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Given a classifier $C$ that gets text as an input and outputs a posterior distribution $p_1\dots p_n$ on $n$ possible topics.

In other words, for each user post, I have a list of probabilities $\{p_i\}$ that represent the chance that the user was writing about topic $i$.

I would like to calculate weights $w_i=f(p_i)$ such that the weight would be negative if the user is very not likely to write about a topic, and positive if the user is very likely to write about a topic.

What would be the standard way to do this transformation ?

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You could use the Logit function as a start, i.e

$$ w_i = \log \left( \frac{p_i}{1-p_i}\right)$$

The weights will have a range of about $[-8, 8]$

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  • $\begingroup$ I was thinking about using the logit but I quite alot of time $p_i$ is very close to zero, which causes the weights to explode to negative infinity $\endgroup$
    – Uri Goren
    Apr 5, 2016 at 16:15

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