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Re: [computer-go] 9x9 Ratings
Remi.Coulom wrote:
> Antti Huima wrote:
>
>> Regarding the explanation of the iteration algorithm, what you
>> ultimately want is to find a local or global maximum of the likelihood
>> of the observed series of results. There are standard methods for this
>> kind of optimization, the easiest one being maybe the standard gradient
>> descent. I used standard gradient descent for my implementation if I
>> recall correctly.
>
> Another very powerful technique to find the maximum likelihood is
> Minorization-Maximization. Implementation is very simple, and
> performance is tremendously better than gradient descent. I
> implemented this technique in an Elo-rating tool. You can find out
> more on that page:
> http://remi.coulom.free.fr/Bayesian-Elo/
> The links at the bottom of the page point to discussions and
> explanations of the algorithms.
So the Minorization-Maximization method is based on deriving lower and
upper bounds and employing them, yes? I must admit the paper to which
there was a link from the bottom of the page was too technical for me to
read through.
Is the performance better when compared to all forms of gradient
descent, or the basic one? Does your ELO function based likelihood have
multiple local maxima, or is there only one maximal point (in which case
the conjugate gradient descent could be quite efficient)?
I had never performance problems in our pool rating system---every
single game tended to change the overall system so little that gradient
descent went from the previous maximum to the new maximum rapidly.
My apologies for the apparent fact that the link to computer go is
becoming indirect.
--
Antti Huima (Mr.)
Director, Conformiq Tools
mobile: +358 40 528 8667
email: antti.huima@xxxxxxxxxxxxxxxxx
Conformiq Software Ltd.
Stella Terra, Lars Sonckin kaari 16
FIN-02600 Espoo, Finland
tel: +358 10 286 6300
fax: +358 10 286 6309
http://www.conformiq.com/
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