Tensor Product Neural Networks for Functional ANOVA Model

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 so called components, is one of the most popular tools for interpretable AI, and recently, various neural network models have been developed for estimating each component in the functional ANOVA model. However, such neural networks are highly unstable when estimating components 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 interpretable model which guarantees a unique functional ANOVA decomposition and thus is able to estimate each component stably. We call our proposed model ANOVA-NODE since it is a modification of Neural Oblivious Decision Ensembles (NODE) for the functional ANOVA model. Theoretically, we prove that ANOVA-NODE can approximate a smooth function well. Additionally, we experimentally show that ANOVA-NODE provides 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 network models do.

META-ANOVA: Screening interactions for interpretable machine learning

There are two things to be considered when we evaluate predictive models. One is prediction accuracy,and the other is interpretability. Over the recent decades, many prediction models of high performance, such as ensemble-based models and deep neural networks, have been developed. However, these models are often too complex, making it difficult to intuitively interpret their predictions. This complexity in interpretation limits their use in many real-world fields that require accountability, such as medicine, finance, and college admissions. In this study, we develop a novel method called Meta-ANOVA to provide an interpretable model for any given prediction model. The basic idea of Meta-ANOVA is to transform a given black-box prediction model to the functional ANOVA model. A novel technical contribution of Meta-ANOVA is a procedure of screening out unnecessary interaction before transforming a given black-box model to the functional ANOVA model. This screening procedure allows the inclusion of higher order interactions in the transformed functional ANOVA model without computational difficulties. We prove that the screening procedure is asymptotically consistent. Through various experiments with synthetic and real-world datasets, we empirically demonstrate the superiority of Meta-ANOVA