Convex Poincaré inequality
= Convex Poincaré inequality
{c}
For <independent random variables> supported on $[0,1]$ and a differentiable <convex function> $f$,
$$
\operatorname{Var}(f(X))\leq\mathbb E\lVert\nabla f(X)\rVert^2.
$$
= Convex Poincaré inequality
{c}
For <independent random variables> supported on $[0,1]$ and a differentiable <convex function> $f$,
$$
\operatorname{Var}(f(X))\leq\mathbb E\lVert\nabla f(X)\rVert^2.
$$