From 5d8bbb2f3748e721d57dff4f3048f226b98b4fc7 Mon Sep 17 00:00:00 2001
From: Petr Baudis
Date: Thu, 11 Mar 2010 21:37:45 +0100
Subject: [PATCH] tex: Strength Estimator cleanups

tex/gostyle.tex  44 +++++++++++++++++++++++++
1 file changed, 25 insertions(+), 19 deletions()
diff git a/tex/gostyle.tex b/tex/gostyle.tex
index e6bd684..2632628 100644
 a/tex/gostyle.tex
+++ b/tex/gostyle.tex
@@ 738,29 +738,34 @@ The neural network part of the project is written using the libfann C library\ci
First, we have used our framework to analyse correlations of pattern vectors
and playing strength. Like in other competitively played board games, Go players
receive realworld rating based on tournament games, and rank based on their
rating.\footnote{Elolike rating system \cite{GoR} is usually used,
+receive realworld {\em rating number} based on tournament games,
+and {\em rank} based on their rating.%
+\footnote{Elolike rating system \cite{GoR} is usually used,
corresponding to even win chances for game of two players with the same rank,
and about 2:3 win chance for stronger in case of one rank difference.}%
\footnote{Professional ranks and dan ranks in some Asia countries may
be assigned differently.} The amateur ranks range from 30kyu (beginner) to
1kyu (intermediate) and then follows 1dan to 7dan (9dan in some systems;
toplevel player). Multiple independent realworld ranking scales exist
(geographically based) and online servers maintain their own user ranking;
the difference can be up to several stones.

As the source game collection, we use Go Teaching Ladder
reviews\footnote{The reviews contain comments and variations  we consider only the actual played game.}
+be assigned differently.}
+The amateur ranks range from 30kyu (beginner) to 1kyu (intermediate)
+and then follows 1dan to 7dan\footnote{9dan in some systems.} (toplevel player).
+Multiple independent realworld ranking scales exist
+(geographically based), also online servers maintain their own user ranking;
+the difference between scales can be up to several ranks and the rank
+distributions also differ. \cite{RankComparison}
+
+As the source game collection, we use Go Teaching Ladder reviews archive%
+\footnote{The reviews contain comments and variations  we consider only the main
+variation with the actual played game.}
\cite{GTL}  this collection contains 7700 games of players with strength ranging
from 30k to 4d; we consider only even games with clear rank information, and then
randomly separate 770 games as a testing set. Since the rank information is provided
by the users and may not be consistent, we are forced to take a simplified look
at the ranks, discarding the differences between various systems and thus increasing
error in our model.\footnote{Since
our results seem satisfying, we did not pursue to try another collection;
+from 30kyu to 4dan; we consider only even games with clear rank information,
+and then randomly separate 770 games as a testing set.
+Since the rank information is provided by the users and may not be consistent,
+we are forced to take a simplified look at the ranks,
+discarding the differences between various systems and thus somewhat
+increasing error in our model.\footnote{Since our results seem satisfying,
+we did not pursue to try another collection;
one could e.g. look at game archives of some Go server.}
First, we have created a single pattern vector for each rank, from 30k to 4d;
+First, we have created a single pattern vector for each rank, from 30kyu to 4dan;
we have performed PCA analysis on the pattern vectors, achieving nearperfect
rank correspondence in the first PCA dimension%
\footnote{The eigenvalue of the second dimension was four times smaller,
@@ 768,10 +773,11 @@ with no discernable structure revealed within the lowerorder eigenvectors.}
(figure \ref{fig:strength_pca}).
We measure the accuracy of strength approximation by the first dimension
using Pearson's $r$ (see \ref{pearson}), yielding satisfying value $r=0.979$.
+using Pearson's $r$ (see \ref{pearson}), yielding quite satisfying value of $r=0.979$
+implying extremely strong correlation.
Using the eigenvector position directly for classification
of players within the test group yields MSE TODO, thus providing
reasonably satisfying accuracy.
+reasonably satisfying accuracy by itself.
To further enhance the strength estimator accuracy,
we have tried to train a NN classifier on our train set, consisting

2.10.5.GIT