Assessing Deep Neural Networks as Probability Estimators

Yu Pan, Kwo Sen Kuo, Michael L. Rilee, Hongfeng Yu

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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.

Original languageEnglish (US)
Title of host publicationProceedings - 2021 IEEE International Conference on Big Data, Big Data 2021
EditorsYixin Chen, Heiko Ludwig, Yicheng Tu, Usama Fayyad, Xingquan Zhu, Xiaohua Tony Hu, Suren Byna, Xiong Liu, Jianping Zhang, Shirui Pan, Vagelis Papalexakis, Jianwu Wang, Alfredo Cuzzocrea, Carlos Ordonez
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages9
ISBN (Electronic)9781665439022
StatePublished - 2021
Event2021 IEEE International Conference on Big Data, Big Data 2021 - Virtual, Online, United States
Duration: Dec 15 2021Dec 18 2021

Publication series

NameProceedings - 2021 IEEE International Conference on Big Data, Big Data 2021


Conference2021 IEEE International Conference on Big Data, Big Data 2021
Country/TerritoryUnited States
CityVirtual, Online


  • Bayesian Inference
  • Deep Neural Networks
  • Density and Sparsity
  • Generative Model
  • Uncertainty

ASJC Scopus subject areas

  • Information Systems and Management
  • Artificial Intelligence
  • Computer Vision and Pattern Recognition
  • Information Systems


Dive into the research topics of 'Assessing Deep Neural Networks as Probability Estimators'. Together they form a unique fingerprint.

Cite this