-
Previous Article
Comparisons of different methods for balanced data classification under the discrete non-local total variational framework
- MFC Home
- This Issue
- Next Article
Kernel-based online gradient descent using distributed approach
Shantou University, No. 243 Daxue Rd., Shantou, Guangdong, China |
In this paper we study the kernel-based online gradient descent with least squares loss without an explicit regularization term. Our approach is novel by controlling the expectation of the K-norm of $ f_t $ using an iterative process. Then we use distributed learning to improve our result.
References:
[1] |
X. Chen and Y. Lei,
Refined Bounds for online pairwise learning algorithm, Neurocomputing, 275 (2018), 2656-2665.
doi: 10.1016/j.neucom.2017.11.049. |
[2] |
F. Cucker and S. Smale,
On the mathematical foundations of learning, Bull. Amer. Math. Soc., 39 (2001), 1-49.
doi: 10.1090/S0273-0979-01-00923-5. |
[3] |
J. Duchi, E. Hazan and Y. Singer,
Adaptive subgradient methods for online learning and stochastic optimization, Journal of Machine Learning Research, 12 (2011), 2121-2159.
|
[4] |
T. Hu,
Online regression with varying gaussians and non-identical distributions, Analysis and Applications, 9 (2011), 395-408.
doi: 10.1142/S0219530511001923. |
[5] |
J. Kiefer and J. Wolfowitz,
Stochastic estimation of the maximum of a regression function, Ann. Math. Statist., 23 (1952), 462-466.
doi: 10.1214/aoms/1177729392. |
[6] |
S. B. Lin, X Guo and D. X. Zhou, Distributed learning with regularized least squares, Journal of Machine Learning Research, 18 (2017), Paper No. 92, 31 pp. |
[7] |
M. Pontil, Y. Ying and D. X. Zhou, Error analysis for online gradient descent algorithms in reproducing kernel Hilbert space, Technical Report, Department of Computer Science, University College London, (2005). |
[8] |
H. Robbins and S. Monro,
A stochastic approximation method, Ann. Math. Statist., 22 (1951), 400-407.
doi: 10.1214/aoms/1177729586. |
[9] |
S. Smale and Y. Yao,
Online learning algorithms, Found. Comput. Math., 6 (2006), 145-170.
doi: 10.1007/s10208-004-0160-z. |
[10] |
S. Smale and D. X. Zhou,
Online learning with Markov sampling, Analysis and Applications, 7 (2009), 87-113.
doi: 10.1142/S0219530509001293. |
[11] |
S. Vijayakumar, A. D'Souza and S. Schaal,
Incremental online learning in high dimensions, Neural Computation, 17 (2005), 2602-2634.
doi: 10.1162/089976605774320557. |
[12] |
C. Wang and T Hu,
Online minimum error entropy algorithm with unbounded sampling, Analysis and Applications, 17 (2019), 293-322.
doi: 10.1142/S0219530518500148. |
[13] |
J. Xu, Z. Zheng, Z. Fan and W. Liu, Online personalized QoS prediction approach for cloud services, 4th International Conference on Cloud Computing and Intelligence Systems, 2016.
doi: 10.1109/CCIS.2016.7790220. |
[14] |
Y. Yao, L. Losasco and A. Caponnetto,
Early stopping in gradient descent boosting, Constr. Approx., 26 (2007), 289-315.
doi: 10.1007/s00365-006-0663-2. |
[15] |
Y. Ying and M. Pontil,
Online pairwise learning algorithms, Found. Comput. Math., 28 (2016), 743-777.
doi: 10.1162/NECO_a_00817. |
[16] |
Y. Ying and D. X. Zhou,
Online regularized classification algorithm, IEEE, trans. Inform. Theory, 52 (2006), 4775-4788.
doi: 10.1109/TIT.2006.883632. |
[17] |
Z. H. Zhou, N. V. Chawla, Y. Jin and G. J. Williams,
Big data opportunities and challenges: Discussions from data analytics perspective, IEEE Computational Intelligence Magazine, 9 (2014), 62-74.
|
show all references
References:
[1] |
X. Chen and Y. Lei,
Refined Bounds for online pairwise learning algorithm, Neurocomputing, 275 (2018), 2656-2665.
doi: 10.1016/j.neucom.2017.11.049. |
[2] |
F. Cucker and S. Smale,
On the mathematical foundations of learning, Bull. Amer. Math. Soc., 39 (2001), 1-49.
doi: 10.1090/S0273-0979-01-00923-5. |
[3] |
J. Duchi, E. Hazan and Y. Singer,
Adaptive subgradient methods for online learning and stochastic optimization, Journal of Machine Learning Research, 12 (2011), 2121-2159.
|
[4] |
T. Hu,
Online regression with varying gaussians and non-identical distributions, Analysis and Applications, 9 (2011), 395-408.
doi: 10.1142/S0219530511001923. |
[5] |
J. Kiefer and J. Wolfowitz,
Stochastic estimation of the maximum of a regression function, Ann. Math. Statist., 23 (1952), 462-466.
doi: 10.1214/aoms/1177729392. |
[6] |
S. B. Lin, X Guo and D. X. Zhou, Distributed learning with regularized least squares, Journal of Machine Learning Research, 18 (2017), Paper No. 92, 31 pp. |
[7] |
M. Pontil, Y. Ying and D. X. Zhou, Error analysis for online gradient descent algorithms in reproducing kernel Hilbert space, Technical Report, Department of Computer Science, University College London, (2005). |
[8] |
H. Robbins and S. Monro,
A stochastic approximation method, Ann. Math. Statist., 22 (1951), 400-407.
doi: 10.1214/aoms/1177729586. |
[9] |
S. Smale and Y. Yao,
Online learning algorithms, Found. Comput. Math., 6 (2006), 145-170.
doi: 10.1007/s10208-004-0160-z. |
[10] |
S. Smale and D. X. Zhou,
Online learning with Markov sampling, Analysis and Applications, 7 (2009), 87-113.
doi: 10.1142/S0219530509001293. |
[11] |
S. Vijayakumar, A. D'Souza and S. Schaal,
Incremental online learning in high dimensions, Neural Computation, 17 (2005), 2602-2634.
doi: 10.1162/089976605774320557. |
[12] |
C. Wang and T Hu,
Online minimum error entropy algorithm with unbounded sampling, Analysis and Applications, 17 (2019), 293-322.
doi: 10.1142/S0219530518500148. |
[13] |
J. Xu, Z. Zheng, Z. Fan and W. Liu, Online personalized QoS prediction approach for cloud services, 4th International Conference on Cloud Computing and Intelligence Systems, 2016.
doi: 10.1109/CCIS.2016.7790220. |
[14] |
Y. Yao, L. Losasco and A. Caponnetto,
Early stopping in gradient descent boosting, Constr. Approx., 26 (2007), 289-315.
doi: 10.1007/s00365-006-0663-2. |
[15] |
Y. Ying and M. Pontil,
Online pairwise learning algorithms, Found. Comput. Math., 28 (2016), 743-777.
doi: 10.1162/NECO_a_00817. |
[16] |
Y. Ying and D. X. Zhou,
Online regularized classification algorithm, IEEE, trans. Inform. Theory, 52 (2006), 4775-4788.
doi: 10.1109/TIT.2006.883632. |
[17] |
Z. H. Zhou, N. V. Chawla, Y. Jin and G. J. Williams,
Big data opportunities and challenges: Discussions from data analytics perspective, IEEE Computational Intelligence Magazine, 9 (2014), 62-74.
|
[1] |
Ning Zhang, Qiang Wu. Online learning for supervised dimension reduction. Mathematical Foundations of Computing, 2019, 2 (2) : 95-106. doi: 10.3934/mfc.2019008 |
[2] |
Shuhua Wang, Zhenlong Chen, Baohuai Sheng. Convergence of online pairwise regression learning with quadratic loss. Communications on Pure and Applied Analysis, 2020, 19 (8) : 4023-4054. doi: 10.3934/cpaa.2020178 |
[3] |
Aude Hofleitner, Tarek Rabbani, Mohammad Rafiee, Laurent El Ghaoui, Alex Bayen. Learning and estimation applications of an online homotopy algorithm for a generalization of the LASSO. Discrete and Continuous Dynamical Systems - S, 2014, 7 (3) : 503-523. doi: 10.3934/dcdss.2014.7.503 |
[4] |
Roberto C. Alamino, Nestor Caticha. Bayesian online algorithms for learning in discrete hidden Markov models. Discrete and Continuous Dynamical Systems - B, 2008, 9 (1) : 1-10. doi: 10.3934/dcdsb.2008.9.1 |
[5] |
Marc Bocquet, Alban Farchi, Quentin Malartic. Online learning of both state and dynamics using ensemble Kalman filters. Foundations of Data Science, 2021, 3 (3) : 305-330. doi: 10.3934/fods.2020015 |
[6] |
Soheila Garshasbi, Brian Yecies, Jun Shen. Microlearning and computer-supported collaborative learning: An agenda towards a comprehensive online learning system. STEM Education, 2021, 1 (4) : 225-255. doi: 10.3934/steme.2021016 |
[7] |
G. Calafiore, M.C. Campi. A learning theory approach to the construction of predictor models. Conference Publications, 2003, 2003 (Special) : 156-166. doi: 10.3934/proc.2003.2003.156 |
[8] |
Ran Ma, Lu Zhang, Yuzhong Zhang. A best possible algorithm for an online scheduling problem with position-based learning effect. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021144 |
[9] |
Yudong Li, Yonggang Li, Bei Sun, Yu Chen. Zinc ore supplier evaluation and recommendation method based on nonlinear adaptive online transfer learning. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021193 |
[10] |
D. Warren, K Najarian. Learning theory applied to Sigmoid network classification of protein biological function using primary protein structure. Conference Publications, 2003, 2003 (Special) : 898-904. doi: 10.3934/proc.2003.2003.898 |
[11] |
Alan Beggs. Learning in monotone bayesian games. Journal of Dynamics and Games, 2015, 2 (2) : 117-140. doi: 10.3934/jdg.2015.2.117 |
[12] |
Yangyang Xu, Wotao Yin, Stanley Osher. Learning circulant sensing kernels. Inverse Problems and Imaging, 2014, 8 (3) : 901-923. doi: 10.3934/ipi.2014.8.901 |
[13] |
Christian Soize, Roger Ghanem. Probabilistic learning on manifolds. Foundations of Data Science, 2020, 2 (3) : 279-307. doi: 10.3934/fods.2020013 |
[14] |
Mauro Maggioni, James M. Murphy. Learning by active nonlinear diffusion. Foundations of Data Science, 2019, 1 (3) : 271-291. doi: 10.3934/fods.2019012 |
[15] |
Nicolás M. Crisosto, Christopher M. Kribs-Zaleta, Carlos Castillo-Chávez, Stephen Wirkus. Community resilience in collaborative learning. Discrete and Continuous Dynamical Systems - B, 2010, 14 (1) : 17-40. doi: 10.3934/dcdsb.2010.14.17 |
[16] |
Gernot Holler, Karl Kunisch. Learning nonlocal regularization operators. Mathematical Control and Related Fields, 2022, 12 (1) : 81-114. doi: 10.3934/mcrf.2021003 |
[17] |
Sriram Nagaraj. Optimization and learning with nonlocal calculus. Foundations of Data Science, 2022 doi: 10.3934/fods.2022009 |
[18] |
Minlong Lin, Ke Tang. Selective further learning of hybrid ensemble for class imbalanced increment learning. Big Data & Information Analytics, 2017, 2 (1) : 1-21. doi: 10.3934/bdia.2017005 |
[19] |
Ziju Shen, Yufei Wang, Dufan Wu, Xu Yang, Bin Dong. Learning to scan: A deep reinforcement learning approach for personalized scanning in CT imaging. Inverse Problems and Imaging, 2022, 16 (1) : 179-195. doi: 10.3934/ipi.2021045 |
[20] |
Ting Hu. Kernel-based maximum correntropy criterion with gradient descent method. Communications on Pure and Applied Analysis, 2020, 19 (8) : 4159-4177. doi: 10.3934/cpaa.2020186 |
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]