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Synthesis of Statistical Knowledge from Time-Dependent Data
March 1991 (vol. 13 no. 3)
pp. 265-271
A general approach to analyzing multivariate time-dependent system processes with discrete-valued (both nominal and ordinal) and/or continuous-valued outcomes is presented. The approach is based on an event-covering method which selects (or covers) a subspace from the outcome space of an n-tuple of variables for estimation purposes. From the covered subspace, statistically interdependent events are selected as statistical knowledge for forecasting unknown events. The event-covering method presented is based on the use of restricted variables with only a subset of the outcomes considered. An extension to the event-covering method based on the selection of joint outcomes is discussed. The testing of this method using climatic data and simulated data which model situations in real life is described. The experiments show that the method is able to detect statistically relevant information, describe it in a meaningful and comprehensible way, and use this information for a reliable estimation (or forecast) of the missing values that will occur at some future time.
[1] B. Abraham and J. Ledolter,Statistical Methods for Forecasting. New York: Wiley, 1983.
[2] Y. M. M. Bishop, S. E. Fienberg, and P. W. Holland,Discrete Multivariate Analysis: Theory and Practice. Cambridge, MA: MIT Press, 1975.
[3] G. E. P. Box, and G. M. Jenkins,Time Series Analysis, Forecasting and Control. San Francisco, CA: Holden Day, 1970.
[4] K. C. C. Chan, A. K. C. Wong, and D. K. Y. Chiu, "Observer: A probabilistic learning system for ordered events," inPattern Recognition(Lecture Notes in Computer Science, Vol. 301), J. Kittler, Ed. New York: Springer-Verlag, 1988, pp. 507-516.
[5] K. C. C. Chan, "Inductive learning in the presence of uncertainty," Ph.D. dissertation, Dep. Syst. Design Eng., Univ. Waterloo, Canada, 1989.
[6] D. K. Y. Chiu, Pattern Analysis Using Event-Covering, Ph.D. Thesis, Dept. of Systems Design Engineering, University of Waterloo, Canada, 1986.
[7] D. K. Y. Chiu and A. K. C. Wong, "Synthesizing knowledge: A cluster analysis approach using event-covering,"IEEE Trans. Syst., Man, Cybern., vol. SMC-16, no. 2, pp. 251-259, Mar./Apr. 1986.
[8] D. K. Y. Chiu, B. Cheung, and A. K. C. Wong, "Information synthesis based on hierarchical maximum entropy discretization,"J. Experimental Theoretical Artificial Intell., vol. 2, pp. 117-129, 1990.
[9] R. Christensen, "Entropy minimax, a non-Bayesian approach to probability estimation from empirical data," inProc. IEEE Int. Conf. Cybernetics and Society, 1973, pp. 321-325.
[10] H. Cramer,Mathematical Methods of Statistics. Princeton, NJ: Princeton University Press, 1946.
[11] T. G. Ditterich and R. S. Michalski, "Discovering patterns in sequences of events,"Artificial Intell., vol. 25, pp. 187-232, 1985.
[12] N. R. Draper and H. Smith,Applied Regression Analysis. New York: Wiley, 1966.
[13] S. E. Fienberg,The Analysis of Cross-Classified Categorical Data. Cambridge, MA: MIT Press, 1980.
[14] B. Fingleton, Models of Category Counts. Cambridge University Press, Cambridge, 1984.
[15] S. J. Haberman, "The analysis of residuals in cross-classified tables,"Biometrics, vol. 29, pp. 205-220, 1973.
[16] J. G. Kalbfleisch,Probability and Statistical Inference. New York: Springer-Verlag, 1985.
[17] M. Lascurain, "On maximum entropy discretization and its applications in pattern recognition," Ph.D. dissertation, Dep. Syst. Design Eng., Univ. Waterloo, Ont., Canada, 1983.
[18] S. G. Makridakis and S. C. Wheelwright, Eds.,Forecasting(Studies in Management Sciences, Vol. 12). Amsterdam, The Netherlands: North-Holland, 1979.
[19] S. G. Makridakis and S. C. Wheelwright, Eds.,The Handbook of Forecasting, A Management's Guide. New York: Wiley, 1982.
[20] R. S. Michalski, H. Ko, and K. Chen, "Qualitative prediction: The SPARC/G methodology for inductively describing and predicting discrete processes," inExpert Systems, P. Dufour and A. van Lamsmeeerde, Eds. New York: Academic, 1986.
[21] B. R. Mitchell,European Historical Statistics 1750-1975, 2nd ed. New York: Facts on File, 1980.
[22] E. Mortimer, "Blaise Pascal: The life and work of a realist," inMathematics, An Introduction to Its Spirits and Use(Readings from Scientific American). San Francisco, CA: Freeman, 1979.
[23] C. R. Rao,Advanced Statistical Methods in Biometric Research. New York: Wiley, 1952.
[24] A. C. Sanderson and A. K. C. Wong, "Pattern trajectory analysis of non-stationary multivariate data,"IEEE Trans. Syst., Man, Cybern., vol. SMC-10, no. 7, pp. 384-392, 1980.
[25] T. E. Unny, U. S. Panu, C. D. MacInnes, and A. K. C. Wong, "Pattern analysis and synthesis of time-dependent hydrologic data,"Advances in Hydrosci., vol. 12, pp. 195-295, 1978.
[26] D. C. C. Wang and A. K. C. Wong, "Classification of discrete data with feature space transformation,"IEEE Trans. Automat. Contr., vol. AC-24, no. 3, pp. 434-437, 1979.
[27] A. K. C. Wong and L. Goldforb, "Pattern recognition of relational structures," inPattern Recognition Theory in Applications(NATO Advanced Study Institutes Series), J. Kittler, K. S. Fu, and L. P. Pau, Eds. Dordrect, The Netherlands: D. Reidel, 1982, pp. 157-175.
[28] A. K. C. Wong and D. K. Y. Chiu, "Synthesizing statistical knowledge from incomplete mixed-mode data,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-9, no. 6, pp. 796-805, Nov. 1987.
[29] A. K. C. Wong and D. K. Y. Chiu, "An event-covering method for effective probabilistic inference,"Pattern Recognition, vol. 20, no. 2, pp. 245-255, 1987.
[30] A. K. C. Wong and D. C. C. Wang, "DECA: A discrete-valued data clustering algorithm,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-1, no. 4, pp. 342-349, 1979.
[31] A. K. C. Wong and T. S. Liu, "Typicality, diversity, and feature pattern of an ensemble,"IEEE Trans. Comput., vol. C-24, no. 2, pp. 158-181, Feb. 1975.
[32] N. Wrigley,Categorical Data Analysis for Geographers and Environmental Scientists. London: Longman, 1985.
Index Terms:
statistical knowledge; time-dependent data; multivariate time-dependent system processes; event-covering method; outcome space; statistically interdependent events; climatic data; simulated data; forecasting theory; statistics; time series
Citation:
D.K.Y. Chiu, A.K.C. Wong, K.C.C. Chan, "Synthesis of Statistical Knowledge from Time-Dependent Data," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 3, pp. 265-271, Mar. 1991, doi:10.1109/34.75513