Abstract
Multi-task learning (MTL) aims to enhance the generalization performance of supervised regression or classification by learning multiple related tasks simultaneously. In this paper, we aim to extend the current MTL techniques to high dimensional data sets with structured input and structured output (SISO), where the SI means the input features are structured and the SO means the tasks are structured. We investigate a completely ignored problem in MTL with SISO data: the interplay of structured feature selection and task relationship modeling. We hypothesize that combining the structure information of features and task relationship inference enables us to build more accurate MTL models. Based on the hypothesis, we have designed an efficient learning algorithm, in which we utilize a task covariance matrix related to the model parameters to capture the task relationship. In addition, we design a regularization formulation for incorporating the structured input features in MTL. We have developed an efficient iterative optimization algorithm to solve the corresponding optimization problem. Our algorithm is based on the accelerated first order gradient method in conjunction with the projected gradient scheme. Using two real-world data sets, we demonstrate the utility of the proposed learning methods.
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Notes
GBM, glioblastoma; AO, anaplastic oligodendroglioma.
Stability score measures the variation in voxel activity across the 58 training stimuli.
MTLPTR selects the same feature set for all tasks due to the block regularization, hence a single number is reported.
The 13 genes’ KEGG IDs: 534, 535, 536, 1067, 1068, 2211, 2224, 2229, 2284, 3262, 4978, 5068, 7190.
References
Argyriou A, Micchelli A, Pontil M, Ying Y (2007) A spectral regularization framework for multi-task structure learning. In: NIPS
Argyriou A, Evgeniou T, Pontil M (2006) Multi-task feature learning. In: NIPS
Bakker B, Heskes T (2003) Task clustering and gating for bayesian multitask learning. J Mach Learn Res 4:83–99
Bolón-Canedo V, Snchez-Maroón N, Alonso-Betanzos A (2012) A review of feature selection methods on synthetic data. Knowledge and information systems, pp 1–37, ISSN 0219–1377
Bonilla EV, Chai KM, Williams CKI (2007) Multi-task gaussian process prediction. In: NIPS
Bouguila N, Ziou D (2011) A countably infinite mixture model for clustering and feature selection. Knowl Inf Syst, pp 1–20, ISSN 0219–1377. doi:10.1007/s10115-011-0467-4
Boyd S, Vandenberghe L (2004) Convex optimization. Cambridge University Press, Cambridge
Chang C, Lin C (2001) Libsvm: a library for support vector machines. Software available at http://www.csie.ntu.edu.tw/~cjlin/libsvm
Chapelle O, Shivaswamy PK, Vadrevu S, Weinberger KQ, Zhang Y, Tseng BL (2010) Multi-task learning for boosting with application to web search ranking. In: KDD, pp 1189–1198
Chen J, Liu J, Jieping Y (2010) Learning incoherent sparse and low-rank patterns from multiple tasks. In: The sixteenth ACM SIGKDD international conference on knowledge discovery and data mining (SIGKDD, 2010)
Chen J, Zhou J, Ye J (2011) Integrating low-rank and group-sparse structures for robust multi-task learning. In: KDD, pp 42–50
Chen W, Yuan Y, Zhang L (2010) Scalable influence maximization in social networks under the linear threshold model. In: ICDM, pp 88–97
Chen X, Pan W, Kwok JT, Carbonell JG (2009) Accelerated gradient method for multi-task sparse learning problem. In: IEEE international conference on data mining (ICDM09), pp 746–751, ISSN 1550–4786
Evgeniou T, Pontil M (2004) Regularized multi-task learning. In: KDD, pp 109–117
Evgeniou T, Micchelli CA, Pontil M (2005) Learning multiple tasks with kernel methods. J Mach Learn Res 6:615–637
Fei H, Huan J (2010) Boosting with structure information in the functional space: an application to graph classification. In: Proceedings of the ACM SIGKDD international conference on knowledge discovery and data mining (SIGKDD)
Fei H, Quanz B, Huan J (2010) Regularization and feature selection for networked features. In: Proceedings of the 19th ACM conference on information and, knowledge management (CIKM’10)
Fellbaum C (1998) WordNet: an electronic lexical database. The MIT Press, Cambridge
Gomez J-C, Boiy E, Moens M-F (2012) Highly discriminative statistical features for email classification. Knowl Inf Syst 31(1):23–53
Jacob L, Bach F, Vert J-P (2009) Clustered multi-task learning: a convex formulation. In: Advances in neural information processing systems (NIPS09)
Jalali A, Ravikumar P, Sanghavi S, Ruan C (2010) A dirty model for multi-task learning. In: Proceedings of the advances in neural information processing systems (NIPS 2010), pp 964–972
Ji S, Ye J (2009) An accelerated gradient method for trace norm minimization. In: ICML ’09: Proceedings of the 26th annual international conference on machine learning. ACM, New York, NY, USA, pp 457–464, ISBN 978-1-60558-516-1. http://doi.acm.org/10.1145/1553374.1553434
Kanehisa M, Goto S, Hattori M, Aoki-Kinoshita KF, Itoh M, Kawashima S, Katayama T, Araki M, Hirakawa M (2006) From genomics to chemical genomics: new developments in KEGG. Nucleic Acids Res 34:D354–D357
Kato T, Kashima H, Asai K, Sugiyama M (2007) Multi-task learning via conic programming. In: NIPS
Kong X, Yu PS (2012) gMLC: a multi-label feature selection framework for graph classification. Knowl Inf Syst 31(2):281–305
Levy S (2001) Interactive 3-d visualization of particle systems with partiview. In: Proceedings of the international astronomical union symposium on astrophysical supercomputing using particles, vol 208
Li C, Li H (2008) Network-constrained regularization and variable selection for analysis of genomic data. Bioinformatics 24(9):1175–1182
Liu H, Palatucci M, Zhang J (2009) Blockwise coordinate descent procedures for the multi-task lasso, with applications to neural semantic basis discovery. In: Proceedings of the 26th international conference on machine learning (ICML 2009)
Liu J, Ji S, Ye J (2009) Multi-task feature learning via efficient \(\ell _{2,1}\)-norm minimization. In: Uncertainty in artificial intelligence
Lounici K, Pontil M, Van De Geer S (2009) Taking advantage of sparsity in multi-task learning. Knowl Inf Syst 20(1):109–348
Mitchell TM, Shinkareva SV, Andrew A et al (2008) Predicting human brain activity associated with the meanings of nouns. Science 320:1191–1195
Nesterov Y (2003) Introductory lectures on convex optimization: a basic course, pp 25–32
Nesterov Y (2007) Gradient methods for minimizing composite objective function. CORE Disc Paper 76:265–286
Nutt CL, Mani DR, Betensky RA et al (2003) Gene expression-based classification of malignant gliomas correlates better with survival than histological classification. Cancer Res 63:1602–1607
National Institute of Health (2010) Metastatic cancer. http://www.cancer.gov/cancertopics/factsheet/Sites-Types/metastatic
Quattoni A, Carreras X, Collins M, Darrell T (2009) An efficient projection for l1, infinity regularization. In: Proceedings of the 26th international conference on machine learning (ICML 2009)
Romero DM, Meeder B, Kleinberg JM (2011) Differences in the mechanics of information diffusion across topics: idioms, political hashtags, and complex contagion on twitter. In: WWW, pp 695–704
Sandler T, Talukdar PP, Ungar LH (2008) Regularized learning with networks of features. In: NIPS08
Schwaighofer A, Volker T, Yu K (2004) Learning gaussian process kernels via hierarchical bayes. In: In advances in neural information processing systems, NIPS. MIT Press, pp 1209–1216
Singh D, Febbo PG et al (2002) Gene expression correlates of clinical prostate cancer behavior. Cancer cell 1(2):203–209, ISSN 1535–6108
Su AI, Welsh JB, Sapinoso LM et al (2001) Molecular classification of human carcinomas by use of gene expression signatures. Cancer Res 15(20):7388–7393
Vapnik VN (1995) The nature of statistical learning theory. Springer, Berlin
Vivanco I, Sawyers CL (2002) The phosphatidylinositol 3-kinase akt pathway in human cancer. Nat Rev Cancer 2(7):489–501
Xu Z, Kersting K (2011) Multi-task learning with task relations. In: ICDM, pp 884–893
Yang J, Leskovec J (2010) Modeling information diffusion in implicit networks. In: ICDM, pp 599–608
Yu H, Yang J (2001) A direct LDA algorithm for high-dimensional data with application to face recognition. Pattern Recognit 34(10):2067–2070
Yu S, Tresp V, Yu K (2007) Robust multi-task learning with t-processes. In: Proceedings of the 24th international conference on machine learning, ICML ’07. ACM, New York, NY, USA, pp 1103–1110
Yuan C (2011) Multi-task learning for bayesian matrix factorization. In: ICDM, pp 924–931
Zhang Y, Yeung D-Y (2009) A convex formulation for learning task relationships in multi-task learning. In: Proceedings of the 26th conference on uncertainty in artificial intelligence (UAI 2009), pp 733–742
Zhang Y, Yeung D-Y, Xu Q (2010) Probabilistic multi-task feature selection. In: Proceedings of the advances in neural information processing systems (NIPS 2010), pp 2559–2567
Bouguila N, Ziou D (2011) A countably infinite mixture model for clustering and feature selection. Knowl Inf Syst, pp 1–20, ISSN 0219–1377. doi:10.1007/s10115-011-0467-4
Zhou J, Yuan L, Liu J, Ye J (2011) A multi-task learning formulation for predicting disease progression. In: KDD, pp 814–822
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This work has been supported by the National Science Foundation under Grant No. 0845951.
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Fei, H., Huan, J. Structured feature selection and task relationship inference for multi-task learning. Knowl Inf Syst 35, 345–364 (2013). https://doi.org/10.1007/s10115-012-0543-4
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DOI: https://doi.org/10.1007/s10115-012-0543-4