{"type":"ScholarlyArticle","title":"Online Kernel Selection via Incremental Sketched Kernel Alignment","authors":[{"name":"Xiao Zhang","slug":"xiao-zhang","given":"Xiao","family":"Zhang","affiliation":"School of Computer Science and Technology , Tianjin University , Tianjin 300350 , China"},{"name":"Shizhong Liao","slug":"shizhong-liao","given":"Shizhong","family":"Liao","affiliation":"School of Computer Science and Technology , Tianjin University , Tianjin 300350 , China"}],"abstract":"In contrast to offline kernel selection, online kernel selection must rise to the new challenges of passing the training set once, selecting optimal kernels and updating hypotheses at each round, enjoying a sublinear regret bound for online kernel learning, and requiring a constant maintenance time complexity at each round and an efficient overall time complexity integrated with online kernel learning. However, most of existing online kernel selection approaches can not meet the new challenges. To address this issue, we propose a novel online kernel selection approach via the incremental sketched kernel alignment criterion, which meets all the new challenges. We first define the incremental sketched kernel alignment (ISKA) criterion, which estimates the kernel alignment and can be computed incrementally  and efficiently. When applying the proposed ISKA criterion to online kernel selection, we adopt the subclass coherence to maintain the hypothesis space, select the optimal kernel at each round using the median of the ISKA criterion estimates, and update the hypothesis following the online gradient decent method. We prove that the ISKA criterion is an unbiased estimate of the maximum mean discrepancy, enjoys the optimal logarithmic regret bound for online kernel learning, and has a constant maintenance time complexity at each round and a logarithmic overall time complexity integrated with online kernel learning. Empirical studies demonstrate that the proposed online kernel selection approach is computationally efficient while maintaining comparable accuracy for online kernel learning.","doi":"10.24963/ijcai.2018/433","url":"https://ijcai.org/proceedings/2018/433","pdf":"https://ijcai.org/proceedings/2018/0433.pdf","markdown":"https://ijcai.org/proceedings/2018/433.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/433","volume":{"slug":"2018","title":"Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2018","url":"https://ijcai.org/proceedings/2018/","year":2018,"location":"Stockholm","dates":"13-19 July 2018","editors":"Jérôme Lang","isbn":"978-0-9992411-2-7","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2018"},"section":"Machine Learning","track":"Main track","number":433,"pages":{"first":3118,"last":3124},"keywords":["Machine Learning: Learning Theory","Machine Learning: Kernel Methods","Machine Learning: Classification","Machine Learning: Online Learning"],"videos":[],"references":[{"position":1,"raw":"[Anguita et al., 2009] Davide Anguita, Alessandro Ghio, Sandro Ridella, and Dario Sterpi. k-fold cross validation for error rate estimate in support vector machines. In Pro- ceedings of the 2009 International Conference on Data Mining, pages 291-297, 2009.","title":"k-fold cross validation for error rate estimate in support vector machines","authors":"Davide Anguita, Alessandro Ghio, Sandro Ridella, Dario Sterpi","year":"2009","venue":"Proceedings of the 2009 International Conference on Data Mining","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Bartlett and Mendelson, 2002] Peter L Bartlett and Shahar Mendelson. Rademacher and Gaussian complexities: Risk bounds and structural results. Journal of Machine Learn- ing Research, 3:463-482, 2002.","title":"Rademacher and Gaussian complexities: Risk bounds and structural results","authors":"L Peter, Shahar Bartlett, Mendelson","year":"2002","venue":"Journal of Machine Learning Research","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Caponnetto and De Vito, 2007] A. Caponnetto and E. De Vito. Optimal rates for the regularized least- squares algorithm. Foundations of Computational Mathematics, 7(3):331-368, 2007.","title":"Optimal rates for the regularized leastsquares algorithm","authors":"De Caponnetto, ; A Vito, E De Caponnetto, Vito","year":"2007","venue":"Foundations of Computational Mathematics","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Cesa-Bianchi et al., 2010] Nicolò Cesa-Bianchi, Shai Shalev-Shwartz, and Ohad Shamir. Online learning of noisy data with kernels. In Proceedings of the 23rd Conference on Learning Theory, pages 218-230, 2010.","title":"Online learning of noisy data with kernels","authors":"Nicolò Cesa-Bianchi, Shai Shalev-Shwartz, Ohad Shamir","year":"2010","venue":"Proceedings of the 23rd Conference on Learning Theory","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Chen et al., 2016] Badong Chen, Junli Liang, Nanning Zheng, and José C Príncipe. Kernel least mean square with adaptive kernel size. Neurocomputing, 191:95-106, 2016.","title":"Kernel least mean square with adaptive kernel size","authors":"Badong Chen, Junli Liang, Nanning Zheng, José C Príncipe","year":"2016","venue":"Neurocomputing","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Cortes et al., 2012] Corinna Cortes, Mehryar Mohri, and Afshin Rostamizadeh. Algorithms for learning kernels based on centered alignment. Journal of Machine Learn- ing Research, 13:795-828, 2012.","title":"Algorithms for learning kernels based on centered alignment","authors":"Corinna Cortes, Mehryar Mohri, Afshin Rostamizadeh","year":"2012","venue":"Journal of Machine Learning Research","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Foster et al., 2015] Dylan J Foster, Alexander Rakhlin, and Karthik Sridharan. Adaptive online learning. In Ad- vances in Neural Information Processing Systems 28, pages 3375-3383, 2015.","title":"Adaptive online learning","authors":"Dylan J Foster, Alexander Rakhlin, Karthik Sridharan","year":"2015","venue":"Advances in Neural Information Processing Systems","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Foster et al., 2017] Dylan J Foster, Satyen Kale, Mehryar Mohri, and Karthik Sridharan. Parameter-free online learning via model selection. In Advances in Neural Infor- mation Processing Systems 30, pages 6022-6032, 2017.","title":"Parameter-free online learning via model selection","authors":"Dylan J Foster, Satyen Kale, Mehryar Mohri, Karthik Sridharan","year":"2017","venue":"Advances in Neural Information Processing Systems","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Gretton et al., 2012] Arthur Gretton, Karsten M Borgwardt, Malte J Rasch, Bernhard Schölkopf, and Alexander Smola. A kernel two-sample test. Journal of Machine Learning Research, 13:723-773, 2012.","title":"A kernel two-sample test","authors":"Arthur Gretton, Karsten M Borgwardt, J Malte, Bernhard Rasch, Alexander Schölkopf, Smola","year":"2012","venue":"Journal of Machine Learning Research","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Hazan, 2016] Elad Hazan. Introduction to online convex optimization. Foundations and Trends R in Optimization, 2(3-4):157-325, 2016.","title":"Introduction to online convex optimization","authors":"Elad Hazan","year":"2016","venue":"Foundations and Trends R in Optimization","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Hu et al., 2015] Junjie Hu, Haiqin Yang, Irwin King, Michael R Lyu, and Anthony Man-Cho So. Kernelized online imbalanced learning with fixed budgets. In Pro- ceedings of the 29th AAAI Conference on Artificial Intelli- gence, pages 2666-2672, 2015.","title":"Kernelized online imbalanced learning with fixed budgets","authors":"Junjie Hu, Haiqin Yang, Irwin King, Anthony Man-Cho Michael R Lyu, So","year":"2015","venue":"Proceedings of the 29th AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Kandola et al., 2002] J. Kandola, J. Shawe-Taylor, and N. Cristianini. On the extensions of kernel alignment. Technical Report Technical report 120, University of Lon- don, 2002.","title":"On the extensions of kernel alignment","authors":"J Kandola, J Shawe-Taylor, N Cristianini","year":"2002","venue":null,"doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Kivinen et al., 2001] Jyrki Kivinen, Alex J Smola, and Robert C Williamson. Online learning with kernels. In Advances in Neural Information Processing Systems 14, pages 785-792, 2001.","title":"Online learning with kernels","authors":"Kivinen","year":"2001","venue":"Advances in Neural Information Processing Systems","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Liu and Liao, 2015] Yong Liu and Shizhong Liao. Eigen- values ratio for kernel selection of kernel methods. In Pro- ceedings of the 29th AAAI Conference on Artificial Intelli- gence, pages 2814-2820, 2015.","title":"Eigenvalues ratio for kernel selection of kernel methods","authors":"Yong Liu, Shizhong Liao","year":"2015","venue":"Proceedings of the 29th AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Nguyen et al., 2017] Tu Dinh Nguyen, Trung Le, Hung Bui, and Dinh Q. Phung. Large-scale online kernel learning with random feature reparameterization. In Proceedings of the 26th International Joint Conference on Artificial In- telligence, pages 2543-2549, 2017.","title":"Large-scale online kernel learning with random feature reparameterization","authors":"Trung Tu Dinh Nguyen, Hung Le, Dinh Q Bui, Phung","year":"2017","venue":"Proceedings of the 26th International Joint Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":"/proceedings/2017/354"},{"position":16,"raw":"[Orabona et al., 2008] Francesco Orabona, Joseph Keshet, and Barbara Caputo. The projectron: A bounded kernel- based perceptron. In Proceedings of the 25th International Conference on Machine learning, pages 720-727, 2008.","title":"The projectron: A bounded kernelbased perceptron","authors":"Francesco Orabona, Joseph Keshet, Barbara Caputo","year":"2008","venue":"Proceedings of the 25th International Conference on Machine learning","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Reisinger et al., 2008] Joseph Reisinger, Peter Stone, and Risto Miikkulainen. Online kernel selection for Bayesian reinforcement learning. In Proceedings of the 25th In- ternational Conference on Machine Learning, pages 816- 823, 2008.","title":"Online kernel selection for Bayesian reinforcement learning","authors":"Joseph Reisinger, Peter Stone, Risto Miikkulainen","year":"2008","venue":"Proceedings of the 25th International Conference on Machine Learning","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Richard et al., 2009] Cédric Richard, José Carlos M Bermudez, and Paul Honeine. Online prediction of time series data with kernels. IEEE Transactions on Signal Processing, 57(3):1058-1067, 2009.","title":"Online prediction of time series data with kernels","authors":"Cédric Richard, José, Carlos M Bermudez, Paul Honeine","year":"2009","venue":"IEEE Transactions on Signal Processing","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Shalev-Shwartz, 2011] Shai Shalev-Shwartz. Online learn- ing and online convex optimization. Foundations and Trends R in Machine Learning, 4(2):107-194, 2011.","title":"Online learning and online convex optimization","authors":"Shai Shalev-Shwartz","year":"2011","venue":"Foundations and Trends R in Machine Learning","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Sinha and Duchi, 2016] Aman Sinha and John C Duchi. Learning kernels with random features. In Advances in Neural Information Processing Systems 29, pages 1298- 1306, 2016.","title":"Learning kernels with random features","authors":"Duchi Sinha, Aman Sinha, John C Duchi","year":"2016","venue":"Advances in Neural Information Processing Systems","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Sun et al., 2012] Yi Sun, Faustino Gomez, and Jürgen Schmidhuber. On the size of the online kernel sparsifi- cation dictionary. In Proceedings of the 29th International Conference on Machine Learning, pages 329-336, 2012.","title":"On the size of the online kernel sparsification dictionary","authors":"Yi Sun, Faustino Gomez, Jürgen Schmidhuber","year":"2012","venue":"Proceedings of the 29th International Conference on Machine Learning","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Tropp, 2004] Joel A Tropp. Greed is good: Algorithmic results for sparse approximation. IEEE Transactions on Information Theory, 50(10):2231-2242, 2004.","title":"Greed is good: Algorithmic results for sparse approximation","authors":"Joel A Tropp","year":"2004","venue":"IEEE Transactions on Information Theory","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Vitter, 1985] Jeffrey S Vitter. Random sampling with a reservoir. ACM Transactions on Mathematical Software, 11(1):37-57, 1985.","title":"Random sampling with a reservoir","authors":"S Jeffrey, Vitter","year":"1985","venue":"ACM Transactions on Mathematical Software","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Yang et al., 2012] Tianbao Yang, Mehrdad Mahdavi, Rong Jin, Jinfeng Yi, and Steven C.H. Hoi. Online kernel se- lection: Algorithms and evaluations. In Proceedings of the 26th AAAI Conference on Artificial Intelligence, pages 22-26, 2012.","title":"Online kernel selection: Algorithms and evaluations","authors":"Tianbao Yang, Mehrdad Mahdavi, Rong Jin, Jinfeng Yi, Steven C H Hoi","year":"2012","venue":"Proceedings of the 26th AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Zhao et al., 2011] Peilin Zhao, Rong Jin, Tianbao Yang, and Steven C.H. Hoi. Online AUC maximization. In Pro- ceedings of the 28th International Conference on Machine Learning, pages 233-240, 2011.","title":"Online AUC maximization","authors":"Peilin Zhao, Rong Jin, Tianbao Yang, Steven C H Hoi","year":"2011","venue":"Proceedings of the 28th International Conference on Machine Learning","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}