Glossary

This document contains and describes all implementation-relevant names and concepts.

Game, Value Function, and Normalization

A cooperative Game is an object, which implements a value_function for a set $\mathcal{N}$ of n_players. A value function $\nu: \mathcal{P}(N) \rightarrow \mathbb{R}$ maps each coalition $S \subseteq \mathcal{N}$ to a real-valued output by implementing the logic / behavior of a cooperative game (what is the worth of a coalition in a game). A value function does not need to map the empty set $\emptyset$ to zero, but a normalized Game does. Normalization is the process of shifting the output of the value function to return zero for the empty set. Any value function can be normalized by centering its output $\nu_0(S) = \nu(S) - \nu(\emptyset)$ $\forall S \subseteq \mathcal{N}$.

Coalition and CoalitionMatrix

A coalition is a binary vector denoting presence and absence of a player in the setting of a cooperative Game. We implement a coalition as a numpy.ndarray array of type bool of shape (n_players,). Multiple coalitions make up a CoalitionMatrix of shape (n_coalitions, n_players). Approximators or Computation methods call Games with these binary matrices since it's computationally efficient to create.

Approximators

An Approximator is a method that can estimate any kind of InteractionValues without needing to enumerate the whole set of all possible coalitions, but uses black-box access to the underlying model/game (this is different from Computers).

Computers

A computer is a method that can calculate exact InteractionValues for a machine learning model or game.

Exact Computer

An ExactComputer is a computer, that uses naive enumeration of all possible coalitions $S \subseteq \mathcal{N}$ to compute the exact InteractionValues. This can be done for any game with black-box access.

Model-Specific Computer

A model-specific computer is a computer, that leverages the structure of a machine learning model to compute the exact InteractionValues, without the need of enumerating all possible coalitions $S \subseteq \mathcal{N}$. Examples are the TreeSHAPIQ.

Explainer

An Explainer is an object which computes any kind of InteractionValues for a machine learning model. Therein, an explainer may use an approximator or a computer. The key is that an explainer needs to convert the machine learning model into an explanation game. This is usually achieved with an imputer.

Imputer

An Imputer is an object which turns a machine learning model into a cooperative game in the setting of model explanation.