| ... | ... | @@ -106,7 +106,8 @@ Herein, we will represent the the probabilities for the weights in terms of Gaus |
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At this stage, the model is not trained at all. What happens as we see examples? Lets show the model the very first example (blue circle below). In the Bayesian learning, we use the likelihood function, p(y|x,w) -- probability of getting the true y value given the wights and the example. With the example we pass, the calculated likelihood is shown below (left). The true weights are shown as "+" for comparison. Here, the calculated likelihood estimates that the weights of the model should be around this zone. By using the likelihood and our prior, we now calculate the posterior probabilities, given in the middle:
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<img src="uploads/47f290dd30648b9cf47e1c597fc45a11/br2.png" width="600">
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<img src="uploads/056765b94996330d69d7dc932f5576b0/br2.png" width="600">
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Samples of models withdrawn from the posterior distribution is given on the right. Here we see that the lines start to accumulate around the observation already.
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