
92.04 ± 0.10
80.52 ± 0.49
35.03 ± 1.25
75.20
5
Table 1: Best test accuracy under Random Bag and Cluster Bag constructions (mean ± std over three runs, %). The best result for each bag size and average is bold. Ranks use average accuracy with standard competition ranking. † indicates severe overfitting caused by negative loss values, with predictions collapsing to a single class.
Dataset
Method
16
32
64
128
Average
Rank
CIFAR-10
PM
91.00 ± 0.40
70.37 ± 0.32
65.38 ± 1.14
61.35 ± 0.52
72.03
4
DSQ
90.98 ± 0.16
74.24 ± 0.57
73.78 ± 1.11
68.83 ± 1.43
76.96
3
LLP-PVC
91.85 ± 0.13
89.18 ± 0.11
81.44 ± 0.61
66.78 ± 0.54
82.31
2
LLP-FC
58.53 ± 0.36
49.40 ± 0.64
49.00 ± 0.42
64.55 ± 1.15
55.37
7
ROT
92.93 ± 0.07
90.71 ± 0.11
61.53 ± 3.70
38.24 ± 1.22
70.85
5
EasyLLP
47.72 ± 1.40
37.40 ± 0.61
28.82 ± 2.44
24.09 ± 1.58
34.51
10
Table 2: Best test accuracy under α -First Bag construction (mean ± std over three runs, %). The best result for each bag size and average is bold. Ranks use average accuracy with standard competition ranking.
Method
Accuracy ↑
Macro-F1 ↑
Balanced Acc. ↑
Weighted-F1 ↑
PM
77.35±13.10
29.11±10.74
32.70±10.01
74.46±15.73
DSQ
92.39±1.33
56.89±7.65
60.08±8.30
92.70±1.57
LLP-PVC
92.82±1.94
58.42±4.31
61.63±4.27
91.58±2.33
LLP-FC
75.11±9.57
26.26±4.28
27.12±4.46
72.46±11.60
ROT
94.05±0.65
56.11±7.56
56.82±7.74
93.35±1.17
EasyLLP
37.98±8.32
11.51±1.77
14.50±0.85
39.28±3.11
Table 3: Test performance on KU-Optofil PBC (mean ± std over three runs, %). The best result in each column is bold.
Figure 2: Effect of the order parameter on prediction performance and runtime per epoch across different bag construction strategies and bag sizes. Runtime was measured on a single NVIDIA A100-SXM4-40GB GPU with an AMD EPYC 7742 64-Core Processor.
Appendix figures & tables3 assets
Supplementary material from the paper’s appendix.
Appendix
Symbol
Meaning
X
Input space.
Y={1,…,q}
Label space.
q
Number of classes.
m
Bag size.
Δq−1
The (q−1) -dimensional probability simplex {(p1,…,pq)∈Rq∣pk≥0,∑k=1qpk=1} .
xj∈X
The j -th instance in a bag.
Appendix
Table 4: Notation used in the paper.
Abbreviation
Meaning
WSL
Weakly supervised learning
LLP
Learning from label proportions
PMD
Poisson multinomial distribution
MM
Moment matching
LLP-MM
LLP via Moment Matching
Appendix
Table 5: Abbreviations used in the paper.
Bag
Method
16
32
64
128
Random
LLP-GAN
92.96±0.09
88.96±0.35
78.07±1.31
58.14±2.94
MM+GAN
93.56±0.19
91.18±0.22
80.69±1.17
67.41±1.41
Cluster
LLP-GAN
92.81±0.15
90.37±0.16
85.16±0.77
76.27±0.91
MM+GAN
93.62±0.05
91.79±0.16
87.17±0.38
76.53±1.93
α -First
LLP-GAN
91.04±0.59
74.75±0.55
69.52±4.12
66.25±2.23
MM+GAN
93.39±0.08
88.12±1.09
77.09±4.17
73.13±5.62
Appendix
Table 6: Best test accuracy on CIFAR-10 with GAN-based representation learning (mean ± std over three runs, %). The best result in each paired comparison is bold.
Learning from Label Proportions (LLP) is a weakly supervised problem in which the training data comprise bags, that is, groups of instances, each annotated only with bag-level class label proportions, and the objective is to learn a classifier that predicts instance-level labels. This setting is widely applicable when privacy constraints limit access to instance-level annotations or when fine-grained labeling is costly or impractical. In this work, we introduce a method that leverages Dual proportion Constraints (LLP-DC) during training, enforcing them at both the bag and instance levels. Specifically, the bag-level training aligns the mean prediction with the given proportion, and the instance-level training aligns hard pseudo-labels that satisfy the proportion constraint, where a minimum-cost maximum-flow algorithm is used to generate hard pseudo-labels. Extensive experimental results across various benchmark datasets empirically validate that LLP-DC consistently improves over previous LLP methods across datasets and bag sizes. The code is publicly available at https://github.com/TianhaoMa5/CV PR2026_Findings_LLP_DC.
Tianhao Ma, Ximing Li, Changchun Li +1
The University of Tokyo, Japan · College of Computer Science and Technology, Jilin University, China · Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University, China +1
Prior work on partial labels learning (PLL) has shown that learning is possible even when each instance is associated with a bag of labels, rather than a single accurate but costly label. However, the necessary conditions for learning with partial labels remain unclear, and existing PLL methods are effective only in specific scenarios. In this work, we mathematically characterize the settings in which PLL is feasible. In addition, we present PL A-kNN, an adaptive nearest-neighbors algorithm for PLL that is effective in general scenarios and enjoys strong performance guarantees. Experimental results corroborate that PL A-kNN can outperform state-of-the-art methods in general PLL scenarios.
Nicolas A. Errandonea, Santiago Mazuelas, Jose A. Lozano +1
Basque Center for Applied Mathematics, Bilbao, Spain · Ikerbasque, Basque Foundation for Science · University of the Basque Country, Spain +1
Semi-supervised learning (SSL) often suffers under class imbalance, where pseudo-labeling amplifies majority bias and suppresses minority performance. We address this issue with a lightweight framework that, to our knowledge, is the first to introduce Proportion Loss from learning from label proportions (LLP) into SSL as a regularization term. Proportion Loss aligns model predictions with the global class distribution, mitigating bias across both majority and minority classes. To further stabilize training, we formulate a stochastic variant that accounts for fluctuations in mini-batch composition. Experiments on the Long-tailed CIFAR-10 benchmark show that integrating Proportion Loss into FixMatch and ReMixMatch consistently improves performance over the baselines across imbalance severities and label ratios, and achieves competitive or superior results compared to existing CISSL methods, particularly under scarce-label conditions.