Consider a convex function $f(x) = x^2$
Let $E_{AV} = \frac{1}{M} \sum_{m=1}^{M} \mathbb{E}_x [(y_m(x) - f(x))^2]$ be average expected sum-of-squares error of the members of an ensemble model
Let $E_{ENS} = \mathbb{E}_x [(\frac{1}{M} \sum_{m=1}^{M} y_m(x) - f(x))^2]$ be the expected error of an ensemble model.
How can we show that $\mathbb{E}_{ENS} \le \mathbb{E}_{AV}$ by applying Jensen Inequality?
$(\frac{1}{M} \sum_{m=1}^{M} (y_m(x) - f(x)))^2 \leq \frac{1}{M} \sum_{m=1}^{M} (y_m(x) - f(x))^2$ by Jensen's Inequality applied to the uniform measure on $\{1,2,...,M\}$. Now just take expectation on both sides.