Understanding Uncertainty Maps in Vision with Statistical Testing

Quantitative descriptions of confidence intervals and uncertainties of the predictions of a model are needed in many applications in vision and machine learning. Mechanisms that enable this for deep neural network (DNN) models are slowly becoming available, and occasionally, being integrated within production systems. But the literature is sparse in terms of how to perform statistical tests with the uncertainties produced by these overparameterized models. For two models with a similar accuracy profile, is the former model's uncertainty behavior better in a statistically significant sense compared to the second model? For high resolution images, performing hypothesis tests to generate meaningful actionable information (say, at a user specified significance level
$\alpha=0.05)$
is difficult but needed in both mission critical settings and elsewhere. In this paper, specifically for uncertainties defined on images, we show how revisiting results from Random Field theory (RFT) when paired with DNN tools (to get around computational hurdles) leads to efficient frameworks that can provide a hypothesis test capabilities, not otherwise available, for uncertainty maps from models used in many vision tasks. We show via many different experiments the viability of this framework.