Explaining Machine Learning Predictive Models through Conditional Expectation Methods

TL;DR

This paper introduces MUCE, a model-agnostic, local explainability method that extends ICE to multivariate feature interactions to reveal how predictions change in a localized neighborhood. By pairing MUCE with a modified ICE for single observations and two quantitative indices—stability and uncertainty—the approach provides both graphical explanations and numeric measures of local behavior and reliability. Validations on synthetic 2D/3D and transformed real-world datasets show MUCE effectively captures complex local dynamics, including feature interactions and behavior near decision boundaries, while the indices offer concise summaries to compare features. The work contributes a practical toolkit for trustworthy, transparent predictions in high-stakes contexts and suggests directions for future comparisons with established XAI methods and extensions to non-tabular data.

Abstract

The rapid adoption of complex Artificial Intelligence (AI) and Machine Learning (ML) models has led to their characterization as black boxes due to the difficulty of explaining their internal decision-making processes. This lack of transparency hinders users' ability to understand, validate and trust model behavior, particularly in high-risk applications. Although explainable AI (XAI) has made significant progress, there remains a need for versatile and effective techniques to address increasingly complex models. This work introduces Multivariate Conditional Expectation (MUCE), a model-agnostic method for local explainability designed to capture prediction changes from feature interactions. MUCE extends Individual Conditional Expectation (ICE) by exploring a multivariate grid of values in the neighborhood of a given observation at inference time, providing graphical explanations that illustrate the local evolution of model predictions. In addition, two quantitative indices, stability and uncertainty, summarize local behavior and assess model reliability. Uncertainty is further decomposed into uncertainty+ and uncertainty- to capture asymmetric effects that global measures may overlook. The proposed method is validated using XGBoost models trained on three datasets: two synthetic (2D and 3D) to evaluate behavior near decision boundaries, and one transformed real-world dataset to test adaptability to heterogeneous feature types. Results show that MUCE effectively captures complex local model behavior, while the stability and uncertainty indices provide meaningful insight into prediction confidence. MUCE, together with the ICE modification and the proposed indices, offers a practical contribution to local explainability, enabling both graphical and quantitative insights that enhance the interpretability of predictive models and support more trustworthy and transparent decision-making.

Figures (15)

• Figure 1: Cross-like scenario. 2D synthetic dataset with 400 observations and two features (F1, F2). The negative class is represented by green circles and the positive class by orange crosses. The red dashed line represents the class boundary. The dark red diamonds indicate four representative data observations selected to be explained with the XAI methods proposed in Sections \ref{['sec:ice']} and \ref{['sec:muce']}.
• Figure 2: Ellipsoidal scenario: 3D synthetic dataset with 400 observations and three features (F1, F2, F3). The negative class is represented by green circles and the positive class by orange crosses. The pink surface represents the ellipsoidal class boundary. The dark red diamond indicates the representative data observation to be explained with the XAI methods proposed in Sections \ref{['sec:ice']} and \ref{['sec:muce']}.
• Figure 3: 2D projections of the synthetic 3D dataset (ellipsoidal scenario): (a) XY plane projection (F1-F2), (b) XZ plane projection (F1-F3), and (c) YZ plane projection (F2-F3). The negative class is represented by green circles and the positive class by orange crosses. The red dashed line represents the projected class boundary. The dark red diamond indicates the representative data observation selected for further analysis.
• Figure 4: Spatial distribution of the observations according to their assigned cardinal direction, derived from latitude and longitude. The dashed lines represent the median values used to divide the geographic space into four quadrants.
• Figure 5: MUCE algorithm overview for three features: $F_{i}=F1$ and $F_{j}=\{F2, F3\}$. The exploration begins at the observation (black circle) in the first iteration (green plane), and observations are generated over $F_{j}$ (white circles). Among the newly generated values, the maximum and minimum predicted values are selected (solid circles), and the other generated values are discarded (dashed circles). This exploration is repeated $t_{1}$ times, and the final selected maximum and minimum observations (blue and yellow circles, respectively) are used as starting observations for the next iteration, in addition to adding $F_{i}\pm\epsilon_{i}$ (purple plane).