Mixtures of Transparent Local Models

TL;DR

This paper introduces a mixture of transparent local models that are interpretable and adaptable to local variations, providing rigorous risk bounds and demonstrating competitiveness with existing methods on synthetic and real data.

Contribution

It proposes a novel mixture of transparent local models with a new loss function and establishes PAC-Bayesian risk bounds for classification and regression tasks.

Findings

Effective in modeling local variations with transparency

Provides theoretical risk bounds for the proposed models

Shows competitive performance on real datasets

Abstract

The predominance of machine learning models in many spheres of human activity has led to a growing demand for their transparency. The transparency of models makes it possible to discern some factors, such as security or non-discrimination. In this paper, we propose a mixture of transparent local models as an alternative solution for designing interpretable (or transparent) models. Our approach is designed for the situations where a simple and transparent function is suitable for modeling the label of instances in some localities/regions of the input space, but may change abruptly as we move from one locality to another. Consequently, the proposed algorithm is to learn both the transparent labeling function and the locality of the input space where the labeling function achieves a small risk in its assigned locality. By using a new multi-predictor (and multi-locality) loss function, we established rigorous PAC-Bayesian risk bounds for the case of binary linear classification problem and that of linear regression. In both cases, synthetic data sets were used to illustrate how the learning algorithms work. The results obtained from real data sets highlight the competitiveness of our approach compared to other existing methods as well as certain opaque models. Keywords: PAC-Bayes, risk bounds, local models, transparent models, mixtures of local transparent models.