These intervals were shown to be in agreement with the cumulative Gaussian distribution when using the radial and NP kernels, but not always for the Bessel or Laplacian kernels, highlighting that the kernel choice has to be made in the light of both models performance and reliability of the predicted variances.
The table shows the final values of C, p, and τ for each channel and the particular kernel choice.
A kernel choice of 7x7 can be processed within 27 sec for a volume consisting of 512x512 A-scans and within 112 s for 1024x1024 A-scans.
Then, depending on the kernel choice, SVMs may have additional hyper-parameters; e.g., the polynomial kernel requires a parameter p that defines the degree of the polynomial while the RBF kernel requires the parameter τ which controls the wideness in an exponential Gaussian-like function.
For in depth analysis regarding the smoothing techniques, bandwidth selection, kernel choices, and LP programs, see the works of Daraio and Simar (2005; 2007b; 2007Bădinădin et al., (2012 20100) and Mastromarco and Simar (2014).
For example, the performance of SVM approach is very sensitive to kernel choices and other parameters including the soft margin parameter and feature normalization method.
After performing a small set of experiments with pilot runs evaluating a number of kernel choices, we decided to use a radial basis kernel, K (x, y ) = exp { | | x - y | | 2 / σ 2 }, where | | X | | = < x, x > = x T x, over a linear or polynomial kernel.
Wavelet is a popular method of choice in many fields because of the flexibility it provides in terms of choice of kernel selection which in turn reflects different time and frequency resolutions.
The GL estimate, λ ˆ n GL is programmed with the Gaussian kernel, with the choice η = 0.5 and with the bandwidths family H = { D − 1 : D = 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 18, 20, 22, 25, 30, 35, 40, 45, 50 }, which has shown a robust behavior on various simulations, for the present considered size of n ( n ≈ 40 ).
Using kernel regression, the choice of the appropriate degree of smoothing is important, which depends on the sample size.
Studies suggest that most unimodal densities perform about the same as the other when used as a kernel, and the choice between kernels can be made on other grounds such as computational efficiency.
