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Beyond MAP: Making Multiple Predictions: Diversity, DPPs and more.

Beyond MAP: Making Multiple Predictions: Diversity, DPPs and more. Dhruv Batra Virginia Tech. Alex Kulesza Univ. of Michigan. Dennis Park UC Irvine. Deva Ramanan UC Irvine. Schedule. Schedule. 1. Please interrupt & ask q uestions!. 2. All slides available online. Local Ambiguity.

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Beyond MAP: Making Multiple Predictions: Diversity, DPPs and more.

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  1. Beyond MAP: Making Multiple Predictions: Diversity, DPPs and more. Dhruv BatraVirginia Tech Alex KuleszaUniv. of Michigan Dennis ParkUC Irvine Deva RamananUC Irvine

  2. Schedule (C) Dhruv Batra

  3. Schedule 1. Please interrupt & ask questions! 2. All slides available online. (C) Dhruv Batra

  4. Local Ambiguity (C) Dhruv Batra slide credit: Fei-Fei Li, Rob Fergus & Antonio Torralba

  5. Graphical Models to the Rescue! y1 MAP Inference y2 … Person xn Table Plate Most Likely Assignment (C) Dhruv Batra

  6. Vision in 2000s (C) Dhruv Batra

  7. Graphical Models in Vision Segmentation Object Recognition / Pose Estimation Left image Right image Disparity map Motion Flow Geometric Labelling Stereo Denoising (C) Dhruv Batra

  8. Alpha-Expansion (C) Dhruv Batra Simulated Annealing

  9. Dollar et al., BMVC 2009

  10. (C) Dhruv Batra

  11. Problems Model-Class is Wrong! -- Approximation Error • Human Body ≠ Tree (C) Dhruv Batra Figure Courtesy: [Yang & Ramanan ICCV ‘11]

  12. Problems Model-Class is Wrong! Not Enough Training Data! -- Approximation Error -- Estimation Error (C) Dhruv Batra

  13. Problems Model-Class is Wrong! Not Enough Training Data! MAP is NP-Hard -- Approximation Error -- Estimation Error -- Optimization Error (C) Dhruv Batra

  14. Biggest Problem Model-Class is Wrong! Not Enough Training Data! MAP is NP-Hard Inherent Ambiguity -- Approximation Error -- Estimation Error -- Optimization Error -- Bayes Error ? ? Rotating clockwise / anti-clockwise? Old Lady looking left / Young woman looking away? One instance / Two instances? (C) Dhruv Batra

  15. Problems Single Prediction = Uncertainty Mismanagement Model-Class is Wrong! Not Enough Training Data! MAP is NP-Hard Inherent Ambiguity -- Approximation Error -- Estimation Error -- Optimization Error -- Bayes Error Make Multiple Predictions! (C) Dhruv Batra

  16. Multiple Predictions (Diverse) M-Best MAP Dhruv10:45 – 11:30 Dennis9:30 – 10:15 Flerova et al., 2011 Fromeret al., 2009 Yanover et al., 2003 (C) Dhruv Batra

  17. Multiple Predictions x x x x x x x x x x x x x Sampling Porway & Zhu, 2011 TU & Zhu, 2002 Rich History Deva1:30 – 2:00-pm (C) Dhruv Batra

  18. Multiple Predictions DeterminentalPoint Process Alex2:00 – 3:153:45 – 4:30 Build a new model over sets that prefers diverse set (C) Dhruv Batra

  19. Multiple Predictions DeterminentalPoint Process (Diverse) M-Best MAP Sampling Porway & Zhu, 2011 TU & Zhu, 2002 Rich History Alex2:00 – 3:153:45 – 4:30 Build a new model over sets that prefers diverse set Flerova et al., 2011 Fromeret al., 2009 Yanover et al., 2003 (C) Dhruv Batra

  20. Multiple Predictions DeterminentalPoint Process (Diverse) M-Best MAP Sampling Porway & Zhu, 2011 TU & Zhu, 2002 Rich History Build a new model over sets that prefers diverse set Flerova et al., 2011 Fromeret al., 2009 Yanover et al., 2003 (C) Dhruv Batra

  21. Schedule (C) Dhruv Batra All slides available online.

  22. Notation andReview of CRFs (C) Dhruv Batra

  23. Conditional Random Fields X1 • Discrete random variables • Factorized Model X2 1 1 10 0 kx1 10 0 … 10 10 Xi Xn 0 10 kxk Node Energies / Local Costs Edge Energies / Distributed Prior (C) Dhruv Batra

  24. MAP Inference • In general NP-hard [Shimony ‘94] Approximate Inference • Heuristics: Loopy BP [Pearl, ‘88] • Greedy: α-Expansion [Boykov ’01, Komodakis ‘05] • LP Relaxations: [Schlesinger ‘76, Wainwright ’05, Sontag ’08, Batra ‘10] • QP/SDP Relaxations: [Ravikumar ’06, Kumar ‘09] (C) Dhruv Batra

  25. MAP Integer Program kx1 (C) Dhruv Batra

  26. MAP Integer Program 1 0 0 0 kx1 (C) Dhruv Batra

  27. MAP Integer Program 0 1 0 0 kx1 (C) Dhruv Batra

  28. MAP Integer Program 0 0 1 0 kx1 (C) Dhruv Batra

  29. MAP Integer Program 0 0 0 1 kx1 (C) Dhruv Batra

  30. MAP Integer Program 0 0 0 1 kx1 k2x1 (C) Dhruv Batra

  31. MAP Integer Program 0 0 0 1 kx1 k2x1 (C) Dhruv Batra

  32. MAP Integer Program Graphcuts, BP, Expansion, etc (C) Dhruv Batra

  33. MAP Integer Program • LP view Graphcuts, BP, Expansion, etc MAP (C) Dhruv Batra

  34. Schedule (C) Dhruv Batra All slides available online.

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