get_S_causal_steps function

Get the steps for generating MC samples for coalitions following a causal ordering

get_S_causal_steps(S, causal_ordering, confounding, as_string = FALSE)

Arguments

• S: Integer matrix of dimension n_coalitions_valid x m, where n_coalitions_valid equals the total number of valid coalitions that respect the causal ordering given in causal_ordering and m equals the total number of features.

• 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.

• confounding: Logical vector. Not applicable for (regular) non-causal or asymmetric explanations. confounding is a vector of logicals specifying whether confounding is assumed or not for each component in the causal_ordering. If NULL (default), then no assumption about the confounding structure is made and explain

  computes asymmetric/symmetric conditional Shapley values, depending on the value of asymmetric. If confounding is a single logical, i.e., FALSE or TRUE, then this assumption is set globally for all components in the causal ordering. Otherwise, confounding must be a vector of logicals of the same length as causal_ordering, indicating the confounding assumption for each component. When confounding is specified, then explain computes asymmetric/symmetric causal Shapley values, depending on the value of asymmetric. The approach cannot be regression_separate and regression_surrogate as the regression-based approaches are not applicable to the causal Shapley value methodology.

• as_string: Boolean. If the returned object is to be a list of lists of integers or a list of vectors of strings.

Returns

Depends on the value of the parameter as_string. If a string, then results[j] is a vector specifying the process of generating the samples for coalition j. The length of results[j] is the number of steps, and results[j][i] is a string of the form features_to_sample|features_to_condition_on. If the features_to_condition_on part is blank, then we are to sample from the marginal distribution. For as_string == FALSE, then we rather return a vector where results[[j]][[i]] contains the elements Sbar and S representing the features to sample and condition on, respectively.

Author(s)

Lars Henry Berge Olsen