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Parametric Copula-GP model for analyzing multidimensional neuronal and behavioral relationships

Fig 4

Comparison of the Copula-GP model against the non-parametric information estimators, performed on three benchmarking datasets A Multivariate Gaussian. B Multivariate Student T. C Multivariate Gaussian y (same as A), morphed into another distribution with a tail dependence, while . In each row, the plots show: i. the probability density plots from each dataset: the unconditional dependency structure p(u) (left) and conditional dependency structures at the beginning and the end of the parameter domain dom x = [0, 1] (middle and right, respectively). ii. conditional entropy H(y|x); the black line shows the true values, the red line—Copula-GP, the orange line—BI-KSG; Note, that MINE is not included in this comparison, as it does not produce estimates of H(y|x). iii. mutual information I(x, y); black line—true value; red—Copula-GP (solid: MC integration (12); dashed: estimated MI (13)); orange—BI-KSG; green—KSG; blue—MINE (dotted: 100 HU, dashed: 200 HU, solid: 500 HU). Gray intervals show either standard error of mean (SE, 6 repetitions), or for integrated variables. Note, that MINE estimates are sensitive to the choice of hyper-parameters (e.g. number of hidden units, shown in different line styles).

doi: https://doi.org/10.1371/journal.pcbi.1009799.g004