Tensor Product Neural Networks for Functional ANOVA Model
This addresses interpretability issues in AI for users needing reliable model decompositions, though it is incremental as it builds on existing neural network methods for functional ANOVA.
The paper tackles the instability in estimating components of functional ANOVA models with neural networks by proposing ANOVA-TPNN, which guarantees a unique decomposition and provides more stable and accurate component estimation, as shown empirically with improved stability under varying training data and initial parameters.
Interpretability for machine learning models is becoming more and more important as machine learning models become more complex. The functional ANOVA model, which decomposes a high-dimensional function into a sum of lower dimensional functions (commonly referred to as components), is one of the most popular tools for interpretable AI, and recently, various neural networks have been developed for estimating each component in the functional ANOVA model. However, such neural networks are highly unstable when estimating each component since the components themselves are not uniquely defined. That is, there are multiple functional ANOVA decompositions for a given function. In this paper, we propose a novel neural network which guarantees a unique functional ANOVA decomposition and thus is able to estimate each component stably and accurately. We call our proposed neural network ANOVA Tensor Product Neural Network (ANOVA-TPNN) since it is motivated by the tensor product basis expansion. Theoretically, we prove that ANOVA-TPNN can approximate any smooth function well. Empirically, we show that ANOVA-TPNN provide much more stable estimation of each component and thus much more stable interpretation when training data and initial values of the model parameters vary than existing neural networks do.