The Partial Response Network: a neural network nomogram
This provides an interpretable alternative to black-box models for binary classification in domains requiring transparency, though it is incremental as it builds on existing GANN and SENN frameworks.
The paper tackles the problem of interpretability in neural networks for tabular data by proposing the Partial Response Network (PRN), which derives an interpretable model from a Multi-layer Perceptron (MLP) using ANOVA decomposition and logistic Lasso for feature selection, achieving competitive performance against state-of-the-art methods like GBM, SVM, and Random Forests on benchmark data.
Among interpretable machine learning methods, the class of Generalised Additive Neural Networks (GANNs) is referred to as Self-Explaining Neural Networks (SENN) because of the linear dependence on explicit functions of the inputs. In binary classification this shows the precise weight that each input contributes towards the logit. The nomogram is a graphical representation of these weights. We show that functions of individual and pairs of variables can be derived from a functional Analysis of Variance (ANOVA) representation, enabling an efficient feature selection to be carried by application of the logistic Lasso. This process infers the structure of GANNs which otherwise needs to be predefined. As this method is particularly suited for tabular data, it starts by fitting a generic flexible model, in this case a Multi-layer Perceptron (MLP) to which the ANOVA decomposition is applied. This has the further advantage that the resulting GANN can be replicated as a SENN, enabling further refinement of the univariate and bivariate component functions to take place. The component functions are partial responses hence the SENN is a partial response network. The Partial Response Network (PRN) is equally as transparent as a traditional logistic regression model, but capable of non-linear classification with comparable or superior performance to the original MLP. In other words, the PRN is a fully interpretable representation of the MLP, at the level of univariate and bivariate effects. The performance of the PRN is shown to be competitive for benchmark data, against state-of-the-art machine learning methods including GBM, SVM and Random Forests. It is also compared with spline-based Sparse Additive Models (SAM) showing that a semi-parametric representation of the GAM as a neural network can be as effective as the SAM though less constrained by the need to set spline nodes.