# Efficient Post-Hoc Uncertainty Calibration via Variance-Based Smoothing

arXiv: https://arxiv.org/abs/2503.15583 · HTML: https://mlsanity.com/paper/2503.15583/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 28 references that are in the map.
- First posted on arXiv 19 Mar 2025.

## Builds on (most cited first, 17 of 17)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [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)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Relational Knowledge Distillation](https://mlsanity.com/paper/1904.05068/) (2019)
- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (2018)
- [Network In Network](https://mlsanity.com/paper/1312.4400/) (2013)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [Empirical Evaluation of Rectified Activations in Convolutional Network](https://mlsanity.com/paper/1505.00853/) (2015)
- [Beyond temperature scaling: Obtaining well-calibrated multiclass probabilities with Dirichlet calibration](https://mlsanity.com/paper/1910.12656/) (2019)
- [Understanding disentangling in β-VAE](https://mlsanity.com/paper/1804.03599/) (2018)
- [Putting An End to End-to-End: Gradient-Isolated Learning of Representations](https://mlsanity.com/paper/1905.11786/) (2019)
- [A Simple Approach to Improve Single-Model Deep Uncertainty via Distance-Awareness](https://mlsanity.com/paper/2205.00403/) (2022)
- [Deep Sub-Ensembles for Fast Uncertainty Estimation in Image Classification](https://mlsanity.com/paper/1910.08168/) (2019)
- [Posterior Uncertainty Quantification in Neural Networks using Data Augmentation](https://mlsanity.com/paper/2403.12729/) (2024)

## Built on by (most cited first, 3 of 3)

- [On the Tightness and Computational Tractability of Higher-Dimensional Confidence Sequences](https://mlsanity.com/paper/2610.03727/) (2026)
- [FALCON-Discover: Discovering Concentrated False-Confidence Regions for Calibration](https://mlsanity.com/paper/2607.18278/) (2026)
- [When Has a Bayesian Neural Network Sampled Enough? Adaptive Inference Time with Statistical Guarantees](https://mlsanity.com/paper/2610.12212/) (2026)

## Abstract (arXiv)

Since state-of-the-art uncertainty estimation methods are often computationally demanding, we investigate whether incorporating prior information can improve uncertainty estimates in conventional deep neural networks. Our focus is on machine learning tasks where meaningful predictions can be made from sub-parts of the input. For example, in speaker classification, the speech waveform can be divided into sequential patches, each containing information about the same speaker. We observe that the variance between sub-predictions serves as a reliable proxy for uncertainty in such settings. Our proposed variance-based scaling framework produces competitive uncertainty estimates in classification while being less computationally demanding and allowing for integration as a post-hoc calibration tool. This approach also leads to a simple extension of deep ensembles, improving the expressiveness of their predicted distributions.