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 language | English (US) |
|---|---|
| Title of host publication | KDD 2017 - Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining |
| Publisher | Association for Computing Machinery |
| Pages | 1255-1264 |
| Number of pages | 10 |
| Volume | Part F129685 |
| ISBN (Electronic) | 9781450348874 |
| DOIs | |
| State | Published - Aug 13 2017 |
| Event | 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2017 - Halifax, Canada Duration: Aug 13 2017 → Aug 17 2017 |
Other
| Other | 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2017 |
|---|---|
| Country | Canada |
| City | Halifax |
| Period | 8/13/17 → 8/17/17 |
Keywords
- Co-grouping structured sparsity
- Function-on-function regression
- Generalized Schatten norm
- Multi-task learning
ASJC Scopus subject areas
- Software
- Information Systems
Cite this
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 proceeding › Conference contribution
}
TY - GEN
T1 - Multi-task function-on-function regression with co-grouping structured sparsity
AU - Yang, Pei
AU - Tan, Qi
AU - He, Jingrui
PY - 2017/8/13
Y1 - 2017/8/13
N2 - 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.
AB - 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.
KW - Co-grouping structured sparsity
KW - Function-on-function regression
KW - Generalized Schatten norm
KW - Multi-task learning
UR - http://www.scopus.com/inward/record.url?scp=85029109625&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85029109625&partnerID=8YFLogxK
U2 - 10.1145/3097983.3098133
DO - 10.1145/3097983.3098133
M3 - Conference contribution
VL - Part F129685
SP - 1255
EP - 1264
BT - KDD 2017 - Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining
PB - Association for Computing Machinery
ER -