Additive feature attribution methods

As explained in [@lundbergUnifiedApproachInterpreting] additive feature attribution methods are those methods that use an explanation model which is a linear function of binary variables, i.e.

$$g\left(z^{\prime }\right)={\varphi }_0+\sum _{i=1}^M{\varphi }_i{z}_i^{\prime }$$

where $z^{\prime }\in \{0,1{\}}^M$ is the number of simplified input features, and ${\varphi }_i\in \mathbb{R}$, which models the effect that each feature has on the final outcome. The summation of al these effects approximates the output $f(x)$ of the original opaque model.

In other words, differently from generating counterfactual examples, which explanation is given by a counterexample, additive feature attribution methods explain the decision by assigning to each feature a score, showing which are the feature that contributed the most to the final prediction.

Note that simplified inputs of the original $x$ are defined as points $x^{\prime }$ such that $h_x(x^{\prime })=x$ ($h_x$ being a specific function to the current input $x$). This is an approach that is used by a lot of methods.

For example, in LIME [@ribeiroWhyShouldTrust2016] they use an additive feature attribution method since they locally approximate the prediction of the model around a given prediction using a local linear explanation model.

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tags: ai-explainability