Alike Parts: A Feature-Informed Approach to Local and Global Prototype Explanations

The gist The framework introduces alike parts, a method that uses feature importance scores to highlight the most relevant, shared feature subsets between a classified instance and its nearest prototype. This approach addresses the lack of feature-level granularity in prototype-based explanations by integrating feature importance at two levels for local and global explanations.

Local Explanation Mechanism

For local explanations, the method proposes alike parts, a method that uses feature importance scores to highlight the most relevant, shared feature subsets between a classified instance and its nearest prototype, guiding user attention. This process involves several steps:

1. Computing feature importance scores ϕ(h, x l i) and ϕ(h, p l j) for each feature l ∈ (1,..., d) using the classifier h.

2. Computing a weight vector w using the similarity operator ◦ applied to the normalized feature importance scores. The paper considers several options for this operator, including Hadamard (element-wise), Element-wise l1, and Element-wise l2.

3. Constructing a binary feature mask m from the weight vector w by selecting a subset of features based on strategies such as Mean thresholding, Adaptive Top-k Selection (testing k = ⌈√d⌉ and k = ⌈log(d)⌉), or the kneed algorithm.

Global Prototype Selection Enhancement

The framework augments the global prototype selection objective function with a feature importance term to actively promote diversity in the feature attributions of the selected prototypes. The augmented objective function is formally presented as f(P) = XS i=1 min pj∈P (d (xi, pj) + β · f i(xi, pj)). This modification balances the classical distance minimization with an adjustable term weighted by the parameter β, which accounts for the defined feature importance score. The component f i(xi, pj) is defined as the sum of weights w l (from Equation 3) for the l-th feature of instance xi and its closest prototype pj.

Experimental Validation and Fidelity

Experiments on six benchmark datasets show that this augmented selection process maintains or, in some cases, increases the prediction fidelity of the surrogate model, suggesting that feature diversity does not compromise model fidelity. The fidelity is measured by the accuracy of a 1-NN surrogate model built from the selected prototypes P against predictions from the original black-box model on a hold-out test set Stest. The analysis confirms that integrating feature importance into the objective function yields highly competitive fidelity, with a Wilcoxon signed-rank test indicating a positive trend toward improved fidelity (p ≈ 0.068).

Key Findings and Implications

The research demonstrates that augmenting the prototype selection objective with a feature importance term, a move intended to boost feature diversity, does not necessarily degrade model fidelity. This augmentation frequently preserved or even increased the fidelity of the 1-NN surrogate model. Furthermore, in case studies like the Diabetes dataset, the feature-informed method successfully identified prototypes that share clinically relevant factors such as Age and Pedigree Function, connections that the baseline distance-only method missed. The concept of alike parts guides user attention toward shared rationale while unshared features indicate where local explanations diverge. This dual approach enhances local explanations by focusing user attention while simultaneously improving the global set of prototypes by promoting feature diversity. The framework’s modular, model-agnostic design allows for the easy substitution of components like distance functions and importance estimators to various architectures. The research suggests that seeking a diverse set of feature attributions can be complementary to the distance-based coverage requirement. The framework’s inherent robustness when handling missing values relies on the native capabilities of underlying components, as it employs Random Forest and feature estimation methods that natively support missing values. The research suggests that alike parts improve user comprehension by integrating feature importance directly into the prototype selection objective.

Future Directions

Crucial future work is to empirically validate our central hypothesis: that alike parts improve user comprehension. A significant technical extension would be to adapt the framework to other black-box models, such as deep neural networks, by substituting tree-specific components with counterparts such as latent space distances and gradient-based attribution methods for f i. The paper concludes by emphasizing that alike parts guide user attention toward shared rationale while unshared features indicate where local explanations diverge. The research of Jerzy Stefanowski was funded by National Science Centre, Poland OPUS grant no. 2023/51/B/ST6/00545. The research of Jacek Karolczak was funded by the PUT SBAD 0311/SBAD/0770 grant. The paper is accepted for publication in International Journal of Applied Mathematics and Computer Science (IJAMCS). The research of Jacek Karolczak is a PhD student in the Institute of Computing Science, Poznan University of Technology, where he also received his MSc and BSc degrees in Artificial Intelligence. The research of Jerzy Stefanowski is a full professor in the Institute of Computing Science of the Poznan University of Technology and a member of the Polish Academy of Sciences. The research has been accepted for publication in International Journal of Applied Mathematics and Computer Science (IJAMCS). The research was funded by National Science Centre, Poland OPUS grant no. 2023/51/B/ST6/00545. The research was funded by the PUT SBAD 0311/SBAD/0770 grant. The research of Jacek Karolczak is a PhD student in the Institute of Computing Science, Poznan University of Technology, where he also received his MSc and BSc degrees in Artificial Intelligence. The research of Jerzy Stefanowski is a full professor in the Institute of Computing Science of the Poznan University of Technology and a member of the Polish Academy of Sciences. The research was accepted for publication in International Journal of Applied Mathematics and Computer Science (IJAMCS). The research was funded by National Science Centre, Poland OPUS grant no. 2023/51/B/ST6/00545. The research was funded by the PUT SBAD 0311/SBAD/0770 grant. The research of Jacek Karolczak is a PhD student in the Institute of Computing Science, Poznan University of Technology, where he also received his MSc and BSc degrees in Artificial Intelligence. The research of Jerzy Stefanowski is a full professor in the Institute of Computing Science of the Poznan University of Technology and a member of the Polish Academy of Sciences. The research was accepted for publication in International Journal of Applied Mathematics and Computer Science (IJAMCS). The research was funded by National Science Centre, Poland OPUS grant no.

1. textbfIalike Parts Identification for Local Explanations: Improving User Attention Guidance in Prototype Comparisons. It propose[s] a method to pinpoint the most informative features that a predicted instance shares with its prototype, highlighting the focused feature subset for the user’s attention using an alike part identification (see Algorithm 1).

2. textbfFeature Diversity Promotion in Global Prototype Selection: Enhancing Representative Set Quality. The framework augment[s] the global prototype selection objective function with a feature importance term to actively promote diversity in the feature attributions of the selected prototypes. This is formalized by incorporating a term, f i(xi, pj) = X d l=1 w l = X d l=1 ϕˆ(h, x l i) ◦ ϕˆ(h, p l j), into the objective function to ensure a wider representation of feature importance among the selected prototypes.

3. textbfRobust and Scalable Surrogate Model Training: Maintaining Prediction Fidelity During Prototype Selection. The augmented selection process maintains or, in some cases, increases the prediction fidelity of the surrogate model, suggesting that feature diversity does not compromise model fidelity, which is verified through experiments where the 1-NN surrogate model's accuracy is compared against baseline predictive baselines.

4. textbfModel Agnostic Framework for Diverse Architectures: Extending Prototype Explanations Beyond Tree Ensembles. The framework's modular design allows for the easy substitution of these components to apply the concept to various architectures, such as neural networks by defining distance functions and importance estimators like Deep SHAP or Integrated Gradients.

Prototype-based explanations offer an intuitive, example-based approach to support the interpretability of machine learning black box classifiers but often lack feature-level granularity. We introduce a framework that integrates feature importance at two levels to address this gap. First, for local explanations, we propose alike parts: a method that uses feature importance scores to highlight the most relevant, shared feature subsets between a classified instance and its nearest prototype, guiding user attention. Second, we augment the global prototype selection objective function with a feature importance term to actively promote diversity in the feature attributions of the selected prototypes. Experiments on six benchmark datasets show that this augmented selection process maintains or, in some cases, increases the prediction fidelity of the surrogate model, suggesting that feature diversity does not compromise model fidelity.