compute_MSEv_eval_crit: Mean squared error of the contribution function 'v(S)'

In shapr: Prediction Explanation with Dependence-Aware Shapley Values

Mean squared error of the contribution function v(S)

Description

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).

Usage

compute_MSEv_eval_crit(
  internal,
  dt_vS,
  MSEv_uniform_comb_weights,
  MSEv_skip_empty_full_comb = TRUE
)

Arguments

internal	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.
dt_vS	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.
MSEv_uniform_comb_weights	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.
MSEv_skip_empty_full_comb	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.

Details

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.

Value

List containing:

MSEv

A 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_explicand

A data.table with the mean squared error for each explicand, i.e., only averaged over the coalitions.

MSEv_coalition

A 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.

Author(s)

Lars Henry Berge Olsen

References

• Frye, C., de Mijolla, D., Begley, T., Cowton, L., Stanley, M., & Feige, I. (2021). Shapley explainability on the data manifold. In International Conference on Learning Representations.

• Olsen, L. H., Glad, I. K., Jullum, M., & Aas, K. (2022). Using Shapley values and variational autoencoders to explain predictive models with dependent mixed features. Journal of machine learning research, 23(213), 1-51

• Olsen, L. H. B., Glad, I. K., Jullum, M., & Aas, K. (2024). A comparative study of methods for estimating model-agnostic Shapley value explanations. Data Mining and Knowledge Discovery, 1-48

shapr documentation built on Aug. 25, 2025, 5:11 p.m.