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One Dimensional Modeling and Learning

Published

Author(s)

J E. Devaney

Abstract

This paper introduces four new algorithms, the M-algorithm, the L-algorithm, the S-algorithm and the T-algorithm, which enable recognition of distributional functions without doing a fit of the data to the distribution. These algorithms workbest for large sample sizes, such as $500$ to $50,000$ points. These techniques rest on the concept of an equation signature, which is a coefficient independent property of an equation, and hence enable searching for all instances of an equation type at the same time. The M-algorithm can differentiate even very similar distributions. Additionally it provides accurate values for the distribution location and variation parameters. The L-algorithm can tell if two distributions are the same, even if the distribution type is unknown. Both can also tell if the location and/or variation parameters of the distribution are changing. The S-algorithm can detect whether a distribution is symmetric or not and provide an estimate of its asymmetry. The T-algorithm provides an estimate of the tail length of the distribution. A method to visualize the attributes of a database in terms of distributions, the D-plot, is presented. Applications of these algorithms include detecting redundancy in decision tables and improving machine learning.
Citation
NIST Interagency/Internal Report (NISTIR) - 6168
Report Number
6168

Keywords

constructive induction, D-plot, distribution finding, L-algorithm, learning, M-algorithm, one dimensional modeling, probability plotting, S-algorithm, T-algorithm

Citation

Devaney, J. (2008), One Dimensional Modeling and Learning, NIST Interagency/Internal Report (NISTIR), National Institute of Standards and Technology, Gaithersburg, MD (Accessed June 19, 2024)

Issues

If you have any questions about this publication or are having problems accessing it, please contact reflib@nist.gov.

Created October 16, 2008