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A best estimator wrt. some loss function is an estimator that minimizes the average value of that loss function.⇒

Optimizing (ie. training) an estimator with input data will result in different results depending on the distribution of data points: wherever there is a high density of data points, the optimizer will reduce the error there, possibly incurring greater error where the density of data points is lower.⇒

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 $$ f_{opt} = \mathrm{arg min}_f \int P(x) \int P(x\mid m) L(x,f(m))\;dx\;dm $$⇒