# SCOD: From Heuristics to Theory

arXiv: https://arxiv.org/abs/2403.16916 · HTML: https://mlsanity.com/paper/2403.16916/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 44 references that are in the map.
- First posted on arXiv 25 Mar 2024.

## Builds on (most cited first, 29 of 29)

- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [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)
- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [ImageNet-21K Pretraining for the Masses](https://mlsanity.com/paper/2104.10972/) (2021)
- [Out-of-Distribution Detection with Deep Nearest Neighbors](https://mlsanity.com/paper/2204.06507/) (2022)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [ReAct: Out-of-distribution Detection With Rectified Activations](https://mlsanity.com/paper/2111.12797/) (2021)
- [Scaling Out-of-Distribution Detection for Real-World Settings](https://mlsanity.com/paper/1911.11132/) (2019)
- [ViM: Out-Of-Distribution with Virtual-logit Matching](https://mlsanity.com/paper/2203.10807/) (2022)
- [Open-Set Recognition: a Good Closed-Set Classifier is All You Need?](https://mlsanity.com/paper/2110.06207/) (2021)
- [On the Importance of Gradients for Detecting Distributional Shifts in the Wild](https://mlsanity.com/paper/2110.00218/) (2021)
- [OpenOOD: Benchmarking Generalized Out-of-Distribution Detection](https://mlsanity.com/paper/2210.07242/) (2022)
- [Learning Confidence for Out-of-Distribution Detection in Neural Networks](https://mlsanity.com/paper/1802.04865/) (2018)
- [MOS: Towards Scaling Out-of-distribution Detection for Large Semantic Space](https://mlsanity.com/paper/2105.01879/) (2021)
- [Extremely Simple Activation Shaping for Out-of-Distribution Detection](https://mlsanity.com/paper/2209.09858/) (2022)
- [Reducing Network Agnostophobia](https://mlsanity.com/paper/1811.04110/) (2018)
- [Adversarial Reciprocal Points Learning for Open Set Recognition](https://mlsanity.com/paper/2103.00953/) (2021)
- [In or Out? Fixing ImageNet Out-of-Distribution Detection Evaluation](https://mlsanity.com/paper/2306.00826/) (2023)
- [Is Out-of-Distribution Detection Learnable?](https://mlsanity.com/paper/2210.14707/) (2022)
- [Training OOD Detectors in their Natural Habitats](https://mlsanity.com/paper/2202.03299/) (2022)
- [Optimal strategies for reject option classifiers](https://mlsanity.com/paper/2101.12523/) (2021)
- [DOCTOR: A Simple Method for Detecting Misclassification Errors](https://mlsanity.com/paper/2106.02395/) (2021)
- [RankFeat: Rank-1 Feature Removal for Out-of-distribution Detection](https://mlsanity.com/paper/2209.08590/) (2022)
- [Augmenting Softmax Information for Selective Classification with Out-of-Distribution Data](https://mlsanity.com/paper/2207.07506/) (2022)
- [A Unified Benchmark for the Unknown Detection Capability of Deep Neural Networks](https://mlsanity.com/paper/2112.00337/) (2021)
- [The Devil is in the Wrongly-classified Samples: Towards Unified Open-set Recognition](https://mlsanity.com/paper/2302.04002/) (2023)
- [Plugin estimators for selective classification with out-of-distribution detection](https://mlsanity.com/paper/2301.12386/) (2023)

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

- [Selective Classification Under Distribution Shifts](https://mlsanity.com/paper/2405.05160/) (2024)
- [Evaluating Epistemic Uncertainty: Beyond OOD Detection and Active Learning](https://mlsanity.com/paper/2607.14817/) (2026)
- [Filtering instances and rejecting predictions to obtain reliable models in healthcare](https://mlsanity.com/paper/2510.24368/) (2025)

## Abstract (arXiv)

This paper addresses the problem of designing reliable prediction models that abstain from predictions when faced with uncertain or out-of-distribution samples - a recently proposed problem known as Selective Classification in the presence of Out-of-Distribution data (SCOD). We make three key contributions to SCOD. Firstly, we demonstrate that the optimal SCOD strategy involves a Bayes classifier for in-distribution (ID) data and a selector represented as a stochastic linear classifier in a 2D space, using i) the conditional risk of the ID classifier, and ii) the likelihood ratio of ID and out-of-distribution (OOD) data as input. This contrasts with suboptimal strategies from current OOD detection methods and the Softmax Information Retaining Combination (SIRC), specifically developed for SCOD. Secondly, we establish that in a distribution-free setting, the SCOD problem is not Probably Approximately Correct learnable when relying solely on an ID data sample. Third, we introduce POSCOD, a simple method for learning a plugin estimate of the optimal SCOD strategy from both an ID data sample and an unlabeled mixture of ID and OOD data. Our empirical results confirm the theoretical findings and demonstrate that our proposed method, POSCOD, out performs existing OOD methods in effectively addressing the SCOD problem.