SlideShare a Scribd company logo
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
<latexit sha1_base64="n+xr3jkNc+0CjJ75U0Z2bnxc7js=">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</latexit><latexit sha1_base64="n+xr3jkNc+0CjJ75U0Z2bnxc7js=">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</latexit><latexit sha1_base64="n+xr3jkNc+0CjJ75U0Z2bnxc7js=">AAADDHicjVHLShxBFD12jK8YncSlm8ZB0EWGbhEUISBkEZcKGRVsHap7amYKqx9UVytD07+QP8kuu5BtfsCFCGaf/IW3yhJMJJhquurUufecqls3LqQodRDcTHgvJl9OTc/Mzr2af72w2Hrz9rDMK5XwbpLLXB3HrORSZLyrhZb8uFCcpbHkR/H5BxM/uuCqFHn2SY8LfpqyYSYGImGaqF7r42WvTpud95HkA722d79EI6brcWMiZ3WUMj1SaV1lksVc8n7TREoMR3rdLWf1u7DptdpBJ7DDfwpCB9pwYz9vXSNCHzkSVEjBkUETlmAo6TtBiAAFcaeoiVOEhI1zNJgjbUVZnDIYsec0D2l34tiM9saztOqETpH0K1L6WCVNTnmKsDnNt/HKOhv2X9619TR3G9MaO6+UWI0Rsc/pHjL/V2dq0Rhg29YgqKbCMqa6xLlU9lXMzf1HVWlyKIgzuE9xRTixyod39q2mtLWbt2U2/stmGtbsE5db4be5JTU4/LudT8HhRicMOuHBZnt307V6BstYwRr1cwu72MM+uuT9BVe4xU/vs/fV++Z9v0/1JpxmCX8M78cdoxSt4w==</latexit><latexit sha1_base64="G30nvnJkyKBlKcCymNnrqTxJgV4=">AAACtXicjVLLSgMxFD0dX7VWrWs3g0VwVTJudCnowmUF+4BaZCZNa+y8TDJCKf6AWz9O/AP9C2/iCGoRzTAzJ+fec5KbmyiPpTaMvVS8peWV1bXqem2jXtvc2m7UuzorFBcdnsWZ6kehFrFMRcdIE4t+rkSYRLHoRdNTG+/dC6Vlll6aWS6GSThJ5Vjy0BDVvm40WYu54S+CoARNlCNrPOMKI2TgKJBAIIUhHCOEpmeAAAw5cUPMiVOEpIsLPKBG2oKyBGWExE7pO6HZoGRTmltP7dScVonpVaT0sU+ajPIUYbua7+KFc7bsb95z52n3NqN/VHolxBrcEPuX7jPzvzpbi8EYx64GSTXljrHV8dKlcKdid+5/qcqQQ06cxSOKK8LcKT/P2Xca7Wq3Zxu6+KvLtKyd8zK3wJvdJfU3+NnNRdA9bAWsFVwwVLGLPRxQG49wgnO00SHLER7x5J15t97dxz3wKuWF2MG34el34YWM3A==</latexit><latexit sha1_base64="aQ6VNeX17tKdKtbSum7ouo/KEII=">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</latexit><latexit sha1_base64="aQ6VNeX17tKdKtbSum7ouo/KEII=">AAADAXicjVLLahsxFD2evhLXbdxusxlqCumiZqablkAgkEWzTCB+gCc2mrFsC2seaDQpZphf6J90113pV3QRAu0++YteKWNoYkqrYaSjc+850pUUZlLk2vOuGs6Dh48eP9nabj5tPXu+037R6udpoSLei1KZqmHIci5FwntaaMmHmeIsDiUfhMsjEx9ccJWLNDnTq4yfx2yeiJmImCZq0v74aVLG1f5BIPlM7x3fDsGC6XJVmci4DGKmFyoui0SykEs+rapAiflCv6mHcfnWrybtjtf1bHM3gV+DDup2krYvEWCKFBEKxOBIoAlLMOT0jeDDQ0bcOUriFCFh4xwVmqQtKItTBiN2Sf2cZqOaTWhuPHOrjmgVSb8ipYvXpEkpTxE2q7k2Xlhnw/7Nu7SeZm8rGsPaKyZWY0Hsv3TrzP/VmVo0ZvhgaxBUU2YZU11UuxT2VMzO3T+q0uSQEWfwlOKKcGSV63N2rSa3tZuzZTZ+bTMNa+ZRnVvgxuySLti/f52boP+u63td/9TDFnbxCnt0je9xiGOcoEeWX/ADP/HL+ex8db7dPgWnUb+Jl7jTnO+/AS2lrHk=</latexit><latexit sha1_base64="+iaWb8t9MW732eOHdR8CMqoyYM8=">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</latexit><latexit sha1_base64="n+xr3jkNc+0CjJ75U0Z2bnxc7js=">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</latexit><latexit sha1_base64="n+xr3jkNc+0CjJ75U0Z2bnxc7js=">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</latexit><latexit sha1_base64="n+xr3jkNc+0CjJ75U0Z2bnxc7js=">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</latexit><latexit sha1_base64="n+xr3jkNc+0CjJ75U0Z2bnxc7js=">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</latexit><latexit sha1_base64="n+xr3jkNc+0CjJ75U0Z2bnxc7js=">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</latexit><latexit sha1_base64="n+xr3jkNc+0CjJ75U0Z2bnxc7js=">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</latexit>
wm<latexit sha1_base64="opxQNj2swkpdqHZm1SeBabun9/4=">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</latexit><latexit sha1_base64="opxQNj2swkpdqHZm1SeBabun9/4=">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</latexit><latexit sha1_base64="opxQNj2swkpdqHZm1SeBabun9/4=">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</latexit><latexit sha1_base64="opxQNj2swkpdqHZm1SeBabun9/4=">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</latexit>
Mk<latexit sha1_base64="V0qzsExbnNA+b2pD24RDP3NMMUo=">AAACxnicjVHLSsNAFD2Nr1pfVZdugkVwVRIp6LLgphuhom2FWkoyndbQvJhMlFIEf8Ctfpr4B/oX3hmnoBbRCUnOnHvPmbn3+mkYZNJxXgvWwuLS8kpxtbS2vrG5Vd7eaWdJLhhvsSRMxJXvZTwMYt6SgQz5VSq4F/kh7/jjUxXv3HKRBUl8KScp70XeKA6GAfMkURdn/XG/XHGqjl72PHANqMCsZlJ+wTUGSMCQIwJHDEk4hIeMni5cOEiJ62FKnCAU6DjHPUqkzSmLU4ZH7Ji+I9p1DRvTXnlmWs3olJBeQUobB6RJKE8QVqfZOp5rZ8X+5j3VnupuE/r7xisiVuKG2L90s8z/6lQtEkOc6BoCqinVjKqOGZdcd0Xd3P5SlSSHlDiFBxQXhJlWzvpsa02ma1e99XT8TWcqVu2Zyc3xrm5JA3Z/jnMetI+qrlN1z2uVes2Muog97OOQ5nmMOhpookXeIzziCc9Ww4qt3Lr7TLUKRrOLb8t6+AAtH5Ai</latexit><latexit sha1_base64="V0qzsExbnNA+b2pD24RDP3NMMUo=">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</latexit><latexit sha1_base64="V0qzsExbnNA+b2pD24RDP3NMMUo=">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</latexit><latexit sha1_base64="V0qzsExbnNA+b2pD24RDP3NMMUo=">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</latexit>
k<latexit sha1_base64="MaenEFsKtSUOisFFlS12vTNpRAI=">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</latexit><latexit sha1_base64="MaenEFsKtSUOisFFlS12vTNpRAI=">AAACxHicjVHLSsNAFD2Nr1pfVZdugkVwVRIp6LIgiMsW7ANqkWQ6raHTJEwmQin6A27128Q/0L/wzjgFtYhOSHLm3HvOzL03TEWUKc97LThLyyura8X10sbm1vZOeXevnSW5ZLzFEpHIbhhkXEQxb6lICd5NJQ8moeCdcHyu4507LrMoia/UNOX9STCKo2HEAkVUc3xTrnhVzyx3EfgWVGBXIym/4BoDJGDIMQFHDEVYIEBGTw8+PKTE9TEjThKKTJzjHiXS5pTFKSMgdkzfEe16lo1prz0zo2Z0iqBXktLFEWkSypOE9WmuiefGWbO/ec+Mp77blP6h9ZoQq3BL7F+6eeZ/dboWhSHOTA0R1ZQaRlfHrEtuuqJv7n6pSpFDSpzGA4pLwswo5312jSYzteveBib+ZjI1q/fM5uZ417ekAfs/x7kI2idV36v6zVqlXrOjLuIAhzimeZ6ijks00DLej3jCs3PhCCdz8s9Up2A1+/i2nIcPSAaPYg==</latexit><latexit sha1_base64="MaenEFsKtSUOisFFlS12vTNpRAI=">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</latexit><latexit sha1_base64="MaenEFsKtSUOisFFlS12vTNpRAI=">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</latexit>
K<latexit sha1_base64="Zoz/5QEOWbZ/Nm7/Z1wf/UlhXR4=">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</latexit><latexit sha1_base64="Zoz/5QEOWbZ/Nm7/Z1wf/UlhXR4=">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</latexit><latexit sha1_base64="Zoz/5QEOWbZ/Nm7/Z1wf/UlhXR4=">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</latexit><latexit sha1_base64="Zoz/5QEOWbZ/Nm7/Z1wf/UlhXR4=">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</latexit>
M =
XK
k=1
Mk
<latexit sha1_base64="vDpCUpTnsJnTuCbeJVpKVfhI1js=">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</latexit><latexit sha1_base64="vDpCUpTnsJnTuCbeJVpKVfhI1js=">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</latexit><latexit sha1_base64="vDpCUpTnsJnTuCbeJVpKVfhI1js=">AAAC5HicjVHLSsNAFD2Nr/qOunRhsAiuSqKCbgqCG0EKFWwrtLUkcapD8yIzEaR06c6duPUH3Oq3iH+gf+GdMYIPRCckOXPuPWfm3uslARfStp8Lxsjo2PhEcXJqemZ2bt5cWGyIOEt9VvfjIE6PPVewgEesLrkM2HGSMjf0Atb0+nsq3rxgqeBxdCQvE9YJ3bOI97jvSqK65krVqlhtkYXtKA54yKXoDvoVZ3gyOBha1W6/a5bssq2X9RM4OSghX7XYfEIbp4jhI0MIhgiScAAXgp4WHNhIiOtgQFxKiOs4wxBTpM0oi1GGS2yfvme0a+VsRHvlKbTap1MCelNSWlgjTUx5KWF1mqXjmXZW7G/eA+2p7nZJfy/3ComVOCf2L91H5n91qhaJHnZ0DZxqSjSjqvNzl0x3Rd3c+lSVJIeEOIVPKZ4S9rXyo8+W1ghdu+qtq+MvOlOxau/nuRle1S1pwM73cf4EjY2yY5edw63S7mY+6iKWsYp1muc2drGPGurkfYV7PODR6BnXxo1x+55qFHLNEr4s4+4Nzi+boQ==</latexit><latexit sha1_base64="vDpCUpTnsJnTuCbeJVpKVfhI1js=">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</latexit>
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
k=1<latexit sha1_base64="lFWluioy0kF5xBwAEpS4DtmWbOY=">AAAC2HicjVHLSsNAFD2Nr1pf1S7dBIvgqiQi2I1QcCOIUME+sK0lSac1NC+SiVBCwJ249Qfc6heJf6B/4Z0xBbWITsjMmXPvOTN3rhk4dsQ17TWnzM0vLC7llwsrq2vrG8XNrWbkx6HFGpbv+GHbNCLm2B5rcJs7rB2EzHBNh7XM8bGIt25YGNm+d8EnAeu5xsizh7ZlcKL6xVI3Oesn47Sb0nykp1fJadovlrWKJoc6C/QMlJGNul98QRcD+LAQwwWDB07YgYGIvg50aAiI6yEhLiRkyzhDigJpY8pilGEQO6Z5RLtOxnq0F56RVFt0ikN/SEoVu6TxKS8kLE5TZTyWzoL9zTuRnuJuE1rNzMslluOa2L9008z/6kQtHENUZQ021RRIRlRnZS6xfBVxc/VLVZwcAuIEHlA8JGxJ5fSdVamJZO3ibQ0Zf5OZghV7K8uN8S5uSQ3Wf7ZzFjT3K7pW0c8PyrVq1uo8trGDPernIWo4QR0N8p7gEU94Vi6VW+VOuf9MVXKZpoRvQ3n4AMJ6l3A=</latexit><latexit sha1_base64="lFWluioy0kF5xBwAEpS4DtmWbOY=">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</latexit><latexit sha1_base64="lFWluioy0kF5xBwAEpS4DtmWbOY=">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</latexit><latexit sha1_base64="lFWluioy0kF5xBwAEpS4DtmWbOY=">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</latexit>
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=">AAACyXicjVHLSsNAFD2Nr1pfVZdugkVwVRIRdFlwI7ipYB/Qikym0xqbl8lErMWVP+BWf0z8A/0L74xTUIvohCRnzr3nzNx7vSTwM+k4rwVrZnZufqG4WFpaXlldK69vNLM4T7lo8DiI07bHMhH4kWhIXwainaSChV4gWt7wSMVbNyLN/Dg6k6NEnIdsEPl9nzNJVLM7YGHILsoVp+roZU8D14AKzKrH5Rd00UMMjhwhBCJIwgEYMno6cOEgIe4cY+JSQr6OC9yjRNqcsgRlMGKH9B3QrmPYiPbKM9NqTqcE9KaktLFDmpjyUsLqNFvHc+2s2N+8x9pT3W1Ef894hcRKXBL7l26S+V+dqkWij0Ndg081JZpR1XHjkuuuqJvbX6qS5JAQp3CP4ilhrpWTPttak+naVW+Zjr/pTMWqPTe5Od7VLWnA7s9xToPmXtV1qu7pfqXmmFEXsYVt7NI8D1DDMepokPcVHvGEZ+vEurZurbvPVKtgNJv4tqyHD61DkYQ=</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 !

More Related Content

What's hot

Static white box testing lecture 12
Static white box testing lecture 12Static white box testing lecture 12
Static white box testing lecture 12
Abdul Basit
 
Formal Approaches to SQA.pptx
Formal Approaches to SQA.pptxFormal Approaches to SQA.pptx
Formal Approaches to SQA.pptx
KarthigaiSelviS3
 
Software Coding- Software Coding
Software Coding- Software CodingSoftware Coding- Software Coding
Software Coding- Software Coding
Nikhil Pandit
 
Software Testing - Part 1 (Techniques, Types, Levels, Methods, STLC, Bug Life...
Software Testing - Part 1 (Techniques, Types, Levels, Methods, STLC, Bug Life...Software Testing - Part 1 (Techniques, Types, Levels, Methods, STLC, Bug Life...
Software Testing - Part 1 (Techniques, Types, Levels, Methods, STLC, Bug Life...
Ankit Prajapati
 
Software reliability growth model
Software reliability growth modelSoftware reliability growth model
Software reliability growth model
Himanshu
 
Black box testing or behavioral testing
Black box testing or behavioral testingBlack box testing or behavioral testing
Black box testing or behavioral testing
Slideshare
 
Software review
Software reviewSoftware review
Software review
amjad_09
 
Domain model
Domain modelDomain model
Domain model
Eagle Eyes
 
Tipos de-pruebas
Tipos de-pruebasTipos de-pruebas
Tipos de-pruebas
Carlos Godoy Fajardo
 
Fundamentals of Software Engineering
Fundamentals of Software Engineering Fundamentals of Software Engineering
Fundamentals of Software Engineering
Madhar Khan Pathan
 
Calidad de software Unidad 1
Calidad de software Unidad 1Calidad de software Unidad 1
Calidad de software Unidad 1
José Gutiérrez Díaz
 
Rayleigh model
Rayleigh modelRayleigh model
Rayleigh model
Roy Antony Arnold G
 
Reliability growth models
Reliability growth modelsReliability growth models
Reliability growth models
Roy Antony Arnold G
 
Algorithmic Software Cost Modeling
Algorithmic Software Cost ModelingAlgorithmic Software Cost Modeling
Algorithmic Software Cost Modeling
Kasun Ranga Wijeweera
 
Unit 5 testing -software quality assurance
Unit 5  testing -software quality assuranceUnit 5  testing -software quality assurance
Unit 5 testing -software quality assurance
gopal10scs185
 
Empirical Software Engineering
Empirical Software EngineeringEmpirical Software Engineering
Empirical Software Engineering
RahimLotfi
 
White box testing
White box testingWhite box testing
White box testing
Neethu Tressa
 
Software Engineering (Metrics for Process and Projects)
Software Engineering (Metrics for Process and Projects)Software Engineering (Metrics for Process and Projects)
Software Engineering (Metrics for Process and Projects)
ShudipPal
 
verification and validation
verification and validationverification and validation
verification and validation
Dinesh Pasi
 
Chapter 8 software testing
Chapter 8 software testingChapter 8 software testing
Chapter 8 software testing
despicable me
 

What's hot (20)

Static white box testing lecture 12
Static white box testing lecture 12Static white box testing lecture 12
Static white box testing lecture 12
 
Formal Approaches to SQA.pptx
Formal Approaches to SQA.pptxFormal Approaches to SQA.pptx
Formal Approaches to SQA.pptx
 
Software Coding- Software Coding
Software Coding- Software CodingSoftware Coding- Software Coding
Software Coding- Software Coding
 
Software Testing - Part 1 (Techniques, Types, Levels, Methods, STLC, Bug Life...
Software Testing - Part 1 (Techniques, Types, Levels, Methods, STLC, Bug Life...Software Testing - Part 1 (Techniques, Types, Levels, Methods, STLC, Bug Life...
Software Testing - Part 1 (Techniques, Types, Levels, Methods, STLC, Bug Life...
 
Software reliability growth model
Software reliability growth modelSoftware reliability growth model
Software reliability growth model
 
Black box testing or behavioral testing
Black box testing or behavioral testingBlack box testing or behavioral testing
Black box testing or behavioral testing
 
Software review
Software reviewSoftware review
Software review
 
Domain model
Domain modelDomain model
Domain model
 
Tipos de-pruebas
Tipos de-pruebasTipos de-pruebas
Tipos de-pruebas
 
Fundamentals of Software Engineering
Fundamentals of Software Engineering Fundamentals of Software Engineering
Fundamentals of Software Engineering
 
Calidad de software Unidad 1
Calidad de software Unidad 1Calidad de software Unidad 1
Calidad de software Unidad 1
 
Rayleigh model
Rayleigh modelRayleigh model
Rayleigh model
 
Reliability growth models
Reliability growth modelsReliability growth models
Reliability growth models
 
Algorithmic Software Cost Modeling
Algorithmic Software Cost ModelingAlgorithmic Software Cost Modeling
Algorithmic Software Cost Modeling
 
Unit 5 testing -software quality assurance
Unit 5  testing -software quality assuranceUnit 5  testing -software quality assurance
Unit 5 testing -software quality assurance
 
Empirical Software Engineering
Empirical Software EngineeringEmpirical Software Engineering
Empirical Software Engineering
 
White box testing
White box testingWhite box testing
White box testing
 
Software Engineering (Metrics for Process and Projects)
Software Engineering (Metrics for Process and Projects)Software Engineering (Metrics for Process and Projects)
Software Engineering (Metrics for Process and Projects)
 
verification and validation
verification and validationverification and validation
verification and validation
 
Chapter 8 software testing
Chapter 8 software testingChapter 8 software testing
Chapter 8 software testing
 

Similar to Distribution Aligning Refinery of Pseudo-label for Imbalanced Semi-supervised Learning

On the Impact of sameAs on Schema Matching
On the Impact of sameAs on Schema MatchingOn the Impact of sameAs on Schema Matching
On the Impact of sameAs on Schema Matching
Joe Raad
 
M2m: Imbalanced Classification via Major-to-minor Translation (CVPR 2020)
M2m: Imbalanced Classification via Major-to-minor Translation (CVPR 2020)M2m: Imbalanced Classification via Major-to-minor Translation (CVPR 2020)
M2m: Imbalanced Classification via Major-to-minor Translation (CVPR 2020)
ALINLAB
 
Adaptive Classification of Imbalanced Data using ANN with Particle of Swarm O...
Adaptive Classification of Imbalanced Data using ANN with Particle of Swarm O...Adaptive Classification of Imbalanced Data using ANN with Particle of Swarm O...
Adaptive Classification of Imbalanced Data using ANN with Particle of Swarm O...
ijtsrd
 
COMP_GroupA2.pptx
COMP_GroupA2.pptxCOMP_GroupA2.pptx
COMP_GroupA2.pptx
shivrajdeshmukh22
 
Implementation of Prototype Based Credal Classification approach For Enhanced...
Implementation of Prototype Based Credal Classification approach For Enhanced...Implementation of Prototype Based Credal Classification approach For Enhanced...
Implementation of Prototype Based Credal Classification approach For Enhanced...
IRJET Journal
 
6145-Article Text-9370-1-10-20200513.pdf
6145-Article Text-9370-1-10-20200513.pdf6145-Article Text-9370-1-10-20200513.pdf
6145-Article Text-9370-1-10-20200513.pdf
chalachew5
 
Semi-supervised Learning Survey - 20 years of evaluation
Semi-supervised Learning Survey - 20 years of evaluationSemi-supervised Learning Survey - 20 years of evaluation
Semi-supervised Learning Survey - 20 years of evaluation
subarna89
 
End to-end semi-supervised object detection with soft teacher ver.1.0
End to-end semi-supervised object detection with soft teacher ver.1.0End to-end semi-supervised object detection with soft teacher ver.1.0
End to-end semi-supervised object detection with soft teacher ver.1.0
taeseon ryu
 
A Systematic Review on the Educational Data Mining and its Implementation in ...
A Systematic Review on the Educational Data Mining and its Implementation in ...A Systematic Review on the Educational Data Mining and its Implementation in ...
A Systematic Review on the Educational Data Mining and its Implementation in ...
United International Journal for Research & Technology
 
Valuation of Startups: A Machine Learning Perspective
Valuation of Startups: A Machine Learning PerspectiveValuation of Startups: A Machine Learning Perspective
Valuation of Startups: A Machine Learning Perspective
Maria Garkavenko
 
Data Mining Techniques in Higher Education an Empirical Study for the Univer...
Data Mining Techniques in Higher Education an Empirical Study  for the Univer...Data Mining Techniques in Higher Education an Empirical Study  for the Univer...
Data Mining Techniques in Higher Education an Empirical Study for the Univer...
IJMER
 
Research Presentation keynote (not yet result)
Research Presentation keynote (not yet result)Research Presentation keynote (not yet result)
Research Presentation keynote (not yet result)
Riniort Huang
 
Galambos_SlidesNEAIR2015
Galambos_SlidesNEAIR2015Galambos_SlidesNEAIR2015
Galambos_SlidesNEAIR2015
Nora Galambos, PhD
 
Ethical Implications of Student Plagiarism in Myanmar
Ethical Implications of Student Plagiarism in MyanmarEthical Implications of Student Plagiarism in Myanmar
Ethical Implications of Student Plagiarism in Myanmar
ijtsrd
 
Clustering Students of Computer in Terms of Level of Programming
Clustering Students of Computer in Terms of Level of ProgrammingClustering Students of Computer in Terms of Level of Programming
Clustering Students of Computer in Terms of Level of Programming
Editor IJCATR
 
A SURVEY OF METHODS FOR HANDLING DISK DATA IMBALANCE
A SURVEY OF METHODS FOR HANDLING DISK DATA IMBALANCEA SURVEY OF METHODS FOR HANDLING DISK DATA IMBALANCE
A SURVEY OF METHODS FOR HANDLING DISK DATA IMBALANCE
IJCI JOURNAL
 
Exploring Peer Prestige in Academic Hiring Networks Brown Bag
Exploring Peer Prestige in Academic Hiring Networks Brown BagExploring Peer Prestige in Academic Hiring Networks Brown Bag
Exploring Peer Prestige in Academic Hiring Networks Brown Bag
Andrea Wiggins
 
Chinese Named Entity Recognition with Graph-based Semi-supervised Learning Model
Chinese Named Entity Recognition with Graph-based Semi-supervised Learning ModelChinese Named Entity Recognition with Graph-based Semi-supervised Learning Model
Chinese Named Entity Recognition with Graph-based Semi-supervised Learning Model
Lifeng (Aaron) Han
 
Using ID3 Decision Tree Algorithm to the Student Grade Analysis and Prediction
Using ID3 Decision Tree Algorithm to the Student Grade Analysis and PredictionUsing ID3 Decision Tree Algorithm to the Student Grade Analysis and Prediction
Using ID3 Decision Tree Algorithm to the Student Grade Analysis and Prediction
ijtsrd
 
Extending the Student’s Performance via K-Means and Blended Learning
Extending the Student’s Performance via K-Means and Blended Learning Extending the Student’s Performance via K-Means and Blended Learning
Extending the Student’s Performance via K-Means and Blended Learning
IJEACS
 

Similar to Distribution Aligning Refinery of Pseudo-label for Imbalanced Semi-supervised Learning (20)

On the Impact of sameAs on Schema Matching
On the Impact of sameAs on Schema MatchingOn the Impact of sameAs on Schema Matching
On the Impact of sameAs on Schema Matching
 
M2m: Imbalanced Classification via Major-to-minor Translation (CVPR 2020)
M2m: Imbalanced Classification via Major-to-minor Translation (CVPR 2020)M2m: Imbalanced Classification via Major-to-minor Translation (CVPR 2020)
M2m: Imbalanced Classification via Major-to-minor Translation (CVPR 2020)
 
Adaptive Classification of Imbalanced Data using ANN with Particle of Swarm O...
Adaptive Classification of Imbalanced Data using ANN with Particle of Swarm O...Adaptive Classification of Imbalanced Data using ANN with Particle of Swarm O...
Adaptive Classification of Imbalanced Data using ANN with Particle of Swarm O...
 
COMP_GroupA2.pptx
COMP_GroupA2.pptxCOMP_GroupA2.pptx
COMP_GroupA2.pptx
 
Implementation of Prototype Based Credal Classification approach For Enhanced...
Implementation of Prototype Based Credal Classification approach For Enhanced...Implementation of Prototype Based Credal Classification approach For Enhanced...
Implementation of Prototype Based Credal Classification approach For Enhanced...
 
6145-Article Text-9370-1-10-20200513.pdf
6145-Article Text-9370-1-10-20200513.pdf6145-Article Text-9370-1-10-20200513.pdf
6145-Article Text-9370-1-10-20200513.pdf
 
Semi-supervised Learning Survey - 20 years of evaluation
Semi-supervised Learning Survey - 20 years of evaluationSemi-supervised Learning Survey - 20 years of evaluation
Semi-supervised Learning Survey - 20 years of evaluation
 
End to-end semi-supervised object detection with soft teacher ver.1.0
End to-end semi-supervised object detection with soft teacher ver.1.0End to-end semi-supervised object detection with soft teacher ver.1.0
End to-end semi-supervised object detection with soft teacher ver.1.0
 
A Systematic Review on the Educational Data Mining and its Implementation in ...
A Systematic Review on the Educational Data Mining and its Implementation in ...A Systematic Review on the Educational Data Mining and its Implementation in ...
A Systematic Review on the Educational Data Mining and its Implementation in ...
 
Valuation of Startups: A Machine Learning Perspective
Valuation of Startups: A Machine Learning PerspectiveValuation of Startups: A Machine Learning Perspective
Valuation of Startups: A Machine Learning Perspective
 
Data Mining Techniques in Higher Education an Empirical Study for the Univer...
Data Mining Techniques in Higher Education an Empirical Study  for the Univer...Data Mining Techniques in Higher Education an Empirical Study  for the Univer...
Data Mining Techniques in Higher Education an Empirical Study for the Univer...
 
Research Presentation keynote (not yet result)
Research Presentation keynote (not yet result)Research Presentation keynote (not yet result)
Research Presentation keynote (not yet result)
 
Galambos_SlidesNEAIR2015
Galambos_SlidesNEAIR2015Galambos_SlidesNEAIR2015
Galambos_SlidesNEAIR2015
 
Ethical Implications of Student Plagiarism in Myanmar
Ethical Implications of Student Plagiarism in MyanmarEthical Implications of Student Plagiarism in Myanmar
Ethical Implications of Student Plagiarism in Myanmar
 
Clustering Students of Computer in Terms of Level of Programming
Clustering Students of Computer in Terms of Level of ProgrammingClustering Students of Computer in Terms of Level of Programming
Clustering Students of Computer in Terms of Level of Programming
 
A SURVEY OF METHODS FOR HANDLING DISK DATA IMBALANCE
A SURVEY OF METHODS FOR HANDLING DISK DATA IMBALANCEA SURVEY OF METHODS FOR HANDLING DISK DATA IMBALANCE
A SURVEY OF METHODS FOR HANDLING DISK DATA IMBALANCE
 
Exploring Peer Prestige in Academic Hiring Networks Brown Bag
Exploring Peer Prestige in Academic Hiring Networks Brown BagExploring Peer Prestige in Academic Hiring Networks Brown Bag
Exploring Peer Prestige in Academic Hiring Networks Brown Bag
 
Chinese Named Entity Recognition with Graph-based Semi-supervised Learning Model
Chinese Named Entity Recognition with Graph-based Semi-supervised Learning ModelChinese Named Entity Recognition with Graph-based Semi-supervised Learning Model
Chinese Named Entity Recognition with Graph-based Semi-supervised Learning Model
 
Using ID3 Decision Tree Algorithm to the Student Grade Analysis and Prediction
Using ID3 Decision Tree Algorithm to the Student Grade Analysis and PredictionUsing ID3 Decision Tree Algorithm to the Student Grade Analysis and Prediction
Using ID3 Decision Tree Algorithm to the Student Grade Analysis and Prediction
 
Extending the Student’s Performance via K-Means and Blended Learning
Extending the Student’s Performance via K-Means and Blended Learning Extending the Student’s Performance via K-Means and Blended Learning
Extending the Student’s Performance via K-Means and Blended Learning
 

More from ALINLAB

Trajectory-wise Multiple Choice Learning for Dynamics Generalization in Reinf...
Trajectory-wise Multiple Choice Learning for Dynamics Generalization in Reinf...Trajectory-wise Multiple Choice Learning for Dynamics Generalization in Reinf...
Trajectory-wise Multiple Choice Learning for Dynamics Generalization in Reinf...
ALINLAB
 
Learning bounds for risk-sensitive learning
Learning bounds for risk-sensitive learningLearning bounds for risk-sensitive learning
Learning bounds for risk-sensitive learning
ALINLAB
 
CSI: Novelty Detection via Contrastive Learning on Distributionally Shifted I...
CSI: Novelty Detection via Contrastive Learning on Distributionally Shifted I...CSI: Novelty Detection via Contrastive Learning on Distributionally Shifted I...
CSI: Novelty Detection via Contrastive Learning on Distributionally Shifted I...
ALINLAB
 
Polynomial Tensor Sketch for Element-wise Matrix Function (ICML 2020)
Polynomial Tensor Sketch for Element-wise Matrix Function (ICML 2020)Polynomial Tensor Sketch for Element-wise Matrix Function (ICML 2020)
Polynomial Tensor Sketch for Element-wise Matrix Function (ICML 2020)
ALINLAB
 
Context-aware Dynamics Model for Generalization in Model-Based Reinforcement ...
Context-aware Dynamics Model for Generalization in Model-Based Reinforcement ...Context-aware Dynamics Model for Generalization in Model-Based Reinforcement ...
Context-aware Dynamics Model for Generalization in Model-Based Reinforcement ...
ALINLAB
 
Self-supervised Label Augmentation via Input Transformations (ICML 2020)
Self-supervised Label Augmentation via Input Transformations (ICML 2020)Self-supervised Label Augmentation via Input Transformations (ICML 2020)
Self-supervised Label Augmentation via Input Transformations (ICML 2020)
ALINLAB
 

More from ALINLAB (6)

Trajectory-wise Multiple Choice Learning for Dynamics Generalization in Reinf...
Trajectory-wise Multiple Choice Learning for Dynamics Generalization in Reinf...Trajectory-wise Multiple Choice Learning for Dynamics Generalization in Reinf...
Trajectory-wise Multiple Choice Learning for Dynamics Generalization in Reinf...
 
Learning bounds for risk-sensitive learning
Learning bounds for risk-sensitive learningLearning bounds for risk-sensitive learning
Learning bounds for risk-sensitive learning
 
CSI: Novelty Detection via Contrastive Learning on Distributionally Shifted I...
CSI: Novelty Detection via Contrastive Learning on Distributionally Shifted I...CSI: Novelty Detection via Contrastive Learning on Distributionally Shifted I...
CSI: Novelty Detection via Contrastive Learning on Distributionally Shifted I...
 
Polynomial Tensor Sketch for Element-wise Matrix Function (ICML 2020)
Polynomial Tensor Sketch for Element-wise Matrix Function (ICML 2020)Polynomial Tensor Sketch for Element-wise Matrix Function (ICML 2020)
Polynomial Tensor Sketch for Element-wise Matrix Function (ICML 2020)
 
Context-aware Dynamics Model for Generalization in Model-Based Reinforcement ...
Context-aware Dynamics Model for Generalization in Model-Based Reinforcement ...Context-aware Dynamics Model for Generalization in Model-Based Reinforcement ...
Context-aware Dynamics Model for Generalization in Model-Based Reinforcement ...
 
Self-supervised Label Augmentation via Input Transformations (ICML 2020)
Self-supervised Label Augmentation via Input Transformations (ICML 2020)Self-supervised Label Augmentation via Input Transformations (ICML 2020)
Self-supervised Label Augmentation via Input Transformations (ICML 2020)
 

Recently uploaded

Online toll plaza booking system project report.doc.pdf
Online toll plaza booking system project report.doc.pdfOnline toll plaza booking system project report.doc.pdf
Online toll plaza booking system project report.doc.pdf
Kamal Acharya
 
Online airline reservation system project report.pdf
Online airline reservation system project report.pdfOnline airline reservation system project report.pdf
Online airline reservation system project report.pdf
Kamal Acharya
 
readers writers Problem in operating system
readers writers Problem in operating systemreaders writers Problem in operating system
readers writers Problem in operating system
VADAPALLYPRAVEENKUMA1
 
EAAP2023 : Durabilité et services écosystémiques de l'élevage ovin de montagne
EAAP2023 : Durabilité et services écosystémiques de l'élevage ovin de montagneEAAP2023 : Durabilité et services écosystémiques de l'élevage ovin de montagne
EAAP2023 : Durabilité et services écosystémiques de l'élevage ovin de montagne
idelewebmestre
 
Jet Propulsion and its working principle.pdf
Jet Propulsion and its working principle.pdfJet Propulsion and its working principle.pdf
Jet Propulsion and its working principle.pdf
KIET Group of Institutions
 
杨洋李一桐做爱视频流出【网芷:ht28.co】国产国产午夜精华>>>[网趾:ht28.co】]<<<
杨洋李一桐做爱视频流出【网芷:ht28.co】国产国产午夜精华>>>[网趾:ht28.co】]<<<杨洋李一桐做爱视频流出【网芷:ht28.co】国产国产午夜精华>>>[网趾:ht28.co】]<<<
杨洋李一桐做爱视频流出【网芷:ht28.co】国产国产午夜精华>>>[网趾:ht28.co】]<<<
amzhoxvzidbke
 
Response & Safe AI at Summer School of AI at IIITH
Response & Safe AI at Summer School of AI at IIITHResponse & Safe AI at Summer School of AI at IIITH
Response & Safe AI at Summer School of AI at IIITH
IIIT Hyderabad
 
lecture10-efficient-scoring.ppmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmt
lecture10-efficient-scoring.ppmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmtlecture10-efficient-scoring.ppmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmt
lecture10-efficient-scoring.ppmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmt
RAtna29
 
Thermodynamics Digital Material basics subject
Thermodynamics Digital Material basics subjectThermodynamics Digital Material basics subject
Thermodynamics Digital Material basics subject
JigneshChhatbar1
 
SCADAmetrics Instrumentation for Sensus Water Meters - Core and Main Training...
SCADAmetrics Instrumentation for Sensus Water Meters - Core and Main Training...SCADAmetrics Instrumentation for Sensus Water Meters - Core and Main Training...
SCADAmetrics Instrumentation for Sensus Water Meters - Core and Main Training...
Jim Mimlitz, P.E.
 
Ship Repair Occupational Health & Safety.ppt
Ship Repair Occupational Health & Safety.pptShip Repair Occupational Health & Safety.ppt
Ship Repair Occupational Health & Safety.ppt
MgZin3
 
Traffic Engineering-MODULE-1 vtu syllabus.pptx
Traffic Engineering-MODULE-1 vtu syllabus.pptxTraffic Engineering-MODULE-1 vtu syllabus.pptx
Traffic Engineering-MODULE-1 vtu syllabus.pptx
mailmad391
 
CONFINED SPACE ENTRY TRAINING FOR OIL INDUSTRY ppt
CONFINED SPACE ENTRY TRAINING FOR OIL INDUSTRY pptCONFINED SPACE ENTRY TRAINING FOR OIL INDUSTRY ppt
CONFINED SPACE ENTRY TRAINING FOR OIL INDUSTRY ppt
ASHOK KUMAR SINGH
 
GUIA_LEGAL_CHAPTER-9_COLOMBIAN ELECTRICITY (1).pdf
GUIA_LEGAL_CHAPTER-9_COLOMBIAN ELECTRICITY (1).pdfGUIA_LEGAL_CHAPTER-9_COLOMBIAN ELECTRICITY (1).pdf
GUIA_LEGAL_CHAPTER-9_COLOMBIAN ELECTRICITY (1).pdf
ProexportColombia1
 
GJ WASTE TO ENERGY KOCHI PROJECT v6.pptx
GJ WASTE TO ENERGY KOCHI PROJECT v6.pptxGJ WASTE TO ENERGY KOCHI PROJECT v6.pptx
GJ WASTE TO ENERGY KOCHI PROJECT v6.pptx
rogginethomas
 
Trends in Computer Aided Design and MFG.
Trends in Computer Aided Design and MFG.Trends in Computer Aided Design and MFG.
Trends in Computer Aided Design and MFG.
Tool and Die Tech
 
RECENT DEVELOPMENTS IN RING SPINNING.pptx
RECENT DEVELOPMENTS IN RING SPINNING.pptxRECENT DEVELOPMENTS IN RING SPINNING.pptx
RECENT DEVELOPMENTS IN RING SPINNING.pptx
peacesoul123
 
Time-State Analytics: MinneAnalytics 2024 Talk
Time-State Analytics: MinneAnalytics 2024 TalkTime-State Analytics: MinneAnalytics 2024 Talk
Time-State Analytics: MinneAnalytics 2024 Talk
Evan Chan
 
OSHA LOTO training, LOTO, lock out tag out
OSHA LOTO training, LOTO, lock out tag outOSHA LOTO training, LOTO, lock out tag out
OSHA LOTO training, LOTO, lock out tag out
Ateeb19
 
Metrology Book, Bachelors in Mechanical Engineering
Metrology Book, Bachelors in Mechanical EngineeringMetrology Book, Bachelors in Mechanical Engineering
Metrology Book, Bachelors in Mechanical Engineering
leakingvideo
 

Recently uploaded (20)

Online toll plaza booking system project report.doc.pdf
Online toll plaza booking system project report.doc.pdfOnline toll plaza booking system project report.doc.pdf
Online toll plaza booking system project report.doc.pdf
 
Online airline reservation system project report.pdf
Online airline reservation system project report.pdfOnline airline reservation system project report.pdf
Online airline reservation system project report.pdf
 
readers writers Problem in operating system
readers writers Problem in operating systemreaders writers Problem in operating system
readers writers Problem in operating system
 
EAAP2023 : Durabilité et services écosystémiques de l'élevage ovin de montagne
EAAP2023 : Durabilité et services écosystémiques de l'élevage ovin de montagneEAAP2023 : Durabilité et services écosystémiques de l'élevage ovin de montagne
EAAP2023 : Durabilité et services écosystémiques de l'élevage ovin de montagne
 
Jet Propulsion and its working principle.pdf
Jet Propulsion and its working principle.pdfJet Propulsion and its working principle.pdf
Jet Propulsion and its working principle.pdf
 
杨洋李一桐做爱视频流出【网芷:ht28.co】国产国产午夜精华>>>[网趾:ht28.co】]<<<
杨洋李一桐做爱视频流出【网芷:ht28.co】国产国产午夜精华>>>[网趾:ht28.co】]<<<杨洋李一桐做爱视频流出【网芷:ht28.co】国产国产午夜精华>>>[网趾:ht28.co】]<<<
杨洋李一桐做爱视频流出【网芷:ht28.co】国产国产午夜精华>>>[网趾:ht28.co】]<<<
 
Response & Safe AI at Summer School of AI at IIITH
Response & Safe AI at Summer School of AI at IIITHResponse & Safe AI at Summer School of AI at IIITH
Response & Safe AI at Summer School of AI at IIITH
 
lecture10-efficient-scoring.ppmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmt
lecture10-efficient-scoring.ppmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmtlecture10-efficient-scoring.ppmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmt
lecture10-efficient-scoring.ppmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmt
 
Thermodynamics Digital Material basics subject
Thermodynamics Digital Material basics subjectThermodynamics Digital Material basics subject
Thermodynamics Digital Material basics subject
 
SCADAmetrics Instrumentation for Sensus Water Meters - Core and Main Training...
SCADAmetrics Instrumentation for Sensus Water Meters - Core and Main Training...SCADAmetrics Instrumentation for Sensus Water Meters - Core and Main Training...
SCADAmetrics Instrumentation for Sensus Water Meters - Core and Main Training...
 
Ship Repair Occupational Health & Safety.ppt
Ship Repair Occupational Health & Safety.pptShip Repair Occupational Health & Safety.ppt
Ship Repair Occupational Health & Safety.ppt
 
Traffic Engineering-MODULE-1 vtu syllabus.pptx
Traffic Engineering-MODULE-1 vtu syllabus.pptxTraffic Engineering-MODULE-1 vtu syllabus.pptx
Traffic Engineering-MODULE-1 vtu syllabus.pptx
 
CONFINED SPACE ENTRY TRAINING FOR OIL INDUSTRY ppt
CONFINED SPACE ENTRY TRAINING FOR OIL INDUSTRY pptCONFINED SPACE ENTRY TRAINING FOR OIL INDUSTRY ppt
CONFINED SPACE ENTRY TRAINING FOR OIL INDUSTRY ppt
 
GUIA_LEGAL_CHAPTER-9_COLOMBIAN ELECTRICITY (1).pdf
GUIA_LEGAL_CHAPTER-9_COLOMBIAN ELECTRICITY (1).pdfGUIA_LEGAL_CHAPTER-9_COLOMBIAN ELECTRICITY (1).pdf
GUIA_LEGAL_CHAPTER-9_COLOMBIAN ELECTRICITY (1).pdf
 
GJ WASTE TO ENERGY KOCHI PROJECT v6.pptx
GJ WASTE TO ENERGY KOCHI PROJECT v6.pptxGJ WASTE TO ENERGY KOCHI PROJECT v6.pptx
GJ WASTE TO ENERGY KOCHI PROJECT v6.pptx
 
Trends in Computer Aided Design and MFG.
Trends in Computer Aided Design and MFG.Trends in Computer Aided Design and MFG.
Trends in Computer Aided Design and MFG.
 
RECENT DEVELOPMENTS IN RING SPINNING.pptx
RECENT DEVELOPMENTS IN RING SPINNING.pptxRECENT DEVELOPMENTS IN RING SPINNING.pptx
RECENT DEVELOPMENTS IN RING SPINNING.pptx
 
Time-State Analytics: MinneAnalytics 2024 Talk
Time-State Analytics: MinneAnalytics 2024 TalkTime-State Analytics: MinneAnalytics 2024 Talk
Time-State Analytics: MinneAnalytics 2024 Talk
 
OSHA LOTO training, LOTO, lock out tag out
OSHA LOTO training, LOTO, lock out tag outOSHA LOTO training, LOTO, lock out tag out
OSHA LOTO training, LOTO, lock out tag out
 
Metrology Book, Bachelors in Mechanical Engineering
Metrology Book, Bachelors in Mechanical EngineeringMetrology Book, Bachelors in Mechanical Engineering
Metrology Book, Bachelors in Mechanical Engineering
 

Distribution Aligning Refinery of Pseudo-label for Imbalanced Semi-supervised Learning

  • 1. 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
  • 2. • 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
  • 3. • 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
  • 4. • Assumption: class distribution of labeled and unlabeled data is highly imbalanced Imbalanced Semi-supervised Learning Imbalanced CIFAR-10 3
  • 5. • 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
  • 6. • 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 <latexit sha1_base64="n+xr3jkNc+0CjJ75U0Z2bnxc7js=">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</latexit><latexit sha1_base64="n+xr3jkNc+0CjJ75U0Z2bnxc7js=">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</latexit><latexit sha1_base64="n+xr3jkNc+0CjJ75U0Z2bnxc7js=">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</latexit><latexit sha1_base64="G30nvnJkyKBlKcCymNnrqTxJgV4=">AAACtXicjVLLSgMxFD0dX7VWrWs3g0VwVTJudCnowmUF+4BaZCZNa+y8TDJCKf6AWz9O/AP9C2/iCGoRzTAzJ+fec5KbmyiPpTaMvVS8peWV1bXqem2jXtvc2m7UuzorFBcdnsWZ6kehFrFMRcdIE4t+rkSYRLHoRdNTG+/dC6Vlll6aWS6GSThJ5Vjy0BDVvm40WYu54S+CoARNlCNrPOMKI2TgKJBAIIUhHCOEpmeAAAw5cUPMiVOEpIsLPKBG2oKyBGWExE7pO6HZoGRTmltP7dScVonpVaT0sU+ajPIUYbua7+KFc7bsb95z52n3NqN/VHolxBrcEPuX7jPzvzpbi8EYx64GSTXljrHV8dKlcKdid+5/qcqQQ06cxSOKK8LcKT/P2Xca7Wq3Zxu6+KvLtKyd8zK3wJvdJfU3+NnNRdA9bAWsFVwwVLGLPRxQG49wgnO00SHLER7x5J15t97dxz3wKuWF2MG34el34YWM3A==</latexit><latexit sha1_base64="aQ6VNeX17tKdKtbSum7ouo/KEII=">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</latexit><latexit sha1_base64="aQ6VNeX17tKdKtbSum7ouo/KEII=">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</latexit><latexit sha1_base64="+iaWb8t9MW732eOHdR8CMqoyYM8=">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</latexit><latexit sha1_base64="n+xr3jkNc+0CjJ75U0Z2bnxc7js=">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</latexit><latexit sha1_base64="n+xr3jkNc+0CjJ75U0Z2bnxc7js=">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</latexit><latexit sha1_base64="n+xr3jkNc+0CjJ75U0Z2bnxc7js=">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</latexit><latexit sha1_base64="n+xr3jkNc+0CjJ75U0Z2bnxc7js=">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</latexit><latexit sha1_base64="n+xr3jkNc+0CjJ75U0Z2bnxc7js=">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</latexit><latexit sha1_base64="n+xr3jkNc+0CjJ75U0Z2bnxc7js=">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</latexit> wm<latexit sha1_base64="opxQNj2swkpdqHZm1SeBabun9/4=">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</latexit><latexit sha1_base64="opxQNj2swkpdqHZm1SeBabun9/4=">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</latexit><latexit sha1_base64="opxQNj2swkpdqHZm1SeBabun9/4=">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</latexit><latexit sha1_base64="opxQNj2swkpdqHZm1SeBabun9/4=">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</latexit> Mk<latexit sha1_base64="V0qzsExbnNA+b2pD24RDP3NMMUo=">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</latexit><latexit sha1_base64="V0qzsExbnNA+b2pD24RDP3NMMUo=">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</latexit><latexit sha1_base64="V0qzsExbnNA+b2pD24RDP3NMMUo=">AAACxnicjVHLSsNAFD2Nr1pfVZdugkVwVRIp6LLgphuhom2FWkoyndbQvJhMlFIEf8Ctfpr4B/oX3hmnoBbRCUnOnHvPmbn3+mkYZNJxXgvWwuLS8kpxtbS2vrG5Vd7eaWdJLhhvsSRMxJXvZTwMYt6SgQz5VSq4F/kh7/jjUxXv3HKRBUl8KScp70XeKA6GAfMkURdn/XG/XHGqjl72PHANqMCsZlJ+wTUGSMCQIwJHDEk4hIeMni5cOEiJ62FKnCAU6DjHPUqkzSmLU4ZH7Ji+I9p1DRvTXnlmWs3olJBeQUobB6RJKE8QVqfZOp5rZ8X+5j3VnupuE/r7xisiVuKG2L90s8z/6lQtEkOc6BoCqinVjKqOGZdcd0Xd3P5SlSSHlDiFBxQXhJlWzvpsa02ma1e99XT8TWcqVu2Zyc3xrm5JA3Z/jnMetI+qrlN1z2uVes2Muog97OOQ5nmMOhpookXeIzziCc9Ww4qt3Lr7TLUKRrOLb8t6+AAtH5Ai</latexit><latexit sha1_base64="V0qzsExbnNA+b2pD24RDP3NMMUo=">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</latexit> k<latexit sha1_base64="MaenEFsKtSUOisFFlS12vTNpRAI=">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</latexit><latexit sha1_base64="MaenEFsKtSUOisFFlS12vTNpRAI=">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</latexit><latexit sha1_base64="MaenEFsKtSUOisFFlS12vTNpRAI=">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</latexit><latexit sha1_base64="MaenEFsKtSUOisFFlS12vTNpRAI=">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</latexit> K<latexit sha1_base64="Zoz/5QEOWbZ/Nm7/Z1wf/UlhXR4=">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</latexit><latexit sha1_base64="Zoz/5QEOWbZ/Nm7/Z1wf/UlhXR4=">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</latexit><latexit sha1_base64="Zoz/5QEOWbZ/Nm7/Z1wf/UlhXR4=">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</latexit><latexit sha1_base64="Zoz/5QEOWbZ/Nm7/Z1wf/UlhXR4=">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</latexit> M = XK k=1 Mk <latexit sha1_base64="vDpCUpTnsJnTuCbeJVpKVfhI1js=">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</latexit><latexit sha1_base64="vDpCUpTnsJnTuCbeJVpKVfhI1js=">AAAC5HicjVHLSsNAFD2Nr/qOunRhsAiuSqKCbgqCG0EKFWwrtLUkcapD8yIzEaR06c6duPUH3Oq3iH+gf+GdMYIPRCckOXPuPWfm3uslARfStp8Lxsjo2PhEcXJqemZ2bt5cWGyIOEt9VvfjIE6PPVewgEesLrkM2HGSMjf0Atb0+nsq3rxgqeBxdCQvE9YJ3bOI97jvSqK65krVqlhtkYXtKA54yKXoDvoVZ3gyOBha1W6/a5bssq2X9RM4OSghX7XYfEIbp4jhI0MIhgiScAAXgp4WHNhIiOtgQFxKiOs4wxBTpM0oi1GGS2yfvme0a+VsRHvlKbTap1MCelNSWlgjTUx5KWF1mqXjmXZW7G/eA+2p7nZJfy/3ComVOCf2L91H5n91qhaJHnZ0DZxqSjSjqvNzl0x3Rd3c+lSVJIeEOIVPKZ4S9rXyo8+W1ghdu+qtq+MvOlOxau/nuRle1S1pwM73cf4EjY2yY5edw63S7mY+6iKWsYp1muc2drGPGurkfYV7PODR6BnXxo1x+55qFHLNEr4s4+4Nzi+boQ==</latexit><latexit sha1_base64="vDpCUpTnsJnTuCbeJVpKVfhI1js=">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</latexit><latexit sha1_base64="vDpCUpTnsJnTuCbeJVpKVfhI1js=">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</latexit> 4
  • 7. • 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 k=1<latexit sha1_base64="lFWluioy0kF5xBwAEpS4DtmWbOY=">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</latexit><latexit sha1_base64="lFWluioy0kF5xBwAEpS4DtmWbOY=">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</latexit><latexit sha1_base64="lFWluioy0kF5xBwAEpS4DtmWbOY=">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</latexit><latexit sha1_base64="lFWluioy0kF5xBwAEpS4DtmWbOY=">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</latexit> Inferred or estimated
  • 8. • 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>
  • 9. • 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=">AAACyXicjVHLSsNAFD2Nr1pfVZdugkVwVRIRdFlwI7ipYB/Qikym0xqbl8lErMWVP+BWf0z8A/0L74xTUIvohCRnzr3nzNx7vSTwM+k4rwVrZnZufqG4WFpaXlldK69vNLM4T7lo8DiI07bHMhH4kWhIXwainaSChV4gWt7wSMVbNyLN/Dg6k6NEnIdsEPl9nzNJVLM7YGHILsoVp+roZU8D14AKzKrH5Rd00UMMjhwhBCJIwgEYMno6cOEgIe4cY+JSQr6OC9yjRNqcsgRlMGKH9B3QrmPYiPbKM9NqTqcE9KaktLFDmpjyUsLqNFvHc+2s2N+8x9pT3W1Ef894hcRKXBL7l26S+V+dqkWij0Ndg081JZpR1XHjkuuuqJvbX6qS5JAQp3CP4ilhrpWTPttak+naVW+Zjr/pTMWqPTe5Od7VLWnA7s9xToPmXtV1qu7pfqXmmFEXsYVt7NI8D1DDMepokPcVHvGEZ+vEurZurbvPVKtgNJv4tqyHD61DkYQ=</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>
  • 10. • 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 !