Source-linked AI summary
GLocalX -- From Local to Global Explanations of Black Box AI Models
Mattia Setzu, Riccardo Guidotti, Anna Monreale, Franco Turini, Dino Pedreschi, Fosca Giannotti
TL;DR
Black-box models achieve strong accuracy but remain difficult to understand, motivating interpretable explanations for high-stakes decisions. GLocalX hierarchically aggregates local logical rules into compact global explanations, achieving high fidelity and low complexity while competing with global explainers.
Problem
Accurate nonlinear models often have opaque internal structures, creating transparency concerns in sensitive and critical applications.
Method
GLocalX is a model-agnostic local-first method that hierarchically merges local logical rules into global explanations of black-box behavior.
Results
GLocalX provides faithful and simple models, outperforming trivial rule unions and competing with natively global explainers, especially in complexity.
Takeaways & Limitations
The results suggest that accuracy and comprehensibility can often be achieved together, including in constrained settings with limited or unavailable data.
Takeaways & Limitations
The approach assumes local decision boundaries are sufficiently simple and that similar explanations can be composed into more general ones.
Abstract
from arXiv · showhide
Artificial Intelligence (AI) has come to prominence as one of the major components of our society, with applications in most aspects of our lives. In this field, complex and highly nonlinear machine learning models such as ensemble models, deep neural networks, and Support Vector Machines have consistently shown remarkable accuracy in solving complex tasks. Although accurate, AI models often are "black boxes" which we are not able to understand. Relying on these models has a multifaceted impact and raises significant concerns about their transparency. Applications in sensitive and critical domains are a strong motivational factor in trying to understand the behavior of black boxes. We propose to address this issue by providing an interpretable layer on top of black box models by aggregating "local" explanations. We present GLocalX, a "local-first" model agnostic explanation method. Starting from local explanations expressed in form of local decision rules, GLocalX iteratively generalizes them into global explanations by hierarchically aggregating them. Our goal is to learn accurate yet simple interpretable models to emulate the given black box, and, if possible, replace it entirely. We validate GLocalX in a set of experiments in standard and constrained settings with limited or no access to either data or local explanations. Experiments show that GLocalX is able to accurately emulate several models with simple and small models, reaching state-of-the-art performance against natively global solutions. Our findings show how it is often possible to achieve a high level of both accuracy and comprehensibility of classification models, even in complex domains with high-dimensional data, without necessarily trading one property for the other. This is a key requirement for a trustworthy AI, necessary for adoption in high-stakes decision making applications.
1. Introduction
GLocalX addresses the difficulty of explaining accurate but opaque models by aggregating local rule-based explanations into a global interpretable model. Its hierarchical approach seeks high fidelity and low complexity, including when data or local explanations are limited.
- GLocalX frames global explanation as a Local to Global problem, using local explanations to overcome limitations of purely global approaches.
- The method assumes logical explanations, locally simple decision boundaries, and composable explanations for similar instances.
- GLocalX hierarchically merges local logical rules while accounting for black-box fidelity and rule complexity.
- GLocalX achieves high fidelity and low complexity across black-box models and datasets, outperforming trivial rule unions and competing with global explainers.
- The evaluation includes settings with restricted local rules or no available data, reflecting proprietary-model and privacy-constrained use cases.
2. Related Work
Prior work includes global interpretable models and post-hoc approximations, while newer local methods explain individual black-box decisions. These approaches motivate a framework that aggregates local explanations into global ones.
- Existing explainability methods distinguish global explanations of overall black-box logic from local explanations of individual decisions.
- Interpretable-by-design approaches include decision trees and rule-based classifiers that directly solve classification with transparent models.
- Post-hoc global methods train interpretable models or extract rules by querying or analyzing black-box models, including Trepan and InTrees.
- Local methods such as LIME, SHAP, and LORE explain individual predictions using simplified spaces, feature contributions, or neighborhood models.
3. Local to Global Explanation Problem
The Local to Global Explanation Problem seeks a compact rule-based theory that describes a black box's overall decision logic from local explanations. GLocalX generalizes locally faithful rules into a global explanation while retaining interpretability.
- A classifier maps feature-valued instances to labels, while the black box may be inaccessible internally or uninterpretable to humans.
- Each local explanation is represented as a conjunctive decision rule whose premises describe the reason for the black box's outcome.
- The local-to-global problem combines explanations of individual black-box decisions to recover the classifier's overall logic.
- The target explanation theory is a set of logical decision rules that emulates the black box globally.
- Because local explanations are faithful only near their instances, aggregation must refine them into a theory that approximates global decision behavior.
4. Local to Global Hierarchy of Explanation Theories
GLocalX hierarchically merges local rule explanations into a global theory, using similarity, quality checks, and complementary join and cut operations to balance fidelity with simplicity.
- Global explanation construction: GLocalX iteratively merges local explanation theories into a global rule-based theory that emulates the black box while remaining simple and interpretable.The resulting theory can also explain individual black-box decisions, although global manipulation may reduce accuracy relative to local explanations.
- Hierarchical merging: The algorithm sorts candidate theories by similarity, samples data batches, merges the most similar acceptable pair, and stops when no qualifying merge remains.Batch-based merging favors diverse merge behaviors, while the quality criterion verifies that a merge improves the selected objective.
- Finding similar theories: Theory similarity is based on Jaccard similarity between their covered instances, capturing both premise overlap and shared coverage.An explanation covers an instance when its rule premise is satisfied; a theory covers an instance when at least one contained explanation does.
- Join and cut operators: Join generalizes non-conflicting rules, whereas cut specializes conflicting rules by removing overlaps and confining weaker rules to high-fidelity subspaces.Together, the operators approximately entail the input theories while balancing generalization, fidelity, and complexity.
- Merge quality: GLocalX evaluates merge quality with BIC, treating rule fidelity as model likelihood and average rule length as model complexity.Low-fidelity rules can also be trimmed using a relative fidelity percentile threshold.
5. Experiments
The experiments evaluate GLocalX on benchmark and proprietary datasets against black-box and native global baselines, including settings with restricted rules or no available explanation data.
- Experimental setup: GLocalX is evaluated on adult, compas, german, and proprietary diva datasets against DNN, Random Forest, and SVM black boxes where supported.DNNs and SVMs are used only on datasets where their performance is adequate; german and diva use Random Forests.
- Experimental setup: The experiments compare GLocalX with natively global interpretable frameworks and assess fidelity and complexity across standard benchmark settings.The black boxes are trained with grid searches and three-fold cross-validation, while evaluation uses held-out Xts data.
- Constrained settings: GLocalX is also tested with only a restricted number of local rules and, in the synthetic GLocalX* setting, without Xle data.GLocalX* generates training data from an estimated feature distribution and examines learning from local rules plus minimal distributional information.
- Dataset constraints: The proprietary diva dataset cannot be publicly released because of privacy and legal concerns.This limits direct public access to one of the evaluated real-world datasets.
5.2. Evaluation Measures
The evaluation distinguishes fidelity and accuracy from explanation complexity, measuring how well an explanation theory emulates the black box and solves the classification task.
- Fidelity measures how accurately the explanation theory emulates the black box’s predictions.It is defined over the predictions returned by the explanation theory and black box.
- Explanation complexity is assessed through theory size and mean rule length.Size counts explanations in the theory, while length is the mean number of premises per rule.
- Accuracy measures how well the explanation theory or black box predicts the real labels.This metric addresses whether the transparent model can solve the classification problem and potentially replace the black box.
- Experiments train black boxes and extract local explanations on designated datasets, then evaluate fidelity on Xts and complexity on models learned from Xle.The setup uses Xbb for black-box training, Xle for local explanations and global interpretable models, and Xts for fidelity evaluation.
5.3. Empirical Motivation of the Local to Global Explanation Problem
The experiments motivate local-to-global explanation by showing that directly trained interpretable models can remain less accurate than black boxes while becoming too complex to interpret.
- Directly trained decision trees can have high accuracy but usually remain less accurate than the black-box classifiers.
- Decision-tree explanations can also have high size and average rule length, making the transparent model non-interpretable in practice.
- GLocalX is presented as reaching comparable fidelity while maintaining an admissible explanation complexity using a much smaller portion of the data.
- GLocalX achieves fidelity 0.86 with six rules inferred from 1,515 starting local explanations for the COMPAS random-forest example.
- The COMPAS example shows longer non-recidivous rules involving several defendant attributes, whereas recidivous rules use only prior imprisonment and offenses.
- The qualitative analysis identifies higher recidivism-related values among African-American defendants than Caucasian defendants in the covered groups.
5.5. Impact of the Filter Parameter
Filtering changes GLocalX’s fidelity and complexity trade-off: fewer retained rules can reduce size, but an intermediate filter setting produces the best combined performance.
- Fidelity is lowest around αq = 75 and peaks around αq = 95, indicating that retaining many rules can mislead predictions.
- Increasing the filter parameter consistently decreases explanation size while slightly increasing explanation length across datasets and black boxes.
- The authors attribute possible fidelity degradation to poor rules that perform well on individual batches leaking into the final model.
- αq = 95 gives the best combined fidelity, size, and length performance, suggesting that few rules can mimic global black-box behavior.
5.6. Effect of the Number of Local Rules
GLocalX remains usable with fewer local explanation rules: under αq = 50, fidelity varies little and can slightly improve as the sampled input set changes.
- With αq = 50, GLocalX shows only small fidelity fluctuations as the fraction of available local rules varies.
- Across sampled rule fractions, fidelity shows an overall slight improvement, supporting use with smaller rule sets.
- Figure 2 compares fidelity and explanation size for varying numbers of local rules against fidelity using all available rules.
- The filter parameter should be tuned jointly for required fidelity, explanation size, and the number of input rules.
5.7. Effectiveness of the Global Explainers
GLocalX produces compact global rule explanations with fidelity comparable to strong global explainers, including when data are unavailable. Its hierarchical merging outperforms simply unioning local rules while balancing fidelity and complexity.
- GLocalX achieves fidelity within 0.1 of the best global explainer while producing substantially smaller rule sets than cpar and decision trees.Its rule sets are one order of magnitude smaller than cpar and one or two orders smaller than decision trees.
- GLocalX learns consistently shorter rules than decision trees, although pdt and cpar obtain shorter rules on this metric.
- GLocalX substantially outperforms the union baseline, showing that local rules require processing to remove useless or misleading aspects.
- GLocalX* retains similar fidelity without data, with worst-case fidelity only 3% below GLocalX.
- Friedman tests reject equivalence among methods for fidelity, size, and length at p-values below 0.05, 0.0001, and 0.0005, respectively.
5.8. Replacing the Black Box with a Global Explainer
The replacement experiment evaluates whether GLocalX can predict real dataset labels rather than only imitate black-box labels. GLocalX trails some competitors in accuracy but has low fidelity–accuracy gaps, supporting its use as a transparent predictor within the tested settings.
- The experiment measures held-out test accuracy, fidelity–accuracy differences, and explanation size and length for global explainers used as black-box replacements.
- GLocalX accuracy is up to 7% lower on compas and 15% lower on adult than some competing explainers.
- Decision-tree ∆acc is highly unstable, ranging from −0.264 to 0.027.
- GLocalX, cpar, and pdt show lower variance than the other explainers in fidelity–accuracy differences.
- GLocalX has the lowest ∆acc among the compared models, approximately 1.5 times lower than cpar and 2.8 times lower than decision trees.Lower ∆acc indicates greater stability between black-box fidelity and dataset-label accuracy.
6. Conclusions
The paper concludes that GLocalX converts local logical explanations into faithful and simple global models, with potential use as transparent predictors. It identifies extensions toward richer rules, other domains, alternative merging strategies, and causal explanations.
- GLocalX hierarchically derives global logical-rule explanations from local explanations while addressing both fidelity and explanation complexity.
- The results suggest that GLocalX is faithful and simple, outperforms trivial rule union, and is competitive with native global explainers in complexity.
- GLocalX explanation theories might serve directly as transparent predictors with performance similar to other global predictors.
- Future work includes fuzzy and non-CNF rules, non-logical domains such as text and images, new merging functions, and causal explanations.