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1

We want a distribution over $w$, don't we? Yes. You want to obtain a distribution over the parameters, which models the uncertainty about the parameters. This distribution over the parameters can induce a probability distribution over the possible functions consistent with your data. Why is $a$ integrated out here and not $w$? This is just the definition ...


0

You have two dependent variables $a$ and $w$. So, there is a joint distribution $p(w, a)$. You can make a marginalization by one of them, pretty much as you did in your second formula. $$p(w) = \int p(w, a)da$$ $$p(w) = \int p(w | a)p(a)da$$ The only difference in this case, the calculation made for the specific point $x_i, y_i$, which is empathized by sub-...


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Your description of what is going on is more or less correct, although I am not completely sure that you have really understood it, given your last question. So, let me enumerate the steps. The computation of the posterior is often intractable (given that the evidence, i.e. the denominator of the right-hand side of the Bayes' rule, might be numerically ...


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The likelihood depends on the task that you are solving, so this is similar to traditional neural networks (in fact, even these neural networks have a probabilistic/Bayesian interpretation!). For binary classification, you should probably use a Bernoulli, which, in practice, corresponds to using a sigmoid with a binary cross-entropy (you can show that the ...


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