#1




Questions on the Bayesian Prior
I asked the TA this during the lecture but I am not sure I understood his answer.
Say in gradient descent (or perceptron) we start with an initial guess for w. Then we proceed to modify w as we process the training data till we get a satisfactory w. I believe our initial w is not the same as the "Bayesian prior". Why is that? Is it because we are guessing an actual number instead of imposing a probability distribution on the values for w? How would gradient descent change if we modeled w as a Bayesian? In perceptron, when we change w based on a data point that contradicts w's predictions, that is not the same as "conditioning on data"? Why? Also, somewhat related, I think: Prof AbuMostafa explained in the last lecture the second condition where it would be ok to assume a Bayesian Prior. The way I understood it was that if we had enough data points that successive updates would eventually dilute our (perhaps poor estimate of the) original prior, then we're OK? Is my understanding correct? So is that similar to saying our Eout will be low if M is large enough? 
#2




Re: Questions on the Bayesian Prior
Quote:
If we had a prior, and we used gradient descent to pick the hypothesis with the maximum posterior, it would be working on an augmented error of sorts, part of which comes from the prior and plays the role of a regularizer. Quote:
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#3




Re: Questions on the Bayesian Prior
Thanks for the clarifications, Professor!

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