How to visualize the equation used by cubic polynomial regression SVM?

I would like to know how I can view the equation and model parameters for a trained correlation model.

Currently, I have a cubic SVM model that can predict the response sufficiently well, and I need to know how the parameters have been combined and which combination of parameters have the larger influence to the result.

Answer 1

[MathWorks Support Team]

You can refer to the "Nonlinear SVM Regression: Dual Formula" section of the following documentation link to see the equation being used by the cubic polynomial SVM:

https://www.mathworks.com/help/stats/understanding-support-vector-machine-regression.html

As you can see, the equation is rather complicated (i.e. not a simple cubic polynomial equation form) and involves parameters such as alpha, beta and all the support vectors. (the "cubic" refers to the way the Gram matrix, G(xi,xj) is created)

While you would not be able to visualize the whole equation, you can access all the parameters used in the formula above by accessing the properties of your model:

>> alpha = model.RegressionSVM.Alpha
>> beta = model.RegressionSVM.Beta
>> supportVectors = model.RegressionSVM.SupportVectors

For visualization, you can make use of this model to compute predictions and plot the results, or compute residuals from the predictions and plot those.

Regarding visualizing the relative influence of each parameter, there is not a simple way that I can think of. However, you can use partial dependence plot to help you visualize the effect of each predictor on predictions from the model:

>> plotPartialDependence(model.RegressionSVM,2)

www.mathworks.com/help/stats/regressiontree.plotpartialdependence.html