I am also adding some material here about influence.
Bill
Influence in go
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Bill Spight
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Influence in go
This is a place for talking about influence in go. I have submitted a presentation for the go symposium this weekend. Any questions or comments that people have can go here.
I am also adding some material here about influence.
Bill
I am also adding some material here about influence.
Bill
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins
Visualize whirled peas.
Everything with love. Stay safe.
At some point, doesn't thinking have to go on?
— Winona Adkins
Visualize whirled peas.
Everything with love. Stay safe.
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hyperpape
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Re: Influence in go
Where is my watch-checking emoticon?Bill Spight wrote:I am also adding some material here about influence.
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Bill Spight
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Re: Influence in go
The presentation is Saturday at 1:00 p. m. EDT. Check back then. (I wanted to start this topic so the organizers would have the URL.)
I may post some things in advance.
Meanwhile, see this topic: http://www.lifein19x19.com/forum/viewto ... =15&t=1341
I may post some things in advance.
Meanwhile, see this topic: http://www.lifein19x19.com/forum/viewto ... =15&t=1341
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins
Visualize whirled peas.
Everything with love. Stay safe.
At some point, doesn't thinking have to go on?
— Winona Adkins
Visualize whirled peas.
Everything with love. Stay safe.
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EdLee
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Bill Spight
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Re: Influence in go
In the decades since Zobrist introduced an influence function in his go program, go programmers and others interested in influence have not come to a consensus about how to estimate it. I don't know, either.
However, I have come up with a first approximation, which looks promising.
This diagram shows part of the hypothesized influence of the Black stone. The four adjacent points each have influence of 1, the points two steps away have influence of ½, those three steps away have influence of ¼, those four steps away have influence of 1/8, etc. (I did not show the influence past three steps.)
This calculation must be modified to reflect the strength of the stones. The estimate for the tengen stone is almost 16 pts., but that is probably too high. It is a good approximation for a 4-4 stone, however, yielding a komi of 8, which is pretty close.
However, I have come up with a first approximation, which looks promising.
This diagram shows part of the hypothesized influence of the Black stone. The four adjacent points each have influence of 1, the points two steps away have influence of ½, those three steps away have influence of ¼, those four steps away have influence of 1/8, etc. (I did not show the influence past three steps.)
This calculation must be modified to reflect the strength of the stones. The estimate for the tengen stone is almost 16 pts., but that is probably too high. It is a good approximation for a 4-4 stone, however, yielding a komi of 8, which is pretty close.
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins
Visualize whirled peas.
Everything with love. Stay safe.
At some point, doesn't thinking have to go on?
— Winona Adkins
Visualize whirled peas.
Everything with love. Stay safe.
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Bill Spight
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Re: Influence in go
Here is an example of it in use.
Estimated count: 0.7 for White.
indicates a neutral point.
Here I considered a point likely area if its net influence was 1/3 or greater in favor of one player. Among the open points, there are 82 likely Black points and 89 likely White points.
This function does not handle edges or corners well. The 3 neutral points in the bottom right, bottom left, and top left corners probably belong to the surrounding group. The points in the top right corner and top side are another matter. There is room for an invasion.
Estimated net count: 4.1 for Black.
82 likely Black points, 79 likely White points.
Net territory estimate: 5.4 (for Black).
Final diagram:
I chose the ranges {-1, -1/3} for White influence, {-1/3, 1/3} for neutral points, and {1/3, 1} for Black influence as a simple tripartite division. A division into points with net Black influence and net White influence seems too precise to me.
Even though the overall net influence is 5.4 for Black, there are 84 open points in the Black range and 84 open points in the White range. (There are 92 points in the neutral range.) 19 points are in the opposite area at the end of the game, so that's an error rate for specific points of about 11%.
The count estimate of 5.4 for Black seems reasonable, given the final score of +9 and the fact that Black has sente.
Game Record:
Estimated count: 0.7 for White.
indicates a neutral point.Here I considered a point likely area if its net influence was 1/3 or greater in favor of one player. Among the open points, there are 82 likely Black points and 89 likely White points.
This function does not handle edges or corners well. The 3 neutral points in the bottom right, bottom left, and top left corners probably belong to the surrounding group. The points in the top right corner and top side are another matter. There is room for an invasion.
Estimated net count: 4.1 for Black.
82 likely Black points, 79 likely White points.
Net territory estimate: 5.4 (for Black).
Final diagram:
I chose the ranges {-1, -1/3} for White influence, {-1/3, 1/3} for neutral points, and {1/3, 1} for Black influence as a simple tripartite division. A division into points with net Black influence and net White influence seems too precise to me.
Even though the overall net influence is 5.4 for Black, there are 84 open points in the Black range and 84 open points in the White range. (There are 92 points in the neutral range.) 19 points are in the opposite area at the end of the game, so that's an error rate for specific points of about 11%.
The count estimate of 5.4 for Black seems reasonable, given the final score of +9 and the fact that Black has sente.
Game Record:
Last edited by Bill Spight on Mon Aug 06, 2012 1:18 pm, edited 10 times in total.
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins
Visualize whirled peas.
Everything with love. Stay safe.
At some point, doesn't thinking have to go on?
— Winona Adkins
Visualize whirled peas.
Everything with love. Stay safe.
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cyclops
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Re: Influence in go
This Spight series: 4, 8, 11 ... how does it continue. If n is the number of terms then Spight Influence = 16 - 8*(n+2)/2^n . As Bill stated this grows quickly to 16 for large n.Bill Spight wrote: .... This diagram shows part of the hypothesized influence of the Black stone. The four adjacent points each have influence of 1, the points two steps away have influence of ½, those three steps away have influence of ¼, those four steps away have influence of 1/8, etc. (I did not show the influence past three steps.) ....
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RobertJasiek
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Re: Influence in go
What is the purpose of still pursuing influence as a visual / light / lattice distance model? If calculation time complexity is important, then even Wolf's stone proximity model seems a slightly better alternative but also has too little relation to reality.
However, all those naive models fail to describe what influence actually is: degrees of connectivity, life and territory (see Joseki 2 Strategy). For this precise model, the calculation time complexity is high (at least, if exact values for the degrees are sought).
For the sake of having good purposes, a small calculation time complexity and a close relation to reality, there is the mobility difference concept (see in the aforementioned source; variations of the concept are straightforward).
So let me ask again: What are the purposes of Bill's model? Why would they not be better fulfilled by my models? How to overcome the missing relation between Bill's model and the basic influence aspects connection, life, territory? Could a model not inherently relying on those basic aspects have justification (other than as a pure thought experiment) in comparison to models relying on them?
Considering the mighty threat title, let me make it clear again: Influence in go is (in its precise and general form) defined in terms of either player's degrees of n-connectivity, m-life and t-territory, per intersection and due to stones as sources of influence.
However, all those naive models fail to describe what influence actually is: degrees of connectivity, life and territory (see Joseki 2 Strategy). For this precise model, the calculation time complexity is high (at least, if exact values for the degrees are sought).
For the sake of having good purposes, a small calculation time complexity and a close relation to reality, there is the mobility difference concept (see in the aforementioned source; variations of the concept are straightforward).
So let me ask again: What are the purposes of Bill's model? Why would they not be better fulfilled by my models? How to overcome the missing relation between Bill's model and the basic influence aspects connection, life, territory? Could a model not inherently relying on those basic aspects have justification (other than as a pure thought experiment) in comparison to models relying on them?
Considering the mighty threat title, let me make it clear again: Influence in go is (in its precise and general form) defined in terms of either player's degrees of n-connectivity, m-life and t-territory, per intersection and due to stones as sources of influence.
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Bill Spight
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Re: Influence in go
The main purpose is to estimate the current count. A secondary purpose is to estimate the degree to which each point currently "belongs" to either player. (Note that these are not probability estimates.)RobertJasiek wrote:So let me ask again: What are the purposes of Bill's model?
No reason at all.Why would they not be better fulfilled by my models?
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins
Visualize whirled peas.
Everything with love. Stay safe.
At some point, doesn't thinking have to go on?
— Winona Adkins
Visualize whirled peas.
Everything with love. Stay safe.
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RobertJasiek
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Re: Influence in go
I recommend t-territory for that purpose.Bill Spight wrote:The main purpose is to estimate the current count.
This can mean connected, alive (if a stone is placed there) or territory. I recommend my model:) Some intersections will be neutral for some degree(s). E.g., an intersection can be neutral with respect to connectivity if either player's stone played there would be 0-connected to some friendly stones.A secondary purpose is to estimate the degree to which each point currently "belongs" to either player.
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Bill Spight
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Re: Influence in go
Example 2.
Estimated count: 0.2 for Black.
Estimated net count: 9.3 for White
Given the final result, the estimation of -9.3 seems too big for White.
Game Record:
{More to come}
Estimated count: 0.2 for Black.
Estimated net count: 9.3 for White
Given the final result, the estimation of -9.3 seems too big for White.
Game Record:
{More to come
}
Last edited by Bill Spight on Mon Aug 06, 2012 1:58 pm, edited 4 times in total.
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins
Visualize whirled peas.
Everything with love. Stay safe.
At some point, doesn't thinking have to go on?
— Winona Adkins
Visualize whirled peas.
Everything with love. Stay safe.
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topazg
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Re: Influence in go
I'm following this with some interest, but I do have an observation of concern on this statement (and others like it) - Without access to the discussions between professionals on the game in question, how do we know that this isn't an accurate assumption, where White's theoretical advantage was slowly removed by suboptimal play?Bill Spight wrote:Given the final result, the estimation of -9.3 seems too big for White.
I think we'd need a considerable sample size before its possible to start evaluating the accuracy of the estimations - even then, there are lots of other factors - if your model overestimates certain situations and underestimate others, you could end up predicting jigo correctly, to feel that the model performed well, when it actually performed equally badly in both directions. I'm not saying the model _did_ perform badly, but it can be hard to separate the possibilities without really extensive examples putting models against games and observing the way the model changed over time in the game. It would be quite interesting to see how the evaluation changed every 6 moves from move 60 to the end for example, and comparing moyo games to territorial games where neither side made any clear blunder, so that the behaviour of your model over time in different situations can be compared.
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RobertJasiek
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Re: Influence in go
By doing positional judgements...! :)topazg wrote:how do we know that this isn't an accurate assumption
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topazg
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Re: Influence in go
Wasn't that rather my point?RobertJasiek wrote:By doing positional judgements...!topazg wrote:how do we know that this isn't an accurate assumption
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Bill Spight
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Re: Influence in go
I think that we can trust pro play more than we can trust the estimates.topazg wrote:I'm following this with some interest, but I do have an observation of concern on this statement (and others like it) - Without access to the discussions between professionals on the game in question, how do we know that this isn't an accurate assumption, where White's theoretical advantage was slowly removed by suboptimal play?Bill Spight wrote:Given the final result, the estimation of -9.3 seems too big for White.
My purpose here is not statistical. The estimates are both crude and biased.I think we'd need a considerable sample size before its possible to start evaluating the accuracy of the estimations - even then, there are lots of other factors - if your model overestimates certain situations and underestimate others, you could end up predicting jigo correctly, to feel that the model performed well, when it actually performed equally badly in both directions.
I am.I'm not saying the model _did_ perform badly,
There are known problems with it.
Influence in this approach is proportional to the strength of the stones. Dead stones exert no influence, half-dead stones exert half influence, etc. In general, we have no way of determining the strength of stones.
Influence needs to be corrected for overconcentration. The whole board calculations that I actually use do so by capping Black or White influence for each point at 1. In theory, that is not enough of a correction. However, since stones strengthen each other, fully correcting for overconcentration without correcting for strengthening would yield poor results. Besides, it is not like either correction is known.
Interaction with the edge and corner is complex. You can clearly see in both games how the corner points are considered neutral. Normally, we expect the edge to increase the influence of a stone. OTOH, if the opponent gets an effective play near the same edge point, its influence is enhanced, as well.
This influence function is also a gote function. Sente has an effect. In a sense, it collapses the influence function, but its effect is not huge. Still, to apply the function, you should correct for sente, if possible. (For instance, in the second game, Black has sente against the top left corner. I know that, and you know that, but does the average 5 kyu know that? Does a computer program know that?)
The idea of making evaluations at different points in the game is a good one. I chose around move 100 in these games because of Jowa's advice to evaluate the position at moves 30, 50, and 100. I think he stopped there because later in the game it is more difficult to overcome an inferior position against an equal opponent.but it can be hard to separate the possibilities without really extensive examples putting models against games and observing the way the model changed over time in the game. It would be quite interesting to see how the evaluation changed every 6 moves from move 60 to the end for example, and comparing moyo games to territorial games where neither side made any clear blunder, so that the behaviour of your model over time in different situations can be compared.
I'll go back and add some estimates at earlier points in the example games.
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins
Visualize whirled peas.
Everything with love. Stay safe.
At some point, doesn't thinking have to go on?
— Winona Adkins
Visualize whirled peas.
Everything with love. Stay safe.