Just a quick note, I find it disappointing that so many point-wise estimators are used in general. If we have a given metric for error, $d\left(y,\hat{y}\right)$, and a prior and likelihood, it seems intuitive that optimization should focus on solving:$$\underset{\hat{y}}{\mathrm{argmin}} \int d\left(y,\hat{y}\right) p\left(x|y\right)p\left(y\right)dy$$But usually you don't see it cast like this, which is a shame because you can end up with the wrong peak and bad overfit. Plus, you can put all sorts of fun regularizers in the prior, such as variation minimizers. Anyway, bad post, just was living on my mind.
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