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Given probability density functions (PDF) $P(X)$ and $P(X\mid M)$ for a latent variable $X$ and an observable $M$, an optimal estimator for $X$ wrt. the loss function $F$ is given by $$ f_{opt} = \mathrm{arg min}_f \int P(x) \int P(x\mid m) L(x,f(m))\;dx\;dm $$