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Given the following scenario from another post of mine where we are building a matrix that expresses the probability of first order transitions from one character to another in an english text.

We take a book, and count the number of times the letter 'e' occurs in that book -- say 15,000. Then we count the number of times the next letter is 'f' -- say, 200. With this in hand, we put

$M(\text{'e'}, \text{'f'}) = 200/15000 = 1.33\%$.

Say instead we want to normalize this conditional probability to a range between 0 - 1, but discluding the absolute values 0 or 1 (only getting infinitesimely close to each extreme). Is there an accepted way to use a sigmoid function for this sort of normalization of a probability?

I don't know if this is a common practice, however, I think it would be useful in an AI application I am working on.

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    @Dan: The percent sign had gone missing because it wasn't escaped.2011-09-15
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    joriki, I see. I still don't understand the question because 200/15000 = 1.33% is already between 0 and 1. Maybe it is about using the sigmoid to normalize a likelihood _ratio_?2011-09-15
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    @Dan: See my answer for how I understood the question to be intended. By the way, I don't get notified unless you put the '@' in front of the username.2011-09-15

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