# Out of Distribution Detection, Generalization, and Robustness Triangle with Maximum Probability Theorem

arXiv: https://arxiv.org/abs/2203.12145 · HTML: https://mlsanity.com/paper/2203.12145/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 46 references that are in the map.
- First posted on arXiv 23 Mar 2022.

## Builds on (most cited first, 17 of 17)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (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)
- [Deep Learning for Classical Japanese Literature](https://mlsanity.com/paper/1812.01718/) (2018)
- [Generalized ODIN: Detecting Out-of-distribution Image without Learning from Out-of-distribution Data](https://mlsanity.com/paper/2002.11297/) (2020)
- [Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One](https://mlsanity.com/paper/1912.03263/) (2019)
- [How to Train Your Energy-Based Models](https://mlsanity.com/paper/2101.03288/) (2021)
- [Improved Contrastive Divergence Training of Energy Based Models](https://mlsanity.com/paper/2012.01316/) (2020)
- [MOOD: Multi-level Out-of-distribution Detection](https://mlsanity.com/paper/2104.14726/) (2021)
- [Understanding and Improving Convolutional Neural Networks via Concatenated Rectified Linear Units](https://mlsanity.com/paper/1603.05201/) (2016)
- [A General Framework For Detecting Anomalous Inputs to DNN Classifiers](https://mlsanity.com/paper/2007.15147/) (2020)
- [Maximum Probability Theorem: A Framework for Probabilistic Learning](https://mlsanity.com/paper/1910.09417/) (2019)

## Abstract (arXiv)

Maximum Probability Framework, powered by Maximum Probability Theorem, is a recent theoretical development in artificial intelligence, aiming to formally define probabilistic models, guiding development of objective functions, and regularization of probabilistic models. MPT uses the probability distribution that the models assume on random variables to provide an upper bound on the probability of the model. We apply MPT to challenging out-of-distribution (OOD) detection problems in computer vision by incorporating MPT as a regularization scheme in the training of CNNs and their energy-based variants. We demonstrate the effectiveness of the proposed method on 1080 trained models, with varying hyperparameters, and conclude that the MPT-based regularization strategy stabilizes and improves the generalization and robustness of base models in addition to enhanced OOD performance on CIFAR10, CIFAR100, and MNIST datasets.