# Detecting Errors and Estimating Accuracy on Unlabeled Data with Self-training Ensembles

arXiv: https://arxiv.org/abs/2106.15728 · HTML: https://mlsanity.com/paper/2106.15728/

## Key facts

- Cited by 54 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 47 references that are in the map.
- First posted on arXiv 29 Jun 2021.

## Builds on (most cited first, 21 of 21)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [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)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [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)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Deep Ensembles: A Loss Landscape Perspective](https://mlsanity.com/paper/1912.02757/) (2019)
- [To Trust Or Not To Trust A Classifier](https://mlsanity.com/paper/1805.11783/) (2018)
- [Addressing Failure Prediction by Learning Model Confidence](https://mlsanity.com/paper/1910.04851/) (2019)
- [Assessing Generalization of SGD via Disagreement](https://mlsanity.com/paper/2106.13799/) (2021)
- [Are Labels Always Necessary for Classifier Accuracy Evaluation?](https://mlsanity.com/paper/2007.02915/) (2020)
- [The iWildCam 2020 Competition Dataset](https://mlsanity.com/paper/2004.10340/) (2020)
- [What Does Rotation Prediction Tell Us about Classifier Accuracy under Varying Testing Environments?](https://mlsanity.com/paper/2106.05961/) (2021)
- [Estimating Generalization under Distribution Shifts via Domain-Invariant Representations](https://mlsanity.com/paper/2007.03511/) (2020)
- [Estimating Accuracy from Unlabeled Data: A Probabilistic Logic Approach](https://mlsanity.com/paper/1705.07086/) (2017)
- [Estimating the Accuracies of Multiple Classifiers Without Labeled Data](https://mlsanity.com/paper/1407.7644/) (2014)
- [Unsupervised Risk Estimation Using Only Conditional Independence Structure](https://mlsanity.com/paper/1606.05313/) (2016)

## Built on by (most cited first, 30 of 54)

- [Large Language Model Routing with Benchmark Datasets](https://mlsanity.com/paper/2309.15789/) (2023)
- [Leveraging Unlabeled Data to Predict Out-of-Distribution Performance](https://mlsanity.com/paper/2201.04234/) (2022)
- [Agreement-on-the-Line: Predicting the Performance of Neural Networks under Distribution Shift](https://mlsanity.com/paper/2206.13089/) (2022)
- [Predicting Out-of-Distribution Error with the Projection Norm](https://mlsanity.com/paper/2202.05834/) (2022)
- [RLSbench: Domain Adaptation Under Relaxed Label Shift](https://mlsanity.com/paper/2302.03020/) (2023)
- [On the Strong Correlation Between Model Invariance and Generalization](https://mlsanity.com/paper/2207.07065/) (2022)
- [Confidence and Dispersity Speak: Characterising Prediction Matrix for Unsupervised Accuracy Estimation](https://mlsanity.com/paper/2302.01094/) (2023)
- [A Survey on Evaluation of Out-of-Distribution Generalization](https://mlsanity.com/paper/2403.01874/) (2024)
- [Estimating and Explaining Model Performance When Both Covariates and Labels Shift](https://mlsanity.com/paper/2209.08436/) (2022)
- [Energy-based Automated Model Evaluation](https://mlsanity.com/paper/2401.12689/) (2024)
- [A Note on "Assessing Generalization of SGD via Disagreement"](https://mlsanity.com/paper/2202.01851/) (2022)
- [Detecting Label Errors by using Pre-Trained Language Models](https://mlsanity.com/paper/2205.12702/) (2022)
- [(Almost) Provable Error Bounds Under Distribution Shift via Disagreement Discrepancy](https://mlsanity.com/paper/2306.00312/) (2023)
- [Demystifying Disagreement-on-the-Line in High Dimensions](https://mlsanity.com/paper/2301.13371/) (2023)
- [LOVM: Language-Only Vision Model Selection](https://mlsanity.com/paper/2306.08893/) (2023)
- [Understanding new tasks through the lens of training data via exponential tilting](https://mlsanity.com/paper/2205.13577/) (2022)
- [A Bag-of-Prototypes Representation for Dataset-Level Applications](https://mlsanity.com/paper/2303.13251/) (2023)
- [Label-Free Model Evaluation with Semi-Structured Dataset Representations](https://mlsanity.com/paper/2112.00694/) (2021)
- [Sequential Harmful Shift Detection Without Labels](https://mlsanity.com/paper/2412.12910/) (2024)
- [Estimating Model Performance Under Covariate Shift Without Labels](https://mlsanity.com/paper/2401.08348/) (2024)
- [AETTA: Label-Free Accuracy Estimation for Test-Time Adaptation](https://mlsanity.com/paper/2404.01351/) (2024)
- [MANO: Exploiting Matrix Norm for Unsupervised Accuracy Estimation Under Distribution Shifts](https://mlsanity.com/paper/2405.18979/) (2024)
- [Confidence-based Estimators for Predictive Performance in Model Monitoring](https://mlsanity.com/paper/2407.08649/) (2024)
- [Selecting which Dense Retriever to use for Zero-Shot Search](https://mlsanity.com/paper/2309.09403/) (2023)
- [Leveraging Ensemble Diversity for Robust Self-Training in the Presence of Sample Selection Bias](https://mlsanity.com/paper/2310.14814/) (2023)
- [Advancing Deep Active Learning & Data Subset Selection: Unifying Principles with Information-Theory Intuitions](https://mlsanity.com/paper/2401.04305/) (2024)
- [Predicting the Performance of Foundation Models via Agreement-on-the-Line](https://mlsanity.com/paper/2404.01542/) (2024)
- [HAPI: A Large-scale Longitudinal Dataset of Commercial ML API Predictions](https://mlsanity.com/paper/2209.08443/) (2022)
- [Improving the Reliability for Confidence Estimation](https://mlsanity.com/paper/2210.06776/) (2022)
- [CAME: Contrastive Automated Model Evaluation](https://mlsanity.com/paper/2308.11111/) (2023)

## Abstract (arXiv)

When a deep learning model is deployed in the wild, it can encounter test data drawn from distributions different from the training data distribution and suffer drop in performance. For safe deployment, it is essential to estimate the accuracy of the pre-trained model on the test data. However, the labels for the test inputs are usually not immediately available in practice, and obtaining them can be expensive. This observation leads to two challenging tasks: (1) unsupervised accuracy estimation, which aims to estimate the accuracy of a pre-trained classifier on a set of unlabeled test inputs; (2) error detection, which aims to identify mis-classified test inputs. In this paper, we propose a principled and practically effective framework that simultaneously addresses the two tasks. The proposed framework iteratively learns an ensemble of models to identify mis-classified data points and performs self-training to improve the ensemble with the identified points. Theoretical analysis demonstrates that our framework enjoys provable guarantees for both accuracy estimation and error detection under mild conditions readily satisfied by practical deep learning models. Along with the framework, we proposed and experimented with two instantiations and achieved state-of-the-art results on 59 tasks. For example, on iWildCam, one instantiation reduces the estimation error for unsupervised accuracy estimation by at least 70% and improves the F1 score for error detection by at least 4.7% compared to existing methods.