# QuantProb: Generalizing Probabilities along with Predictions for a Pre-trained Classifier

arXiv: https://arxiv.org/abs/2304.12766 · HTML: https://mlsanity.com/paper/2304.12766/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 45 references that are in the map.
- First posted on arXiv 25 Apr 2023.

## Builds on (most cited first, 24 of 24)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Images](https://mlsanity.com/paper/1412.1897/) (2014)
- [Revisiting the Calibration of Modern Neural Networks](https://mlsanity.com/paper/2106.07998/) (2021)
- [Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness](https://mlsanity.com/paper/2006.10108/) (2020)
- [Open-Set Recognition: a Good Closed-Set Classifier is All You Need?](https://mlsanity.com/paper/2110.06207/) (2021)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [Verified Uncertainty Calibration](https://mlsanity.com/paper/1909.10155/) (2019)
- [Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control](https://mlsanity.com/paper/2110.01052/) (2021)
- [To Trust Or Not To Trust A Classifier](https://mlsanity.com/paper/1805.11783/) (2018)
- [Beyond Pinball Loss: Quantile Methods for Calibrated Uncertainty Quantification](https://mlsanity.com/paper/2011.09588/) (2020)
- [Calibrated Multiple-Output Quantile Regression with Representation Learning](https://mlsanity.com/paper/2110.00816/) (2021)
- [Improving Conditional Coverage via Orthogonal Quantile Regression](https://mlsanity.com/paper/2106.00394/) (2021)
- [Calibrated ensembles can mitigate accuracy tradeoffs under distribution shift](https://mlsanity.com/paper/2207.08977/) (2022)
- [Single Layer Predictive Normalized Maximum Likelihood for Out-of-Distribution Detection](https://mlsanity.com/paper/2110.09246/) (2021)
- [Estimation and Applications of Quantiles in Deep Binary Classification](https://mlsanity.com/paper/2102.06575/) (2021)

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

- [Quantile Activation: Correcting a Failure Mode of ML Models](https://mlsanity.com/paper/2405.11573/) (2024)

## Abstract (arXiv)

Quantification of Uncertainty in predictions is a challenging problem. In the classification settings, although deep learning based models generalize well, class probabilities often lack reliability. Calibration errors are used to quantify uncertainty, and several methods exist to minimize calibration error. We argue that between the choice of having a minimum calibration error on original distribution which increases across distortions or having a (possibly slightly higher) calibration error which is constant across distortions, we prefer the latter We hypothesize that the reason for unreliability of deep networks is - The way neural networks are currently trained, the probabilities do not generalize across small distortions. We observe that quantile based approaches can potentially solve this problem. We propose an innovative approach to decouple the construction of quantile representations from the loss function allowing us to compute quantile based probabilities without disturbing the original network. We achieve this by establishing a novel duality property between quantiles and probabilities, and an ability to obtain quantile probabilities from any pre-trained classifier. While post-hoc calibration techniques successfully minimize calibration errors, they do not preserve robustness to distortions. We show that, Quantile probabilities (QuantProb), obtained from Quantile representations, preserve the calibration errors across distortions, since quantile probabilities generalize better than the naive Softmax probabilities.