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Manuscript Title: Delta 2.0: a program for finding dependencies in tables of data.
Authors: H. Pi, C. Peterson
Program title: DELTA 2.0.
Catalogue identifier: ACVP_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 83(1994)293
Programming language: C.
Computer: DEC Alpha 3000.
Operating system: DEC OSF 1.3.
RAM: 170K words
Word size: 32
Keywords: General purpose, Statistical methods, Data analysis, Dependencies, Correlations, Nonlinear systems, Embedding dimension, Artificial neural Network.
Classification: 4.13.

Nature of problem:
Analysis of experimental data for determining dependencies among the measured variables and establishing noise levels. This is a frequently occurring task in natural sciences. Standard methods for these problems are typically limited to linear dependencies like using correlation matrices. Many problems in physics are nonlinear by nature and hence require analysis methods that are not limited to linear approximations.

Solution method:
The core of the algorithm is based on the delta-test [1], which establishes dependency structures by exploiting the properties of continuous functions. The method, which in contrast to standard correlation methods is not confined to linear dependencies, forms conditional probabilities from data tables, which are then extrapolated to the infinite resolution limit. From these limit values one reads off relative dependencies, noise levels and embedding dimensions. The method is very useful when it comes to single out most relevant input variables for artificial neural network processing. Also, in this case the approach can be used to track residual dependencies of the output errors. The degree of nonlinearity is estimated by comparing the delta- test noise reading with the variance of the residuals of the linear multiple regression model.

Restrictions:
The only restriction of the complexity for an application is set by available memory and CPU time. A table of M variables with N measurements each requires a storage of M x N double precision numbers. The corresponding CPU time grows like M**2N. For a problem with M=5 (one independent and 4 dependent variables) and N=1000 this amounts to 35 CPU seconds on a DEC Alpha 3000/300. For users equipped with X11 some of the informative results can be displayed with interactive graphics. (X plot graphic package)