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→作为分布差异的有效信息
<math>
<math>
P(\tilde{X}|\tilde{Y}=Y_0,f)=\frac{P(\tilde{X},\tilde{Y_0})}{P(\tilde{Y_0})}=\frac{P(\tilde{X_0})P(\tilde{Y_0}|\tilde{X})}{P(\tilde{Y_0})}=\frac{P(\tilde{Y_0}|\tilde{X})}{N\cdot P(\tilde{Y_0})}
P(\tilde{X}|\tilde{Y}=Y_0,f)=\frac{P(\tilde{X},\tilde{Y_0})}{P(\tilde{Y_0})}=\frac{P(\tilde{X_0})P(\tilde{Y_0}|\tilde{X})}{P(\tilde{Y_0})}=\frac{P(\tilde{Y_0}|\tilde{X})}{\#(\mathcal{X})\cdot P(\tilde{Y_0})}
</math>
</math>
<math>
<math>
ei(f,Y_0)=-D_{KL}(U||P(\tilde{X}|\tilde{Y}=Y_0,f)=\log N+\frac{1}{N}\sum_{\tilde{X}}\log\frac{P(\tilde{Y_0}|\tilde{X})}{P(\tilde{Y_0})}
ei(f,Y_0)=-D_{KL}(U||P(\tilde{X}|\tilde{Y}=Y_0,f)=\log \#(\mathcal{X})+\frac{1}{\#(\mathcal{X})}\sum_{\tilde{X}}\log\frac{P(\tilde{Y_0}|\tilde{X})}{P(\tilde{Y_0})}
</math>
</math>
<math>
<math>
EI=\frac{1}{N}\sum_{\tilde{X},\tilde{Y_0}}P(\tilde{Y_0}|\tilde{X})\log\frac{P(\tilde{Y_0}|\tilde{X})}{P(\tilde{Y_0})}=\mathbb{E}_{P(\tilde{Y_0}|\tilde{X})}(ei(f,Y_0))-\log N
EI=\frac{1}{\#(\mathcal{X})}\sum_{\tilde{X},\tilde{Y_0}}P(\tilde{Y_0}|\tilde{X})\log\frac{P(\tilde{Y_0}|\tilde{X})}{P(\tilde{Y_0})}=\mathbb{E}_{P(\tilde{Y_0}|\tilde{X})}(ei(f,Y_0))-\log \#(\mathcal{X})
</math>
</math>