Feedforward neural networks as statistical models 

Andrew McIerney, Maths & Stats Department, University of Limerick, Ireland

Abstract
Feedforward neural networks (FNNs) are typically viewed as “pure prediction” algorithms, and their strong predictive performance has led to their use in many machine-learning applications. However, quite simply, FNNs are non-linear regression models, where the covariates are mapped to the response through a series of weighted summations and non-linear functions. Their success in predictivity can be attributed, at least in part, to their ability to capture complex relationships through the modelling of higher-order interactions. However, their flexibility comes with an interpretability trade-off; thus, FNNs have been historically less popular among statisticians, who tend to use more interpretable additive models. Nevertheless, classical statistical theory such as significance testing and uncertainty quantification is still relevant for FNNs. Supplementing FNNs with methods of statistical inference, model selection and the covariate-effect visualisations, can shift the focus away from “black-box” prediction and make FNNs more akin to traditional statistical models. This can pave the way towards more inferential analysis, and, hence, increase the utility of the FNN within the statistician's toolbox.

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