On Balancing between Optimal and Proportional categorical predictions

Wenxue Huang ¹,
Yuanyi Pan ^{2
,
,}

1.
Department of Mathematics, Guangzhou University Guangzhou, Guangdong 510006, China;
2.
Kochava Inc 414 Church Street, Suite 306 Sandpoint, Idaho 83864, USA

Received: 01 May 2015 Published: 01 January 2016

Abstract
Full Text(HTML)

A bias-variance dilemma in categorical data mining and analysis is the fact that a prediction method can aim at either maximizing the overall point-hit accuracy without constraint or with the constraint of minimizing the distribution bias. However, one can hardly achieve both at the same time. A scheme to balance these two prediction objectives is proposed in this article. An experiment with a real data set is conducted to demonstrate some of the scheme's characteristics. Some basic properties of the scheme are also discussed.
- Bias-variance dilemma,
- categorical data,
- optimal prediction,
- proportional prediction,
- point estimation,
- conditional distribution
Citation: Wenxue Huang, Yuanyi Pan. On Balancing between Optimal and Proportional categorical predictions[J]. Big Data and Information Analytics, 2016, 1(1): 129-137. doi: 10.3934/bdia.2016.1.129

Related Papers:

Abstract

A bias-variance dilemma in categorical data mining and analysis is the fact that a prediction method can aim at either maximizing the overall point-hit accuracy without constraint or with the constraint of minimizing the distribution bias. However, one can hardly achieve both at the same time. A scheme to balance these two prediction objectives is proposed in this article. An experiment with a real data set is conducted to demonstrate some of the scheme's characteristics. Some basic properties of the scheme are also discussed.

References

[1]	[ A. C. Acock, Working with missing values, Journal of Marriage and Family, 67(2005), 1012-1028.
[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.
[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]	[ Survey of Family Expenditures-1996, STATCAN, 1998.
[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.
[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.
[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.
[13]	[ P. T. V. Hippel, Regression with missing Ys:An improved strategy for analyzing multiply imputed data, Sociological Methodology, 37(2007), 83-117.
[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.
[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.
[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.
[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.
[21]	[ Z. Mark and Y. Baram, The bias-variance dilemma of the Monte Carlo method, Artificial Neural Networks,ICANN, 2130(2001), 141-147.
[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 accuracyinformativeness trade-off, Journal of Experimental Psychology:General, 124(1995), 424-432.
[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.
[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.