Model agnostic local variable importance for locally dependent relationships

Global variable importance measures are commonly used to interpret machine learning model results. Local variable importance techniques assess how variables contribute to individual observations rather than the entire dataset. Current methods typically fail to accurately reflect locally dependent relationships between variables and instead focus on marginal importance values. 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, contains improvements 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 and properly reduces bias in regions where variables do not affect the response.