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2016 | OriginalPaper | Buchkapitel

Learning Diverse Models: The Coulomb Structured Support Vector Machine

verfasst von : Martin Schiegg, Ferran Diego, Fred A. Hamprecht

Erschienen in: Computer Vision – ECCV 2016

Verlag: Springer International Publishing

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Abstract

In structured prediction, it is standard procedure to discriminatively train a single model that is then used to make a single prediction for each input. This practice is simple but risky in many ways. For instance, models are often designed with tractability rather than faithfulness in mind. To hedge against such model misspecification, it may be useful to train multiple models that all are a reasonable fit to the training data, but at least one of which may hopefully make more valid predictions than the single model in standard procedure. We propose the Coulomb Structured SVM (CSSVM) as a means to obtain at training time a full ensemble of different models. At test time, these models can run in parallel and independently to make diverse predictions. We demonstrate on challenging tasks from computer vision that some of these diverse predictions have significantly lower task loss than that of a single model, and improve over state-of-the-art diversity encouraging approaches.

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Fußnoten
1
Note that this is almost always true once we have a sufficient number of independent features, see the function counting theorem [23].
 
2
Note that we want to approximate this problem in a high dimensional space instead of only 3 dimensions.
 
3
Note that we assume electrostatic charges on the parameters, and not the training samples as done in [37].
 
Literatur
1.
Zurück zum Zitat Tsochantaridis, I., Joachims, T., Hofmann, T., Altun, Y.: Large margin methods for structured and interdependent output variables. JMLR 6, 1453–1484 (2005)MathSciNetMATH Tsochantaridis, I., Joachims, T., Hofmann, T., Altun, Y.: Large margin methods for structured and interdependent output variables. JMLR 6, 1453–1484 (2005)MathSciNetMATH
2.
Zurück zum Zitat Nowozin, S., Lampert, C.H.: Structured learning and prediction in computer vision. Found. Trends Comput. Graph. Vis. 6(3–4), 185–365 (2011)MATH Nowozin, S., Lampert, C.H.: Structured learning and prediction in computer vision. Found. Trends Comput. Graph. Vis. 6(3–4), 185–365 (2011)MATH
3.
Zurück zum Zitat Yanover, C., Weiss, Y.: Finding the M most probable configurations in arbitrary graphical models. In: NIPS 2003, pp. 289–296 (2003) Yanover, C., Weiss, Y.: Finding the M most probable configurations in arbitrary graphical models. In: NIPS 2003, pp. 289–296 (2003)
4.
Zurück zum Zitat Papandreou, G., Yuille, A.L.: Perturb-and-map random fields: using discrete optimization to learn and sample from energy models. In: ICCV (2011) Papandreou, G., Yuille, A.L.: Perturb-and-map random fields: using discrete optimization to learn and sample from energy models. In: ICCV (2011)
5.
Zurück zum Zitat Batra, D., Yadollahpour, P., Guzman-Rivera, A., Shakhnarovich, G.: Diverse M-best solutions in Markov random fields. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds.) ECCV 2012, Part V. LNCS, vol. 7576, pp. 1–16. Springer, Heidelberg (2012) Batra, D., Yadollahpour, P., Guzman-Rivera, A., Shakhnarovich, G.: Diverse M-best solutions in Markov random fields. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds.) ECCV 2012, Part V. LNCS, vol. 7576, pp. 1–16. Springer, Heidelberg (2012)
6.
Zurück zum Zitat Guzman-Rivera, A., Batra, D., Kohli, P.: Multiple choice learning: learning to produce multiple structured outputs. In: NIPS, pp. 1808–1816 (2012) Guzman-Rivera, A., Batra, D., Kohli, P.: Multiple choice learning: learning to produce multiple structured outputs. In: NIPS, pp. 1808–1816 (2012)
7.
Zurück zum Zitat Guzman-Rivera, A., Kohli, P., Batra, D., Rutenbar, R.A.: Efficiently enforcing diversity in multi-output structured prediction. In: AISTATS (2014) Guzman-Rivera, A., Kohli, P., Batra, D., Rutenbar, R.A.: Efficiently enforcing diversity in multi-output structured prediction. In: AISTATS (2014)
8.
Zurück zum Zitat Gane, A., Hazan, T., Jaakkola, T.: Learning with maximum a-posteriori perturbation models. In: AISTATS, pp. 247–256 (2014) Gane, A., Hazan, T., Jaakkola, T.: Learning with maximum a-posteriori perturbation models. In: AISTATS, pp. 247–256 (2014)
9.
Zurück zum Zitat Yadollahpour, P., Batra, D., Shakhnarovich, G.: Discriminative re-ranking of diverse segmentations. In: CVPR (2013) Yadollahpour, P., Batra, D., Shakhnarovich, G.: Discriminative re-ranking of diverse segmentations. In: CVPR (2013)
10.
Zurück zum Zitat Gimpel, K., Batra, D., Dyer, C., Shakhnarovich, G.: A systematic exploration of diversity in machine translation. In: EMNLP (2013) Gimpel, K., Batra, D., Dyer, C., Shakhnarovich, G.: A systematic exploration of diversity in machine translation. In: EMNLP (2013)
11.
Zurück zum Zitat Roig, G., Boix, X., de Nijs, R., Ramos, S., Kühnlenz, K., Van Gool, L.: Active MAP inference in CRFs for efficient semantic segmentation. In: ICCV (2013) Roig, G., Boix, X., de Nijs, R., Ramos, S., Kühnlenz, K., Van Gool, L.: Active MAP inference in CRFs for efficient semantic segmentation. In: ICCV (2013)
12.
Zurück zum Zitat Maji, S., Hazan, T., Jaakkola, T.: Active boundary annotation using random map perturbations. In: AISTATS (2014) Maji, S., Hazan, T., Jaakkola, T.: Active boundary annotation using random map perturbations. In: AISTATS (2014)
13.
Zurück zum Zitat Premachandran, V., Tarlow, D., Batra, D.: Empirical minimum bayes risk prediction: how to extract an extra few % performance from vision models with just three more parameters. In: CVPR (2014) Premachandran, V., Tarlow, D., Batra, D.: Empirical minimum bayes risk prediction: how to extract an extra few % performance from vision models with just three more parameters. In: CVPR (2014)
14.
Zurück zum Zitat Kirillov, A., Savchynskyy, B., Schlesinger, D., Vetrov, D., Rother, C.: Inferring m-best diverse labelings in a single one. In: ICCV, pp. 1814–1822 (2015) Kirillov, A., Savchynskyy, B., Schlesinger, D., Vetrov, D., Rother, C.: Inferring m-best diverse labelings in a single one. In: ICCV, pp. 1814–1822 (2015)
15.
Zurück zum Zitat Hazan, T., Maji, S., Jaakkola, T.: On sampling from the Gibbs distribution with random maximum a-posteriori perturbations. In: NIPS, pp. 1268–1276 (2013) Hazan, T., Maji, S., Jaakkola, T.: On sampling from the Gibbs distribution with random maximum a-posteriori perturbations. In: NIPS, pp. 1268–1276 (2013)
16.
Zurück zum Zitat Chen, C., Kolmogorov, V., Zhu, Y., Metaxas, D., Lampert, C.: Computing the M most probable modes of a graphical model. In: AISTATS, pp. 161–169 (2013) Chen, C., Kolmogorov, V., Zhu, Y., Metaxas, D., Lampert, C.: Computing the M most probable modes of a graphical model. In: AISTATS, pp. 161–169 (2013)
17.
Zurück zum Zitat Chen, C., Liu, H., Metaxas, D., Zhao, T.: Mode estimation for high dimensional discrete tree graphical models. In: NIPS, pp. 1323–1331 (2014) Chen, C., Liu, H., Metaxas, D., Zhao, T.: Mode estimation for high dimensional discrete tree graphical models. In: NIPS, pp. 1323–1331 (2014)
18.
19.
Zurück zum Zitat Lucchi, A., Li, Y., Smith, K., Fua, P.: Structured image segmentation using kernelized features. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds.) ECCV 2012, Part II. LNCS, vol. 7573, pp. 400–413. Springer, Heidelberg (2012) Lucchi, A., Li, Y., Smith, K., Fua, P.: Structured image segmentation using kernelized features. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds.) ECCV 2012, Part II. LNCS, vol. 7573, pp. 400–413. Springer, Heidelberg (2012)
20.
Zurück zum Zitat Lou, X., Hamprecht, F.A.: Structured learning for cell tracking. In: NIPS (2011) Lou, X., Hamprecht, F.A.: Structured learning for cell tracking. In: NIPS (2011)
21.
Zurück zum Zitat Li, Y.F., Zhou, Z.H.: Towards making unlabeled data never hurt. IEEE Trans. PAMI 37(1), 175–188 (2015)CrossRef Li, Y.F., Zhou, Z.H.: Towards making unlabeled data never hurt. IEEE Trans. PAMI 37(1), 175–188 (2015)CrossRef
22.
Zurück zum Zitat Lampert, C.H.: Maximum margin multi-label structured prediction. In: NIPS, pp. 289–297 (2011) Lampert, C.H.: Maximum margin multi-label structured prediction. In: NIPS, pp. 289–297 (2011)
23.
Zurück zum Zitat Cover, T.M.: Geometrical and statistical properties of systems of linear inequalities with applications in pattern recognition. IEEE Trans. Electron. Comput. EC–14(3), 326–334 (1965)CrossRefMATH Cover, T.M.: Geometrical and statistical properties of systems of linear inequalities with applications in pattern recognition. IEEE Trans. Electron. Comput. EC–14(3), 326–334 (1965)CrossRefMATH
24.
Zurück zum Zitat Mitchell, T.M.: Machine Learning, 1st edn. McGraw-Hill Inc., New York (1997)MATH Mitchell, T.M.: Machine Learning, 1st edn. McGraw-Hill Inc., New York (1997)MATH
25.
Zurück zum Zitat Herbrich, R., Graepel, T., Williamson, R.C.: The structure of version space. Technical report MSR-TR-2004-63, Microsoft Research, July 2004 Herbrich, R., Graepel, T., Williamson, R.C.: The structure of version space. Technical report MSR-TR-2004-63, Microsoft Research, July 2004
26.
27.
Zurück zum Zitat Graepel, T., Herbrich, R.: The kernel Gibbs sampler. In: NIPS, pp. 514–520 (2001) Graepel, T., Herbrich, R.: The kernel Gibbs sampler. In: NIPS, pp. 514–520 (2001)
28.
Zurück zum Zitat Sacks, J., Welch, W.J., Mitchell, T.J., Wynn, H.P.: Design and analysis of computer experiments. Stat. Sci. 4, 409–423 (1989)MathSciNetCrossRefMATH Sacks, J., Welch, W.J., Mitchell, T.J., Wynn, H.P.: Design and analysis of computer experiments. Stat. Sci. 4, 409–423 (1989)MathSciNetCrossRefMATH
29.
Zurück zum Zitat Hardin, R., Sloane, N.: A new approach to the construction of optimal designs. J. Stat. Plann. Infer. 37(3), 339–369 (1993)MathSciNetCrossRefMATH Hardin, R., Sloane, N.: A new approach to the construction of optimal designs. J. Stat. Plann. Infer. 37(3), 339–369 (1993)MathSciNetCrossRefMATH
30.
Zurück zum Zitat Conway, J.H., Sloane, N.J.A.: Sphere-packings, Lattices, and Groups. Springer, New York (1987)MATH Conway, J.H., Sloane, N.J.A.: Sphere-packings, Lattices, and Groups. Springer, New York (1987)MATH
33.
Zurück zum Zitat Claxton, T., Benson, G.: Stereochemistry and seven coordination. Can. J. Chem. 44(2), 157–163 (1966)CrossRef Claxton, T., Benson, G.: Stereochemistry and seven coordination. Can. J. Chem. 44(2), 157–163 (1966)CrossRef
34.
Zurück zum Zitat Erber, T., Hockney, G.: Equilibrium configurations of n equal charges on a sphere. J. Phys. A: Math. Gen. 24(23), L1369 (1991)CrossRef Erber, T., Hockney, G.: Equilibrium configurations of n equal charges on a sphere. J. Phys. A: Math. Gen. 24(23), L1369 (1991)CrossRef
35.
Zurück zum Zitat Lakhbab, H., EL Bernoussi, S., EL Harif, A.: Energy minimization of point charges on a sphere with a spectral projected gradient method. Int. J. Sci. Eng. Res. 3(5) (2012) Lakhbab, H., EL Bernoussi, S., EL Harif, A.: Energy minimization of point charges on a sphere with a spectral projected gradient method. Int. J. Sci. Eng. Res. 3(5) (2012)
37.
Zurück zum Zitat Hochreiter, S., Mozer, M.C., Obermayer, K.: Coulomb classifiers: generalizing support vector machines via an analogy to electrostatic systems. In: NIPS, pp. 561–568 (2003) Hochreiter, S., Mozer, M.C., Obermayer, K.: Coulomb classifiers: generalizing support vector machines via an analogy to electrostatic systems. In: NIPS, pp. 561–568 (2003)
38.
Zurück zum Zitat Ratliff, N.D., Bagnell, J.A., Zinkevich, M.A.: (Online) Subgradient methods for structured prediction. In: AISTATS (2007) Ratliff, N.D., Bagnell, J.A., Zinkevich, M.A.: (Online) Subgradient methods for structured prediction. In: AISTATS (2007)
39.
Zurück zum Zitat Prasad, A., Jegelka, S., Batra, D.: Submodular meets structured: finding diverse subsets in exponentially-large structured item sets. In: NIPS, pp. 2645–2653 (2014) Prasad, A., Jegelka, S., Batra, D.: Submodular meets structured: finding diverse subsets in exponentially-large structured item sets. In: NIPS, pp. 2645–2653 (2014)
40.
Zurück zum Zitat Batra, D., Kowdle, A., Parikh, D., Luo, J., Chen, T.: iCoseg: interactive co-segmentation with intelligent scribble guidance. In: CVPR (2010) Batra, D., Kowdle, A., Parikh, D., Luo, J., Chen, T.: iCoseg: interactive co-segmentation with intelligent scribble guidance. In: CVPR (2010)
41.
Zurück zum Zitat Everingham, M., Van Gool, L., Williams, C.K.I., Winn, J., Zisserman, A.: The PASCAL visual object classes challenge. Int. J. Comput. Vis. 88, 303–338 (2010)CrossRef Everingham, M., Van Gool, L., Williams, C.K.I., Winn, J., Zisserman, A.: The PASCAL visual object classes challenge. Int. J. Comput. Vis. 88, 303–338 (2010)CrossRef
42.
Zurück zum Zitat Tsai, Y.H., Yang, J., Yang, M.H.: Decomposed learning for joint object segmentation and categorization. In: BMVC (2013) Tsai, Y.H., Yang, J., Yang, M.H.: Decomposed learning for joint object segmentation and categorization. In: BMVC (2013)
43.
Zurück zum Zitat Lee, T., Fidler, S., Dickinson, S.: Learning to combine mid-level cues for object proposal generation. In: CVPR, pp. 1680–1688 (2015) Lee, T., Fidler, S., Dickinson, S.: Learning to combine mid-level cues for object proposal generation. In: CVPR, pp. 1680–1688 (2015)
44.
Zurück zum Zitat Wang, S., Fidler, S., Urtasun, R.: Lost shopping! monocular localization in large indoor spaces. In: ICCV (2015) Wang, S., Fidler, S., Urtasun, R.: Lost shopping! monocular localization in large indoor spaces. In: ICCV (2015)
45.
Zurück zum Zitat Müller, A.C., Behnke, S.: PyStruct - learning structured prediction in python. JMLR 15, 2055–2060 (2014)MathSciNetMATH Müller, A.C., Behnke, S.: PyStruct - learning structured prediction in python. JMLR 15, 2055–2060 (2014)MathSciNetMATH
46.
Zurück zum Zitat Kolmogorov, V.: Convergent tree-reweighted message passing for energy minimization. IEEE Trans. PAMI 28(10), 1568–1583 (2006)CrossRef Kolmogorov, V.: Convergent tree-reweighted message passing for energy minimization. IEEE Trans. PAMI 28(10), 1568–1583 (2006)CrossRef
47.
Zurück zum Zitat Rother, C., Minka, T., Blake, A., Kolmogorov, V.: Cosegmentation of image pairs by histogram matching-incorporating a global constraint into MRFs. In: CVPR, pp. 993–1000 (2006) Rother, C., Minka, T., Blake, A., Kolmogorov, V.: Cosegmentation of image pairs by histogram matching-incorporating a global constraint into MRFs. In: CVPR, pp. 993–1000 (2006)
48.
Zurück zum Zitat Koltun, V.: Efficient inference in fully connected CRFs with Gaussian edge potentials. In: NIPS (2011) Koltun, V.: Efficient inference in fully connected CRFs with Gaussian edge potentials. In: NIPS (2011)
Metadaten
Titel
Learning Diverse Models: The Coulomb Structured Support Vector Machine
verfasst von
Martin Schiegg
Ferran Diego
Fred A. Hamprecht
Copyright-Jahr
2016
DOI
https://doi.org/10.1007/978-3-319-46487-9_36