Prototypical Explanations

What are prototypical explanations?

Prototypical explanations are examples-based explanations (called prototypes) that represent all the data. Prototypes can be used independently from a machine learning model to describe the data, but they can also be used to create an interpretable model or to make a black-box model interpretable.

MMD-critic is a popular prototypical explanation algorithm that compares the actual data distribution $D = \{ X_1, X_2, ...., X_N \}$ and the selected prototypes' distribution $P = \{P_1, P_2, ..., P_m \}$. MMD-critic selects prototypes that minimize the discrepancy between the two distributions.

The figure below shows prototypes in a data distribution. The prototypes are data points that cover the data distribution.

Maximum mean discrepancy (MMD)

The maximum mean discrepancy (MMD) measures the difference or discrepancy between two distributions. We want to evaluate whether the selected prototype distribution $P$ differs from the data distribution $D$. The following formula shows how to calculate the squared MMD ($MMD^2$ ...