# Dual feature-based and example-based explanation methods

## TL;DR

This paper introduces a new method for explaining machine learning models using a dual representation of data points and convex combinations.

## Contribution

The novelty lies in using a dual dataset and convex hulls for both feature-based and example-based explanations.

## Key findings

- The dual linear surrogate model provides accurate feature importance values through matrix calculations.
- The approach is a modification of LIME and allows for example-based explanations inherently.
- Numerical experiments on real datasets validate the effectiveness of the proposed method.

## Abstract

A new approach to the local and global explanation based on selecting a convex hull constructed for the finite number of points around an explained instance is proposed. 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. A code of proposed algorithms is available. The proposed results are fundamental and can be used in various application areas. They do not involve specific human subjects and human data.