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I'm currently reading Thomas Hofmamms paper on Probabilistic Latent Semantic Analysis.

He includes a formula for the E step in Expectation Maximisation, but has proposed an alternative to this step which looks like

$P(z;d,w) = \dfrac{[P(z)P(d|z)P(w|z)]^\beta}{\sum_{z'\in \mathcal{Z}}[P(z')P(d|z')P(w|z')]^\beta}$

I'm sure I have seen this formula in the context of something else, where it is known by a much more common name. Issue is I can't remember, and googling Tempered EM provides no useful results

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  • $\begingroup$ What are you asking exactly? Do you want to know the name of this formula? $\endgroup$
    – gung - Reinstate Monica
    Commented Mar 18, 2015 at 1:12
  • $\begingroup$ Sorry, I was trying to think what the context I've seen before may have been. The poster below said it was simulated annealing, which was what I was looking for $\endgroup$
    – Kom
    Commented Mar 18, 2015 at 11:54

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A similar 'cooling schedule' comes up in Simulated Annealing. $\beta$ is a temperature parameter.

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  • $\begingroup$ Thanks very much, I thought it was simulated annealing, but couldn't see the related formula on Wikipedia. Thank you. $\endgroup$
    – Kom
    Commented Mar 18, 2015 at 11:53

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