Find the value of $Z$ from the log expression of 0-1 error decomposition.

23 Views Asked by At

I am trying to interpret the calculation of 0-1 error for classification from the following link (p. 44). With the expression given below, I need help in finding out the value of $Z$.

$$\bar h = \text{argmin}_u \mathbb{E}_s[\mathrm{KL}(u, h)]$$

This turns out to be the geometric mean:

$$ \begin{aligned} \log\frac{\bar h}{1 - \bar h} &= \mathbb{E}_s\left[\log \frac{h}{1 - h}\right] \\ \bar h &= \frac{1}{Z} \exp\left(\mathbb{E}_s[\log h]\right), \end{aligned} $$

where $\mathbb{E}_s$ is the expected value.