Explainable Neural Networks with Guarantees: A Sparse Estimation Approach

TL;DR

This paper presents SparXnet, an explainable neural network that combines sparse feature selection with complex relationship modeling, providing interpretability and strong theoretical guarantees without sacrificing predictive accuracy.

Contribution

The paper introduces SparXnet, a neural network architecture that automatically selects important features and offers theoretical generalization bounds, advancing explainability in neural networks.

Findings

SparXnet achieves feature sparsity with comparable predictive performance.

Theoretical analysis shows linear generalization bounds in the number of features.

Experimental results validate interpretability and effectiveness on real-world data.

Abstract

Balancing predictive power and interpretability has long been a challenging research area, particularly in powerful yet complex models like neural networks, where nonlinearity obstructs direct interpretation. This paper introduces a novel approach to constructing an explainable neural network that harmonizes predictiveness and explainability. Our model, termed SparXnet, is designed as a linear combination of a sparse set of jointly learned features, each derived from a different trainable function applied to a single 1-dimensional input feature. Leveraging the ability to learn arbitrarily complex relationships, our neural network architecture enables automatic selection of a sparse set of important features, with the final prediction being a linear combination of rescaled versions of these features. We demonstrate the ability to select significant features while maintaining comparable predictive performance and direct interpretability through extensive experiments on synthetic and real-world datasets. We also provide theoretical analysis on the generalization bounds of our framework, which is favorably linear in the number of selected features and only logarithmic in the number of input features. We further lift any dependence of sample complexity on the number of parameters or the architectural details under very mild conditions. Our research paves the way for further research on sparse and explainable neural networks with guarantee.