Support vector regression
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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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Support Vector Regression

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Support vector regression

Support Vector Regression

ArturAkbarov


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


Model over fit

Model over-fit


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))


Support vector regression

Thank you for your attention


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