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Fig. 3 | International Journal for Equity in Health

Fig. 3

From: Can government subsidies and public mechanisms alleviate the physical and mental health vulnerability of China’s urban and rural residents?

Fig. 3

The gap of the urban-rural economic index and public health service index for each province and city in the three regions of China. Note: Based on the availability of data, only thirty provinces of China are shown in the figures for this study. Based on the methods presented by [65, 66], the equivalence is shown by: \({g}_{ME}\left(X,W\right)=-E\left[\mathit{\log}p\left(g(Wx)\right)\right]\triangleq H(z)=E\left[\sum_{i=1}^m\log p\left({y}_i\right)\right]+\mathit{\log}\left|\mathit{\det}W\right|-E\left[\log p(x)\right]\propto Tlog\left|\mathit{\det}W\right|+\sum_{t=1}^T\sum_{i=1}^m\mathit{\log}p\left({w}_i{x}_t\right).\) 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

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