Generalized Additive Models (GAMs) can be used to create non-linear glass-box (i.e. explicitly interpretable) models, where the predictive function is fully observable over the complete input space. However, glass-box interpretability itself does not allow for the incorporation of expert knowledge from the modeller. In this paper, we present ParamBoost, a novel GAM whose shape functions (i.e. mappings from individual input features to the output) are learnt using a Gradient Boosting algorithm that fits cubic polynomial functions at leaf nodes. ParamBoost incorporates several constraints commonly used in parametric analysis to ensure well-refined shape functions. These constraints include: (i) continuity of the shape functions and their derivatives (up to C2); (ii) monotonicity; (iii) convexity; (iv) feature interaction constraints; and (v) model specification constraints. Empirical results show that the unconstrained ParamBoost model consistently outperforms state-of-the-art GAMs across several real-world datasets. We further demonstrate that modellers can selectively impose required constraints at a modest trade-off in predictive performance, allowing the model to be fully tailored to application-specific interpretability and parametric-analysis requirements.

It is desirable to restrict the number of components (i.e., encourage sparsity) for

The Rashomon set is the set of models that are approximately as good as the best model in the class. That is, it is the set of all good models.

Previous works attempting to close this gap have failed to fully investigate the exponentially growing number of feature combinations which deep networks consider automatically during training. In this work, we develop a tractable selection algorithm to efficiently identify the necessary feature combinations byleveraging techniques infeature interaction detection. Our proposed Sparse Interaction AdditiveNetworks (SIAN) construct abridge from thesesimple andinterpretable models tofullyconnected neuralnetworks.

However, NAMs (likeallGAMs), are not causal models.

They perform similarly to existing state-of-the-art generalized additive models in accuracy,but are more flexible because theyare based on neural nets instead ofboosted trees.