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An Efficient Message-Passing Algorithm for the M-Best MAP Problem

An Efficient Message-Passing Algorithm for the M-Best MAP Problem. Dhruv Batra . (Currently) Research Assistant Professor TTI-Chicago. (Spring 2013) Assistant Professor Virginia Tech. Local Ambiguity. Graphical Models. Hat. x 1. x 2. MAP Inference. …. x n. C at.

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An Efficient Message-Passing Algorithm for the M-Best MAP Problem

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  1. An Efficient Message-Passing Algorithm for the M-Best MAP Problem Dhruv Batra • (Currently) • Research Assistant ProfessorTTI-Chicago • (Spring 2013) • Assistant ProfessorVirginia Tech

  2. Local Ambiguity • Graphical Models Hat x1 x2 MAP Inference … xn Cat Most Likely AssignmentMAP Problem (C) Dhruv Batra

  3. Global Ambiguity • “While hunting in Africa, I shot an elephant in my pajamas. How an elephant got into my pajamas, I’ll never know!” • Groucho Marx (1930) (C) Dhruv Batra

  4. M-Best MAP • Useful for: • Generating multiple hypotheses when model is inaccurate • Passing on hypotheses to next stage in cascade • Show multiple solutions to users • Generalization of MAP, thus NP-Hard (C) Dhruv Batra

  5. History (C) Dhruv Batra

  6. History (C) Dhruv Batra

  7. History (C) Dhruv Batra

  8. History • This Work[Batra UAI ’12] ? (C) Dhruv Batra

  9. Contributions • First message-passing alg for solving M-Best MAP LP of [Fromer & Globerson NIPS09] • Guaranteed to get exact solution to LP • Orders of magnitude faster than a generic LP solver LP-solver Time (sec) Our Approach Better #Nodes (C) Dhruv Batra

  10. Outline M M=2  M>2 Schemes • Partition Enumeration Scheme [Fromer & Globerson NIPS09] • Others • Details in Paper Cycles (C) Dhruv Batra

  11. Background x1 • Over-Complete Representation x2 … … kx1 0 0 0 0 1 1 0 0 … kxk Xi xn … … … … … 0 1 0 0 1 0 0 0 … kx1 (C) Dhruv Batra

  12. Background x1 • Over-Complete Representation x2 … Xi xn … … 100000000000 010000000000 (C) Dhruv Batra k2x1

  13. Background • MAP Integer Program (C) Dhruv Batra

  14. Background • MAP Linear Program • Properties • If LP-opt is integral, MAP is found • LP always integral for trees • Efficient message-passing schemes for solving LP (C) Dhruv Batra

  15. Outline M Cycles (C) Dhruv Batra

  16. M-Best MAP LP: Tree Spanning-Tree Inequality [Fromer & Globerson NIPS09] (C) Dhruv Batra

  17. M-Best MAP LP: Tree Generic LP-solver: CPLEX [Fromer & Globerson NIPS09] ~ 106x 106 (C) Dhruv Batra

  18. M-Best MAP LP: Tree Similarity-Augmented Energy • Lagrangian Relaxation Dualize 2-PassBelief Propagation (C) Dhruv Batra

  19. M-Best MAP LP: Tree • Lagrangian Relaxation • Dual Problem upergradient Ascent 2nd Best MAP energy Concave (Non-smooth) Lower-Bound on 2nd Best MAP energy (C) Dhruv Batra

  20. M-Best MAP LP: Tree • Lagrangian Relaxation • Dual Problem upergradient Ascent primal point Primal Block Dual Block dual point (C) Dhruv Batra

  21. M-Best MAP LP: Tree • Lagrangian Relaxation • Dual Problem • Guarantees • Suitable choice of stepsize solves Lagrangian[Shor ‘85] • LP => StrongDuality upergradient Ascent (C) Dhruv Batra

  22. Outline M Cycles (C) Dhruv Batra

  23. M-Best MAP LP: Loopy-MRFs , , … (C) Dhruv Batra

  24. M-Best MAP LP: Loopy-MRFs Dualize Problems 1. Exponentially many Lagrangian Terms 2. Collection of factors not a tree , , … (C) Dhruv Batra

  25. Exponentially Many Terms Dynamic Constraint Management upergradient Ascent Tree Subset primal point primal point Primal Block Dual Block … dual point dual point (C) Dhruv Batra

  26. Exponentially Many Terms Dynamic Constraint Management upergradient Ascent Tree Subset primal point Max-Weight Spanning TreeSame as [Fromer & Globerson] Primal Block Dual Block , … dual point , (C) Dhruv Batra

  27. Loopy Graph Problems 1. Exponentially many Lagrangian Terms 2. Collection of factors not a tree Dual Decomposition … (C) Dhruv Batra

  28. M-Best MAP LP: Loopy-MRFs • Guarantees • Dynamic Supergradient Ascent w/ Max-Violation Oracle solves Lagrangian Relaxation [Emiel & Sagastizabal ‘08] • LP => Strong Duality (C) Dhruv Batra

  29. Experiments • Synthetic Data • Trees • Grid Graphs • Energies sampled from Gaussians • Methods • STEELARS: Spanning TREE LAgrangian Relaxation Scheme [Proposed] • STRIPES [Fromer & Globerson NIPS09] • BMMF [Yanover & Weiss NIPS03] • NILSSON [Nilsson Stat. & Comp. 98] (C) Dhruv Batra

  30. Results: Tree-MRFs Better (C) Dhruv Batra

  31. Results: Loopy-MRFs Better (C) Dhruv Batra

  32. Extension: Diverse M-Best Task-Specific Diversity • Diverse M-Best Solutions in MRFsBatra, Yadollahpour, Guzman, ShakhnarovichECCV 2012 (C) Dhruv Batra

  33. Extension: Diverse M-Best • Interactive Segmentation Image + Scribbles 2nd Best Mode MAP 2nd Best MAP 1-2 Nodes Flipped 100-500 Nodes Flipped (C) Dhruv Batra

  34. Extension: Diverse M-Best Input MAP Best Mode (C) Dhruv Batra

  35. Conclusions • First message-passing alg for solving M-Best MAP LP • Guaranteed to get exact solution to LP • Orders of magnitude faster than a generic LP solver • Extension: • Diverse M-Best Solutions in MRFsBatra, Yadollahpour, Guzman, ShakhnarovichECCV 2012 (C) Dhruv Batra

  36. Thank you! (C) Dhruv Batra

  37. Results: Tree-MRFs (C) Dhruv Batra

  38. Quality of Solutions: Loopy-MRFs (C) Dhruv Batra

  39. Results: Loopy-MRFs (C) Dhruv Batra

  40. Applications • What can we do with multiple solutions? • More choices for “human/expert in the loop” (C) Dhruv Batra

  41. Applications • What can we do with multiple solutions? • More choices for “human/expert in the loop” • Input to next system in cascade Top M Top M Step 1 Step 2 Step 3 hypotheses hypotheses (C) Dhruv Batra

  42. Applications • What can we do with multiple solutions? • More choices for “human in the loop” • Rank solutions ~10,000 [Carreira and Sminchisescu, CVPR10] State-of-art segmentation on PASCAL Challenge 2011 (C) Dhruv Batra

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