메뉴 건너뛰기




Volumn 39, Issue 2, 2017, Pages 227-241

Algorithm-Dependent Generalization Bounds for Multi-Task Learning

Author keywords

generalization; inductive bias; learning theory; learning to learn; Multi Task learning; regularization; stability

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; LEARNING SYSTEMS; LINEARIZATION; PARAMETER ESTIMATION;

EID: 85009732680     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPAMI.2016.2544314     Document Type: Article
Times cited : (134)

References (54)
  • 1
    • 85121045899 scopus 로고
    • Multitask learning: A knowledge-based source of inductive bias
    • R. Caruna, "Multitask learning: A knowledge-based source of inductive bias, " in Proc. Int. Conf. Mach. Learn., 1993, pp. 41-48.
    • (1993) Proc. Int. Conf. Mach. Learn , pp. 41-48
    • Caruna, R.1
  • 2
    • 70450188142 scopus 로고    scopus 로고
    • Boosted multi-Task learning for face verification with applications to web image and video search
    • X. Wang, C. Zhang, and Z. Zhang, "Boosted multi-Task learning for face verification with applications to web image and video search, " in Proc. IEEE Conf. Comput. Vis. Pattern Recog., 2009, pp. 142-149.
    • (2009) Proc IEEE Conf. Comput. Vis. Pattern Recog , pp. 142-149
    • Wang, X.1    Zhang, C.2    Zhang, Z.3
  • 3
    • 77955999539 scopus 로고    scopus 로고
    • Multi-Task warped gaussian process for personalized age estimation
    • Y. Zhang and D.-Y. Yeung, "Multi-Task warped gaussian process for personalized age estimation, " in Proc. IEEE Conf. Comput. Vis. Pattern Recog., 2010, pp. 2622-2629.
    • (2010) Proc IEEE Conf. Comput. Vis. Pattern Recog , pp. 2622-2629
    • Zhang, Y.1    Yeung, D.-Y.2
  • 6
    • 56449095373 scopus 로고    scopus 로고
    • A unified architecture for natural language processing: Deep neural networks with multitask learning
    • R. Collobert and J. Weston, "A unified architecture for natural language processing: Deep neural networks with multitask learning, " in Proc. 25th Int. Conf. Mach. Learn., 2008, pp. 160-167.
    • (2008) Proc. 25th Int. Conf. Mach. Learn , pp. 160-167
    • Collobert, R.1    Weston, J.2
  • 7
    • 55149088329 scopus 로고    scopus 로고
    • Convex multi-Task feature learning
    • A. Argyriou, T. Evgeniou, and M. Pontil, "Convex multi-Task feature learning, " Mach. Learn., vol. 73, no. 3, pp. 243-272, 2008.
    • (2008) Mach. Learn , vol.73 , Issue.3 , pp. 243-272
    • Argyriou, A.1    Evgeniou, T.2    Pontil, M.3
  • 9
    • 84916931592 scopus 로고    scopus 로고
    • Convex discriminative multitask clustering
    • Jan
    • X.-L. Zhang, "Convex discriminative multitask clustering, " IEEE Trans. Pattern Anal. Mach. Intell., vol. 37, no. 1, pp. 28-40, Jan. 2015.
    • (2015) IEEE Trans. Pattern Anal. Mach. Intell , vol.37 , Issue.1 , pp. 28-40
    • Zhang, X.-L.1
  • 10
    • 84875472724 scopus 로고    scopus 로고
    • A convex formulation for learning a shared predictive structure from multiple tasks
    • May
    • J. Chen, L. Tang, J. Liu, and J. Ye, "A convex formulation for learning a shared predictive structure from multiple tasks, " IEEE Trans. Pattern Anal. Mach. Intell., vol. 35, no. 5, pp. 1025-1038, May 2013.
    • (2013) IEEE Trans. Pattern Anal. Mach. Intell , vol.35 , Issue.5 , pp. 1025-1038
    • Chen, J.1    Tang, L.2    Liu, J.3    Ye, J.4
  • 11
    • 14344277592 scopus 로고    scopus 로고
    • A model of inductive bias learning
    • J. Baxter, "A model of inductive bias learning, " J. Artif. Intell. Res., vol. 12, no. 1, pp. 149-198, 2000.
    • (2000) J. Artif. Intell. Res , vol.12 , Issue.1 , pp. 149-198
    • Baxter, J.1
  • 13
    • 27844439373 scopus 로고    scopus 로고
    • A framework for learning predictive structures from multiple tasks and unlabeled data
    • R. K. Ando and T. Zhang, "A framework for learning predictive structures from multiple tasks and unlabeled data, " J. Mach. Learn. Res., vol. 6, pp. 1817-1853, 2005.
    • (2005) J. Mach. Learn. Res , vol.6 , pp. 1817-1853
    • Ando, R.K.1    Zhang, T.2
  • 14
    • 30744438843 scopus 로고    scopus 로고
    • Bounds for linear multi-Task learning
    • A. Maurer, "Bounds for linear multi-Task learning, " J. Mach. Learn. Res., vol. 7, pp. 117-139, 2006.
    • (2006) J. Mach. Learn. Res , vol.7 , pp. 117-139
    • Maurer, A.1
  • 15
    • 67349277101 scopus 로고    scopus 로고
    • Transfer bounds for linear feature learning
    • A. Maurer, "Transfer bounds for linear feature learning, " Mach. Learn., vol. 75, no. 3, pp. 327-350, 2009.
    • (2009) Mach. Learn , vol.75 , Issue.3 , pp. 327-350
    • Maurer, A.1
  • 18
  • 20
    • 0031235711 scopus 로고    scopus 로고
    • Covering numbers for realvalued function classes
    • Sep
    • P. Bartlett, S. Kulkarni, and S. Posner, "Covering numbers for realvalued function classes, " IEEE Trans. Inf. Theory, vol. 43, no. 5, pp. 1721-1724, Sep. 1997.
    • (1997) IEEE Trans. Inf. Theory , vol.43 , Issue.5 , pp. 1721-1724
    • Bartlett, P.1    Kulkarni, S.2    Posner, S.3
  • 21
    • 0347067948 scopus 로고    scopus 로고
    • Covering number bounds of certain regularized linear function classes
    • T. Zhang, "Covering number bounds of certain regularized linear function classes, " J. Mach. Learn. Res., vol. 2, pp. 527-550, 2002.
    • (2002) J. Mach. Learn. Res , vol.2 , pp. 527-550
    • Zhang, T.1
  • 22
    • 0038105204 scopus 로고    scopus 로고
    • Capacity of reproducing kernel spaces in learning theory
    • Jul
    • D.-X. Zhou, "Capacity of reproducing kernel spaces in learning theory, " IEEE Trans. Inf. Theory, vol. 49, no. 7, pp. 1743-1752, Jul. 2003.
    • (2003) IEEE Trans. Inf. Theory , vol.49 , Issue.7 , pp. 1743-1752
    • Zhou, D.-X.1
  • 24
    • 0035397715 scopus 로고    scopus 로고
    • Rademacher penalties and structural risk minimization
    • Jul
    • V. Koltchinskii, "Rademacher penalties and structural risk minimization, " IEEE Trans. Inf. Theory, vol. 47, no. 5, pp. 1902-1914, Jul. 2001.
    • (2001) IEEE Trans. Inf. Theory , vol.47 , Issue.5 , pp. 1902-1914
    • Koltchinskii, V.1
  • 25
    • 0038453192 scopus 로고    scopus 로고
    • Rademacher and Gaussian complexities: Risk bounds and structural results
    • P. L. Bartlett and S. Mendelson, "Rademacher and Gaussian complexities: Risk bounds and structural results, " J. Mach. Learn. Res., vol. 3, pp. 463-482, 2003.
    • (2003) J. Mach. Learn. Res , vol.3 , pp. 463-482
    • Bartlett, P.L.1    Mendelson, S.2
  • 26
    • 0038368335 scopus 로고    scopus 로고
    • Stability and generalization
    • O. Bousquet and A. Elisseeff, "Stability and generalization, " J. Mach. Learn. Res., vol. 2, pp. 499-526, 2002.
    • (2002) J. Mach. Learn. Res , vol.2 , pp. 499-526
    • Bousquet, O.1    Elisseeff, A.2
  • 27
    • 84960102659 scopus 로고    scopus 로고
    • Multi-Task learning and algorithmic stability
    • Y. Zhang, "Multi-Task learning and algorithmic stability, " in Proc. 29th AAAI Conf. Artif. Intell., 2015, pp. 3181-3187.
    • (2015) Proc. 29th AAAI Conf. Artif. Intell , pp. 3181-3187
    • Zhang, Y.1
  • 28
    • 84908489084 scopus 로고    scopus 로고
    • Stability of multi-Task kernel regression algorithms
    • J. Audiffren and H. Kadri, "Stability of multi-Task kernel regression algorithms, " in Proc. ACML, 2013, pp. 1-16.
    • (2013) Proc. ACML , pp. 1-16
    • Audiffren, J.1    Kadri, H.2
  • 29
    • 33745847104 scopus 로고    scopus 로고
    • Leave-one-out error and stability of learning algorithms with applications
    • A. Elisseeff and M. Pontil, "Leave-one-out error and stability of learning algorithms with applications, " NATO Sci. Series Sub Series iii Comput. Syst. Sci., vol. 190, pp. 111-130, 2003.
    • (2003) NATO Sci. Series Sub Series Iii Comput. Syst. Sci , vol.190 , pp. 111-130
    • Elisseeff, A.1    Pontil, M.2
  • 32
    • 79251515185 scopus 로고    scopus 로고
    • Trace norm regularization: Reformulations, algorithms, and multi-Task learning
    • T. K. Pong, P. Tseng, S. Ji, and J. Ye, "Trace norm regularization: Reformulations, algorithms, and multi-Task learning, " SIAM J. Optimization, vol. 20, no. 6, pp. 3465-3489, 2010.
    • (2010) SIAM J. Optimization , vol.20 , Issue.6 , pp. 3465-3489
    • Pong, T.K.1    Tseng, P.2    Ji, S.3    Ye, J.4
  • 33
    • 84898036145 scopus 로고    scopus 로고
    • Excess risk bounds for multitask learning with trace norm regularization
    • M. Pontil and A. Maurer, "Excess risk bounds for multitask learning with trace norm regularization, " in Proc. COLT, 2013, pp. 55-76.
    • (2013) Proc. COLT , pp. 55-76
    • Pontil, M.1    Maurer, A.2
  • 34
  • 36
    • 71149094644 scopus 로고    scopus 로고
    • A convex formulation for learning shared structures from multiple tasks
    • J. Chen, L. Tang, J. Liu, and J. Ye, "A convex formulation for learning shared structures from multiple tasks, " in Proc. 26th Annu. Int. Conf. Mach. Learn., 2009, pp. 137-144.
    • (2009) Proc. 26th Annu. Int. Conf. Mach. Learn , pp. 137-144
    • Chen, J.1    Tang, L.2    Liu, J.3    Ye, J.4
  • 37
    • 84862271988 scopus 로고    scopus 로고
    • Infinite predictor subspace models for multitask learning
    • P. Rai and H. Daume, "Infinite predictor subspace models for multitask learning, " in Proc. 13th Int. Conf. Artif. Intell. Statist., 2010, pp. 613-620.
    • (2010) Proc. 13th Int. Conf. Artif. Intell. Statist , pp. 613-620
    • Rai, P.1    Daume, H.2
  • 38
    • 85162400077 scopus 로고    scopus 로고
    • Clustered multi-Task learning via alternating structure optimization
    • J. Zhou, J. Chen, and J. Ye, "Clustered multi-Task learning via alternating structure optimization, " in Proc. Adv. Neural Inf. Process. Syst. 24, 2011, pp. 702-710.
    • (2011) Proc. Adv. Neural Inf. Process. Syst , vol.24 , pp. 702-710
    • Zhou, J.1    Chen, J.2    Ye, J.3
  • 39
    • 84867114266 scopus 로고    scopus 로고
    • Learning task grouping and overlap in multi-Task learning
    • A. Kumar and H. Daume, "Learning task grouping and overlap in multi-Task learning, " in Proc. 29th Int. Conf. Mach. Learn., 2012, pp. 1383-1390.
    • (2012) Proc. 29th Int. Conf. Mach. Learn , pp. 1383-1390
    • Kumar, A.1    Daume, H.2
  • 42
    • 0033566418 scopus 로고    scopus 로고
    • Algorithmic stability and sanity-check bounds for leave-one-out cross-validation
    • M. Kearns and D. Ron, "Algorithmic stability and sanity-check bounds for leave-one-out cross-validation, " Neural Comput., vol. 11, no. 6, pp. 1427-1453, 1999.
    • (1999) Neural Comput , vol.11 , Issue.6 , pp. 1427-1453
    • Kearns, M.1    Ron, D.2
  • 44
    • 0000595627 scopus 로고    scopus 로고
    • Some applications of concentration inequalities to statistics
    • P. Massart, "Some applications of concentration inequalities to statistics, " in Proc. Annales de la Faculte des Sci. de Toulouse, 2000, pp. 245-303.
    • (2000) Proc. Annales de la Faculte des Sci. de Toulouse , pp. 245-303
    • Massart, P.1
  • 45
    • 0001703864 scopus 로고
    • On the density of families of sets
    • N. Sauer, "On the density of families of sets, " J. Combinatorial Theory, Series A, vol. 13, no. 1, pp. 145-147, 1972.
    • (1972) J. Combinatorial Theory, Series A , vol.13 , Issue.1 , pp. 145-147
    • Sauer, N.1
  • 46
    • 0000660999 scopus 로고
    • The sizes of compact subsets of hilbert space and continuity of Gaussian processes
    • R. M. Dudley, "The sizes of compact subsets of hilbert space and continuity of Gaussian processes, " J. Functional Anal., vol. 1, no. 3, pp. 290-330, 1967.
    • (1967) J. Functional Anal , vol.1 , Issue.3 , pp. 290-330
    • Dudley, R.M.1
  • 47
    • 84898471955 scopus 로고    scopus 로고
    • Beyond the regret minimization barrier: An optimal algorithm for stochastic strongly-convex optimization
    • E. Hazan and S. Kale, "Beyond the regret minimization barrier: An optimal algorithm for stochastic strongly-convex optimization, " in Proc. COLT, 2011, pp. 421-436.
    • (2011) Proc. COLT , pp. 421-436
    • Hazan, E.1    Kale, S.2
  • 48
    • 84867120686 scopus 로고    scopus 로고
    • Making gradient descent optimal for strongly convex stochastic optimization
    • A. Rakhlin, O. Shamir, and K. Sridharan, "Making gradient descent optimal for strongly convex stochastic optimization, " in Proc. 29th Int. Conf. Mach. Learn., 2012, pp. 449-456.
    • (2012) Proc. 29th Int. Conf. Mach. Learn , pp. 449-456
    • Rakhlin, A.1    Shamir, O.2    Sridharan, K.3
  • 50
    • 85009798156 scopus 로고    scopus 로고
    • On the generalization ability of online strongly convex programming algorithms
    • S. M. Kakade and A. Tewari, "On the generalization ability of online strongly convex programming algorithms, " in Proc. 30th Int. Conf. Mach. Learn., 2009, pp. 441-449.
    • (2009) Proc. 30th Int. Conf. Mach. Learn , pp. 441-449
    • Kakade, S.M.1    Tewari, A.2
  • 53
    • 84947403595 scopus 로고
    • Probability inequalities for sums of bounded random variables
    • W. Hoeffding, "Probability inequalities for sums of bounded random variables, " J. Am. Statist. Assoc., vol. 58, no. 301, pp. 13-30, 1963.
    • (1963) J. Am. Statist. Assoc , vol.58 , Issue.301 , pp. 13-30
    • Hoeffding, W.1
  • 54
    • 0001638327 scopus 로고
    • Optimum bounds for the distributions of martingales in Banach spaces
    • I. Pinelis, "Optimum bounds for the distributions of martingales in Banach spaces, " Ann. Probability, vol. 22, pp. 1679-1706, 1994.
    • (1994) Ann. Probability , vol.22 , pp. 1679-1706
    • Pinelis, I.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.