Dual feature-based and example-based explanation methods

TL;DR

The paper addresses explainability for black-box models by introducing a dual feature-based and example-based framework built on convex hull duality. It replaces perturbations in the original feature space with uniform sampling on the unit simplex of convex coefficients derived from the hull of $K$ nearest neighbors around the explainable instance, yielding a dual dataset for a linear surrogate $h(\boldsymbol{\lambda})$. The primal explanation coefficients are recovered from the dual via $\mathbf{aX}=\mathbf{b}$, enabling both feature-based and example-based explanations, with NAM applicable on the dual features to obtain interpretable shape functions. Empirical results on synthetic and real data show robustness to out-of-domain perturbations, improved or competitive accuracy relative to LIME, and coherent example-based explanations, while code availability supports reproducibility. The approach offers a flexible, perturbation-free alternative that can be extended to global explanations and other surrogate models, with practical impact for reliable model interpretation in safety-critical domains.

Abstract

A new approach to the local and global explanation is proposed. It is based on selecting a convex hull constructed for the finite number of points around an explained instance. The convex hull allows us to consider a dual representation of instances in the form of convex combinations of extreme points of a produced polytope. Instead of perturbing new instances in the Euclidean feature space, vectors of convex combination coefficients are uniformly generated from the unit simplex, and they form a new dual dataset. A dual linear surrogate model is trained on the dual dataset. The explanation feature importance values are computed by means of simple matrix calculations. The approach can be regarded as a modification of the well-known model LIME. The dual representation inherently allows us to get the example-based explanation. The neural additive model is also considered as a tool for implementing the example-based explanation approach. Many numerical experiments with real datasets are performed for studying the approach. The code of proposed algorithms is available.

Figures (13)

• Figure 1: An illustration of a case of out-of-domain data when generated points may be out of the training point domain
• Figure 2: Two cases of the explained point location and the convex polytops constructed from $K$ nearest neighbors
• Figure 3: Steps of the algorithm for explanation of a prediction provided by a black-box model at the point depicted by the small triangle
• Figure 4: Generated points in the original LIME (a) and in the proposed dual method (b)
• Figure 5: A scheme of training NAM on the generated set of random vectors $\mathbf{\lambda}$