Provable Guarantees for Understanding Out-of-distribution Detection

Abstract

Out-of-distribution (OOD) detection is important for deploying machine learning models in the real world, where test data from shifted distributions can naturally arise. While a plethora of algorithmic approaches have recently emerged for OOD detection, a critical gap remains in theoretical understanding. In this work, we develop an analytical framework that characterizes and unifies the theoretical understanding for OOD detection. Our analytical framework motivates a novel OOD detection method for neural networks, GEM, which demonstrates both theoretical and empirical superiority. In particular, on CIFAR-100 as in-distribution data, our method outperforms a competitive baseline by 16.57% (FPR95). Lastly, we formally provide provable guarantees and comprehensive analysis of our method, underpinning how various properties of data distribution affect the performance of OOD detection 1 .

Provable Guarantees for Understanding Out-of-Distribution Detection

“…We emphasize that in Theorem 1 µ i and µ out can have arbitrary configurations. We refer the reader to the extended version 2 (Morteza and Li 2021) for the proof of Theorem 1 and detailed discussions on other variants.…”

“…We refer the reader to the extended version (Morteza and Li 2021) for the proof of Proposition 2. The next Corollary explains how the performance of our method decreases by increasing the number of classes.…”

“…Results for OOD detection are averaged over the six OOD test datasets described in section 3. Numbers for individual OOD test datasets are available in the extended version(Morteza and Li 2021). The reported results for baselines are courtesy of(Liu et al 2020).…”

Topological Structure Learning for Weakly-Supervised Out-of-Distribution Detection

“…Lee et al [24] presented a score using the Mahalanobis distance concerning the closest class-conditional distribution in the feature space of the pre-trained network, which verifies that information of feature space also contributes to OOD detection. Morteza and Li [33] derived analytically an optimal form of OOD scoring function called GEM (Gaussian mixture based Energy Measurement), which is provably aligned with the true log-likelihood for OOD detection. However, post-hoc based methods still assign high-confidence predictions to OOD data due to the lack of supervision signals from OOD data [10].…”

“…The performance of the near OOD detection experiment when we take CIFAR-10's testing set and all unlabeled data during training as the test set respectively. ± 2 33. 24.90 ± 0.86 39.44 ± 3.52 24.00 ± 5.81 Detection Error ↓ 16.00 ± 0.23 11.69 ± 0.52 15.75 ± 0.27 11.67 ± 1.62 AUPR-In ↑ 93.13 ± 0.44 95.34 ± 0.44 92.86 ± 0.32 95.65 ± 1.04 AUPR-Out ↑ 84.72 ± 0.50 89.69 ± 1.25 86.01 ± 1.71 92.34 ± 1.97 training sets respectively as D out U .…”