Author: Heiner Marxen
Date: 06:15:44 07/01/02
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On June 30, 2002 at 12:51:20, Uri Blass wrote: >I believe that a good program for this task can help me to improve my >chess program. > >Note that the formula does not have to be linear. Being linear helps, though. In that case the math is simple enough that you may even derive the formula yourself (I once did so). It is a linear regression. >The test for the quality of the prediction is E((y-y')^2) when y' is the >prediction for y based on the varaibles x1,x2,x3,x4,x5 A standard measure of "distance", ok. >A good program for this task may get a file of integers and give me an estimate >for the 6n's integer in the file based on the previous 5 integers. > >It is better if the program gives me not only the prediction but also an >estimate for the distribution of the error. > >Uri I think, I can quite well imagine what you want to do. It is "a sort of" an eval-function. I once tried to do something quite similar: Starting with a chess position, and several indicator values derived from it (like number of pieces, being in check etc) I tried to find an estimator for y = siye of search tree which will be spanned by chest to analyse that chess board for a mate in 4. I derived a large set of test data (measured facts). The linear regression insisted on some of the weights to be negative, which I did not believe should be negative. Also, the estimates were not good enough for my purpose. Then I added some non-linear terms (quadratic ones), as if they were independant linear terms. Again I got some negative weights, I was not willing to accept. Still, quality of the result was not good enough. I suspect that chess boards, together with a few simple derived attributes, do not give smooth enough function to be captured by linear functions. There is however some literature about automatic tuning of evaluation functions. The methods used there might be of interist for you. Otherwise I would propose to try a neural network. Train it with your facts, and have a look at how good it does. Try more facts, look at that results. May be you find something close enough. Then either stick to a neural net simulation, or use it as a basis to derive a mathematical model with some parameters. Start over with this model, where your x-Vector are now the parameters of the model. Try a linear regression. Repeat until exhausted... ;-) Cheers, Heiner
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