Fig. 2
Difference between urban and rural EII and MII in the eastern, central, and western regions of China in 2018 (EII = Economic Inequality Index, MII = Medical Inequality Index). Note: Based on the methods presented by [65, 66], the equivalence is shown by: \({g}_{ME}\left(X,W\right)=-E\left[\log p\left(g(Wx)\right)\right]\triangleq H(z)=E\left[\sum_{i=1}^m\mathit{\log}p\left({y}_i\right)\right]+\mathit{\log}\left|\mathit{\det}W\right|-E\left[\mathit{\log}p(x)\right]\propto Tlog\left|\mathit{\det}W\right|+\sum_{t=1}^T\sum_{i=1}^m\mathit{\log}p\left({w}_i{x}_t\right).\) Where the maximum entropy (ME) based ICA method meets the perspective of a neural network by estimating the demixing matrix WME, which maximizes the entropy H(·) of the nonlinear outputs z = g(y) of a neural network. In particular, using the cumulative distribution function for a nonlinear function g(·), i.e., \({g}_i^{\prime}\left({y}_i\right)=p\left({y}_i\right)\), assures the equivalence between the ME method using WME