TY - GEN
T1 - Multi-task function-on-function regression with co-grouping structured sparsity
AU - Yang, Pei
AU - Tan, Qi
AU - He, Jingrui
N1 - Funding Information:
This work is supported by National Natural Science Foundation of China under Grant No. 61473123, National Science Foundation under Grant No. IIS-1552654, ONR under Grant No. N00014-15-1-2821, and an IBM Faculty Award. The views and conclusions are those of the authors and should not be interpreted as representing the official policies of the funding agencies or the government.
Publisher Copyright:
© 2017 Copyright held by the owner/author(s).
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
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U2 - 10.1145/3097983.3098133
DO - 10.1145/3097983.3098133
M3 - Conference contribution
AN - SCOPUS:85029109625
T3 - Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining
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
T2 - 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2017
Y2 - 13 August 2017 through 17 August 2017
ER -