Semi-Supervised Learning Barnabas Poczos Slides Courtesy: Jerry Zhu, Aarti Singh
Supervised Learning Feature Space Label Space Goal: Optimal predictor (Bayes Rule) depends on unknown P XY , so instead learn a good prediction rule from training data Learning algorithm Labeled 2
Labeled and Unlabeled data “Crystal” “Needle” “Empty” “0” “1” “2” … “Sports” Human expert/ “News” Special equipment/ “Science” Experiment … Cheap and abundant ! Expensive and scarce ! 3
Free-of-cost labels? Luis von Ahn: Games with a purpose (ReCaptcha) Word challenging to OCR (Optical Character Recognition) You provide a free label! 4
Semi-Supervised learning Learning algorithm Supervised learning (SL) “Crystal” Semi-Supervised learning (SSL) Goal: Learn a better prediction rule than based on labeled data alone. 5
Semi-Supervised learning in Humans 6
Can unlabeled data help? Positive labeled data Negative labeled data Unlabeled data Supervised Decision Boundary Semi-Supervised Decision Boundary Assume each class is a coherent group (e.g. Gaussian) Then unlabeled data can help identify the boundary more accurately. 7
Can unlabeled data help? “0” “1” “2” … 7 7 1 1 2 2 9 9 4 4 8 8 3 3 5 5 This embedding can be done by manifold learning algorithms “Similar” data points have “similar” labels 8
Some SSL Algorithms ▪ Self-Training ▪ Generative methods, mixture models ▪ Graph-based methods ▪ Co-Training ▪ Semi-supervised SVM ▪ Many others 9
Notation 10
Self-training 11
Self-training Example Propagating 1-NN 12
Mixture Models for Labeled Data 15
Mixture Models for Labeled Data Estimate the parameters from the labeled data Decision for any test > 1/2 < point not in the labeled dataset 16
Mixture Models for Labeled Data 17
Mixture Models for SSL Data 18
Mixture Models 19
Mixture Models SL vs SSL 20
Mixture Models 21
Gaussian Mixture Models 22
EM for Gaussian Mixture Models 23
Assumption for GMMs 24
Assumption for GMMs 25
Assumption for GMMs 26
Related: Cluster and Label 27
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Graph Based Methods Assumption: Similar unlabeled data have similar labels. 29
Graph Regularization Similarity Graphs: Model local neighborhood relations between data points Assumption: Nodes connected by heavy edges tend to have similar label 30
Graph Regularization If data points i and j are similar (i.e. weight w ij is large), then their labels are similar f i = f j Loss on labeled data Graph based smoothness prior (mean square,0-1) on labeled and unlabeled data 31
Co-training
Co-training Algorithm Co-training (Blum & Mitchell, 1998) (Mitchell, 1999) assumes that (i) features can be split into two sets; (ii) each sub- feature set is sufficient to train a good classifier. • Initially two separate classifiers are trained with the labeled data, on the two sub-feature sets respectively. • Each classifier then classifies the unlabeled data, and ‘teaches’ the other classifier with the few unlabeled examples (and the predicted labels) they feel most confident. • Each classifier is retrained with the additional training examples given by the other classifier, and the process repeats. 33
Co-training Algorithm Blum & Mitchell’98
Semi-Supervised SVMs 35
Semi-Supervised Learning ▪ Generative methods ▪ Graph-based methods ▪ Co-Training ▪ Semi-Supervised SVMs ▪ Many other methods SSL algorithms can use unlabeled data to help improve prediction accuracy if data satisfies appropriate assumptions 36
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