Manifold-valued Dirichlet processes

Hyun Woo Kim, Jia Xu, Baba C. Vemuri, Vikas Singh

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Citations (Scopus)

Abstract

Statistical models for manifold-valued data permit capturing the intrinsic nature of the curved spaces in which the data lie and have been a topic of research for several decades. Typically, these formulations use geodesic curves and distances defined locally for most cases - this makes it hard to design parametric models globally on smooth manifolds. Thus, most (manifold specific) parametric models available today assume that the data lie in a small neighborhood on the manifold. To address this 'locality' problem, we propose a novel nonparametric model which unifies multivariate general linear models (MGLMs) using multiple tangent spaces. Our framework generalizes existing work on (both Euclidean and non-Euclidean) general linear models providing a recipe to globally extend the locally-defined parametric models (using a mixture of local models). By grouping observations into sub-populations at multiple tangent spaces, our method provides insights into the hidden structure (geodesic relationships) in the data. This yields a framework to group observations and discover geodesic relationships between covari-ates X and manifold-valued responses Y, which we call Dirichlet process mixtures of multivariate general linear models (DP-MGLM) on Rie-mannian manifolds. Finally, we present proof of concept experiments to validate our model.

Original languageEnglish
Title of host publication32nd International Conference on Machine Learning, ICML 2015
EditorsDavid Blei, Francis Bach
PublisherInternational Machine Learning Society (IMLS)
Pages1199-1208
Number of pages10
ISBN (Electronic)9781510810587
Publication statusPublished - 2015 Jan 1
Externally publishedYes
Event32nd International Conference on Machine Learning, ICML 2015 - Lile, France
Duration: 2015 Jul 62015 Jul 11

Publication series

Name32nd International Conference on Machine Learning, ICML 2015
Volume2

Conference

Conference32nd International Conference on Machine Learning, ICML 2015
CountryFrance
CityLile
Period15/7/615/7/11

Fingerprint

Experiments
Statistical Models

ASJC Scopus subject areas

  • Human-Computer Interaction
  • Computer Science Applications

Cite this

Kim, H. W., Xu, J., Vemuri, B. C., & Singh, V. (2015). Manifold-valued Dirichlet processes. In D. Blei, & F. Bach (Eds.), 32nd International Conference on Machine Learning, ICML 2015 (pp. 1199-1208). (32nd International Conference on Machine Learning, ICML 2015; Vol. 2). International Machine Learning Society (IMLS).

Manifold-valued Dirichlet processes. / Kim, Hyun Woo; Xu, Jia; Vemuri, Baba C.; Singh, Vikas.

32nd International Conference on Machine Learning, ICML 2015. ed. / David Blei; Francis Bach. International Machine Learning Society (IMLS), 2015. p. 1199-1208 (32nd International Conference on Machine Learning, ICML 2015; Vol. 2).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Kim, HW, Xu, J, Vemuri, BC & Singh, V 2015, Manifold-valued Dirichlet processes. in D Blei & F Bach (eds), 32nd International Conference on Machine Learning, ICML 2015. 32nd International Conference on Machine Learning, ICML 2015, vol. 2, International Machine Learning Society (IMLS), pp. 1199-1208, 32nd International Conference on Machine Learning, ICML 2015, Lile, France, 15/7/6.
Kim HW, Xu J, Vemuri BC, Singh V. Manifold-valued Dirichlet processes. In Blei D, Bach F, editors, 32nd International Conference on Machine Learning, ICML 2015. International Machine Learning Society (IMLS). 2015. p. 1199-1208. (32nd International Conference on Machine Learning, ICML 2015).
Kim, Hyun Woo ; Xu, Jia ; Vemuri, Baba C. ; Singh, Vikas. / Manifold-valued Dirichlet processes. 32nd International Conference on Machine Learning, ICML 2015. editor / David Blei ; Francis Bach. International Machine Learning Society (IMLS), 2015. pp. 1199-1208 (32nd International Conference on Machine Learning, ICML 2015).
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