Quantifying Total Influence between Variables with Information Theoretic and Machine Learning Techniques 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 sensitive only to linear correlations. The total influence between quantities is, therefore, often expressed in terms of the mutual information, which also takes into account the nonlinear effects but is not normalized. 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. As the quality and amount of data available are 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.

Generalised Measures of Multivariate Information Content The entropy of a pair of random variables is commonly depicted using a Venn diagram. This representation is potentially misleading, however, since the multivariate mutual information can be negative. This paper presents new measures of multivariate information content that can be accurately depicted using Venn diagrams for any number of random variables. These measures complement the existing measures of multivariate mutual information and are constructed by considering the algebraic structure of information sharing. It is shown that the distinct ways in which a set of marginal observers can share their information with a nonobserving third party corresponds to the elements of a free distributive lattice. The redundancy lattice from partial information decomposition is then subsequently and independently derived by combining the algebraic structures of joint and shared information content.