Technical Validation of Plot Designs by Use of Deep Learning

Abstract

AbstractWhen does inspecting a certain graphical plot allow for an investigator to reach the right statistical conclusion? Visualizations are commonly used for various tasks in statistics – including model diagnostics and exploratory data analysis – and though attractive due to its intuitive nature, the lack of available methods for validating plots is a major drawback. We propose a new technical validation method for visual reasoning. Our method trains deep neural networks to distinguish between plots simulated under two different data generating mechanisms (null or alternative), and we use the classification accuracy as a technical validation score (TVS). The TVS measures the information content in the plots, and TVS values can be used to compare different plots or different choices of data generating mechanisms, thereby providing a meaningful scale that new visual reasoning procedures can be validated against. We apply the method to three popular diagnostic plots for linear regression, namely scatter plots, quantile-quantile plots and residual plots. We consider various types and degrees of misspecification, as well as different within-plot sample sizes. Our method produces TVSs that increase with increasing sample size and decrease with increasing difficulty, and hence the TVS is a meaningful measure of validity.Keywords: Deep learninggraphical inferencelinear regressionneural networkmodel diagnosticsvisualizationDisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also.