Jump to: navigation, search

Automated Tuning

98 bytes removed, 13:20, 25 September 2020
no edit summary
<span id="Regression"></span>
[[FILE:Linear regression.svg|border|right|thumb|300px|[ Linear Regression] <ref>Random data points and their [ linear regression]. [ Created] with [ Sage] by Sewaqu, November 5, 2010, [ Wikimedia Commons]</ref> ]]
[ Regression analysis] is a [ statistical process] with a substantial overlap with machine learning to [ predict] the value of an [ Y variable] (output), given known value pairs of the X and Y variables. While [ linear regression] deals with continuous outputs, [ logistic regression] covers binary or discrete output, such as win/loss, or win/draw/loss. Parameter estimation in regression analysis can be formulated as the [ minimization] of a [ cost or loss function] over a [ training set] <ref>[ Loss function - Use in statistics - Wkipedia]</ref>, such as [ mean squared error] or [ cross-entropy error function] for [ binary classification] <ref>"Using [ cross-entropy error function] instead of [ sum of squares] leads to faster training and improved generalization", from [ Sargur Srihari], [ Neural Network Training] (pdf)</ref>. The minimization is implemented by [[Iteration|iterative]] optimization [[Algorithms|algorithms]] or [ metaheuristics] such as [ Iterated local search], [ Gauss–Newton algorithm], or [ conjugate gradient method].
<span id="LinearRegression"></span>
==Linear Regression==
{||-| style="vertical-align:top;" | The supervised problem of regression applied to [[Automated Tuning#MoveAdaption|move adaptation]] was used by [[Thomas Nitsche]] in 1982, minimizing the [ mean squared error] of a cost function considering the program’s and a grandmaster’s choice of moves, as mentioned, extended by [[Tony Marsland]] in 1985, and later by the [[Deep Thought]] team. Regression used to [[Automated Tuning#ValueAdaption|adapt desired values]] was described by [[Donald H. Mitchell]] in his 1984 masters thesis on evaluation features in [[Othello]], cited by [[Michael Buro]] <ref>[[Michael Buro]] ('''1995'''). ''[ Statistical Feature Combination for the Evaluation of Game Positions]''. [ JAIR], Vol. 3</ref> <ref>[[Donald H. Mitchell]] ('''1984'''). ''Using Features to Evaluate Positions in Experts' and Novices' Othello Games''. Masters thesis, Department of Psychology, [[Northwestern University]], Evanston, IL</ref>. [[Jens Christensen]] applied [ linear regression] to chess in 1986 to learn [[Point Value|point values]] in the domain of [[Temporal Difference Learning|temporal difference learning]] <ref>[[Jens Christensen]] ('''1986'''). ''[ Learning Static Evaluation Functions by Linear Regression]''. in [[Tom Mitchell]], [[Jaime Carbonell]], [[Ryszard Michalski]] ('''1986'''). ''[ Machine Learning: A Guide to Current Research]''. The Kluwer International Series in Engineering and Computer Science, Vol. 12</ref>. | [[FILE:Linear regression.svg|border|left|thumb|baseline|300px|[ Linear Regression] <ref>Random data points and their [ linear regression]. [ Created] with [ Sage] by Sewaqu, November 5, 2010, [ Wikimedia Commons]</ref> ]] |}
<span id="LogisticRegression"></span>
==Logistic Regression==
{ [[FILE:SigmoidTexelTune.gif|border|right|thumb|300px|link=|[ Logistic function] <ref>[ log-linear 1 / (1 + 10^(-| styles/4)) , s="vertical-align10 to 10] from [https:top;" // Wolfram| Alpha]</ref> ]]  Since the relationship between [[Pawn Advantage, Win Percentage, and Elo|win percentage and pawn advantage]] is assumed to follow a [ logistic model], one may treat static evaluation as [[Neural Networks#Perceptron|single-layer perceptron]] or single [ neuron] [[Neural Networks|ANN]] with the common [ logistic] [ activation function], performing the perceptron algorithm to train it <ref>[ Re: Piece weights with regression analysis (in Russian)] by [[Fabien Letouzey]], [[CCC]], May 04, 2015</ref>. [ Logistic regression] in evaluation tuning was first elaborated by [[Michael Buro]] in 1995 <ref>[[Michael Buro]] ('''1995'''). ''[ Statistical Feature Combination for the Evaluation of Game Positions]''. [ JAIR], Vol. 3</ref>, and proved successful in the game of [[Othello]] in comparison with [[Mathematician#RFisher|Fisher's]] [ linear discriminant] and quadratic [ discriminant] function for [ normally distributed] features, and served as eponym of his Othello program ''Logistello'' <ref>[ LOGISTELLO's Homepage]</ref>. In computer chess, logistic regression was applied by [[Arkadiusz Paterek]] with [[Gosu]] <ref>[[Arkadiusz Paterek]] ('''2004'''). ''Modelowanie funkcji oceniającej w grach''. [[University of Warsaw]], [ zipped ps] (Polish, Modeling of an evaluation function in games)</ref>, later proposed by [[Miguel A. Ballicora]] in 2009 as used by [[Gaviota]] <ref>[ Re: Insanity... or Tal style?] by [[Miguel A. Ballicora]], [[CCC]], April 02, 2009</ref>, independently described by [[Amir Ban]] in 2012 for [[Junior|Junior's]] evaluation learning <ref>[[Amir Ban]] ('''2012'''). ''[ Automatic Learning of Evaluation, with Applications to Computer Chess]''. Discussion Paper 613, [ The Hebrew University of Jerusalem] - Center for the Study of Rationality, [ Givat Ram]</ref>, and explicitly mentioned by [[Álvaro Begué]] in a January 2014 [[CCC]] discussion <ref>[ Re: How Do You Automatically Tune Your Evaluation Tables] by [[Álvaro Begué]], [[CCC]], January 08, 2014</ref>, when [[Peter Österlund]] explained [[Texel's Tuning Method]] <ref>[ The texel evaluation function optimization algorithm] by [[Peter Österlund]], [[CCC]], January 31, 2014</ref>, which subsequently popularized logistic regression tuning in computer chess. [[Vladimir Medvedev|Vladimir Medvedev's]] [[Point Value by Regression Analysis]] <ref>[ Определяем веса шахматных фигур регрессионным анализом / Хабрахабр] by [[Vladimir Medvedev|WinPooh]], April 27, 2015 (Russian)</ref> <ref>[ Piece weights with regression analysis (in Russian)] by [[Vladimir Medvedev]], [[CCC]], April 30, 2015</ref> experiments showed why the [ logistic function] is appropriate, and further used [ cross-entropy] and [ regularization].| [[FILE:SigmoidTexelTune.gif|border|left|thumb|baseline|300px|link=|[ Logistic function] <ref>[ log-linear 1 / (1 + 10^(-s/4)) , s=-10 to 10] from [ Wolfram|Alpha]</ref> ]] |}

Navigation menu