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Support Vector RegressionPowerPoint Presentation

Support Vector Regression

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### Support Vector Regression

ArturAkbarov

Paper

A tutorial on support vector regression

By Smola, A.J and Schölkopf, B.

Statistics and Computing, 14,

pp. 199-222, 2004

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

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

Formulation of SVR problem

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

Non-linear SVR

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

Kernels

- Gaussian radial basis function:
- Polynomial

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

- 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

- LIBSVM – SVM library in different languages.
- Weka – data mining tools.
- R package - “e1071”

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 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

- 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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