ShapValues

A vector $\text{[math]}$ with contributions of each feature to the prediction for every input object and the expected value of the model prediction for the object (average prediction given no knowledge about the object).

$\text{[math]}$ is the contribution of the i-th feature.
$\text{[math]}$ is the expected value of the model prediction.

For a given object the sum $\text{[math]}$ is equal to the prediction on this object.

This is an implementation of the Consistent Individualized Feature Attribution for Tree Ensembles approach.

See the ShapValues file format.

Use the SHAP package to plot the returned values.

Calculation principles

The feature importance $\text{[math]}$ is calculated as follows for each feature $\text{[math]}$ :

$\text{[math]}$

$\text{[math]}$ is the number of input features.
$\text{[math]}$ is the set of all input features.
$\text{[math]}$ is the set of non-zero feature indexes (the features that are being observed and not unknown).
$\text{[math]}$ is the model's prediction for the input $\text{[math]}$ , where $\text{[math]}$ is the expected value of the function conditioned on a subset S of the input features.