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GAMI-Net: An Explainable Neural Network based on Generalized Additive Models with Structured Interactions
Zebin Yang, Aijun Zhang, Agus Sudjianto
TL;DR
Neural networks often lack interpretable decision processes, motivating models that balance prediction and explanation. The paper proposes GAMI-Net, a disentangled additive neural network with structured main effects and interactions, and reports high interpretability with competitive predictive performance against black-box models.
Problem
Neural networks’ decision-making can be difficult to understand and may behave abnormally when data changes slightly, creating a need for interpretable neural models.
Method
GAMI-Net uses additive neural subnetworks for main effects and pairwise interactions, with sparsity, heredity, marginal clarity, and adaptive training.
Results
GAMI-Net is highly interpretable and easily compared with competitive predictive performance to black-box machine-learning models.
Takeaways & Limitations
GAMI-Net provides an intrinsically explainable neural-network model that combines structured effect selection with competitive prediction.
Takeaways & Limitations
The paper identifies extending GAMI-Net as future work, indicating that the presented model remains within its current scope of capabilities.
Abstract
from arXiv · showhide
The lack of interpretability is an inevitable problem when using neural network models in real applications. In this paper, an explainable neural network based on generalized additive models with structured interactions (GAMI-Net) is proposed to pursue a good balance between prediction accuracy and model interpretability. GAMI-Net is a disentangled feedforward network with multiple additive subnetworks; each subnetwork consists of multiple hidden layers and is designed for capturing one main effect or one pairwise interaction. Three interpretability aspects are further considered, including a) sparsity, to select the most significant effects for parsimonious representations; b) heredity, a pairwise interaction could only be included when at least one of its parent main effects exists; and c) marginal clarity, to make main effects and pairwise interactions mutually distinguishable. An adaptive training algorithm is developed, where main effects are first trained and then pairwise interactions are fitted to the residuals. Numerical experiments on both synthetic functions and real-world datasets show that the proposed model enjoys superior interpretability and it maintains competitive prediction accuracy in comparison to the explainable boosting machine and other classic machine learning models.
1 Introduction
The paper addresses the tension between neural networks’ predictive strength and their limited interpretability by proposing GAMI-Net, an intrinsically explainable network with structured main effects and interactions. Its design combines disentangled additive subnetworks with sparsity, heredity, marginal clarity, and adaptive training to retain interpretability while maintaining competitive prediction.
- Motivation: Neural networks can achieve accurate predictions, but their internal decision-making is difficult to understand and may behave abnormally when data changes slightly.These issues motivate intrinsically interpretable neural-network designs rather than relying only on post-hoc explanations.
- Proposed model: GAMI-Net extends explainable neural networks to model both main effects and pairwise interactions with separate additive subnetworks.Each subnetwork uses one input node for a main effect or two input nodes for a pairwise interaction, and the subnetworks are additively combined.
- Interpretability: Sparsity, heredity, and marginal clarity constrain GAMI-Net to retain important effects, include interactions only with important parent effects, and distinguish interactions from their main effects.These constraints support parsimonious and structurally interpretable representations.
- Training: GAMI-Net uses a three-stage adaptive training procedure that trains and prunes main effects, fits and prunes selected interactions, and then jointly fine-tunes them.The procedure first learns main effects before adding important pairwise interactions.
- Evaluation: Experiments on synthetic functions and real-world datasets find GAMI-Net more interpretable than benchmark models while maintaining competitive predictive performance.The paper evaluates GAMI-Net against interpretable and black-box models, including EBM and classic machine-learning models.
2 GAMI-Net Methodology
GAMI-Net represents predictions with additive subnetworks for nonlinear main effects and pairwise interactions, while structured constraints promote sparse, hierarchical, and distinguishable components. Its adaptive procedure fits main effects before interactions and supports direct global and local interpretation.
- Network Architecture: GAMI-Net combines a main-effect module and a pairwise-interaction module whose subnetworks are linearly combined to produce the final output.Main-effect subnetworks fit 1D curves, whereas interaction subnetworks approximate 2D surfaces.
- Network Architecture: Each main effect uses one input node and each pairwise interaction uses two input nodes, with multiple hidden layers enabling flexible nonlinear functions.Categorical variables are preprocessed using one-hot encoding.
- Computational Aspects: GAMI-Net is trained adaptively by estimating main effects first, then selecting and fitting ranked pairwise interactions to residuals under heredity and marginal-clarity constraints.The architecture figure describes sequential estimation, pruning trivial subnetworks, and imposing marginal clarity on interactions.
- Interpretability Constraints: GAMI-Net imposes sparsity, heredity, and marginal clarity constraints to select important effects, structure interactions, and make components mutually distinguishable.Sparsity selects top-ranked effects; weak heredity permits an interaction only when at least one parent main effect is included; marginal clarity regularizes interactions toward orthogonality with parent effects.
- Interpretability Constraints: Sparsity prunes effects with small variation or selects top-s1 main effects and top-s2 pairwise interactions according to their variation measures.The paper motivates pruning as a way to reduce unnecessary complexity and overfitting.
- Interpretability Constraints: Marginal clarity addresses non-identifiability because main effects can be absorbed by child interactions, creating multiple representations and unstable interpretation.The constraint is motivated by orthogonal functional ANOVA decomposition.
- Model Interpretation: GAMI-Net supports direct partial-dependence interpretation and easy local explanations, and is reported as more efficient and interpretable than EBM.These claims are presented as intrinsic interpretability properties of the fitted model.
3 Numerical Experiments
Numerical experiments on synthetic and real-world datasets evaluate GAMI-Net against interpretable and black-box benchmarks using repeated train, validation, and test procedures. The results show strong predictive performance, interpretable effect recovery, and practical advantages over EBM in several settings.
- Experimental setup: Experiments compare GAMI-Net with EBM, spline-based GAM, GLM, MLP, RF, and XGBoost across synthetic and real-world datasets.Predictive performance is measured by RMSE for regression and AUC for binary classification, with experiments repeated 10 times.
- Synthetic function: GAMI-Net outperforms all compared interpretable and black-box models in every tested synthetic-function case.The comparison includes both interpretable models and black-box models such as MLP and RF.
- Synthetic function: Adding pairwise interactions significantly decreases training and validation losses, demonstrating their value beyond the additive main effects.The losses show a training increase and validation decrease when trivial interactions are pruned during fine-tuning.
- Synthetic function: The selected synthetic model contains s1 = 6 main effects and s2 = 2 pairwise interactions, while additional effects offer little benefit and may overfit.The fitted model successfully captures all six main effects and two pairwise interactions, with fitted results close to the ground truth.
- Real-world datasets: On the bank marketing dataset, GAMI-Net produces smoother fitted effects than EBM and supports both global and local interpretation.EBM exhibits difficult-to-understand fluctuations, whereas GAMI-Net’s fitted model is continuous and smooth.
- Real-world datasets: GAMI-Net and EBM are both competitive in predictive power, while GAMI-Net is designed with stronger interpretability considerations and may perform better for smooth effects.The paper states that EBM may perform better for piece-wise constant shape functions.
4 Conclusion
GAMI-Net approximates complex functional relationships with interpretable main-effect and pairwise-interaction subnetworks, while enforcing sparsity, heredity, and marginal clarity. Experiments report competitive predictive performance alongside high interpretability, with future work extending shape constraints and interaction order.
- 4 Conclusion: Sparsity, heredity, and marginal clarity constraints promote parsimony, structurally valid interactions, and separation between effects.The constraints are designed to enhance interpretability and avoid effects-mixing problems.
- 4 Conclusion: The experimental results show competitive predictive performance to black-box machine learning models while retaining high interpretability.The GAMI-Net estimates are also described as easily interpretable.
- 4 Conclusion: Future work includes adding shape constraints such as monotonicity, convexity, or concavity based on prior experience or domain knowledge.These constraints are identified as one direction for extending GAMI-Net.
- 4 Conclusion: Another future direction is incorporating higher-order interactions for more sophisticated developments.