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Coupling Gaussian Process Dynamical Models with Product-of-Experts Kernels

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Artificial Neural Networks and Machine Learning – ICANN 2014 (ICANN 2014)

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Abstract

We describe a new probabilistic model for learning of coupled dynamical systems in latent state spaces. The coupling is achieved by combining predictions from several Gaussian process dynamical models in a product-of-experts fashion. Our approach facilitates modulation of coupling strengths without the need for computationally expensive re-learning of the dynamical models. We demonstrate the effectiveness of the new coupling model on synthetic toy examples and on high-dimensional human walking motion capture data.

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References

  1. Ajallooeian, M., van den Kieboom, J., Mukovskiy, A., Giese, M.A., Ijspeert, A.: A general family of morphed nonlinear phase oscillators with arbitrary limit cycle shape. Physica D: Nonlinear Phenomena 263, 41–56 (2013), http://www.sciencedirect.com/science/article/pii/S0167278913002339

    Article  MATH  MathSciNet  Google Scholar 

  2. Bishop, C.M.: Pattern Recognition and Machine Learning. Springer (2006)

    Google Scholar 

  3. Brand, M., Hertzmann, A.: Style machines. In: Proc. SIGGRAPH 2000, pp. 183–192 (2000)

    Google Scholar 

  4. Chai, J., Hodgins, J.K.: Performance animation from low-dimensional control signals. ACM Trans. Graph. 24(3), 686–696 (2005)

    Article  Google Scholar 

  5. Giese, M.A., Mukovskiy, A., Park, A.-N., Omlor, L., Slotine, J.-J.E.: Real-Time Synthesis of Body Movements Based on Learned Primitives. In: Cremers, D., Rosenhahn, B., Yuille, A.L., Schmidt, F.R. (eds.) Visual Motion Analysis. LNCS, vol. 5604, pp. 107–127. Springer, Heidelberg (2009)

    Google Scholar 

  6. Grassia, F.S.: Practical parameterization of rotations using the exponential map. J. Graph. Tools 3(3), 29–48 (1998), http://dx.doi.org/10.1080/10867651.1998.10487493

    Article  Google Scholar 

  7. Grillner, S., Wallen, P.: Central pattern generators for locomotion, with special reference to vertebrates. Ann. Rev. Neurosci. 8(1), 233–261 (1985)

    Article  Google Scholar 

  8. Grochow, K., Martin, S.L., Hertzmann, A., Popovic, Z.: Style-based inverse kinematics. ACM Trans. Graph. 23(3), 522–531 (2004)

    Article  Google Scholar 

  9. Hinton, G.E.: Products of experts. In: Proc. ICANN 1999, vol. 1, pp. 1–6 (1999)

    Google Scholar 

  10. Ijspeert, A.J., Nakanishi, J., Hoffmann, H., Pastor, P., Schaal, S.: Dynamical movement primitives: Learning attractor models for motor behaviors. Neu. Comp. 25(2), 328–373 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  11. Jebara, T., Kondor, R., Howard, A.: Probability product kernels. J. Mach. Learn. Res. 5, 819–844 (2004)

    MATH  MathSciNet  Google Scholar 

  12. Lawrence, N.D.: Gaussian process latent variable models for visualisation of high dimensional data. In: NIPS 2003 (2003)

    Google Scholar 

  13. Lee, S.H., Sifakis, E., Terzopoulos, D.: Comprehensive biomechanical modeling and simulation of the upper body. ACM Trans. Graph. 99, 99 (2009)

    Google Scholar 

  14. Levine, S., Wang, J.M., Haraux, A., Popović, Z., Koltun, V.: Continuous character control with low-dimensional embeddings. ACM Trans. Graph. 28, 28 (2012)

    Google Scholar 

  15. Lohmiller, W., Slotine, J.J.E.: On contraction analysis for non-linear systems. Automatica 34(6), 683–696 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  16. Mukovskiy, A., Slotine, J.J., Giese, M.: Design of the dynamic stability properties of the collective behavior of articulated bipeds. In: 10th IEEE-RAS Intl. Conf. Humanoid Robots, pp. 66–73 (2010)

    Google Scholar 

  17. Neal, R.: Bayesian Learning for Neural Networks. Ph.D. thesis, Dept. of Computer Science, University of Toronto (1994)

    Google Scholar 

  18. Pearl, J.: Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann (1997)

    Google Scholar 

  19. Petersen, K.B., Pedersen, M.S.: The matrix cookbook (2012), version 20121115

    Google Scholar 

  20. Rasmussen, C.E.: minimize.m (2006), http://learning.eng.cam.ac.uk/carl/code/minimize/

  21. Taubert, N., Endres, D., Christensen, A., Giese, M.A.: Shaking hands in latent space. In: Bach, J., Edelkamp, S. (eds.) KI 2011. LNCS (LNAI), vol. 7006, pp. 330–334. Springer, Heidelberg (2011)

    Google Scholar 

  22. Urtasun, R., Fleet, D.J., Lawrence, N.D.: Modeling human locomotion with topologically constrained latent variable models. In: Elgammal, A., Rosenhahn, B., Klette, R. (eds.) Human Motion 2007. LNCS, vol. 4814, pp. 104–118. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  23. Wang, J.M., Fleet, D.J., Hertzmann, A.: Multifactor gaussian process models for style-content separation. In: ICML, pp. 975–982 (2007)

    Google Scholar 

  24. Wang, J.M., Fleet, D.J., Hertzmann, A.: Gaussian process dynamical models for human motion. IEEE Trans. Pattern Anal. Mach. Intell. 30(2), 283–298 (2008)

    Article  Google Scholar 

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Velychko, D., Endres, D., Taubert, N., Giese, M.A. (2014). Coupling Gaussian Process Dynamical Models with Product-of-Experts Kernels. In: Wermter, S., et al. Artificial Neural Networks and Machine Learning – ICANN 2014. ICANN 2014. Lecture Notes in Computer Science, vol 8681. Springer, Cham. https://doi.org/10.1007/978-3-319-11179-7_76

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  • DOI: https://doi.org/10.1007/978-3-319-11179-7_76

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11178-0

  • Online ISBN: 978-3-319-11179-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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