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< xml version 1.0 > <!-- --> <!-- > <!--Copyright (c) 2003 Nokia. All rights reserved. --> <!-- > <!--The contents of this document are provided as is . --> <!--No warranties of any kind, either express or implied, --> <!--including, but not limited to, the implied warranties --> <!--of merchantability and tness for a particular --> <!--purpose, are made in relation to the accuracy, --> <!--reliability or contents of this document. Nokia --> <!--reserves the right to revise this document or --> <!--withdraw it at any time without prior notice. --> <!-- > <!-- --> <!-- --> <!-- > <!--Version 1.0 20 Mar 2003 --> <!-- > <!-- --> <RDF xmlns http://www.w3.org/1999/02/22-rdf-syntax-ns# xmlns:rdf http://www.w3.org/1999/02/22-rdf-syntax-ns# xmlns:prf http://www.wapforum.org/UAPROF/ccppschema20000405# > <rdf:Description ID Nokia3650 > <prf:component> <rdf:Description ID HardwarePlatform > <rdf:type resource http://www.wapforum.org/UAPROF/ ccppschema-20000405#HardwarePlatform /> <prf:ScreenSize>176 208</prf:ScreenSize> <prf:Model>Nokia3650</prf:Model> <prf:ScreenSizeChar>15 6</prf:ScreenSizeChar> <prf:ColorCapable>Yes</prf:ColorCapable> <prf:BitsPerPixel>12</prf:BitsPerPixel> <prf:TextInputCapable>Yes</prf:TextInputCapable> <prf:ImageCapable>Yes</prf:ImageCapable> <prf:Keyboard>PhoneKeypad</prf:Keyboard> <prf:NumberOfSoftKeys>2</prf:NumberOfSoftKeys> <prf:Vendor>Nokia</prf:Vendor> <prf:SoundOutputCapable>Yes</prf:SoundOutputCapable> <prf:StandardFontProportional>Yes</prf:StandardFontProportional> <prf:PixelsAspectRatio>1 1</prf:PixelsAspectRatio> <prf:OutputCharSet>

As mentioned earlier, one of the potential applications of symbolic regression via genetic programming is sensitivity analysis of nonlinear problems with a potentially large set of candidate input variables These kinds of problems are frequently encountered in the chemical processing industry Sensitivity analysis is also called the problem of input variables selection in machine learning terminology Many problems in the chemical industry are of this type Usually, there are a large number of measurements available at a plant, many of which are redundant or not relevant to the problem that one is trying to solve Engineering knowledge about the problem is usually the rst step in trying to narrow down the number of inputs Sensitivity analysis generates a ranking of all the input variables in terms of how important they are in modeling a certain unknown process.

In linear problems the sensitivity of an input variable is related to the derivative of the output with respect to that variable In nonlinear problems, however, the derivative becomes a local property and has to be integrated over the entire input domain to qualify as sensitivity Since this approach is not really practical in a genetic programming context, the sensitivity of a given input variable can be related to its tness in the population of equations The rationale is that important input variables will be used in equations that have a relatively high tness So, the tness of input variables is related to the tness of the equations they are used in There is, however, a question with respect to credit assignment, that is, what portion of the tness goes to which variable in the equation.

Example 16: The binary erasure channel (BEC) In its most basic form, the transmission of binary information involves sending two different waveforms to identify the symbols 0 and 1 At the receiver, normally an optimum detection operation is used to decide whether the waveform received, affected by ltering and noise in the channel, corresponds to a 0 or a 1 This operation, often called matched lter detection, can sometimes give an indecisive result If con dence in the received symbol is not high, it may be preferable to indicate a doubtful result by means of an erasure symbol Correction of the erasure symbols is then normally carried out by other means in another part of the system In other scenarios the transmitted information is coded, which makes it possible to detect if there are errors in a bit or packet of information.

The easiest approach is to distribute the credit (the tness of the equation) equally over all variables present Provided the population size is large enough, we can take the tness of.