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GLEAMS: Bridging the Gap Between Local and Global Explanations

Giorgio Visani, Vincenzo Stanzione, Damien Garreau

TL;DR

GLEAMS tackles the challenge of providing both local and global explanations for black-box models on tabular data by constructing a global surrogate that is piecewise-linear over axis-aligned partitions of a hyper-rectangle input space. It builds this surrogate through Sobol-based measurement points and recursive splits, yielding local explanations from leaf coefficients and global explanations via volume-weighted aggregation, along with counterfactuals that can be evaluated without further model queries. The method achieves competitive monotonicity against LIME, SHAP, and PDP on real datasets while enabling constant-time explanations for new inputs. This approach offers scalable, human-understandable insights and actionable what-if analyses, with practical implications for transparent decision-making in ML deployments.

Abstract

The explainability of machine learning algorithms is crucial, and numerous methods have emerged recently. Local, post-hoc methods assign an attribution score to each feature, indicating its importance for the prediction. However, these methods require recalculating explanations for each example. On the other side, while there exist global approaches they often produce explanations that are either overly simplistic and unreliable or excessively complex. To bridge this gap, we propose GLEAMS, a novel method that partitions the input space and learns an interpretable model within each sub-region, thereby providing both faithful local and global surrogates. We demonstrate GLEAMS' effectiveness on both synthetic and real-world data, highlighting its desirable properties and human-understandable insights.

GLEAMS: Bridging the Gap Between Local and Global Explanations

TL;DR

GLEAMS tackles the challenge of providing both local and global explanations for black-box models on tabular data by constructing a global surrogate that is piecewise-linear over axis-aligned partitions of a hyper-rectangle input space. It builds this surrogate through Sobol-based measurement points and recursive splits, yielding local explanations from leaf coefficients and global explanations via volume-weighted aggregation, along with counterfactuals that can be evaluated without further model queries. The method achieves competitive monotonicity against LIME, SHAP, and PDP on real datasets while enabling constant-time explanations for new inputs. This approach offers scalable, human-understandable insights and actionable what-if analyses, with practical implications for transparent decision-making in ML deployments.

Abstract

The explainability of machine learning algorithms is crucial, and numerous methods have emerged recently. Local, post-hoc methods assign an attribution score to each feature, indicating its importance for the prediction. However, these methods require recalculating explanations for each example. On the other side, while there exist global approaches they often produce explanations that are either overly simplistic and unreliable or excessively complex. To bridge this gap, we propose GLEAMS, a novel method that partitions the input space and learns an interpretable model within each sub-region, thereby providing both faithful local and global surrogates. We demonstrate GLEAMS' effectiveness on both synthetic and real-world data, highlighting its desirable properties and human-understandable insights.
Paper Structure (19 sections, 9 equations, 4 figures, 1 table, 3 algorithms)

This paper contains 19 sections, 9 equations, 4 figures, 1 table, 3 algorithms.

Table of Contents

  1. Introduction
  2. Description of the method
  3. Measurement points
  4. Splitting criterion
  5. Global surrogate model
  6. GLEAMS
  7. Local explanations.
  8. Global explanations.
  9. Counterfactual explanations.
  10. Experiments on real data
  11. Models.
  12. Methods.
  13. Evaluation.
  14. Results.
  15. Conclusion
  16. ...and 4 more sections

Figures (4)

  • Figure 1: Overview of the global surrogate model construction. Left panel: the black-box model maps the input space (here $\mathcal{X} = [0,1]^2$) to $\mathbb{R}$, which we can visualize as a surface. Middle panel: we generate $N$ Sobol points on $\mathcal{X}$, giving rise to $N$ measurement points on the surface (in blue). Right panel: we fit a piecewise-linear global surrogate model $\hat{f}$ on the measurement points by recursively splitting $\mathcal{X}$.
  • Figure 2: Gleams explanations consist of both: i) Local importance (feature attribution) and ii) counterfactuals, i.e., answering what-if questions. On the left feature importance for a regressor trained on the house sell dataset (Section \ref{['sec:experiments']}), while figure on the right answers to "What if my house was bigger?" Moving along feature sqft_living, for a given example (yellow dot), we can visualize specific values of $f$ (Sobol points in blue) as well as the GLEAMS linear approximations (in green).
  • Figure 3: Evolution of the norm of the cumulative score process. Top panel: measurements of a piecewise-linear model (dark dots) visualized along one axis. Bottom panel: evolution of $\left\lVert B(t)\right\rVert_1$ as a function of $t$ (solid blue line). The process presents a clear maximum, which gives us a candidate split for this axis (vertical red line).
  • Figure 4: Approximating piecewise-linear models with GLEAMS surrogate model. Left panels: example (i), model on the left and GLEAMS surrogate on the right. Right panels: example (ii), model on the left and GLEAMS surrogate on the right.