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Quantifying Total Influence between Variables with Information Theoretic and Machine Learning Techniques

1
Consorzio RFX (CNR, ENEA, INFN, Universita’ di Padova, Acciaierie Venete SpA), Corso Stati Uniti 4, 35127 Padova, Italy
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Associazione EURATOM-ENEA - University of Rome “Tor Vergata”, 00185 Rome, Italy
*
Author to whom correspondence should be addressed.
Presented at the 5th International Electronic Conference on Entropy and Its Applications, 18–30 November 2019; Available online: https://ecea-5.sciforum.net/.
These authors contributed equally to the work.
Proceedings 2020, 46(1), 19; https://doi.org/10.3390/ecea-5-06666
Published: 17 November 2019
The increasingly sophisticated investigations of complex systems require more robust estimates of the correlations between the measured quantities. The traditional Pearson Correlation Coefficient is easy to calculate but is sensitive only to linear correlations. The total influence between quantities is therefore often expressed in terms of the Mutual Information, which takes into account also the nonlinear effects but is not normalised. To compare data from different experiments, the Information Quality Ratio is therefore in many cases of easier interpretation. On the other hand, both Mutual Information and Information Quality Ratio are always positive and therefore cannot provide information about the sign of the influence between quantities. Moreover, they require an accurate determination of the probability distribution functions of the variables involved. Since the quality and amount of data available is not always sufficient to grant an accurate estimation of the probability distribution functions, it has been investigated whether neural computational tools can help and complement the aforementioned indicators. Specific encoders and autoencoders have been developed for the task of determining the total correlation between quantities related by a functional dependence, including information about the sign of their mutual influence. Both their accuracy and computational efficiencies have been addressed in detail, with extensive numerical tests using synthetic data. A careful analysis of the robustness against noise has also been performed. The neural computational tools typically outperform the traditional indicators in practically every respect.
Keywords: Machine Learning Tools; Information Theory; Information Quality Ratio; Total Correlations; Encoders; Autoencoders. Machine Learning Tools; Information Theory; Information Quality Ratio; Total Correlations; Encoders; Autoencoders.
MDPI and ACS Style

Murari, A.; Rossi, R.; Lungaroni, M.; Gaudio, P.; Gelfusa, M. Quantifying Total Influence between Variables with Information Theoretic and Machine Learning Techniques. Proceedings 2020, 46, 19.

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