Evolutionary Polynomial Regression EPR

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Evolutionary Polynomial RegressionEPR
USERS MANUAL Stand-Alone Version 1.0 January
5th, 2006

• Prof. Orazio Giustolisi
• Prof. Dragan A. Savic

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Evolutionary Polynomial RegressionUSERS MANUAL
Outline

• Installing the toolbox
• How to construct the input file
• Starting with EPR
• During the execution
• Output data files
• References

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EPR can work with incomplete output data
record EPR identify the missing value as NaN
(Not a Number) EPR will reconstruct data, by
infilling missing data samples
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EPR perform a number of sub-runs
one for each different length of the model
structure
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Coefficient of Determination
Complexity Indicator (px) selected input values
(Xi) total number of available inputs
NO MOGA strategy
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NO MOGA strategy
Dynamical Modelling
Returned Model
Returned models with different prediction horizons
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MOGA strategy
PARETO Front
All the other diagrams will be displayed at the
end of the run
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EPR saves its results as Excel file (.xls)
located in your work directory

• input data file, bridata.xls
• EPR type Ysum(aiX1X2f(X1)f(X2))ao.
• Function type f(X) No function (Field n. 3).
• Objective function SSE (normal).
• No multi-objective search.
• Bias selected.
• Data scaled.
• Coefficient aj evaluated by a Least Square
  approach.

the returned output Excel file name
is brif00t000000SOGAb1s1LSresults.xls
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Yhat ? model-returned outputs on the training
set
X_scale ? input scale factors
Y_scale ? output scale factors
Ykhat_V ? model-returned outputs on the test set
SSE_V ? SSE value for each model computed on the
Ykhat_V predictions
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CoD_V ? CoD value for each model computed on the
Ykhat_V predictions
SSE ? SSE values for each model on the training
set (1-step ahead)
SSE_Naivy ? SSE value for the naive model
BIC ? BIC (Best Information Criterion) values
for each model on the training set
COD_Naivy ? CoD value for the naive model
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MSE ? Mean Squared Error values for each model
on the training set
AIC ? Akaikes Information Theoretic - AIC
values for each model on the training set
FPE ? Final Prediction Error of Akaike - FPE
values for each model on the training set
GCV ? Generalized Cross Validation - GCV values
for each model on the training set
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CoD ? CoD values for each model on the training
set (1-step ahead)
Y_rec ? Reconstructed data of the training set
Y_V_rec ? Reconstructed data of the test set
Models ? Explicit expression(s) of all the EPR
returned model(s)
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• Berardi, L., Savic, D.A., and Giustolisi, O,
  Investigation of burst-prediction formulas for
  water distribution systems by evolutionary
  computing, , CCWI International Conference,
  vol.2, pp.275-280, 2005. ISBN 09 5391 403 8
• Davidson, J.W., Savic, D.A., and Walters, G.A.,
  Method for Identification of explicit polynmial
  formulae for the friction in turbulent pipe flow,
  Journal of Hydroinformatics, IAHR-IWA, No.2,
  Vo.1, pp.115-126, 1999.
• Efron, B., Bootstrap Methods. Another Look at the
  Jackknife. The Ann. of Statist., 7, pp. 1-26,
  1979.
• Ljung, L., System Identification Theory for the
  User 2e. Prentice-Hall Inc., UpperSaddle River,
  New Jersey, USA, 1999.
• Giustolisi, O., Using genetic programming to
  determine Chèzy resistance coefficient in
  corrugated channels. Journal of Hydroinformatics,
  IAHR-IWA, Vol. 6, No 3, pp. 158173, 2004.
• Giustolisi, O., and Savic, D.A., A novel strategy
  to perform genetic programming Evolutionary
  Polynomial Regression. 6th Int. Conf. on
  Hydroinformatics, Singapore, Liong, Phoon
  Babovic (eds), World Scientific Publishing
  Company, vol.1, pp.787-794, 2004. ISBN
  981-238-787-0.
• Giustolisi, O., Savic, D.A., and Doglioni, A.,
  Data Reconstruction and Forecasting by
  Evolutionary Polynomial Regression, 6th Int.
  Conf. on Hydroinformatics, Singapore, Liong,
  Phoon Babovic (eds), World Scientific
  Publishing Company, vol.2, pp.1245-1252, 2004a.
  ISBN 981-238-787-0.
• Giustolisi, O., Savic, D.A., Doglioni A., and
  Laucelli, D., Knowledge discovery by Evolutionary
  Polynomial Regression, 6th Int. Conf. on
  Hydroinformatics, Singapore, Liong, Phoon
  Babovic (eds), World Scientific Publishing
  Company, vol.2, pp.1647-1654, 2004b. ISBN
  981-238-787-0.
• Giustolisi, O., Doglioni A., and Savic, D.A., A
  multi-model approach to analysis of environmental
  phenomena, invited in Special issue Complexity
  and Integrated Resources Management of
  Environmental Modelling Software Journal,
  Elsevier Science, Netherlands. In press.
• Giustolisi, O., Doglioni, A., Savic, D. and di
  Pierro, F., A new multi-objective strategy to
  support model selection for environmental
  modelling. Fourth International Workshop on
  Environmental Applications of Machine Learning
  (EAML), Bled, Slovenia, accepted for publication,
  2004d.
• Giustolisi, O., Doglioni A., and Laucelli, D.,
  Experimental determination of friction factor for
  corrugated drains, Water Management, ICE, 2005a
  (submitted for publication).
• Giustolisi, O, Laucelli, D., and Savic, D.A., A
  decision support framework for short-time
  rehabilitation planning in water distribution
  systems, CCWI International Conference, vol.1,
  pp.39-44, 2005b. ISBN 09 5391 402 X.
• Goldberg, D.E., Genetic Algorithms in Search,
  Optimization and Machine Learning. Addison
  Wesley, 1989.
• Golub, G.H., and Van Loan, C.F., Matrix
  Computations, The Johns Hopkins University Press
  Ltd., London, 1993.
• Keijzer, M., and Babovic, V., Dimensionally aware
  genetic programming, in Banzhaf, W., Daida, J.,
  Eiben, A. E., Garzon, M. H., Honavar, V.,
  Jakiela, M., Smith, R. E. (eds.), GECCO-99
  Proceedings of the Genetic and Evolutionary
  Computation Conference, July 13-17, 1999,
• Savic, D.A., Giustolisi, O., and Berardi, L.,
  Sewers failure analysis using evolutionary
  computing, Water Management Journal, ICE, UK,
  2005. In press.
• Tikhonov, A.N., Solution of incorrectly
  formulated problems and the regularization
  method, Doklady Akademii Nauk SSSR, No.151,
  pp.501-504, 1963.
• Van Veldhuizen, D.A., and Lamont, G.B.,
  Multi-objective Evolutionary Algorithms Analyzing
  the State-of-the-Art. Evolutionary Computation.
  Vol. 8(2), pp. 125-144, 2000.