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Why curriculum learning & self-paced learning work in big/noisy data: A theoretical perspective
On balancing between optimal and proportional categorical predictions
1. | Department of Mathematics, Guangzhou University, Guangzhou, Guangdong 510006, China |
2. | Kochava Inc, 414 Church Street, Suite 306, Sandpoint, Idaho 83864, United States |
References:
[1] |
A. C. Acock, Working with missing values, Journal of Marriage and Family, 67 (2005), 1012-1028.
doi: 10.1111/j.1741-3737.2005.00191.x. |
[2] |
E. Acuna and C. Rodriguez, The treatment of missing values and its effect in the classifier accuracy, In Classification, Clustering and Data Mining Applications, (2004), 639-647. |
[3] |
G. E. Batista and M. C. Monard, An analysis of four missing data treatment methods for supervised learning, Applied Artificial Intelligence, 17 (2003), 519-533.
doi: 10.1080/713827181. |
[4] |
J. Doak, An Evaluation of Feature Selection Methods and Their Application to Computer Security, UC Davis Department of Computer Science, 1992. |
[5] |
P. Domingos, A unified bias-variance decomposition, In Proceedings of 17th International Conference on Machine Learning. Stanford CA Morgan Kaufmann, 2000, 231-238. |
[6] | |
[7] |
A. Farhangfar, L. Kurgan and J. Dy, Impact of imputation of missing values on classification error for discrete data, Pattern Recognition, 41 (2008), 3692-3705.
doi: 10.1016/j.patcog.2008.05.019. |
[8] |
H. H. Friedman, On bias, variance, 0/1-loss, and the curse-of-dimensionality, Data mining and knowledge discovery, 1 (1997), 55-77. |
[9] |
S. Geman, E. Bienenstock and R. Doursaté, Neural networks and the bias/variance dilemma, Neural computation, 4 (1992), 1-58.
doi: 10.1162/neco.1992.4.1.1. |
[10] |
L. A. Goodman and W. H. Kruskal, Measures of association for cross classification, J. American Statistical Association, 49 (1954), 732-764. |
[11] |
I. Guyon and A. Elisseeff, An introduction to variable and feature selection, J. Mach. Learn. Res., 3 (2003), 1157-1182. |
[12] |
L. Himmelspach and S. Conrad, Clustering approaches for data with missing values: Comparison and evaluation, In Digital Information Management (ICDIM), 2010 Fifth International Conference on,IEEE 2010, 19-28.
doi: 10.1109/ICDIM.2010.5664691. |
[13] |
P. T. V. Hippel, Regression with missing Ys: An improved strategy for analyzing multiply imputed data, Sociological Methodology, 37 (2007), 83-117.
doi: 10.1111/j.1467-9531.2007.00180.x. |
[14] |
W. Huang, Y. Shi and X. Wang, A nomminal association matrix with feature selection for categorical data, Communications in Statistics - Theory and Methods, to appear, 2015. |
[15] |
W. Huang, Y. Pan and J. Wu, Supervised Discretization for Optimal Prediction, Procedia Computer Science, 30 (2014), 75-80.
doi: 10.1016/j.procs.2014.05.383. |
[16] |
G. James and T. Hastie, Generalizations of the Bias/Variance Decomposition for Prediction Error, Dept. Statistics, Stanford Univ., Stanford, CA, Tech. Rep, 1997. |
[17] |
S. Kullback and R. A. Leibler, On information and sufficiency, Annals of Mathematical Statistics, 22 (1951), 79-86.
doi: 10.1214/aoms/1177729694. |
[18] |
R. J. A. Little and D. B. Rubin, Statistical Analysis with Missing Data, John Wiley & Sons, Inc. 1987, New York, NY, USA. |
[19] |
H. Liu and H. Motoda, Feature Selection for Knowledge Discovery and Data Mining, Kluwer Academic Publishers 1998, Norwell, MA, USA.
doi: 10.1007/978-1-4615-5689-3. |
[20] |
J. Luengo, S. García and F. Herrera, On the choice of the best imputation methods for missing values considering three groups of classification methods, Knowledge and information systems, 32 (2012), 77-108.
doi: 10.1007/s10115-011-0424-2. |
[21] |
Z. Mark and Y. Baram, The bias-variance dilemma of the Monte Carlo method, Artificial Neural Networks,ICANN, 2130 (2001), 141-147.
doi: 10.1007/3-540-44668-0_20. |
[22] |
R. Tibshirani, Bias, Variance and Prediction Error for Classification Rules, Citeseer 1996. |
[23] |
I. Yaniv and D. P. Foster, Graininess of judgment under uncertainty: An accuracy-informativeness trade-off, Journal of Experimental Psychology: General, 124 (1995), 424-432.
doi: 10.1037/0096-3445.124.4.424. |
[24] |
L. Yu, K. K. Lai, S. Wang and W. Huang, A bias-variance-complexity trade-off framework for complex system modeling, In Computational Science and Its Applications-ICCSA 2006, Springer, 3980 (2006), 518-527.
doi: 10.1007/11751540_55. |
[25] |
T. Zhou, Z. Kuscsik, J. Liu, M. Medo, J. R. Wakeling and Y. Zhang, Solving the apparent diversity-accuracy dilemma of recommender systems, Proceedings of the National Academy of Sciences, 107 (2010), 4511-4515.
doi: 10.1073/pnas.1000488107. |
show all references
References:
[1] |
A. C. Acock, Working with missing values, Journal of Marriage and Family, 67 (2005), 1012-1028.
doi: 10.1111/j.1741-3737.2005.00191.x. |
[2] |
E. Acuna and C. Rodriguez, The treatment of missing values and its effect in the classifier accuracy, In Classification, Clustering and Data Mining Applications, (2004), 639-647. |
[3] |
G. E. Batista and M. C. Monard, An analysis of four missing data treatment methods for supervised learning, Applied Artificial Intelligence, 17 (2003), 519-533.
doi: 10.1080/713827181. |
[4] |
J. Doak, An Evaluation of Feature Selection Methods and Their Application to Computer Security, UC Davis Department of Computer Science, 1992. |
[5] |
P. Domingos, A unified bias-variance decomposition, In Proceedings of 17th International Conference on Machine Learning. Stanford CA Morgan Kaufmann, 2000, 231-238. |
[6] | |
[7] |
A. Farhangfar, L. Kurgan and J. Dy, Impact of imputation of missing values on classification error for discrete data, Pattern Recognition, 41 (2008), 3692-3705.
doi: 10.1016/j.patcog.2008.05.019. |
[8] |
H. H. Friedman, On bias, variance, 0/1-loss, and the curse-of-dimensionality, Data mining and knowledge discovery, 1 (1997), 55-77. |
[9] |
S. Geman, E. Bienenstock and R. Doursaté, Neural networks and the bias/variance dilemma, Neural computation, 4 (1992), 1-58.
doi: 10.1162/neco.1992.4.1.1. |
[10] |
L. A. Goodman and W. H. Kruskal, Measures of association for cross classification, J. American Statistical Association, 49 (1954), 732-764. |
[11] |
I. Guyon and A. Elisseeff, An introduction to variable and feature selection, J. Mach. Learn. Res., 3 (2003), 1157-1182. |
[12] |
L. Himmelspach and S. Conrad, Clustering approaches for data with missing values: Comparison and evaluation, In Digital Information Management (ICDIM), 2010 Fifth International Conference on,IEEE 2010, 19-28.
doi: 10.1109/ICDIM.2010.5664691. |
[13] |
P. T. V. Hippel, Regression with missing Ys: An improved strategy for analyzing multiply imputed data, Sociological Methodology, 37 (2007), 83-117.
doi: 10.1111/j.1467-9531.2007.00180.x. |
[14] |
W. Huang, Y. Shi and X. Wang, A nomminal association matrix with feature selection for categorical data, Communications in Statistics - Theory and Methods, to appear, 2015. |
[15] |
W. Huang, Y. Pan and J. Wu, Supervised Discretization for Optimal Prediction, Procedia Computer Science, 30 (2014), 75-80.
doi: 10.1016/j.procs.2014.05.383. |
[16] |
G. James and T. Hastie, Generalizations of the Bias/Variance Decomposition for Prediction Error, Dept. Statistics, Stanford Univ., Stanford, CA, Tech. Rep, 1997. |
[17] |
S. Kullback and R. A. Leibler, On information and sufficiency, Annals of Mathematical Statistics, 22 (1951), 79-86.
doi: 10.1214/aoms/1177729694. |
[18] |
R. J. A. Little and D. B. Rubin, Statistical Analysis with Missing Data, John Wiley & Sons, Inc. 1987, New York, NY, USA. |
[19] |
H. Liu and H. Motoda, Feature Selection for Knowledge Discovery and Data Mining, Kluwer Academic Publishers 1998, Norwell, MA, USA.
doi: 10.1007/978-1-4615-5689-3. |
[20] |
J. Luengo, S. García and F. Herrera, On the choice of the best imputation methods for missing values considering three groups of classification methods, Knowledge and information systems, 32 (2012), 77-108.
doi: 10.1007/s10115-011-0424-2. |
[21] |
Z. Mark and Y. Baram, The bias-variance dilemma of the Monte Carlo method, Artificial Neural Networks,ICANN, 2130 (2001), 141-147.
doi: 10.1007/3-540-44668-0_20. |
[22] |
R. Tibshirani, Bias, Variance and Prediction Error for Classification Rules, Citeseer 1996. |
[23] |
I. Yaniv and D. P. Foster, Graininess of judgment under uncertainty: An accuracy-informativeness trade-off, Journal of Experimental Psychology: General, 124 (1995), 424-432.
doi: 10.1037/0096-3445.124.4.424. |
[24] |
L. Yu, K. K. Lai, S. Wang and W. Huang, A bias-variance-complexity trade-off framework for complex system modeling, In Computational Science and Its Applications-ICCSA 2006, Springer, 3980 (2006), 518-527.
doi: 10.1007/11751540_55. |
[25] |
T. Zhou, Z. Kuscsik, J. Liu, M. Medo, J. R. Wakeling and Y. Zhang, Solving the apparent diversity-accuracy dilemma of recommender systems, Proceedings of the National Academy of Sciences, 107 (2010), 4511-4515.
doi: 10.1073/pnas.1000488107. |
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