RE: [computer-go] RE: Bayesian Pattern Ranking for MovePredictionin the Game of Go

["Thore Graepel" <thoreg@xxxxxxxxxxxxx>]

Hi John,

Thanks for your feedback

> Btw, I found some typos in the paper:
>   the definition of h_a should list the domain as \cal{D}, not
> \hat{\cal{G}}.

Yep, you are right.

>   at the bottom of that page you say patterns are added to B,
>   if they're not new.

Yep, that's a mistake.

> I do have some problems understanding section 3
> (not having a good statistics background)
> 
> What is diag()?

The "argument" of the Gaussian density requires a matrix, so diag()
converts a vector to the corresponding diagonal matrix with the diagonal
elements being the elements of the vector. 

> In P(v|c,s), what does random variable s represent?
> Is it dependent on v or not?

s is the vector of score values for each pattern. The expert is assumed
to prefer moves of high value, so p(v|s,c) is the distribution over
moves given the scores of all moves available in that particular board
position. Think of it this way: the probability that a move v is played
depends on the score values s_i of all the moves available in that
position (the one with the highest value s_i being the most likely one).
Now, we observe a move v^* that is played and - using Bayes law - can
update the values of this move and the available alternative moves. Of
course, the value of v^* would increase (because it was chosen by the
expert) and the values of the alternative moves would decrease (because
they were rejected by the expert)

> Are latent scores depending only on a pattern, or also in the context
> they occur in?

We are currently only taking into account the local pattern itself.
However, we are in the process of including a few bits of context
information such as active ko, distance from boarder, liberties of
chains involved etc.

> What does random variable x represent in equation (1)?
> In the first line of (1), are the x() functions the random variables
over
> which the probability is defined?

Suppose s_i represents the (unknown) mean value of pattern i. Then x_i
represents its value for an individual board position for an individual
player. The extra variance of x_i (beta^2) captures the fact that even
if we knew the patterns score value s_i, its actual score would vary
from position to position due to changes in context and player
preference. Hence, x_i varies around its mean s_i.

Here is how you would sample from the distribution p(v|c,s) over moves
for a given position if you knew the values s_i for each pattern i:
Create one Gaussian bump N_i for each available pattern. Each of these
Gaussians is centred at the corresponding s_i and has variance beta^2.
Now sample one instance from each of these Gaussians. If x_j is the
biggest number sampled then pattern j is chosen.
 
> As you can tell, I'd love to see this section expanded and accessible
> to statistics dummies like me:)
> I'll try to read some of Tom Minka's thesis to see if that clarifies
> matters.

Minka's thesis is not exactly an easy ride... Have fun.

> 
> Have you asked Frank how his prediction relates to yours?

>>From what I know, Frank has results for one particular game on his page,
see http://www.moyogo.com/joseki.htm

If these results extend to more games (we tested on 500), which were not
in the training or harvesting sample, I would say that Frank's results
are considerably better than ours. This is not surprising considering
that he learns on 500,000 (versus our 20,000) and uses context for his
smaller patterns (which we have not done so far). Also, in one mail
Frank cautioned against using the very game collection (GoGoD) that we
have been using (Frank, could you explain, why?)

There are many things left for us to try out because we only started
this project four weeks ago...

> 
> And is any of the software that you wrote for harvesting and learning
> available?

We will be thinking about this.

Thore
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