What are the details fitrkernel model and how the predictions are produced?

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Mariam Ahmed
Mariam Ahmed 2020년 11월 9일
편집: Mariam Ahmed 2020년 11월 9일
I am trying to implment my own predict function for a model produced using fitrkernel in which a Gaussian kernel regression model is fit using random feature expansion.
I Have two questions regarding fitrkernel
1) Question 1:
What I understand is that fitrkernel solves for β and b in the linear regression equaition, f(x)=T(x)β+b.
However, the model otuputs the following with no mention of β and b:
RegressionKernel
ResponseName: 'Y'
Learner: 'svm'
NumExpansionDimensions: 128
KernelScale: 1
Lambda: 0.000328947368421053
BoxConstraint: 1
Epsilon: 0.0192374351371386
So, how can I know what are the values of β and b?
2) Question 2:
I looked up the documentation of the model and I found in https://www.mathworks.com/help/stats/fitrkernel.html that Gaussian kernel approximation is done using Random Feature Expansion. That is,
T(x)=m^(−1/2)*exp(iZx′)′ --- Eq(1)
where Z∈ℝ^(m×p) is a sample drawn from N(0,σ^−2) and σ^2 is a kernel scale.
The values for m and σ^2 coresponds to the NumExpansionDimensions and KernelScale name-value pair arguments of fitrkernel, respectively.
However, In Eq(1) the sample Z ~ N(0,σ^−2) is drawn at random, so how the model can predict the same output for the same input all the time? and what is i?

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