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You can use it to estimate model uncertainty, Yarin Gal has some nice writeups on this: https://www.cs.ox.ac.uk/people/yarin.gal/website/blog_3d801a... (in this case using dropout networks as GP approximations).

How would we use a property of networks with random weights to estimate uncertainty of trained models in which which the weights are (as much as we can) trained to be not random?

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