Assessing Deep Neural Networks as Probability Estimators

TL;DR

This paper evaluates how well deep neural networks can estimate classification probabilities and introduces a framework for uncertainty analysis, revealing key factors affecting their probabilistic accuracy.

Contribution

It provides a systematic approach to assess DNNs' probability estimates and identifies factors influencing their uncertainty characterization.

Findings

Likelihood probability density significantly impacts estimation accuracy.

Inter-categorical sparsity affects uncertainty estimation.

Prior probability has less influence on DNN uncertainty.

Abstract

Deep Neural Networks (DNNs) have performed admirably in classification tasks. However, the characterization of their classification uncertainties, required for certain applications, has been lacking. In this work, we investigate the issue by assessing DNNs' ability to estimate conditional probabilities and propose a framework for systematic uncertainty characterization. Denoting the input sample as x and the category as y, the classification task of assigning a category y to a given input x can be reduced to the task of estimating the conditional probabilities p(y|x), as approximated by the DNN at its last layer using the softmax function. Since softmax yields a vector whose elements all fall in the interval (0, 1) and sum to 1, it suggests a probabilistic interpretation to the DNN's outcome. Using synthetic and real-world datasets, we look into the impact of various factors, e.g., probability density f(x) and inter-categorical sparsity, on the precision of DNNs' estimations of p(y|x), and find that the likelihood probability density and the inter-categorical sparsity have greater impacts than the prior probability to DNNs' classification uncertainty.