Structural Modelling with Sparse Kernels

Abstract

A widely acknowledged drawback of many statistical modelling techniques, commonly used in machine learning, is that the resulting model is extremely difficult to interpret. A number of new concepts and algorithms have been introduced by researchers to address this problem. They focus primarily on determining which inputs are relevant in predicting the output. This work describes a transparent, advanced non-linear modelling approach that enables the constructed predictive models to be visualised, allowing model validation and assisting in interpretation. The technique combines the representational advantage of a sparse ANOVA decomposition, with the good generalisation ability of a kernel machine. It achieves this by employing two forms of regularisation: a 1-norm based structural regulariser to enforce transparency, and a 2-norm based regulariser to control smoothness. The resulting model structure can be visualised showing the overall effects of different inputs, their interactions, and the strength of the interactions. The robustness of the technique is illustrated using a range of both artificial and "real world" datasets. The performance is compared to other modelling techniques, and it is shown to exhibit competitive generalisation performance together with improved interpretability.

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