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From: g2kafka@cdf.toronto.edu (Patrick Tierney)
Subject: Re: Arithmetic coding
Message-ID: <D569Kv.InH@cdf.toronto.edu>
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Organization: University of Toronto, Computing Disciplines Facility
References: <3j75gh$flm@tyranno.cs.duke.edu> <3jkhd7$qo0@news.bu.edu>
Date: Thu, 9 Mar 1995 12:05:17 GMT
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In article <3jkhd7$qo0@news.bu.edu>,
Karl Meissner <meissner@space.bu.edu> wrote:
>
>I have used floating point numbers as weights in classifiers and neural
>network GAs.  They seem to work fine for many hard classification problems.
>I don't encode them really.  Each weight is has one site on the
>genetic string.  I do crossover normally.  Mutation is simply a small
>probability that the weight at each site is replaced with a new random weight
>that is uniformly distributed between the min and max weight value.  
>
>I have seen references claiming that using a Gaussian distribution is
>better, either centered around the mid point, or the old weight value,
>but for my application uniform distributions worked fine.
>
Would anyone be able to explain to me how you can convert uniformly
distributed random numbers into normally distributed ones with a
given mean and standard deviation? I spent hours trying to figure
this out, but no luck. I have an application in which I would prefer
to constrain pairs of values to Gaussian distributions with different
means. In effect, for pair (a,b) with a,b in [0,1], generally a < b,
and the mean of a's distribution is 0.4, while the mean of b's is 0.6.
Std. dev = 0.1 in both cases and outliers are clamped at 0 and 1.

I tried using uniform distribution and waiting for the GA to discover
this relationship, but since my fitness function is actually user-
assessment, and this relationship is so crucial to the quality of
output, and yet only two of many variables being optimized overall,
I wanted to include this constraint in the genotype -> phenotype mapping.

Hope this isn't too far off topic.

Patrick Tierney
g2kafka@cdf.toronto.edu


