# Towards Consistent Predictive Confidence through Fitted Ensembles

arXiv: https://arxiv.org/abs/2106.12070 · HTML: https://mlsanity.com/paper/2106.12070/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 38 references that are in the map.
- First posted on arXiv 22 Jun 2021.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (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)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [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)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Delving into Transferable Adversarial Examples and Black-box Attacks](https://mlsanity.com/paper/1611.02770/) (2016)
- [Learning Confidence for Out-of-Distribution Detection in Neural Networks](https://mlsanity.com/paper/1802.04865/) (2018)
- [Mix-n-Match: Ensemble and Compositional Methods for Uncertainty Calibration in Deep Learning](https://mlsanity.com/paper/2003.07329/) (2020)
- [Posterior Network: Uncertainty Estimation without OOD Samples via Density-Based Pseudo-Counts](https://mlsanity.com/paper/2006.09239/) (2020)
- [Out-of-Distribution Detection Using an Ensemble of Self Supervised Leave-out Classifiers](https://mlsanity.com/paper/1809.03576/) (2018)
- [Robust Out-of-distribution Detection for Neural Networks](https://mlsanity.com/paper/2003.09711/) (2020)
- [Universum Prescription: Regularization using Unlabeled Data](https://mlsanity.com/paper/1511.03719/) (2015)
- [Fitted Learning: Models with Awareness of their Limits](https://mlsanity.com/paper/1609.02226/) (2016)

## Built on by (most cited first, 4 of 4)

- [Model merging with SVD to tie the Knots](https://mlsanity.com/paper/2410.19735/) (2024)
- [Towards Realistic Semi-Supervised Learning](https://mlsanity.com/paper/2207.02269/) (2022)
- [A Comprehensive Review of Trends, Applications and Challenges In Out-of-Distribution Detection](https://mlsanity.com/paper/2209.12935/) (2022)
- [Two-stage Modeling for Prediction with Confidence](https://mlsanity.com/paper/2209.08848/) (2022)

## Abstract (arXiv)

Deep neural networks are behind many of the recent successes in machine learning applications. However, these models can produce overconfident decisions while encountering out-of-distribution (OOD) examples or making a wrong prediction. This inconsistent predictive confidence limits the integration of independently-trained learning models into a larger system. This paper introduces separable concept learning framework to realistically measure the performance of classifiers in presence of OOD examples. In this setup, several instances of a classifier are trained on different parts of a partition of the set of classes. Later, the performance of the combination of these models is evaluated on a separate test set. Unlike current OOD detection techniques, this framework does not require auxiliary OOD datasets and does not separate classification from detection performance. Furthermore, we present a new strong baseline for more consistent predictive confidence in deep models, called fitted ensembles, where overconfident predictions are rectified by transformed versions of the original classification task. Fitted ensembles can naturally detect OOD examples without requiring auxiliary data by observing contradicting predictions among its components. Experiments on MNIST, SVHN, CIFAR-10/100, and ImageNet show fitted ensemble significantly outperform conventional ensembles on OOD examples and are possible to scale.