v(S)Compute the mean squared error (MSEv) of the contribution function v(S) as proposed by Frye et al. (2019) and used by Olsen et al. (2022).
compute_MSEv_eval_crit(
internal,
dt_vS,
MSEv_uniform_comb_weights,
MSEv_skip_empty_full_comb = TRUE
)List containing:
MSEvA data.table with the overall MSEv evaluation criterion averaged
over both the coalitions and observations/explicands. The data.table
also contains the standard deviation of the MSEv values for each explicand (only averaged over the coalitions)
divided by the square root of the number of explicands.
MSEv_explicandA data.table with the mean squared error for each
explicand, i.e., only averaged over the coalitions.
MSEv_coalitionA data.table with the mean squared error for each
coalition, i.e., only averaged over the explicands/observations.
The data.table also contains the standard deviation of the MSEv values for
each coalition divided by the square root of the number of explicands.
List.
Holds all parameters, data, functions and computed objects used within explain()
The list contains one or more of the elements parameters, data, objects, iter_list, timing_list,
main_timing_list, output, and iter_timing_list.
Data.table of dimension n_coalitions times n_explain + 1 containing the contribution function
estimates. The first column is assumed to be named id_coalition and containing the ids of the coalitions.
The last row is assumed to be the full coalition, i.e., it contains the predicted responses for the observations
which are to be explained.
Logical.
If TRUE (default), then the function weights the coalitions uniformly when computing the MSEv criterion.
If FALSE, then the function use the Shapley kernel weights to weight the coalitions when computing the MSEv
criterion.
Note that the Shapley kernel weights are replaced by the sampling frequency when not all coalitions are considered.
Logical. If TRUE (default), exclude the empty and grand
coalitions when computing the MSEv evaluation criterion. This is reasonable as they are identical
for all methods, i.e., their contribution function is independent of the method used (special cases not
affected by the approach). If FALSE, include the empty and grand coalitions. In that case,
we recommend setting MSEv_uniform_comb_weights = TRUE; otherwise the large weights for the empty and
grand coalitions will outweigh all others and make the MSEv criterion uninformative.
Lars Henry Berge Olsen
The MSEv evaluation criterion does not rely on access to the true contribution functions or the true Shapley values. A lower value indicates better approximations; however, the scale and magnitude of MSEv are not directly interpretable regarding the precision of the final estimated Shapley values. Olsen et al. (2024) illustrates (Figure 11) a fairly strong linear relationship between MSEv and the MAE between the estimated and true Shapley values in a simulation study. Note: explicands are the observations whose predictions we explain.