Gaussian Kernel
A commonly used characteristic kernel function of the form k(x,y)=exp(-||x-y||^2/(2 sigma^2)); it is the standard kernel choice in the computation of MMD.
Timeline (last 90 days)
If and only if the kernel is a characteristic kernel (such as a Gaussian kernel), MMD(P,Q)=0 is equivalent to P=Q.
Mild conditions usually refer to standard assumptions such as the kernel function being sufficiently smooth and its eigenvalues decaying at a polynomial rate, covering commonly used kernels such as the Gaussian kernel and the Matérn kernel.
When the kernel is a characteristic kernel (e.g., a Gaussian kernel), MMD equals zero if and only if the two distributions are identical.
Gaussian kernels maintain a Gaussian form in both the spatial and frequency domains and are continuously differentiable at all derivatives, so they can be efficiently solved using optimization methods such as gradient descent.
All Facts (4)
If and only if the kernel is a characteristic kernel (such as a Gaussian kernel), MMD(P,Q)=0 is equivalent to P=Q.
50%UnverifiedMild conditions usually refer to standard assumptions such as the kernel function being sufficiently smooth and its eigenvalues decaying at a polynomial rate, covering commonly used kernels such as the Gaussian kernel and the Matérn kernel.
50%UnverifiedWhen the kernel is a characteristic kernel (e.g., a Gaussian kernel), MMD equals zero if and only if the two distributions are identical.
50%UnverifiedGaussian kernels maintain a Gaussian form in both the spatial and frequency domains and are continuously differentiable at all derivatives, so they can be efficiently solved using optimization methods such as gradient descent.
50%