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Self-Paced Learning for Semantic Segmentation M. Pawan Kumar

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

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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 }

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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

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

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

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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

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

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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

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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

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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)

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

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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)

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

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

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

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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)

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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

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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

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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

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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

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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/

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

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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 }

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

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Object Detection CCCP Self-Paced

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Object Detection CCCP Self-Paced

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Object Detection CCCP Self-Paced

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Object Detection CCCP Self-Paced

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Objective valueTest error Object Detection

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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

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Handwritten Digit Recognition - Significant Difference C C C SPL

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Handwritten Digit Recognition - Significant Difference C C C SPL

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Handwritten Digit Recognition - Significant Difference C C C SPL

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Handwritten Digit Recognition - Significant Difference C C C SPL

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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

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

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Motif Finding Average Hamming Distance of Inferred Motifs SPL

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Motif Finding Objective Value SPL

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Motif Finding Test Error SPL

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

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

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

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Noun Phrase Coreference MITRE Loss Pairwise Loss SPL

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Noun Phrase Coreference MITRE Loss Pairwise Loss SPL

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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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