The application of the Maximum Entropy (ME) principle leads to a minimum of the Mutual Information (MI),
I(X,Y), between random variables
X,
Y, which is compatible with prescribed joint expectations and given ME marginal distributions. A sequence of sets of
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The application of the Maximum Entropy (ME) principle leads to a minimum of the Mutual Information (MI),
I(X,Y), between random variables
X,
Y, which is compatible with prescribed joint expectations and given ME marginal distributions. A sequence of sets of joint constraints leads to a hierarchy of lower MI bounds increasingly approaching the true MI. In particular, using standard bivariate Gaussian marginal distributions, it allows for the MI decomposition into two positive terms: the Gaussian MI (
Ig), depending upon the Gaussian correlation or the correlation between ‘Gaussianized variables’, and a non‑Gaussian MI (
Ing), coinciding with joint negentropy and depending upon nonlinear correlations. Joint moments of a prescribed total order
p are bounded within a compact set defined by Schwarz-like inequalities, where
Ing grows from zero at the ‘Gaussian manifold’ where moments are those of Gaussian distributions, towards infinity at the set’s boundary where a deterministic relationship holds. Sources of joint non-Gaussianity have been systematized by estimating
Ing between the input and output from a nonlinear synthetic channel contaminated by multiplicative and non-Gaussian additive noises for a full range of signal-to-noise ratio (
snr) variances. We have studied the effect of varying
snr on
Ig and
Ing under several signal/noise scenarios.
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