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Support Vector Regression. Artur Akbarov. Paper. A tutorial on support vector regression By Smola, A.J and Schölkopf , B. Statistics and Computing, 14, pp . 199-222 , 200 4. Why SVM?.

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Presentation Transcript
paper
Paper

A tutorial on support vector regression

By Smola, A.J and Schölkopf, B.

Statistics and Computing, 14,

pp. 199-222, 2004

why svm
Why SVM?
  • SVM is applied in many different fields including bioinformatics, epidemiology, finance, economics etc.
  • Essentially, it can be applied wherever there is a problem of classification or prediction.
formulation of svr problem
Formulation of SVR problem

Source:http://www.saedsayad.com/support_vector_machine_reg.htm

formulation of svr problem1
Formulation of SVR problem

Source:http://www.saedsayad.com/support_vector_machine_reg.htm

non linear svr
Non-linear SVR

Source:http://www.saedsayad.com/support_vector_machine_reg.htm

parameter estimation
Parameter estimation

Linear SVR:

Non-linear SVR:

kernels
Kernels
  • Gaussian radial basis function:
  • Polynomial
the solution of svr
The solution of SVR
  • Model fitting:
    • Training set – fit the model
    • Validation set – predict using the fitted model,

choose the model with minimum

prediction error.

  • Model testing:
    • Test set – examine the prediction error (model performance, compare different prediction methods)
splitting the data set
Splitting the data set
  • Training and validation sets:
    • Fixed split
    • Random split
    • Cross-validation
      • Split the data into n number of subsets, train on n-1 subsets, validate on the remaining subset, loop over all subsets.
      • Leave-one-out cross validation.
svm library
SVM library
  • LIBSVM – SVM library in different languages.
  • Weka – data mining tools.
  • R package - “e1071”
svm in r
SVM in R
  • install.packages(“e1071”)
  • library(“e1071”)
  • model<-svm(data=D, formula=Y~X1+X2)
  • model<-svm(y=Y,x=X)
  • Y_fit<-predict(model, X)
  • Y_hat<-predict(model, X_new)
svm in r1
SVM in R
  • Other SVM parameters for the svm() function:
    • epsilon = 0.1
    • cost = 1.0, which is C
    • kernel =“linear”, “polynomial”, “radial”, ”sigmoid”.
tuning svm parameters
Tuning SVM parameters
  • best.svm() function uses grid search to find the optimal values for SVM parameters.
  • model<-best.svm(x=X, y=Y, tunecontrol=tune.control(cross=5), cost=c(1:10),epsilon=c(0.05,0.10))
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