Kernel Embeddings of Longitudinal Data

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9992)

Abstract

Longitudinal data is the repeated observations of individuals through time. They often exhibit rich statistical qualities, such as skew or multimodality, that are difficult to capture using traditional parametric methods. To tackle this, we build a non-parametric Markov transition model for longitudinal data. Our approach uses kernel mean embeddings to learn a transition model that can express complex statistical features. We also propose an approximate data subsampling technique based on kernel herding and random Fourier features that allows our method to scale to large longitudinal data sets. We demonstrate our approach on two real world data sets.

References

  1. 1.
    Kanagawa, M., Nishiyama, Y., Gretton, A., Fukumizu, K.: Filtering with state-observation examples via kernel Monte Carlo filter. Neural Comput. 28(2), 382–444 (2014)CrossRefGoogle Scholar
  2. 2.
    Smola, A., Gretton, A., Song, L., Schölkopf, B.: A Hilbert space embedding for distributions. In: Hutter, M., Servedio, R.A., Takimoto, E. (eds.) ALT 2007. LNCS (LNAI), vol. 4754, pp. 13–31. Springer, Heidelberg (2007). doi:10.1007/978-3-540-75225-7_5 CrossRefGoogle Scholar
  3. 3.
    Song, L., Huang, J., Smola, A., Fukumizu, K.: Hilbert space embeddings of conditional distributions with applications to dynamical systems. In: Proceedings of the 26th Annual International Conference on Machine Learning, pp. 961–968. ACM, June 2009Google Scholar
  4. 4.
    McCalman, L.R.: Function embeddings for multi-modal Bayesian inference (2013)Google Scholar
  5. 5.
    Muandet, K., Fukumizu, K., Sriperumbudur, B., Schlkopf, B.: Kernel mean embedding of distributions: a review and beyonds. arXiv preprint arXiv:1605.09522 (2016)
  6. 6.
    Kanagawa, M., Fukumizu, K.: Recovering distributions from Gaussian RKHS embeddings. In: AISTATS, pp. 457–465 (2014)Google Scholar
  7. 7.
    Rahimi, A., Recht, B.: Random features for large-scale kernel machines. In: Advances in Neural Information Processing Systems, pp. 1177–1184 (2007)Google Scholar
  8. 8.
    Majecka, B.: Statistical models of pedestrian behaviour in the forum. Master’s thesis, School of Informatics, University of Edinburgh (2009)Google Scholar
  9. 9.
    GPy: GPy: a Gaussian process framework in python. http://github.com/SheffieldML/GPy

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.School of Information TechnologiesUniversity of SydneySydneyAustralia

Personalised recommendations