Conditional Local Importance by Quantile Expectations

Abstract:

Global variable importance measures are commonly used to interpret the results of machine learning models. Local variable importance techniques assess how variables contribute to individual observations. Current, popular methods, including LIME and SHAP, provide
useful measures of feature contribution in the prediction space, while leaving opportunities for improved characterization of local structure in the model loss space. Additionally, they are not natively adapted for multi-class classification problems. We propose a new model-agnostic method for calculating local variable importance, CLIQUE, that captures locally dependent relationships, provides improved stability over permutation-based methods, and can be directly applied to multi-class classification problems. Simulated and real-world examples show that CLIQUE emphasizes locally dependent information, captures interaction behavior beyond what can be evaluated by correlations, and assigns zero importance in regions where the response is invariant to changes in variables.

Submission Type: Long submission (more than 12 pages of main content)

Changes Since Last Submission:

- We have revised the text throughout the paper to better highlight the distinction between SHAP/LIME and CLIQUE and substantially softened the competitive language between them.
- We have added a more complex regression simulation with known localized effects for 100 features with multivariate correlation imposed (ρ=0.5). When a binary feature z is 1, a linear combination of the first 5 features affects the response, while when z=0, a linear combination of the next 5 features affects the response. These results are included in Section 3.4 and Appendix C and are modeled with an Artificial Neural Network to further expand the model-agnostic demonstrations.
- We have rerun the Lichen dataset using an XGBoost model and included these results in the revision, with the Random Forest results moved to the appendix.
- We have updated Table 1 to include results from 50 Monte Carlo runs in order to obtain means and intervals for the MAE values with respect to 0.
- We have clarified that the computational comparisons included the CV training costs for CLIQUE and provided additional implementation details for transparency.
- We have added a limitations section with a substantially expanded discussion of relevant limitations. In particular, we address out-of-distribution inputs, CV partition sensitivity, and model calibration/hyperparameter tuning. We also include a simple sensitivity analysis examining the number of CV folds for the AND GATE data in Section 3.6.
- We have clarified our use of the term conditional throughout the paper, emphasizing that CLIQUE captures interaction-dependent rather than formal probabilistic conditional structure, and we discuss formal conditional derivations as a meaningful direction for future work.
- We have compared squared-error and absolute-error loss functions for the Regression Interaction data and added these results to the appendix, together with a brief discussion motivating our default use of absolute error. We also reference this comparison briefly in the main text.
- We have trimmed portions of the standard desiderata discussion in the methods section for a more concise narrative and expanded discussion in several of the more novel methodological sections.
- We have included a sensitivity analysis varying several LIME hyperparameters (Appendix A) and revised the text to better clarify our use of DeepSHAP and TreeSHAP.
- We have expanded the Introduction discussion of current state-of-the-art local importance methods, including additional clarification of the relationship between CLIQUE and ICI and expanded background for LIME, SHAP, and ICI.
- We have included an ablation study examining the number of quantiles for the Regression Interaction data in Section 3.6 and updated the text to better justify our selection of 25 quantiles.

Assigned Action Editor: ~Xiaojie_Mao1

Submission Number: 7881