Rio de Janeiro, 11 de Dezembro de 2009. A New Model for Credit Approval Problems: A Neuro-Genetic System with Quantum Insp...
<ul><ul><li>Introduction </li></ul></ul><ul><ul><li>The Problem </li></ul></ul><ul><ul><li>The Algorithm </li></ul></ul><u...
<ul><ul><li>Introduction </li></ul></ul><ul><ul><li>The Problem </li></ul></ul><ul><ul><li>The Algorithm </li></ul></ul><u...
Introduction <ul><li>What does credit approval means? </li></ul>“ The main objective is to separate good from bad customer...
<ul><ul><li>Introduction </li></ul></ul><ul><ul><li>The Problem </li></ul></ul><ul><ul><li>The Algorithm </li></ul></ul><u...
The Problem <ul><li>“  ...  developing a neural network with one hidden layer, to fit problems of binary classification.” ...
The Problem <ul><li>“  ...  developing a neural network with one hidden layer, to fit problems of binary classification.” ...
<ul><ul><li>Introduction </li></ul></ul><ul><ul><li>The Problem </li></ul></ul><ul><ul><li>The Algorithm </li></ul></ul><u...
The Algorithm <ul><li>GQA-BR </li></ul>
The Algorithm <ul><li>Example of a individual with mix representation ... </li></ul>Real Part Binary Part
The Algorithm <ul><li>GQA-BR </li></ul>
The Algorithm <ul><li>Example of generation of a classic individual ... </li></ul>Real Part Binary Part Let “random” be a ...
The Algorithm <ul><li>GQA-BR </li></ul>
The Algorithm <ul><li>Objective Function </li></ul>
The Algorithm <ul><li>GQA-BR </li></ul>
The Algorithm <ul><li>Example of recombination of two classic individual </li></ul>Real Part Binary Part Individual 1 Real...
The Algorithm <ul><li>Example of recombination of two classic individual </li></ul>Binary Part Individual 1 Binary Part In...
The Algorithm <ul><li>Example of recombination of two classic individual </li></ul>Real Part Individual 1 Real Part Indivi...
The Algorithm <ul><li>GQA-BR </li></ul>
The Algorithm <ul><li>Updates of the binary and real parts </li></ul>Real Part Binary Part Real Part Binary Part Quantum I...
The Algorithm <ul><li>Updates of the binary and real parts </li></ul>Binary Part Binary Part Quantum Individual Classic In...
The Algorithm <ul><li>Updates of the binary and real parts </li></ul>Real Part Real Part Quantum Individual Classic Indivi...
<ul><ul><li>Introduction </li></ul></ul><ul><ul><li>The Problem </li></ul></ul><ul><ul><li>The Algorithm </li></ul></ul><u...
Benchmark Case <ul><li>Australian Credit Approval Problem </li></ul><ul><ul><li>Reference:  UCI Machine Learning Repositor...
<ul><ul><li>Introduction </li></ul></ul><ul><ul><li>The Problem </li></ul></ul><ul><ul><li>The Algorithm </li></ul></ul><u...
Results <ul><li>Parameters to Control </li></ul>nh numQuantum numClassic numGeneration C-Crossover  Q-Crossover minGener...
Results <ul><li>Parameters Set </li></ul>nh 20 numQuantum 2 numClassic 400 numGeneration 200 C-Crossover 0,95  0,020*pi ...
Results <ul><li>Results Obtained    3-fold-cross validation </li></ul>Australian Credit Approval
Results <ul><li>Comparasion with other models </li></ul><ul><ul><li>Reference:  Carvalho and Lacerda </li></ul></ul>
Results <ul><li>Comparasion with other models </li></ul><ul><ul><li>Reference:  Jones and Quinlan </li></ul></ul>
<ul><ul><li>Introduction </li></ul></ul><ul><ul><li>The Problem </li></ul></ul><ul><ul><li>The Algorithm </li></ul></ul><u...
Conclusions <ul><li>Some Considerations ... </li></ul><ul><ul><li>Flexibility    </li></ul></ul><ul><ul><ul><li>Potential...
“ Thanks! Obrigado!” André Vargas, Anderson Pinho and Marley Vellasco “ It is more by education than by instruction that w...
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A New Model for Credit Approval Problems: A Neuro-Genetic System with Quantum Inspiration and Binary-Real Representation

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This paper presents a new model for neuro-evolutionary systems. It is a new quantum-inspired evolutionary algorithm with binary-real representation (QIEA-BR) for evolution of a neural network. The proposed model is an extension of the QIEA-R developed for numerical optimization. The Quantum-Inspired Neuro-Evolutionary Computation model (QINEA-BR) is able to completely configure a feed-forward neural network in terms of selecting the relevant input variables, number of neurons in the hidden layer and all existent synaptic weights. QINEA-BR is evaluated in a benchmark problem of financial credit evaluation. The results obtained demonstrate the effectiveness of this new model in comparison with other machine learning and statistical models, providing good accuracy in separating good from bad customers.

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A New Model for Credit Approval Problems: A Neuro-Genetic System with Quantum Inspiration and Binary-Real Representation

  1. 1. Rio de Janeiro, 11 de Dezembro de 2009. A New Model for Credit Approval Problems: A Neuro-Genetic System with Quantum Inspiration and Binary-Real Representation Anderson Pinho, Marley Vellasco e André Vargas
  2. 2. <ul><ul><li>Introduction </li></ul></ul><ul><ul><li>The Problem </li></ul></ul><ul><ul><li>The Algorithm </li></ul></ul><ul><ul><li>Benchmark Case </li></ul></ul><ul><ul><li>Results </li></ul></ul><ul><ul><li>Conclusions </li></ul></ul>A New Model for Credit Approval Problems: A Neuro-Genetic System with Quantum Inspiration and Binary-Real Representation
  3. 3. <ul><ul><li>Introduction </li></ul></ul><ul><ul><li>The Problem </li></ul></ul><ul><ul><li>The Algorithm </li></ul></ul><ul><ul><li>Benchmark Case </li></ul></ul><ul><ul><li>Results </li></ul></ul><ul><ul><li>Conclusions </li></ul></ul>A New Model for Credit Approval Problems: A Neuro-Genetic System with Quantum Inspiration and Binary-Real Representation
  4. 4. Introduction <ul><li>What does credit approval means? </li></ul>“ The main objective is to separate good from bad customers, rejecting credit to customers classified as bad, minimizing risk of the firms and banks.” Many techniques and areas of science has been used for evaluating credit approval problems. We could list: Discriminant Analysis, Logistic Regression, Mathematical Programming, Expert System, Neural Networks, Genetic Programming, Non-Parametric Methods, Model of Time Series, Hybrid Models, Evolutionary Programming, Support Vector Machines, Recursive Partitioning ...
  5. 5. <ul><ul><li>Introduction </li></ul></ul><ul><ul><li>The Problem </li></ul></ul><ul><ul><li>The Algorithm </li></ul></ul><ul><ul><li>Benchmark Case </li></ul></ul><ul><ul><li>Results </li></ul></ul><ul><ul><li>Conclusions </li></ul></ul>A New Model for Credit Approval Problems: A Neuro-Genetic System with Quantum Inspiration and Binary-Real Representation
  6. 6. The Problem <ul><li>“ ... developing a neural network with one hidden layer, to fit problems of binary classification.” </li></ul><ul><ul><li>CATEGORICAL decisions: </li></ul></ul><ul><ul><li>Wich variables we selected in a input layer? </li></ul></ul><ul><ul><li>How many neurons we consider in the hidden layer? </li></ul></ul><ul><ul><li>What kind of activation function must we use throughout the network? Logistic or Hiperbolic? </li></ul></ul><ul><ul><li>NUMERICAL decisions : </li></ul></ul><ul><ul><li>What are the weights of the input layer? </li></ul></ul><ul><ul><li>What are the weights of the output layer? </li></ul></ul><ul><ul><li>What cutt-off point must we use for classification between two classes? </li></ul></ul>
  7. 7. The Problem <ul><li>“ ... developing a neural network with one hidden layer, to fit problems of binary classification.” </li></ul>x 1 x 2 x 3 x n C 1 C 2
  8. 8. <ul><ul><li>Introduction </li></ul></ul><ul><ul><li>The Problem </li></ul></ul><ul><ul><li>The Algorithm </li></ul></ul><ul><ul><li>Benchmark Case </li></ul></ul><ul><ul><li>Results </li></ul></ul><ul><ul><li>Conclusions </li></ul></ul>A New Model for Credit Approval Problems: A Neuro-Genetic System with Quantum Inspiration and Binary-Real Representation
  9. 9. The Algorithm <ul><li>GQA-BR </li></ul>
  10. 10. The Algorithm <ul><li>Example of a individual with mix representation ... </li></ul>Real Part Binary Part
  11. 11. The Algorithm <ul><li>GQA-BR </li></ul>
  12. 12. The Algorithm <ul><li>Example of generation of a classic individual ... </li></ul>Real Part Binary Part Let “random” be a random number generated for each classic individual observated in the quantum population Gene(i)= (Center(i) – Height(i)/2) + Height * random Gene(i)= If random between 0 and (Q-bit 0)^2 then 1 else 0
  13. 13. The Algorithm <ul><li>GQA-BR </li></ul>
  14. 14. The Algorithm <ul><li>Objective Function </li></ul>
  15. 15. The Algorithm <ul><li>GQA-BR </li></ul>
  16. 16. The Algorithm <ul><li>Example of recombination of two classic individual </li></ul>Real Part Binary Part Individual 1 Real Part Binary Part Individual 2 Real Part Binary Part Soon
  17. 17. The Algorithm <ul><li>Example of recombination of two classic individual </li></ul>Binary Part Individual 1 Binary Part Individual 2 Binary Part Soon Let “random” be a random number generated for each classic individual observated in the quantum population Let “Individual 1” be a classic individual inside population of the best. SoonGene(1)= If random > CrossoverProbability then “Change Genes” Else “Don´t Change The Genes”.
  18. 18. The Algorithm <ul><li>Example of recombination of two classic individual </li></ul>Real Part Individual 1 Real Part Individual 2 Real Part Soon Let “random” be a random number generated for each classic individual observated in the quantum population SoonGene(1)= Indiv1Gene(1)+(Indiv2Gene(1)-Indiv1Gene(1))*random Let “Individual 1” be a classic individual inside population of the best.
  19. 19. The Algorithm <ul><li>GQA-BR </li></ul>
  20. 20. The Algorithm <ul><li>Updates of the binary and real parts </li></ul>Real Part Binary Part Real Part Binary Part Quantum Individual Classic Individual
  21. 21. The Algorithm <ul><li>Updates of the binary and real parts </li></ul>Binary Part Binary Part Quantum Individual Classic Individual Quantum Q-Gates “ For the first gene, for example, we grows up the probability of a Q-Bit 1 be choosen, because we have observed a Bit-1 on classic individual from the population of best, wich was choosen randomly”
  22. 22. The Algorithm <ul><li>Updates of the binary and real parts </li></ul>Real Part Real Part Quantum Individual Classic Individual UCenter(1) = Center(1) + (Real(1) – Center(1)) * random UHeight (1) = Height (1) + (MaxHeightBest(1) – Height(1)) * random “ MaxHeightBest is the maximum height observed between all the best individual”
  23. 23. <ul><ul><li>Introduction </li></ul></ul><ul><ul><li>The Problem </li></ul></ul><ul><ul><li>The Algorithm </li></ul></ul><ul><ul><li>Benchmark Case </li></ul></ul><ul><ul><li>Results </li></ul></ul><ul><ul><li>Conclusions </li></ul></ul>A New Model for Credit Approval Problems: A Neuro-Genetic System with Quantum Inspiration and Binary-Real Representation
  24. 24. Benchmark Case <ul><li>Australian Credit Approval Problem </li></ul><ul><ul><li>Reference: UCI Machine Learning Repository </li></ul></ul><ul><ul><li>Characteristics </li></ul></ul><ul><ul><li>690 samples of customers </li></ul></ul><ul><ul><li>307 (55.5%) bad payers and 383 (44.5%) good payers </li></ul></ul><ul><ul><li>14 for explanatory variables </li></ul></ul><ul><ul><li>Missing values are in 5% of customers. </li></ul></ul><ul><ul><li>They were treated by the average or median </li></ul></ul><ul><ul><li>Pre-processing </li></ul></ul><ul><ul><li>Some categorical attributes received 1 of N encodings </li></ul></ul><ul><ul><li>Some continuous were normalized by mean and standard deviation </li></ul></ul><ul><ul><li>The tests and training occurred on a 3-fold-cross validation </li></ul></ul>
  25. 25. <ul><ul><li>Introduction </li></ul></ul><ul><ul><li>The Problem </li></ul></ul><ul><ul><li>The Algorithm </li></ul></ul><ul><ul><li>Benchmark Case </li></ul></ul><ul><ul><li>Results </li></ul></ul><ul><ul><li>Conclusions </li></ul></ul>A New Model for Credit Approval Problems: A Neuro-Genetic System with Quantum Inspiration and Binary-Real Representation
  26. 26. Results <ul><li>Parameters to Control </li></ul>nh numQuantum numClassic numGeneration C-Crossover  Q-Crossover minGeneration updatesGeneration
  27. 27. Results <ul><li>Parameters Set </li></ul>nh 20 numQuantum 2 numClassic 400 numGeneration 200 C-Crossover 0,95  0,020*pi Q-Crossover 0,95 minGeneration 3 updatesGeneration 10
  28. 28. Results <ul><li>Results Obtained  3-fold-cross validation </li></ul>Australian Credit Approval
  29. 29. Results <ul><li>Comparasion with other models </li></ul><ul><ul><li>Reference: Carvalho and Lacerda </li></ul></ul>
  30. 30. Results <ul><li>Comparasion with other models </li></ul><ul><ul><li>Reference: Jones and Quinlan </li></ul></ul>
  31. 31. <ul><ul><li>Introduction </li></ul></ul><ul><ul><li>The Problem </li></ul></ul><ul><ul><li>The Algorithm </li></ul></ul><ul><ul><li>Benchmark Case </li></ul></ul><ul><ul><li>Results </li></ul></ul><ul><ul><li>Conclusions </li></ul></ul>A New Model for Credit Approval Problems: A Neuro-Genetic System with Quantum Inspiration and Binary-Real Representation
  32. 32. Conclusions <ul><li>Some Considerations ... </li></ul><ul><ul><li>Flexibility  </li></ul></ul><ul><ul><ul><li>Potential Predictor, Neurons on Hidden Layer, Cut-off, Weights, Activation Functions </li></ul></ul></ul><ul><ul><li>Exploration and Exploitation  </li></ul></ul><ul><ul><ul><li>This quantum algorithm guarantees good exploration and search of the solution space </li></ul></ul></ul><ul><ul><li>Comparasion  </li></ul></ul><ul><ul><ul><li>BR-NEIQ could replace other models, but not significant better than them </li></ul></ul></ul><ul><ul><li>Adjusting Parameters  </li></ul></ul><ul><ul><ul><li>BR-NEIQ could replace other models, but not significant better than them </li></ul></ul></ul><ul><ul><li>The need of comparasion with others benchmark problems  </li></ul></ul>
  33. 33. “ Thanks! Obrigado!” André Vargas, Anderson Pinho and Marley Vellasco “ It is more by education than by instruction that we can transform the humanity ” Alan Kardec

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