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Self-Paced Learning for Semantic Segmentation M. Pawan Kumar.

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Presentation on theme: "Self-Paced Learning for Semantic Segmentation M. Pawan Kumar."— Presentation transcript:

1 Self-Paced Learning for Semantic Segmentation M. Pawan Kumar

2

3 Self-Paced Learning for Latent Structural SVM Daphne KollerBenjamin Packer M. Pawan Kumar

4 Aim To learn accurate parameters for latent structural SVM Input x Output y Y Deer Hidden Variable h H Y = {Bison, Deer, Elephant, Giraffe, Llama, Rhino }

5 Aim To learn accurate parameters for latent structural SVM Feature (x,y,h) (HOG, BoW) (y*,h*) = max y Y,h H w T (x,y,h) Parameters w

6 Motivation Real Numbers Imaginary Numbers e iπ +1 = 0 Math is for losers !! FAILURE … BAD LOCAL MINIMUM

7 Motivation Real Numbers Imaginary Numbers e iπ +1 = 0 Euler was a Genius!! SUCCESS … GOOD LOCAL MINIMUM

8 Motivation Start with easy examples, then consider hard ones Easy vs. Hard Expensive Easy for human Easy for machine Simultaneously estimate easiness and parameters Easiness is property of data sets, not single instances

9 Outline Latent Structural SVM Concave-Convex Procedure Self-Paced Learning Experiments

10 Latent Structural SVM Training samples x i Ground-truth label y i Loss Function (y i, y i (w), h i (w)) Felzenszwalb et al, 2008, Yu and Joachims, 2009

11 Latent Structural SVM (y i (w),h i (w)) = max y Y,h H w T (x,y,h) min ||w|| 2 + C i (y i, y i (w), h i (w)) Non-convex Objective Minimize an upper bound

12 Latent Structural SVM min ||w|| 2 + C i i max h i w T (x i,y i,h i ) - w T (x i,y,h) (y i, y, h) - i Still non-convexDifference of convex CCCP Algorithm - converges to a local minimum (y i (w),h i (w)) = max y Y,h H w T (x,y,h)

13 Outline Latent Structural SVM Concave-Convex Procedure Self-Paced Learning Experiments

14 Concave-Convex Procedure Start with an initial estimate w 0 Update Update w t+1 by solving a convex problem min ||w|| 2 + C i i w T (x i,y i,h i ) - w T (x i,y,h) (y i, y, h) - i h i = max h H w t T (x i,y i,h)

15 Concave-Convex Procedure Looks at all samples simultaneously Hard samples will cause confusion Start with easy samples, then consider hard ones

16 Outline Latent Structural SVM Concave-Convex Procedure Self-Paced Learning Experiments

17 Self-Paced Learning REMINDER Simultaneously estimate easiness and parameters Easiness is property of data sets, not single instances

18 Self-Paced Learning Start with an initial estimate w 0 Update Update w t+1 by solving a convex problem min ||w|| 2 + C i i w T (x i,y i,h i ) - w T (x i,y,h) (y i, y, h) - i h i = max h H w t T (x i,y i,h)

19 Self-Paced Learning min ||w|| 2 + C i i w T (x i,y i,h i ) - w T (x i,y,h) (y i, y, h) - i

20 Self-Paced Learning min ||w|| 2 + C i v i i w T (x i,y i,h i ) - w T (x i,y,h) (y i, y, h) - i v i {0,1} Trivial Solution

21 Self-Paced Learning v i {0,1} Large KMedium KSmall K min ||w|| 2 + C i v i i - i v i /K w T (x i,y i,h i ) - w T (x i,y,h) (y i, y, h) - i

22 Self-Paced Learning v i [0,1] min ||w|| 2 + C i v i i - i v i /K w T (x i,y i,h i ) - w T (x i,y,h) (y i, y, h) - i Large KMedium KSmall K Biconvex Problem Alternating Convex Search

23 Self-Paced Learning Start with an initial estimate w 0 Update Update w t+1 by solving a convex problem min ||w|| 2 + C i v i i - i v i /K w T (x i,y i,h i ) - w T (x i,y,h) (y i, y, h) - i h i = max h H w t T (x i,y i,h) Decrease K K/

24 Outline Latent Structural SVM Concave-Convex Procedure Self-Paced Learning Experiments

25 Object Detection Feature (x,y,h) - HOG Input x - Image Output y Y Latent h - Box - 0/1 Loss Y = {Bison, Deer, Elephant, Giraffe, Llama, Rhino }

26 Object Detection 271 images, 6 classes 90/10 train/test split 4 folds Mammals Dataset

27 Object Detection CCCP Self-Paced

28 Object Detection CCCP Self-Paced

29 Object Detection CCCP Self-Paced

30 Object Detection CCCP Self-Paced

31 Objective valueTest error Object Detection

32 Handwritten Digit Recognition Feature (x,y,h) - PCA + Projection Input x - Image Output y Y Y = {0, 1, …, 9} Latent h - Rotation MNIST Dataset - 0/1 Loss

33 Handwritten Digit Recognition - Significant Difference C C C SPL

34 Handwritten Digit Recognition - Significant Difference C C C SPL

35 Handwritten Digit Recognition - Significant Difference C C C SPL

36 Handwritten Digit Recognition - Significant Difference C C C SPL

37 Motif Finding Feature (x,y,h) - Ng and Cardie, ACL 2002 Input x - DNA Sequence Output y Y Y = {0, 1} Latent h - Motif Location - 0/1 Loss

38 Motif Finding 40,000 sequences 50/50 train/test split 5 folds UniProbe Dataset

39 Motif Finding Average Hamming Distance of Inferred Motifs SPL

40 Motif Finding Objective Value SPL

41 Motif Finding Test Error SPL

42 Noun Phrase Coreference Feature (x,y,h) - Yu and Joachims, ICML 2009 Input x - NounsOutput y - Clustering Latent h - Spanning Forest over Nouns

43 Noun Phrase Coreference 60 documents 50/50 train/test split 1 predefined fold MUC6 Dataset

44 Noun Phrase Coreference - Significant Improvement - Significant Decrement MITRE Loss Pairwise Loss

45 Noun Phrase Coreference MITRE Loss Pairwise Loss SPL

46 Noun Phrase Coreference MITRE Loss Pairwise Loss SPL

47 Summary Automatic Self-Paced Learning Concave-Biconvex Procedure Generalization to other Latent models – Expectation-Maximization – E-step remains the same – M-step includes indicator variables v i Kumar, Packer and Koller, NIPS 2010


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