Re: computer-go: A little Arithmetic

["Ran Xiao" <ranxiao@xxxxxxxxxxxx>]

I may need to clarify the board representation method in my mind:
    1. Horizontal coordinates are A, B, C, ...;
    2. Vertical coordinates are a, b, c, ...;
    3. An attribute of board position is the combination of the horizontal
       and vertical position, such as Aa, Bc, etc;
    4. Input variables are the attributes (361 total);
    5. The values of an attribute are {B, W, E};
    6. Always in B's move;
    7. Classification or machine learning is based on game's finial result
{W, T, L}.

For example, W won a game, a data record for B's move may look like:
  E,E,E,B,B,W,...,E, L.
A rule for a position, say Aa, should play or not may look like:
  If Aa = E,  Ab = W,  Bb = W => Class = L;
Which states B should not play Aa position, if the conditions are satisfied.

I did not see the above primitive representation is not enough.

Weimin

----- Original Message -----
From: "Nicol N. Schraudolph" <nic@xxxxxxxxxxxxxxxxx>
To: <computer-go@xxxxxxxxxxxxxxxxx>
Sent: Thursday, November 16, 2000 4:55 AM
Subject: Re: computer-go: A little Arithmetic


> If board configurations can be generalized, there should exit a learning
> system that can generalize these configurations. The real odd balls can be
> dealt by 9K programs. If board configuration can not be generalized, no
> learning scheme will work.

Generalizability is not a property of board positions per se, it is
a property of *representations* of board positions.  Learning can only
formulate *short* statements about Go from a million games; to get
anywhere your hypothesis space must contain short statements that
generalize well, i.e., capture useful regularities about Go.  The
primitive representation of board positions you proposed does not
contain such statements.

Example: "don't peep where you can cut" is a short statement that
generalizes well; given good definitions of "peep" and "cut" as
primitives (wherein much trickery of course lies buried), learning
such a rule is easy.  Try to express this rule in terms of raw board
positions, and the universe is not big enough to hold its description,
let alone learn it.

- nic

--
    Dr. Nicol N. Schraudolph
    IDSIA, Galleria 2
    CH-6928 Manno, Switzerland
    http://www.idsia.ch/~nic/