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

  • Dmytro Velychko
  • Dominik Endres
  • Nick Taubert
  • Martin A. Giese
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8681)

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.

Keywords

Gaussian Process Products of Experts Computer Graphics 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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 CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Bishop, C.M.: Pattern Recognition and Machine Learning. Springer (2006)Google Scholar
  3. 3.
    Brand, M., Hertzmann, A.: Style machines. In: Proc. SIGGRAPH 2000, pp. 183–192 (2000)Google Scholar
  4. 4.
    Chai, J., Hodgins, J.K.: Performance animation from low-dimensional control signals. ACM Trans. Graph. 24(3), 686–696 (2005)CrossRefGoogle Scholar
  5. 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. 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 CrossRefGoogle Scholar
  7. 7.
    Grillner, S., Wallen, P.: Central pattern generators for locomotion, with special reference to vertebrates. Ann. Rev. Neurosci. 8(1), 233–261 (1985)CrossRefGoogle Scholar
  8. 8.
    Grochow, K., Martin, S.L., Hertzmann, A., Popovic, Z.: Style-based inverse kinematics. ACM Trans. Graph. 23(3), 522–531 (2004)CrossRefGoogle Scholar
  9. 9.
    Hinton, G.E.: Products of experts. In: Proc. ICANN 1999, vol. 1, pp. 1–6 (1999)Google Scholar
  10. 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)CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    Jebara, T., Kondor, R., Howard, A.: Probability product kernels. J. Mach. Learn. Res. 5, 819–844 (2004)MATHMathSciNetGoogle Scholar
  12. 12.
    Lawrence, N.D.: Gaussian process latent variable models for visualisation of high dimensional data. In: NIPS 2003 (2003)Google Scholar
  13. 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. 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. 15.
    Lohmiller, W., Slotine, J.J.E.: On contraction analysis for non-linear systems. Automatica 34(6), 683–696 (1998)CrossRefMATHMathSciNetGoogle Scholar
  16. 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. 17.
    Neal, R.: Bayesian Learning for Neural Networks. Ph.D. thesis, Dept. of Computer Science, University of Toronto (1994)Google Scholar
  18. 18.
    Pearl, J.: Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann (1997)Google Scholar
  19. 19.
    Petersen, K.B., Pedersen, M.S.: The matrix cookbook (2012), version 20121115Google Scholar
  20. 20.
    Rasmussen, C.E.: minimize.m (2006), http://learning.eng.cam.ac.uk/carl/code/minimize/
  21. 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. 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)CrossRefGoogle Scholar
  23. 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. 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)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Dmytro Velychko
    • 1
    • 2
  • Dominik Endres
    • 1
    • 2
  • Nick Taubert
    • 1
  • Martin A. Giese
    • 1
  1. 1.Section Computational Sensomotorics, Department of Cognitive NeurologyUniversity Clinic Tübingen, CIN, HIH and University of TübingenTübingenGermany
  2. 2.Theoretical Neuroscience, Dept. of PsychologyPhilipps-University MarburgMarburgGermany

Personalised recommendations