Sparse Neural Additive Model: Interpretable Deep Learning with Feature Selection via Group Sparsity

TL;DR

This paper introduces Sparse Neural Additive Models (SNAM), which combine interpretability and feature selection in deep learning through group sparsity, with theoretical guarantees and empirical validation.

Contribution

SNAM extends neural additive models with group sparsity regularization, providing theoretical analysis and practical algorithms for feature selection and interpretability.

Findings

SNAM provably converges to zero training loss.

SNAM achieves asymptotic vanishing estimation error.

SNAM can recover true feature support with proper regularization.

Abstract

Interpretable machine learning has demonstrated impressive performance while preserving explainability. In particular, neural additive models (NAM) offer the interpretability to the black-box deep learning and achieve state-of-the-art accuracy among the large family of generalized additive models. In order to empower NAM with feature selection and improve the generalization, we propose the sparse neural additive models (SNAM) that employ the group sparsity regularization (e.g. Group LASSO), where each feature is learned by a sub-network whose trainable parameters are clustered as a group. We study the theoretical properties for SNAM with novel techniques to tackle the non-parametric truth, thus extending from classical sparse linear models such as the LASSO, which only works on the parametric truth. Specifically, we show that SNAM with subgradient and proximal gradient descents provably converges to zero training loss as $t\to\infty$, and that the estimation error of SNAM vanishes asymptotically as $n\to\infty$. We also prove that SNAM, similar to LASSO, can have exact support recovery, i.e. perfect feature selection, with appropriate regularization. Moreover, we show that the SNAM can generalize well and preserve the `identifiability', recovering each feature's effect. We validate our theories via extensive experiments and further testify to the good accuracy and efficiency of SNAM.