On Dec 20, 2007 11:43 AM, Jason House <[EMAIL PROTECTED]> wrote:
> I seem to have more time to think than to code lately. I believe I've
> derived an alternate update method.
>
Thinking more, I realize I messed up a three things...
For one, Newton-Raphson requires
new gamma - gamma = -*L/**L
instead of
new gamma - gamma = *L/**L
Another,
1/sigma^2 = -**L
instead of
1/sigma^2 = **L
Finally,
**L = sum[ (selection probability)^2 ] - wins
instead of
**L = (estimated wins)^2 - wins
> Using Newton-Raphson method, I derived
> fractional change = (estimation error) * (fractional uncertainty)^2
> new gamma = gamma * (1 + fractional change)
>
A less intuitive form is:
> fractional change = (wins-expected wins) / (expected wins^2 - wins)
> Using Remi's notation, expected wins = gamma*sum(C/E)
>
This becomes:
fractional change =
( wins - sum(selection probability) )
/ ( wins - sum((selection probability)^2) )
selection probability = gamma*C/E
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