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CVPR 2013 Diversity Tutorial Beyond MAP: Making Multiple Predictions: Diversity, DPPs and more. Dhruv Batra Virginia Tech Alex Kulesza Univ. of Michigan.

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Presentation on theme: "CVPR 2013 Diversity Tutorial Beyond MAP: Making Multiple Predictions: Diversity, DPPs and more. Dhruv Batra Virginia Tech Alex Kulesza Univ. of Michigan."— Presentation transcript:

1 CVPR 2013 Diversity Tutorial 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

2 CVPR 2013 Diversity Tutorial Schedule TimeTopicPresenter 9:00 – 9:30Opening Remarks + Need for Multiple Diverse Solutions Dhruv 9:30 – 10:15Multiple Solutions via M-Best MAPDennis 10:15 – 10:45Coffee Break 10:45 – 11:30Multiple Solutions via Diverse M-BestDhruv 12:00 – 1:30Lunch (C) Dhruv Batra2

3 CVPR 2013 Diversity Tutorial TimeTopicPresenter 9:00 – 9:30Opening Remarks + Need for Multiple Diverse Solutions Dhruv 9:30 – 10:15Multiple Solutions via M-Best MAPDennis 10:15 – 10:45Coffee Break 10:45 – 11:30Multiple Solutions via Diverse M-BestDhruv 12:00 – 1:30Lunch 1:30 – 2:00Multiple Solutions via SamplingDeva 2:00 – 3:15Multiple Solutions via DPPsAlex 3:15 – 3:45Coffee Break 3:45 – 4:30DPPs (Continued)Alex 4:30 – 5:00Closing Remarks + What can we do with diverse solutions? Dhruv Schedule (C) Dhruv Batra3 1. Please interrupt & ask questions! 2. All slides available online.

4 CVPR 2013 Diversity Tutorial Local Ambiguity (C) Dhruv Batra4 slide credit: Fei-Fei Li, Rob Fergus & Antonio Torralba

5 CVPR 2013 Diversity Tutorial Graphical Models to the Rescue! (C) Dhruv Batra5 MAP Inference Most Likely Assignment y1y1 y2y2 … xnxn Person Table Plate

6 CVPR 2013 Diversity Tutorial Vision in 2000s (C) Dhruv Batra6

7 CVPR 2013 Diversity Tutorial Graphical Models in Vision (C) Dhruv Batra7 Segmentation Left imageRight imageDisparity map Stereo Geometric Labelling Denoising Motion Flow Object Recognition / Pose Estimation

8 CVPR 2013 Diversity Tutorial (C) Dhruv Batra8 Alpha-Expansion Simulated Annealing

9 CVPR 2013 Diversity Tutorial Dollar et al., BMVC 2009 9

10 CVPR 2013 Diversity Tutorial (C) Dhruv Batra10

11 CVPR 2013 Diversity Tutorial Problems (C) Dhruv Batra11 Model-Class is Wrong! -- Approximation Error Human Body ≠ Tree Figure Courtesy: [Yang & Ramanan ICCV ‘11]

12 CVPR 2013 Diversity Tutorial Problems (C) Dhruv Batra12 Model-Class is Wrong! -- Approximation Error Not Enough Training Data! -- Estimation Error

13 CVPR 2013 Diversity Tutorial Problems (C) Dhruv Batra13 Model-Class is Wrong! -- Approximation Error Not Enough Training Data! -- Estimation Error MAP is NP-Hard -- Optimization Error

14 CVPR 2013 Diversity Tutorial Biggest Problem (C) Dhruv Batra14 Model-Class is Wrong! -- Approximation Error Not Enough Training Data! -- Estimation Error MAP is NP-Hard -- Optimization Error Inherent Ambiguity -- Bayes Error ? ? Old Lady looking left / Young woman looking away? Rotating clockwise / anti-clockwise? One instance / Two instances?

15 CVPR 2013 Diversity Tutorial Problems (C) Dhruv Batra15 Model-Class is Wrong! -- Approximation Error Not Enough Training Data! -- Estimation Error MAP is NP-Hard -- Optimization Error Inherent Ambiguity -- Bayes Error Make Multiple Predictions! Single Prediction = Uncertainty Mismanagement

16 CVPR 2013 Diversity Tutorial Multiple Predictions (C) Dhruv Batra16 Flerova et al., 2011 Fromer et al., 2009 Yanover et al., 2003 (Diverse) M-Best MAP Dhruv 10:45 – 11:30 Dennis 9:30 – 10:15

17 CVPR 2013 Diversity Tutorial Multiple Predictions (C) Dhruv Batra17 Porway & Zhu, 2011 TU & Zhu, 2002 Rich History Sampling xxxxxxxxxxxxx Deva 1:30 – 2:00-pm

18 CVPR 2013 Diversity Tutorial Multiple Predictions (C) Dhruv Batra18 Build a new model over sets that prefers diverse set Determinental Point Process Alex 2:00 – 3:15 3:45 – 4:30

19 CVPR 2013 Diversity Tutorial Multiple Predictions (C) Dhruv Batra19 Build a new model over sets that prefers diverse set Determinental Point Process Alex 2:00 – 3:15 3:45 – 4:30 Porway & Zhu, 2011 TU & Zhu, 2002 Rich History Sampling Flerova et al., 2011 Fromer et al., 2009 Yanover et al., 2003 (Diverse) M-Best MAP

20 CVPR 2013 Diversity Tutorial Multiple Predictions (C) Dhruv Batra20 Build a new model over sets that prefers diverse set Determinental Point Process Porway & Zhu, 2011 TU & Zhu, 2002 Rich History Sampling Flerova et al., 2011 Fromer et al., 2009 Yanover et al., 2003 (Diverse) M-Best MAP

21 CVPR 2013 Diversity Tutorial Schedule TimeTopicPresenter 9:00 – 9:30Opening Remarks + Need for Multiple Diverse Solutions Dhruv 9:30 – 10:15Multiple Solutions via M-Best MAPDennis 10:15 – 10:45Coffee Break 10:45 – 11:30Multiple Solutions via Diverse M-BestDhruv 12:00 – 1:30Lunch 1:30 – 2:00Multiple Solutions via SamplingDeva 2:00 – 3:15Multiple Solutions via DPPsAlex 3:15 – 3:45Coffee Break 3:45 – 4:30DPPs (Continued)Alex 4:30 – 5:00Closing Remarks + What can we do with diverse solutions? Dhruv (C) Dhruv Batra21 All slides available online.

22 CVPR 2013 Diversity Tutorial Notation and Review of CRFs (C) Dhruv Batra22

23 CVPR 2013 Diversity Tutorial Conditional Random Fields Discrete random variables Factorized Model 23(C) Dhruv Batra Node Energies / Local Costs Edge Energies / Distributed Prior X1X1 X2X2 … XnXn XiXi kx1 1 1 10 0 kxk 10 0 0

24 CVPR 2013 Diversity Tutorial MAP Inference In general NP-hard [Shimony ‘94] (C) Dhruv Batra24 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]

25 CVPR 2013 Diversity Tutorial MAP Integer Program (C) Dhruv Batra25 kx1

26 CVPR 2013 Diversity Tutorial MAP Integer Program (C) Dhruv Batra26 kx1 10001000

27 CVPR 2013 Diversity Tutorial MAP Integer Program (C) Dhruv Batra27 kx1 01000100

28 CVPR 2013 Diversity Tutorial MAP Integer Program (C) Dhruv Batra28 kx1 00100010

29 CVPR 2013 Diversity Tutorial MAP Integer Program (C) Dhruv Batra29 kx1 00010001

30 CVPR 2013 Diversity Tutorial MAP Integer Program (C) Dhruv Batra30 kx1 00010001 k 2 x1

31 CVPR 2013 Diversity Tutorial MAP Integer Program (C) Dhruv Batra31 kx1 00010001 k 2 x1

32 CVPR 2013 Diversity Tutorial MAP Integer Program (C) Dhruv Batra32 Graphcuts, BP, Expansion, etc

33 CVPR 2013 Diversity Tutorial MAP Integer Program LP view (C) Dhruv Batra33 MAP Graphcuts, BP, Expansion, etc

34 CVPR 2013 Diversity Tutorial Schedule TimeTopicPresenter 9:00 – 9:30Opening Remarks + Need for Multiple Diverse Solutions Dhruv 9:30 – 10:15Multiple Solutions via M-Best MAPDennis 10:15 – 10:45Coffee Break 10:45 – 11:30Multiple Solutions via Diverse M-BestDhruv 12:00 – 1:30Lunch 1:30 – 2:00Multiple Solutions via SamplingDeva 2:00 – 3:15Multiple Solutions via DPPsAlex 3:15 – 3:45Coffee Break 3:45 – 4:30DPPs (Continued)Alex 4:30 – 5:00Closing Remarks + What can we do with diverse solutions? Dhruv (C) Dhruv Batra34 All slides available online.

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