Canonical gradient
= Canonical gradient
{title2=$\varphi_{\mathrm{eff}}=\Pi_{\mathcal T}\varphi$}
= Efficient influence function
{synonym}
The canonical gradient is the <influence-function representer> in the <statistical tangent space> $\mathcal T$. It equals the <orthogonal projection> onto $\mathcal T$ of any representer. Every other representer differs from it by an element of $\mathcal T^\perp$, so the <Pythagorean theorem in an inner-product space> gives it minimum <variance>. For $\psi(P)=Pa$ in an unrestricted density model with bounded $a$, it is $a-Pa$.