On Jul 24, 2009, at 12:04 PM, Isaac Deutsch <i...@gmx.ch> wrote:
To answer exactly, I need to know more about how you set up your
patterns. If every point gets one, and exactly one 3x3 pattern,
then fixing one 3x3 pattern is required. If some points have no 3x3
pattern, then you're implicitly fixing an "other" pattern to a
value of 1 and then no fixing of a 3x3 pattern is needed.
Just like 3x3 patterns, any orthogonal subset should have one value
fixed...
Does that help?
When teaching a position, all legal positions get a pattern. This
means positions that would be suicidal, ko, or aren't empty get no
pattern. All legal positions get exactly one 3x3 pattern assigned.
What do you mean with orthogonal subset?
Please tell me if you need more information.
Here's a really simple example:
Consider the following 4 patterns:
A: 3rd or 4th line
B: Any other line
X: No adjacent stones in 3x3
Y: Some adjacent stones in 3x3
Now let's arbitrarily assign the following probabilities for some
board position:
AX: 4%
AY: 3%
BX: 2%
BY: 1.5%
One solution for gammas would be:
A: 2
B: 1
X: 4
Y: 3
Another would be
A: 100
B: 50
X: 4
Y: 3
Another would be:
A: 2
B: 1
X: 100
B: 75
Because of how I defined the patterns, selection of A or B is
completely independent of the selection of X or Y. I think of the
feature set a={A,B} as orthogonal to b={X,Y}. Because of this
property, set a can have its gammas multiplied by an arbitrary
constant. Set b can also be multiplied by an arbitrary constant. If we
fix one member of each set to 1 (let's say A and Y), a unique solution
exists:
A: 1
B: 0.5
X: 1.333333333...
Y: 1
It sounds to me like your 3x3 patterns are an orthogonal set relative
to everything else. Because of that, you must pin on 3x3 gamma. You
may need to pin a few more... Note that any set of features where you
don't pick one for every legal move doesn't require pinning because
you implicitly have an "anything else" that is pinned to a value of 1.
I hope that helps!
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