get_max_n_coalitions_causal function

Get the number of coalitions that respects the causal ordering

get_max_n_coalitions_causal(causal_ordering)

Arguments

• causal_ordering: List. Not applicable for (regular) non-causal or asymmetric explanations. causal_ordering is an unnamed list of vectors specifying the components of the partial causal ordering that the coalitions must respect. Each vector represents a component and contains one or more features/groups identified by their names (strings) or indices (integers). If causal_ordering is NULL (default), no causal ordering is assumed and all possible coalitions are allowed. No causal ordering is equivalent to a causal ordering with a single component that includes all features (list(1:n_features)) or groups (list(1:n_groups)) for feature-wise and group-wise Shapley values, respectively. For feature-wise Shapley values and causal_ordering = list(c(1, 2), c(3, 4)), the interpretation is that features 1 and 2 are the ancestors of features 3 and 4, while features 3 and 4 are on the same level. Note: All features/groups must be included in the causal_ordering without any duplicates.

Returns

Integer. The (maximum) number of coalitions that respects the causal ordering.

Details

The function computes the number of coalitions that respects the causal ordering by computing the number of coalitions in each partial causal component and then summing these. We compute the number of coalitions in the $i$th a partial causal component by $2^n - 1$, where $n$ is the number of features in the the $i$th partial causal component and we subtract one as we do not want to include the situation where no features in the $i$th partial causal component are present. In the end, we add 1 for the empty coalition.

Author(s)

Lars Henry Berge Olsen