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In Platt's 1999 paper on turning support vector machine output into a probabilistic score, he says

Bayes rule on two exponentials suggests using a parametric form of a sigmoid

where he cites this paper. I'm still getting up to speed on Bayesian probability, so could someone help me do the math (or point me towards a reference that does) so I can see how the posterior of two exponentials suggests a sigmoid?

To get started, I've tried working through this thesis and looking at specific questions like this one, but I must be missing something fundamental because I can't even get started on the problem.

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  • $\begingroup$ I also found this paper which appears to derive the posterior distribution from an exponential prior on the first page, but I don't know how to relate it to Platt's statement about two priors (or if these are even similar problems). $\endgroup$ May 13 '18 at 18:46

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