[computer-go] ELO Ratings of move pattern

[Rémi Coulom]

Jason House wrote:
>
>
> On Dec 12, 2007 3:09 PM, Álvaro Begué <alvaro.begue at gmail.com 
> <mailto:alvaro.begue at gmail.com>> wrote:
>
>
>
>     On Dec 12, 2007 3:05 PM, Jason House <jason.james.house at gmail.com
>     <mailto:jason.james.house at gmail.com>> wrote:
>
>
>
>         On Dec 12, 2007 2:59 PM, Rémi Coulom
>         <Remi.Coulom at univ-lille3.fr
>         <mailto:Remi.Coulom at univ-lille3.fr>> wrote:
>
>             > Do you mean a plot of the prediction rate with only the
>             > gamma of interest varying?
>
>             No the prediction rate, but the probability of the
>             training data. More
>             precisely, the logarithm of that probability. 
>
>
>         I still don't know what you mean by this.
>
>
>     He probably should use the word "likelihood" instead of
>     "probability". http://en.wikipedia.org/wiki/Likelihood_function
>
>
> Clearly I'm missing something, because I still don't understand.  
> Let's take a simple example of a move is on the 3rd line and has a 
> gamma value of 1.75.  What is the equation or sequence of discrete 
> values that I can take the derivative of?
>
> Doing conditional probabilities based on "move is on 3rd line" and 
> "move is selected" (AKA pure training data) seems to yield a fixed 
> value rather than something approximating a normal distribution.

Consider, in the Elo rating analogy, a player with a win and a loss to 
player whose gamma is 1. There you have P(gamma)=gamma/(1+gamma)², whose 
maximum is at gamma = 1. It is that probability that I am talking about. 
It is the probability that is maximized by the MM algorithm.

Rémi