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Could someone explain in a bit more detail the move from 26 to 27? I don't get the significance of being "worried about optimization" or why/how we cancel p(x)
by subjectHarold 8y ago
Could someone explain in a bit more detail the move from 26 to 27? I don't get the significance of being "worried about optimization" or why/how we cancel p(x). I do get the later point about integration and the convenience of the reformulation. I just don't get why or how it is "allowed".
Sorry if this is obvious but I have been doing a lot of reading on this and have come across this step a few times before...but am just missing some part of every explanation.
- ysleepy 8y agoIt is allowed since we optimize over many instances and all of them are normalized by p(x). This means we can drop it from all of them and they stay proportional and will result in the same optimization result.
- throwaway287391 8y agoBecause we're optimizing (taking an argmax) with respect to theta for some fixed dataset x, the 1/p(x) is just a constant factor -- p(x) is just some number (and a non-negative one, since it's a probability). It's like saying argmax_{theta} 0.87*f(theta) = argmax_{theta} f(theta).