Neural Additive Models (NAMs) (Agarwal et al., and have become the go-to method for problems 2021b) were recently proposed as a class of Neural Networks, requiring high-level predictive power. There has that impose an additivity constraint on the input data been extensive research on how DNNs arrive at and thus allow to directly derive the feature-wise contribution their decisions, however, the inherently uninterpretable onto the generated predictions as a function of the input networks remain up to this day mostly domain. While this indeed yields an exact representation of unobservable "black boxes". In recent years, the the decision making process, NAMs are nevertheless highly field has seen a push towards interpretable neural complex functions that are characterized by hundreds of networks, such as the visually interpretable thousands of parameters and thus fail to address additional Neural Additive Models (NAMs). We propose dimensions of interpretability (Murdoch et al., 2019). To a further step into the direction of intelligibility this end, we propose the use of Structural Neural Additive beyond the mere visualization of feature effects Models (SNAMs) as a way to achieve the same (and and propose Structural Neural Additive Models even better) predictive performance with a fraction of the (SNAMs). A modeling framework that combines parameters required, while providing intelligibility beyond classical and clearly interpretable statistical methods mere visualizations. The contributions of SNAMs can be with the predictive power of neural applications.

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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.