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Related Experiment Video

Updated: Oct 14, 2025

Deep Neural Networks for Image-Based Dietary Assessment

Deep Neural Networks for Image-Based Dietary Assessment

Published on: March 13, 2021

Epistemic uncertainty quantification in deep learning classification by the Delta method.

Geir K Nilsen¹, Antonella Z Munthe-Kaas¹, Hans J Skaug¹

¹Department of Mathematics, University of Bergen, Norway.

Neural Networks : the Official Journal of the International Neural Network Society

|November 8, 2021

Summary

This summary is machine-generated.

We developed an efficient approximation of the Delta method for deep neural networks to quantify epistemic uncertainty. This method accurately estimates uncertainty even with fewer parameters, outperforming traditional approaches.

Keywords:

Deep learning Fisher information Hessian Neural networks Predictive epistemic uncertainty Uncertainty quantification

Related Experiment Videos

Last Updated: Oct 14, 2025

Deep Neural Networks for Image-Based Dietary Assessment

Deep Neural Networks for Image-Based Dietary Assessment

Published on: March 13, 2021

Area of Science:

Machine Learning
Deep Learning
Statistical Modeling

Background:

The Delta method is a standard technique for quantifying epistemic uncertainty in statistical models.
Direct application of the Delta method to deep neural networks is computationally infeasible due to the large number of parameters (P).
L2-regularized deep neural networks are widely used but quantifying their uncertainty remains challenging.

Purpose of the Study:

To propose a computationally efficient approximation of the Delta method for L2-regularized deep neural networks.
To provide theoretical bounds on the approximation error for predictive class probability uncertainty.
To demonstrate the practical utility of the proposed method for uncertainty quantification in image classification tasks.

Main Methods:

An approximation of the Delta method using the top K eigenpairs of the Fisher information matrix.
Efficient computation of approximate eigendecompositions using inverse Hessian, inverse outer-products of gradients, and Sandwich estimators.
Analysis of approximation error bounds for predictive uncertainty.

Main Results:

The approximation error is minimal when the smallest eigenvalue of the Fisher information matrix approaches the L2-regularization rate, even for K << P.
Demonstrated effective uncertainty ranking of images using LeNet and ResNet models on MNIST and CIFAR-10 datasets.
False positives exhibited higher predictive epistemic uncertainty than true positives, indicating supplementary information beyond classification.

Conclusions:

The proposed low-cost Delta method approximation is effective for uncertainty quantification in deep neural networks.
The method provides reliable uncertainty estimates and enables meaningful uncertainty-based image ranking.
Predictive epistemic uncertainty offers valuable insights that complement classification results, particularly for identifying challenging or misclassified samples.