Statistical Analysis of Neural Networks as Applied to Building Energy Prediction

Abstract

It has been shown that a neural network with sufficient hidden units can approximate any continuous function defined on a closed and bounded set. This has inspired the use of neural networks as general nonlinear regression models. As with other nonlinear regression models, tools of conventional statistical analysis can be applied to neural networks to yield a test for the relevance or irrelevance of a free parameter. The test, a version of Wald’s test, can be extended to yield a test for the relevance or irrelevance of an input variable. This test was applied to the building energy use data of the Energy Prediction Shootout II contest. Input variables were selected by initially constructing a neural network model which had many inputs, then cutting out the inputs which were deemed irrelevant on the basis of the Wald test. Time-lagged values were included for some input variables, with the time lag chosen by inspecting the autocovariance function of the candidate variable. The results of the contest entry are summarized, and the benefits of applying Wald’s test to this problem are assessed.