Conditional Local Importance by Quantile Expectations

A new model-agnostic technique called CLIQUE offers a way to measure local variable importance in machine learning models, emphasizing locally dependent relationships and providing more stable results than permutation-based methods, according to a paper posted on arXiv [1]. The method, formally titled "Conditional Local Importance by Quantile Expectations," was submitted by Kelvyn Bladen on 13 November 2024 and last revised on 15 June 2026 [1]. It addresses limitations in widely used interpretation tools such as LIME and SHAP. While those tools measure feature contribution in the prediction space, the paper states they leave "opportunities for improved characterization of local structure in the model loss space" and are not natively adapted for multi-class classification problems [1][2]. CLIQUE is designed to fill that gap by operating in the loss space and handling multi-class settings directly [2]. In decision theory, scoring rules provide a summary measure for evaluating the quality of a probabilistic prediction given the actual outcome, often serving as loss functions for forecasting models [3]. The CLIQUE approach builds on this concept by examining how a model's loss changes locally when variables are perturbed, rather than relying solely on prediction-space perturbations [2]. The paper reports that simulated and real-world examples show CLIQUE "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" [2]. Standard regression models typically assume independent variables are measured without error, an assumption that can lead to inconsistent estimates when measurement error is present [4]. By focusing on conditional distributions in the loss space, CLIQUE aims to provide a more nuanced local importance measure that is robust to such structural complexities [2]. The method is model-agnostic, meaning it can be applied across different machine learning architectures, from simple regressors to complex neural networks such as variational autoencoders, which map inputs to distributions in a latent space to avoid overfitting [5], or generative adversarial networks, where two networks compete in a zero-sum game to generate realistic data [6]. Autoencoders more broadly learn efficient codings of unlabeled data for tasks including dimensionality reduction and anomaly detection [7]. CLIQUE's design allows it to operate across these varied model types without requiring internal access to model parameters [1][2].