# Uncertainty quantification in neural network classifiers -- a local linear approach

arXiv: https://arxiv.org/abs/2303.07114 · HTML: https://mlsanity.com/paper/2303.07114/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 58 references that are in the map.
- First posted on arXiv 10 Mar 2023.

## Builds on (most cited first, 28 of 28)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Underspecification Presents Challenges for Credibility in Modern Machine Learning](https://mlsanity.com/paper/2011.03395/) (2020)
- [A Survey of Deep Learning Techniques for Autonomous Driving](https://mlsanity.com/paper/1910.07738/) (2019)
- [Being Bayesian, Even Just a Bit, Fixes Overconfidence in ReLU Networks](https://mlsanity.com/paper/2002.10118/) (2020)
- [Evaluating model calibration in classification](https://mlsanity.com/paper/1902.06977/) (2019)
- [Posterior Network: Uncertainty Estimation without OOD Samples via Density-Based Pseudo-Counts](https://mlsanity.com/paper/2006.09239/) (2020)
- [Practical Deep Learning with Bayesian Principles](https://mlsanity.com/paper/1906.02506/) (2019)
- [Challenges in Deploying Machine Learning: a Survey of Case Studies](https://mlsanity.com/paper/2011.09926/) (2020)
- [Uncertainty Estimates and Multi-Hypotheses Networks for Optical Flow](https://mlsanity.com/paper/1802.07095/) (2018)
- [Bayesian Uncertainty Estimation for Batch Normalized Deep Networks](https://mlsanity.com/paper/1802.06455/) (2018)
- [Uncertainty-Aware CNNs for Depth Completion: Uncertainty from Beginning to End](https://mlsanity.com/paper/2006.03349/) (2020)
- [Dangers of Bayesian Model Averaging under Covariate Shift](https://mlsanity.com/paper/2106.11905/) (2021)
- [Accelerated Linearized Laplace Approximation for Bayesian Deep Learning](https://mlsanity.com/paper/2210.12642/) (2022)
- [Deep Neural Networks for Improved, Impromptu Trajectory Tracking of Quadrotors](https://mlsanity.com/paper/1610.06283/) (2016)
- [Accurate Prediction and Uncertainty Estimation using Decoupled Prediction Interval Networks](https://mlsanity.com/paper/2202.09664/) (2022)
- [On the sensitivity of pose estimation neural networks: rotation parameterizations, Lipschitz constants, and provable bounds](https://mlsanity.com/paper/2203.09937/) (2022)
- [SLOVA: Uncertainty Estimation Using Single Label One-Vs-All Classifier](https://mlsanity.com/paper/2206.13923/) (2022)

## Built on by (most cited first, 1 of 1)

- [h-calibration: Rethinking Classifier Recalibration with Probabilistic Error-Bounded Objective](https://mlsanity.com/paper/2506.17968/) (2025)

## Abstract (arXiv)

Classifiers based on neural networks (NN) often lack a measure of uncertainty in the predicted class. We propose a method to estimate the probability mass function (PMF) of the different classes, as well as the covariance of the estimated PMF. First, a local linear approach is used during the training phase to recursively compute the covariance of the parameters in the NN. Secondly, in the classification phase another local linear approach is used to propagate the covariance of the learned NN parameters to the uncertainty in the output of the last layer of the NN. This allows for an efficient Monte Carlo (MC) approach for: (i) estimating the PMF; (ii) calculating the covariance of the estimated PMF; and (iii) proper risk assessment and fusion of multiple classifiers. Two classical image classification tasks, i.e., MNIST, and CFAR10, are used to demonstrate the efficiency the proposed method.