In the mathematic literature, kernels can refer to:

• a function used to weight observations. Examples:

  • LIME: the method uses a Gaussian kernel as proximity measure to penalize observations that are far away from the observation we want to explain.

  • SHAP: the method to define effects can be seen as a kernel since it aims at finding Shapley values which are weights per se.

  • KDE: the method estimates a continuous distribution in averaging several kernels centered in each point of the data to be smoothed.

• the inverse image of zero: $ker\{f\} = \{x | f(x)=0\}$

  • Linear regression: there is unicity when $ker\{X\}=0$ (reminder: $\hat \theta = (X^TX)^{-1}X^TY$).