Semi- Supervised Learning

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1 Semi- Supervised Learning Aarti Singh Machine Learning Dec 1, 2011 Slides Courtesy: Jerry Zhu 1

2 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

3 Training data Crystal Needle Empty Human expert/ Special equipment/ Experiment Sports News Science Cheap and abundant! Expensive and scarce!

4 Free- of- cost labels? Luis von Ahn: Games with a purpose (ReCaptcha) Word rejected by OCR (Op1cal Character Recogin1on) You provide a free label!

5 Semi- Supervised learning Learning algorithm Supervised learning (SL) Crystal Semi-Supervised learning (SSL) Goal: Learn a be>er predic?on rule than based on labeled data alone.

6 Semi- Supervised learning in Humans

7 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.

8 Can unlabeled data help? Similar data points have similar labels

9 Some SSL Algorithms Generative methods assume a model for p(x,y) and maximize joint likelihood Mixture models Graph-based methods assume the target function p(y x) is smooth wrt a graph or manifold Graph/Manifold Regularization Multi-view methods multiple independent learners that agree on prediction for unlabeled data Co-training

10 Some SSL Algorithms Generative methods assume a model for p(x,y) and maximize joint likelihood Mixture models Graph-based methods assume the target function p(y x) is smooth wrt a graph or manifold Graph/Manifold Regularization Multi-view methods multiple independent learners that agree on prediction for unlabeled data Co-training

11 Mixture Models

12 Mixture Models > 1/2 <

13 Mixture Models

14 Mixture Models

15 Mixture Models

16 Mixture Models

17 Mixture Models

18 Gaussian Mixture Models

19 EM for Gaussian Mixture Models

20 EM for GMMs: Example Σ 2 Σ 3 Σ 1 µ 1 µ 2 µ 3 P(y = x j,µ 1,µ 2,µ 3,Σ 1,Σ 2,Σ 3,w 1,w 2,w 3 )

21 AKer 1 st itera?on

22 AKer 2 nd itera?on

23 AKer 3 rd itera?on

24 AKer 4 th itera?on

25 AKer 5 th itera?on

26 AKer 6 th itera?on

27 AKer 20 th itera?on

28 Assump?on for GMMs

29 Assump?on for GMMs

30 Assump?on for GMMs

31 Related: Cluster and Label

33 Some SSL Algorithms Generative methods assume a model for p(x,y) and maximize joint likelihood Mixture models Graph-based methods assume the target function p(y x) is smooth wrt a graph or manifold Graph/Manifold Regularization Multi-view methods multiple independent learners that agree on prediction for unlabeled data Co-training

34 Graph Regulariza?on Assumption: Similar unlabeled data have similar labels.

35 Graph Regulariza?on Similarity Graphs: Model local neighborhood relations between data points

36 Graph Regulariza?on 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 (mean square,0-1) Graph based smoothness prior on labeled and unlabeled data If labels are binary +1/-1, Minimization = min-cut on a modified graph - add source and sink nodes with large weight to labeled examples. Blum & Chawla 01 Source +1 Sink -1

37 Some SSL Algorithms Generative methods assume a model for p(x,y) and maximize joint likelihood Mixture models Graph-based methods assume the target function p(y x) is smooth wrt a graph or manifold Graph/Manifold Regularization Multi-view methods multiple independent learners that agree on prediction for unlabeled data Co-training

38 Two views of an Instance

39 Two views of an Instance

40 Two views of an Instance

41 Co- training Algorithm Blum & Mitchell 98

42 Co- training

43 Semi- Supervised Learning Generative methods Mixture models Graph-based methods Manifold Regularization Multi-view methods Co-training Semi-Supervised SVMs assume unlabeled data from different classes have large margin Many other methods SSL algorithms can use unlabeled data to help improve prediction accuracy if data satisfies appropriate assumptions

Semi-supervised Learning

Semi-supervised Learning Piyush Rai CS5350/6350: Machine Learning November 8, 2011 Semi-supervised Learning Supervised Learning models require labeled data Learning a reliable model usually requires plenty