Distribution Aligning Refinery of Pseudo-label
for Imbalanced Semi-supervised Learning
Jaehyung Kim1 Youngbum Hur2 Sejun Park1
Eunho Yang1,3 Sung Ju Hwang1,3 Jinwoo Shin1
1Korea Advanced Institute of Science and Technology (KAIST)
2Samsung Advanced Institute of Technology
3AITRICS

• Goal: reduce the need for labeled data by leveraging unlabeled data
• Common approach for SSL: generating pseudo-labels for unlabeled data
• Generating method and loss function are just different among them
• For example, the prediction of augmented data has been used as pseudo-labels
[Miyato et al., 2018; Berthelot et al., 2019; Sohn et al; 2020]
Semi-supervised Learning (SSL)
[Miyato et al. 2018] Virtual Adversarial Training: A Regularization Method for Supervised and Semi-supervised Learning. In PAMI, 2018
[Berthelot et al. 2019] MixMatch: A Holistic Approach to Semi-supervised Learning. In NeurIPS, 2019
[Sohn et al. 2020] Fixmatch: Simplifying Semi-sueprvised Learning with Consistency and Confidence. In NeurIPS, 2020
Generation method of pseudo-label in MixMatch [Berthelot et al. 2019]
1

• Balanced class distribution is typically assumed in the existing works for SSL
• However, many real-world datasets have an imbalanced class distribution
• Standard training (e.g. ERM) often fails to generalize at the minority classes
[Wang et al., 2017; Cao et al., 2019]
Class Imbalance in Training Data
Species [Van Horn et al. 2019] Places [Wang et al. 2017]
[Wang et al. 2017] Learning to Model the Tail. In NeurIPS, 2017
[Van Horn et al. 2019] The iNaturalist Species Classification and Detection Dataset. In CVPR, 2018
[Cao et al. 2019] Learning Imbalanced Datasets with Label-Distribution-Aware Margin Loss. In NeurIPS, 2019 2

• Assumption: class distribution of labeled and unlabeled data is highly imbalanced
Imbalanced Semi-supervised Learning
Imbalanced CIFAR-10
3

• Assumption: class distribution of labeled and unlabeled data is highly imbalanced
• Under imbalanced SSL scenario, recent SSL methods do not work well
• They generate pseudo-labels of unlabeled data from the model’s biased predictions
• Pseudo-labels are even more severely imbalanced ⟹ degradation on minority classes
Imbalanced Semi-supervised Learning
3
Results on imbalanced CIFAR-10

• Idea: refining the original, biased pseudo-labels from SSL methods
• Distribution of refined pseudo-labels matches the true class distribution of unlabeled data
• Simultaneously, refined pseudo-labels are constrained to be not too far from the original ones
• Refined pseudo-labels are obtained by solving a convex optimization
• : number of unlabeled data for class , : number of classes,
• Weight to preserve more information of high-confident original pseudo-labels
Distribution Aligning Refinery of Pseudo-label (DARP)
wm := H ˆyunlabeled
m
1
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Mk
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4

• For solving the optimization, we propose an efficient iterative algorithm
• It is a coordinate ascent algorithm for solving its Lagrangian dual with a provable guarantee
• Number of unlabeled data can be inferred or simply estimated
Distribution Aligning Refinery of Pseudo-label (DARP)
Simple matrix multiplication
Solved by existing efficient solver
5
{Mk}K
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Inferred or estimated

• Both labeled and unlabeled data have the same class distribution
• Number of unlabeled data is inferred from that of labeled data
• SSL: semi-supervised learning (not consider imbalance), RB: re-balancing (not use unlabeled data)
Experiments: “Same” Class Distributions
DARP improves the accuracy
of all the applied baselines
Biased pseudo-labels
degrade the performance
6*bACC / GM: arithmetic / geometric mean over class-wise accuracy*Larger ⟹ More severely imbalanced<latexit sha1_base64="4JXcQvmS1cZ5PKlmHsv0tSJYNSM=">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</latexit><latexit sha1_base64="4JXcQvmS1cZ5PKlmHsv0tSJYNSM=">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</latexit><latexit sha1_base64="4JXcQvmS1cZ5PKlmHsv0tSJYNSM=">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</latexit><latexit sha1_base64="4JXcQvmS1cZ5PKlmHsv0tSJYNSM=">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</latexit>

• Class distribution of unlabeled data is not same as that of labeled data
• Estimated number of unlabeled data is used for both DARP and ReMixMatch*
• SSL: semi-supervised learning (not consider imbalance), RB: re-balancing (not use unlabeled data)
Experiments: “Different” Class Distributions
7*bACC / GM: arithmetic / geometric mean over class-wise accuracy
As the gap between
distributions is increased,
the improvement from
DAPR is also increased
*Larger ⟹ More severely imbalanced<latexit sha1_base64="4JXcQvmS1cZ5PKlmHsv0tSJYNSM=">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</latexit><latexit sha1_base64="4JXcQvmS1cZ5PKlmHsv0tSJYNSM=">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</latexit><latexit sha1_base64="4JXcQvmS1cZ5PKlmHsv0tSJYNSM=">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</latexit><latexit sha1_base64="4JXcQvmS1cZ5PKlmHsv0tSJYNSM=">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</latexit>

• We investigate imbalanced SSL, which is an important but under-explored
• We identify that current SSL algorithms can be suffered under such a scenario
• We propose a simple, yet effective pseudo-label refining method (DARP)
Summary
In our paper, there are
• Formal derivation and proof
• Detailed analysis
• More experiments
• Results on other dataset
Thank you for your attention !