Abstract

The growing importance of functional data has fueled the rapid development of functional data analysis, which treats the infinite-dimensional data as continuous functions rather than discrete, finite-dimensional vectors. On the other hand, heterogeneity is an intrinsic property of functional data due to the variety of sources to collect the data. In this paper, we propose a novel multi-task function-on-function regression approach to model both the functionality and heterogeneity of data. The basic idea is to simultaneously model the relatedness among tasks and correlations among basis functions by using the co-grouping structured sparsity to encourage similar tasks to behave similarly in shrinking the basis functions. The resulting optimization problem is challenging due to the non-smoothness and non-separability of the co-grouping structured sparsity. We present an efficient algorithm to solve the problem, and prove its separability, convexity, and global convergence. The proposed algorithm is applicable to a wide spectrum of structured sparsity regularized techniques, such as structured l2,p norm and structured Schatten p-norm. The effectiveness of the proposed approach is verified on benchmark functional data sets collected from various domains.

Original languageEnglish (US)
Title of host publicationKDD 2017 - Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining
PublisherAssociation for Computing Machinery
Pages1255-1264
Number of pages10
VolumePart F129685
ISBN (Electronic)9781450348874
DOIs
StatePublished - Aug 13 2017
Event23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2017 - Halifax, Canada
Duration: Aug 13 2017Aug 17 2017

Other

Other23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2017
CountryCanada
CityHalifax
Period8/13/178/17/17

Keywords

  • Co-grouping structured sparsity
  • Function-on-function regression
  • Generalized Schatten norm
  • Multi-task learning

ASJC Scopus subject areas

  • Software
  • Information Systems

Cite this

Yang, P., Tan, Q., & He, J. (2017). Multi-task function-on-function regression with co-grouping structured sparsity. In KDD 2017 - Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (Vol. Part F129685, pp. 1255-1264). Association for Computing Machinery. https://doi.org/10.1145/3097983.3098133

Multi-task function-on-function regression with co-grouping structured sparsity. / Yang, Pei; Tan, Qi; He, Jingrui.

KDD 2017 - Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. Vol. Part F129685 Association for Computing Machinery, 2017. p. 1255-1264.

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

Yang, P, Tan, Q & He, J 2017, Multi-task function-on-function regression with co-grouping structured sparsity. in KDD 2017 - Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. vol. Part F129685, Association for Computing Machinery, pp. 1255-1264, 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2017, Halifax, Canada, 8/13/17. https://doi.org/10.1145/3097983.3098133
Yang P, Tan Q, He J. Multi-task function-on-function regression with co-grouping structured sparsity. In KDD 2017 - Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. Vol. Part F129685. Association for Computing Machinery. 2017. p. 1255-1264 https://doi.org/10.1145/3097983.3098133
Yang, Pei ; Tan, Qi ; He, Jingrui. / Multi-task function-on-function regression with co-grouping structured sparsity. KDD 2017 - Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. Vol. Part F129685 Association for Computing Machinery, 2017. pp. 1255-1264
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