Conceptcharacteristic kernel

Characteristic Kernel

A class of kernel functions whose corresponding mean embedding map is injective, meaning that different distributions have different kernel mean embeddings, which guarantees the validity of MMD as a measure of distributional difference.

Timeline (last 90 days)

Oct 15

If and only if the kernel is a characteristic kernel (such as a Gaussian kernel), MMD(P,Q)=0 is equivalent to P=Q.

Unverified50%

Oct 12

When the kernel is a characteristic kernel (e.g., a Gaussian kernel), MMD equals zero if and only if the two distributions are identical.

Unverified50%

All Facts (2)

Unverified

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%Unverified

When the kernel is a characteristic kernel (e.g., a Gaussian kernel), MMD equals zero if and only if the two distributions are identical.

50%

Source Articles

First Finite-Particle Guarantee for the Optimization Landscape of Overparameterized Weighted MMDOct 15