# Learning Acceptance Regions for Many Classes with Anomaly Detection

arXiv: https://arxiv.org/abs/2209.09963 · HTML: https://mlsanity.com/paper/2209.09963/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 62 references that are in the map.
- First posted on arXiv 20 Sep 2022.

## Builds on (most cited first, 15 of 15)

- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [A Unifying Review of Deep and Shallow Anomaly Detection](https://mlsanity.com/paper/2009.11732/) (2020)
- [Least Ambiguous Set-Valued Classifiers with Bounded Error Levels](https://mlsanity.com/paper/1609.00451/) (2016)
- [Towards Open World Recognition](https://mlsanity.com/paper/1412.5687/) (2014)
- [A Conformal Prediction Approach to Explore Functional Data](https://mlsanity.com/paper/1302.6452/) (2013)
- [Class-prior Estimation for Learning from Positive and Unlabeled Data](https://mlsanity.com/paper/1611.01586/) (2016)
- [Prediction and outlier detection in classification problems](https://mlsanity.com/paper/1905.04396/) (2019)
- [Cautious Deep Learning](https://mlsanity.com/paper/1805.09460/) (2018)
- [Open Category Detection with PAC Guarantees](https://mlsanity.com/paper/1808.00529/) (2018)
- [Density Level Sets: Asymptotics, Inference, and Visualization](https://mlsanity.com/paper/1504.05438/) (2015)
- [On Reject and Refine Options in Multicategory Classification](https://mlsanity.com/paper/1701.02265/) (2017)
- [Consistent Algorithms for Multiclass Classification with a Reject Option](https://mlsanity.com/paper/1505.04137/) (2015)
- [Learning Confidence Sets using Support Vector Machines](https://mlsanity.com/paper/1809.10818/) (2018)
- [Double Sparsity Kernel Learning with Automatic Variable Selection and Data Extraction](https://mlsanity.com/paper/1706.01426/) (2017)

## Abstract (arXiv)

Set-valued classification, a new classification paradigm that aims to identify all the plausible classes that an observation belongs to, can be obtained by learning the acceptance regions for all classes. Many existing set-valued classification methods do not consider the possibility that a new class that never appeared in the training data appears in the test data. Moreover, they are computationally expensive when the number of classes is large. We propose a Generalized Prediction Set (GPS) approach to estimate the acceptance regions while considering the possibility of a new class in the test data. The proposed classifier minimizes the expected size of the prediction set while guaranteeing that the class-specific accuracy is at least a pre-specified value. Unlike previous methods, the proposed method achieves a good balance between accuracy, efficiency, and anomaly detection rate. Moreover, our method can be applied in parallel to all the classes to alleviate the computational burden. Both theoretical analysis and numerical experiments are conducted to illustrate the effectiveness of the proposed method.